Insulator-Based Dielectrophoretic Manipulation of DNA in a Microfluidic Device

by

Lin Gan

A Dissertation Presented in Partial Fulfillment

of the Requirements for the Degree

Doctor of Philosophy

Approved July 2015 by the

Graduate Supervisory Committee:

Alexandra Ros, Chair

Daniel Buttry

Yan Liu

ARIZONA STATE UNIVERSITY

August 2015

i

ABSTRACT

DNA and DNA nanoassemblies such as DNA origamis have large potential in

biosensing, drug delivery, nanoelectronic circuits, and biological computing requiring

suitable methods for migration and precise positioning. Insulator-based dielectrophoresis

(iDEP) provides an efficient and matrix-free approach for manipulation of micro-and

nanometer-sized objects. In order to exploit iDEP for naturally formed DNA and DNA

nanoassemblies, a detailed understanding of the underlying polarization and

dielectrophoretic migration is essential. The shape and the counterion distribution are

considered two essential factors in the polarization mechanism. Here, the

dielectrophoretic behavior of 6-helix bundle (6HxB) and triangle DNA origamis with

identical sequences but substantial topological differences was explored. The

polarizability models were discussed for the two species according to their structural

difference. The experimental observations reveal distinct iDEP trapping behavior in low

frequency AC electric fields in addition to numerical simulations showing a considerable

contribution of the electrophoretic transport of the DNA origami species in the DEP

trapping regions. Furthermore, the polarizabilities of the two species were determined by

measuring the migration times through a potential landscape exhibiting dielectrophoretic

barriers. The resulting migration times correlate to the depth of the dielectrophoretic

potential barrier and the escape characteristics of the DNA origamis according to an

adapted Kramer’s rate model. The orientations of both species in the escape process were

studied. Finally, to study the counterion distribution around the DNA molecules, both λ-

DNA and 6HxB DNA were used in a phosphate buffer containing magnesium, revealing

ii

distinctive negative dielectrophoretic trapping behavior as opposed to positive trapping in

a sodium/potassium phosphate buffer system.

iii

DEDICATION

To my parents, for their love, support, understanding,

respecting my decisions and never asking what took it so long.

To all my friends, for hearing me out, cheering me up,

and always being by my side no matter how far the physical distance is,

and what time zones they are in.

iv

ACKNOWLEDGEMENT

I'd like to show my gratitude to my advisor and doctoral committee chair,

Professor Alexandra Ros for her guidance and support academically and mentor in life

for all the years through my graduate studies.

I also would like to thank Dr. Daniel Buttry and Dr. Yan Liu for the inspiring

discussions and helpful feedbacks.

For building up the instruments and construct Labview program, I want to

sincerely express my thankfulness to Dr. Fernanda Camacho-Alanis, Dr. Tzu-Chiao

Chao, and Jan Klos. Only with your help, could I make the experiment happen.

Great thanks to Dr. Hao Yan and Dr. Yan Liu's group for training me in

synthesizing DNA origamis and for the valuable advice in handling and purification.

I would like to thank Dr. Robert Ros's group for assistance with AFM imaging.

Specifically, gratitude to Olaf Schulz, Alex Ward and Bryant Doss for dedicating hours

in your busy schedules toward teaching me the tricks of the instrument.

Finally, I want to thank all my lab mates and coworkers for all the constructive

suggestions on my work and emotional support in my life. You guys are the best.

v

TABLE OF CONTENTS

Page

LIST OF TABLES ........................................................................................................... viii

LIST OF FIGURES ........................................................................................................... ix

CHAPTER

1. INTRODUCTION .................................................................................................... 1

Significance of the Study of DNA Dielectrophoresis (DEP) ................................ 1

Dissertation Work Methodology ........................................................................... 3

2. THEORY .................................................................................................................. 5

Electrokinesis and Dielectrophoresis (DEP) ......................................................... 5

Common Models for DNA Dielectrophoresis ..................................................... 18

DNA Origami Model ........................................................................................... 22

3. MATERIALS, METHODS AND INSTRUMENTAL .......................................... 28

Chemicals ............................................................................................................ 28

Origami Synthesis and Characterization ............................................................. 28

Microchip Fabrication ......................................................................................... 29

Channel Incubation .............................................................................................. 30

Constructing the Voltage-Supply Instrument and the Software Programming ... 31

Detection ............................................................................................................. 36

Data process ........................................................................................................ 40

4. NUMERICAL MODELING .................................................................................. 41

Introduction ......................................................................................................... 41

vi

CHAPTER Page

Multiphysics Model Set-up ................................................................................. 41

Convection-Diffusion Model .............................................................................. 43

Time Dependent Study ........................................................................................ 44

Electric Field Calculation .................................................................................... 45

5. DEP MANIPULATIONS OF DNA ORIGAMIS................................................... 47

Introduction ......................................................................................................... 47

Results and Discussion ........................................................................................ 48

iDEP Trapping of 6HxB and Triangle Origami ........................................... 48

Extension of the Trapping Area ................................................................... 50

Origami Migration Behavior in iDEP Traps ................................................ 53

Trapping Conditions for 6HxB Dimer ......................................................... 59

Section Summary ................................................................................................ 61

6. DETERMINATION OF THE POLARIZABILITY OF DNA ORIGAMIS .......... 63

6.1 Introduction ................................................................................................... 63

6.2 Results and Discussion .................................................................................. 65

Determination of Origami Polarizabilities ................................................... 65

Orientation of the Origami Species.............................................................. 70

Comparison between 6HxB and Triangle Origami Polarizability ............... 76

Influence of Diffusion on the Escape Process ............................................. 77

Section Summary ................................................................................................ 79

7. EFFECT OF BUFFER VALENCY IN DEP TRAPPING ..................................... 80

vii

CHAPTER Page

Introduction ......................................................................................................... 80

Results and Discussion ........................................................................................ 82

p-DEP and n-DEP for Monovalent and Divalent Buffer ............................. 82

Section Summary ................................................................................................ 85

CONCLUSIONS......................................................................................................... 86

REFERENCES ................................................................................................................. 88

APPENDIX

A CHANNEL INCUBATION METHOD DEVELOPMENT ................................. 102

B DEP MANIPULATION OF 6HxB DIMER ......................................................... 106

C DEVELOPMENT FOR INJECTION DEVICE ................................................... 110

D COPYRIGHT PERMISSIONS ............................................................................. 115

viii

LIST OF TABLES

Table Page

2.3-1. A Summary of Polarizability 𝑍 and Shape Factor 𝑆 Related Equations and

Calculated Parameters Used in Simulations ···················································· 27

6.2-1. Solutions for the Calculated Orientation Angle of the Triangle Origami ··········· 75

ix

LIST OF FIGURES

Figure Page

2.1-1. EOF Profile in Microfluidic Channel and Schematics of Electrical Double Layer

(EDL) ··································································································· 5

2.1-2. Results EOF Measurement ·································································· 8

2.1-3. Schematics of a Negative Charged Particle Surface ··································· 10

2.1-4. Schematic Representation of Particle DEP under Inhomogeneous Electric Fields 15

2.3-1. Schematics of the Shape of 6HxB DNA and Triangle Origami ······················ 22

3.3-1. Schematics of Chip Fabrication ··························································· 30

3.5-1. Schematics of the Control LabVIEW Program from Generation 1 ·················· 32

3.5-2. Schematics of the Voltage Control for Generation 2 ·································· 34

3.6-1. Schematics of the Microfluidic Device ················································· 37

5.2-1. Schematically Depicted and AFM Images of 6HxB and Triangle Origami ········ 48

5.2-2. DEP Trapping Frequency Range under Which DEP Trapping Occurs ············· 49

5.2-3. Snapshots of DEP Trapping in the Insulator-Based Post Array for 6HxB and

Triangle Origami (each for two exemplary frequencies) ····································· 50

5.2-4 Time-Dependent Concentration Profiles from Numerical Simulations ·············· 52

5.2-5. Simulation of Normalized Concentration Profile with only Electrokinesis and with

only DEP ····························································································· 54

5.2-6. Ltrap Plot versus Applied Frequency for the 6HxB and Triangle Origami through

Experiments and Simulation ······································································ 55

5.2-7. Gel Image and AFM Image of the 6HxB origami ······································ 59

x

Figure Page

5.2-8. 6HxB Dimer Trapping ····································································· 60

6.2-1. Schematics of Potential Landscape for DNA Origami Migration through One

Dielectrophoretic Trap ············································································· 66

6.2-2. lnτ versus the Square of the AC Voltages for 6HxB and Triangle Origami ········ 69

6.2-3. Schematics of the Triangle Origami Orientation with Respect to the Electric Field

E⃑⃑ and the Alignment of 6HxB and Triangle Origami against the Electric Field

Streamlines in a set of post arrays ································································ 71

7.2-1. Numerical simulation for ∇E⃑⃑ 2 and n-DEP, p-DEP trapping of λ-DNA with

different Valency buffer ··········································································· 83

7.2-2 n-DEP Trapping of 6HxB Origami ······················································· 84

SI A-1. Comparison between Adsorption of λ-DNA with two Incubation Methods ···· 103

SI B-1. Numerical Simulation for Alternative Device for 6HxB Dimer Trapping ······· 107

SI B-2. Experimental results and Numerical Simulation for 6HxB Dimer in the

Alternative Device ················································································· 108

SI C-1. Fresh Buffer Channel Contaminated by Sample Due to the Hydrodynamic

Resistance ··························································································· 111

SI C-2. Schematics of the Calculation of Hydrodynamic Resistances ····················· 112

SI C-3. A Successful Example of Pinched Injection with Newly Designed Device ····· 114

SI C-4 An example of electropherogram from pinched injection

········································································································ 114

1

CHAPTER 1

1. INTRODUCTION

1.1 Significance of the Study of DNA Dielectrophoresis (DEP)

Naturally formed deoxyribonucleic acid (DNA) carries our genetic information

and its analysis in health, disease diagnosis and the identification of origins of species are

of great interest. During the past decade, various methods for the synthesis of self-

assembled nanoassemblies such as artificial DNA structures have developed. Two-

dimensional (2D) and three-dimensional (3D) structures such as 2D stars (He et al. 2006),

circular structures (Han et al. 2011) as well as 3D rods (Mathieu et al. 2005), cubes

(Chen, Seeman 1991, Kuzuya, Komiyama 2009), spheres (Han et al. 2011) and other

hollow structures (Han et al. 2011, Ke et al. 2009) were successfully synthesized.

Artificial DNA assembles are of great importance for many areas such as genetic

engineering (Breaker 2002), drug delivery (Liu et al. 2012), bioinformatics (Li et al.

2013), molecular biology (Hertweck 2015), DNA nanotechnology (Rothemund 2006)

and medical diagnosis (Esmaeilnejad et al. 2015). Studies dedicated to the analysis,

manipulation, concentration and purification of DNA are in demand due to the

increasingly important applications of natural and artificial DNA forms.

Rapid and reliable separation and analysis methods for biological samples such as

DNA become challenging when only small sample volume and low concentration are

available. Time critical situations such as rapidly degraded samples, repeated sampling

and fast diagnosis pose additional challenges. Miniaturization has benefited creating

portable and sensitive devices that can achieve analyzing samples using low sample

2

volume, reduced time and high throughput (Lapizco-Encinas, Rito-Palomares 2007).

Microfluidic platforms applying dielectrophoeresis (DEP) have become efficient tools for

DNA separation methods such as filtration, liquid-liquid extraction, centrifugation,

adsorption and capillary electrophoresis (Lapizco-Encinas, Rito-Palomares 2007).

DEP is a powerful analytical technique that has the potential in many processing

steps such as pre-concentration, fractionation, separation and purification. Such a

versatile applicability makes DEP an attractive tool to facilitate the analysis of biological

particles and biomolecules. Specifically, DEP occurs when the particles respond to an

inhomogeneous electric field, where the particles in aqueous solution become polarizable

thus exhibiting an induced dipole moment. Since the DEP response for a bioparticle is

based on its intrinsic properties, DEP can serve as a label-free analytical method.

Additionally, compared to other methods such as capillary electrophoresis, DEP is not

limited to the ratio between the analyte charge and friction coefficient (Ying et al. 2004);

Compared to the gel purification methods, DEP is gel-free and can be label-free. The

versatility and the uniqueness of DEP makes it an attractive tool, especially in

combination with other orthogonal analysis techniques and platforms such as Mass

Spectrometry and UV-Vis.

DEP in combination with microfluidic platforms has many successful examples in

DNA manipulation and analysis. Separation (Regtmeier et al. 2007a, Sano et al. 2002,

Kawabata, Washizu 2001) and fractionation (Thomas, Dorfman 2014) prototypes

utilizing DEP in microfluidic platforms provide great potential in developing and mass

producing such devices in industry. However, the theoretical DEP models are

3

underdeveloped and still under debate, especially on the subject of DNA length and

frequency dependence (Henning, Bier & Hoelzel 2010, Zhao 2011b). Knowledge of the

physical principles underlying the migration mechanism and experimental proof is

essential for the development of migration and separation tools for DNA nanostructures.

1.2 Dissertation Work Methodology

This work focuses on the manipulation of artificial DNA nanoassemblies with

DEP and elucidation of the DNA DEP mechanism. This dissertation is dedicated to

revealing the DEP mechanism by the following:

1. Studying the dielectrophoretic behavior of 6-helix bundle (6HxB) and triangle

DNA origamis with identical sequences but large topological differences.

2. Determining the polarizabilities for 6HxB and triangle origami experimentally

and discussing the orientations of both species

3. Validating the effect of multivalent buffers on the effect of DEP trapping

This dissertation is organized into 8 Chapters. Following this introduction,

Chapter 2 explains the theoretical basis prevailing to electrokinetic and dielectrophoretic

migration. Chapter 3 presents the experimental methods used to perform iDEP

manipulation, as well as the construction of the hardware/software employed for the

application of the high voltage device. Chapter 4 illustrates the simulation methodology

to model the electric field and DNA concentration during DEP manipulation. Chapter 5

studies the differences in the DEP trapping behavior of 6HxB and triangle origami.

Chapter 6 present the study of polarizabilities for both species and the knowledge of the

4

orientation of both origami species under electric fields, as well as the surface

conductivity for DNA origami species. Chapter 7 presents the effect of buffer valency on

DEP manipulation. Finally, Chapter 8 represents a summary and suggested future work.

5

CHAPTER 2

2. THEORY

2.1 Electrokinesis and Dielectrophoresis (DEP)

2.1.1 Electroosmosis

When a surface is in contact with a polar aqueous medium, due to various

mechanisms such as ionization and ion adsorption, the material will acquire a surface

electric charge. In the medium, the counterions (in contrast to surface charge) are

attracted to the surface and the co-ions are repelled from the surface. Together with the

random thermal motion of the ions, an electric double layer (EDL), is formed, and the

distribution of the ions follow a "diffuse" behavior (Probstein 2003).

Figure 2.1-1. a) Schematics of electrical double layer (EDL). The solid surface is

negatively charged and the positive charges are electrostatically attracted to the

interface, resulting in the Stern layer. The plane between the Stern layer and diffuse layer

is called the shear plain. The potential at the shear plane is called the zeta potential (𝜁).

b) EOF profile in a microfluidic channel. Applied electric field direction: left to right.

The channel walls are negatively charged and a Debye layer is shown (darker blue) in

contrast with the bulk solution (shallow blue). The flow profile is uniform throughout the

channel and drops rapidly in the diffuse layer to 0 at the interface.

6

The schematics of the electrical double layer is shown in Figure 2.1-1b. At the

interface between the object and the solution, a single layer of counterions is formed. Due

to the hydrated radius of the counterion, the center of the charge cannot directly be

attached to the surface. The distance between the surface and the center of the counterion

define the inner layer, which is called Stern layer. The thickness of the Stern layer

depends on the hydrated radius of the counterions. The plane between the inner layer and

outer layer is called the Stern plane, slipping plane or shear plane, and the electrokinetic

potential at the slipping plane is called the zeta potential (𝜁). The layer between the Stern

plane and the bulk solution is defined as the diffuse layer. The thickness of the Stern

layer and part of the diffuse layer together forms the Debye layer, which is characterized

by a Debye length is expressed as:

𝜆𝐷 = (𝜀0𝜀𝑟𝑘𝐵𝑇

𝑒2 ∑ 𝑛𝑖𝑧𝑖2𝑁

𝑖=1

)1/2 (2.1-1)

where 𝜀0 and 𝜀𝑟 are the vacuum permittivity of the free space and the relative permittivity

of the medium, 𝑘𝐵 is Boltzmann constant, 𝑇 is temperature, 𝑒 is the elementary charge

(1.602 × 10−19 𝐶), 𝑁 is the number of species in the solution, and 𝑛𝑖 is the molar

concentration of a specific species in the bulk solution.

As shown in Figure 2.1-1b, the charge redistribution of the liquid medium occurs

at the liquid-solid interface. As a result, upon application of an external electric field along

the channel, the liquid inside the channel moves by the Coulomb force. The flow caused by

the applied electric field is called electroosmotic flow (EOF). The flow profile is shown in

Figure 2.1-1a, where a uniform velocity profile is formed throughout the cross section of the

7

channel, and the velocity profile drops rapidly to zero at the liquid-solid interface. The

velocity of the electroosmotic flow (�⃑� 𝐸𝑂𝐹) is described by the Smoluchowski equation (von

Smoluchowski 1914):

�⃑� 𝐸𝑂𝐹 = 𝜇𝐸𝑂𝐹�⃑� = −𝜀0𝜀𝑟ζ

𝜂�⃑� (2.1-2)

where 𝜇𝐸𝑂𝐹 is the EOF mobility and η is the dynamic viscosity of the dispersed medium.

EOF is one of the major electrokinetic flows in microfluidic systems, which is also a

parameter to evaluate the surface properties in a microfluidic system. The control of the

EOF in a microchannel is also critical in many types of experiments to improve the

reproducibility between experiments and different substrate types (Abdallah, Ros 2013).

The methods measuring EOF mobility are summarized in the review article

(Wang et al. 2007c).Typical approaches include liquid mass transmission (Vandegoor,

Wanders & Everaerts 1989), flow of detectable analyte measurement (Stevens, Cortes

1983), the sampling zone method (Wang et al. 2007a, Wang et al. 2006), the current-

monitoring method (Huang, Gordon & Zare 1988), the conductivity method (Wanders,

Vandegoor & Everaerts 1993), effective mobility of charged analyte measurement (Wang

et al. 2007b), and the streaming potential method (Reijenga et al. 1983).

The method used for this thesis is termed the current-monitoring method

according to Huang et al. (Huang, Gordon & Zare 1988): A straight microfluidic channel

or capillary is filled with a solution having a certain conductivity (𝜎1). A voltage is

applied to the across the channel length and the current is recorded in real time. A lower

8

conductivity (𝜎2) buffer is exchanged in one of the sample reservoirs and as the voltage is

applied, the solution (𝜎2) from the inlet reservoir will replace the solution in the channel

due to EOF, causing a decrease in the monitored current due to an increase of the

resistance in the channel. When the channel is fully replaced by a lower conductivity (𝜎2)

buffer, the current stays constant. An example of this EOF measurement is shown in

Figure 2.1-2.

Figure 2.1-2. An example of an EOF measurement. The lower conductivity buffer is

exchanged in reservoir at time 0, and after time Δ𝑡, the buffer in the channel is fully

replaced.

The EOF velocity can be calculated as:

�⃑� 𝐸𝑂𝐹 =𝐿

∆𝑡 (2.1-3)

where 𝐿 is the channel length and Δ𝑡 is the time the current decreases, as shown in Figure

2.1-2.

From Eq. 2.1-2,

9

𝜇𝐸𝑂𝐹 =�⃑⃑� 𝐸𝑂𝐹

�⃑� =

𝐿

∆𝑡|�⃑� |=

𝐿2

∆𝑡𝑈 (2.1-4)

where the 𝑈 is the applied voltage along the channel.

2.1.2 Electrophoresis

Electrophoresis is the movement of dispersed charged particles relative to the

surrounding liquid medium under the influence of a spatially uniform electric field

(Lyklema 1995, Hunter 1989). Due to electrophoresis, positively charged particles move

along the electric field lines, negatively charged particles move against the electric field

lines, and neutral particles remain stationary (Lyklema 1995). When the charged particle

moves at constant velocity under the application of a homogenous electric field (�⃑� ), the

electric force is balanced with the viscous drag force, and the electrophoretic velocity of

the particle (�⃑� 𝐸𝑃) is proportional to the applied electric field (Lyklema 1995):

�⃑� 𝐸𝑃 = 𝜇𝐸𝑃�⃑� =𝑞

𝑓�⃑� (2.1-5)

where 𝑞 is the particle charge and 𝑓 is the friction coefficient of the particle. 𝜇𝐸𝑃 is

defined as the electrophoretic mobility, and is often interpreted as (von Smoluchowski

1903):

𝜇𝐸𝑃 =𝜀0𝜀𝑟ζ

𝜂 (2.1-6)

where 𝜂 is the dynamic viscosity of the dispersed medium.

10

Figure 2.1-3. Schematics of a negatively charged particle surface. Zeta potential (ζ) is at

the shear plane. When a uniform electric field (�⃑� ) is applied from left to right as shown in

the image, the particle moves from right to left.

2.1.3 Dielectrophoresis

Dielectrophoresis (DEP) is the movement of a polarizable particle in a non-

uniform electric field (�⃑� ) (Pohl 1978, Jones 2005). The term was first named by Pohl

(Pohl 1978), implied from the Greek word phorein , meaning that the effect was as a

result of dielectric properties.

To study dielectrophoresis, the DEP force is a useful parameter to describe the DEP

behavior. Specifically, when the particle is polarized with an induced dipole moment

𝑝 = 𝑞𝑑 (2.1-7)

11

where 𝑑 is the distance between the center of positive charge +𝑞 and negative charge

−𝑞. Taking a sphere as an example, when the dipole potential (𝛷) is superposed onto the

original electric field �⃑� , the standard electrostatic boundary conditions at the surface of

the sphere (Pethig 2010) must satisfy the following conditions:

(1) On either side of the sphere's surface, the normal component of the gradient of Φ

changes so that 𝜀(𝑑𝛷/𝑑𝑛) remains constant. �⃑� is the unit vector of the radius 𝑅.

(2) 𝛷 is continuous across the boundary defined by the sphere's surface.

(3) In all of the space, 𝛷 satisfies Laplace's equation (∇2𝛷 = 0).

(4) At all distances far beyond the sphere, 𝛷 = −�⃑� 𝑥. where 𝑥 is the distance.

For an isotropic and homogeneous dielectric sphere, when an external electric

field �⃑� is applied at 𝑥 direction, an internal field �⃑� 𝑖 is induced and symmetric about 𝑥.

𝛷𝑖 = −�⃑� 𝑖 𝑥 (2.1-8)

For all space outside the sphere, the field created by the dipole is superposed onto �⃑� . The

polarization is presented as an induced dipole of effective moment 𝑝 = �⃑� 𝑘, where k is a

constant.

The potential caused by the external electric field �⃑� and the induced dipole moment 𝑝 at

any point in space can be expressed as:

𝛷0 = −�⃑� 𝑥 + �⃑� 𝑘

4𝜋𝜀𝑚∗ 𝑟2

∙𝑥

𝑟 (2.1-9)

12

r is the distance at any given direction. if r is not along 𝑥, the angle is given by θ, 𝑥 =

𝑟𝑐𝑜𝑠𝜃.

The radius of the particle is R, and at r = R, Φi = Φ0, and 𝜀𝑝∗ 𝜕𝛷𝑖

𝜕𝑟= 𝜀𝑚

∗ 𝜕𝛷0

𝜕𝑟.

So from Eq. 2.1-8 and 2.1-9 (Pethig 2010),

�⃑� 𝑖 = �⃑� (1 −𝑘

4𝜋𝜀𝑚∗ 𝑟3) (2.1-10)

and

𝜀𝑝∗�⃑� 𝑖 = 𝜀𝑝

∗�⃑� (1 +𝑘

4𝜋𝜀𝑚∗ 𝑟3) (2.1-11)

Through Eq. 2.1-10 and 2.1-11, k can be solved as

𝑘 = 4𝜋𝜀𝑚∗ 𝑅3(

𝜀𝑝∗ −𝜀𝑚

∗

𝜀𝑝∗ +2𝜀𝑚

∗ ) (2.1-13)

and the induced dipole,

𝑝 = 𝑘�⃑� = 4𝜋𝜀𝑚∗ 𝑅3(

𝜀𝑝∗ −𝜀𝑚

∗

𝜀𝑝∗ +2𝜀𝑚

∗ )�⃑� (2.1-14)

The DEP force (𝐹 𝐷𝐸𝑃) acting on the spherical particle is now subjected to a non-uniform

field, which is the algebraic sum of the forces acting on the positive and negative

elements of the induced dipole moment (Pethig 2010).

By performing a first order Taylor series expansion of �⃑� (𝑥 + 𝑑) about 𝑥, (higher-

order can be omitted due to the particle diameter which is much smaller than the scale of

13

the field non-uniformity), and taking the effective length of the dipole as 𝑑 = 2𝑅, the

DEP force can be written as:

𝐹 𝐷𝐸𝑃 = 𝑞 [𝐸(𝑥) + 2𝑅𝜕�⃑�

𝜕𝑥] − 𝑞�⃑� (𝑥) (2.1-15)

where

𝑝 = 𝑞𝑑 = 𝑞 ∙ 2�⃑� (2.1-16)

From Eq. 2.1-15 and 2.1-16,

𝐹 𝐷𝐸𝑃 = 𝑞 ∙ 2�⃑� 𝜕�⃑�

𝜕𝑥 = 𝑝 ∇�⃑� (2.1-17)

Taking Eq. 2.1-14 into 2.1-17,

𝐹 𝐷𝐸𝑃 = 4𝜋𝜀𝑚∗ 𝑅3(

𝜀𝑝∗ −𝜀𝑚

∗

𝜀𝑝∗ +2𝜀𝑚

∗ )�⃑� ∙ ∇�⃑� = 2𝜋𝜀𝑚∗ 𝑅3(

𝜀𝑝∗ −𝜀𝑚

∗

𝜀𝑝∗ +2𝜀𝑚

∗ )(∇�⃑� 2) (2.1-18)

As from Eq. 2.1-18, when the particle permittivity is larger than the permittivity

of the medium, the particle will be attracted to where the ∇�⃑� 2 is highest, which is called

positive DEP (p-DEP) (Medoro et al. 2007). On the contrary, if the particle permittivity is

smaller than the medium, the particle will move to where the ∇�⃑� 2 is lowest, which is

termed negative DEP (n-DEP), as shown in Figure 2.1-4.

The Clausius-Mossotti factor (Pohl 1978) is defined as

𝑓𝑐𝑚 =𝜀𝑝∗ −𝜀𝑚

∗

𝜀𝑝∗ +2𝜀𝑚

∗ (2.1-19)

14

where 𝜀𝑝∗ is the complex permittivity of the particle and 𝜀𝑚

∗ is the complex permittivity of

the medium. Specifically, the complex permittivity is given by 𝜀∗ = 𝜀 − 𝑗𝜎

𝜔, where 𝜀 is

the real part of the complex permittivity, σ is conductivity, and j is the imaginary unit,

𝑗 = √−1.

So Eq. 2.1-19 can be written as

𝑓𝑐𝑚 =𝜀𝑝∗ −𝜀𝑚

∗

𝜀𝑝∗ +2𝜀𝑚

∗ =𝜀𝑝−𝜀𝑚−𝑗(𝜎𝑝−𝜎𝑚)/𝜔

𝜀𝑝+2𝜀𝑚−𝑗(𝜎𝑝+2𝜎𝑚)/𝜔 (2.1-20)

This equation can be written as (Benguigui, Lin 1982):

𝑓𝑐𝑚 =𝜀𝑝−𝜀𝑚

𝜀𝑝+2𝜀𝑚=

3(𝜀𝑚𝜎𝑝−𝜀𝑝𝜎𝑚)

𝜏𝑀𝑊(𝜎𝑝+2𝜎𝑚)2(1+𝜔2𝜏𝑀𝑊

2 ) (2.1-21)

where 𝜏𝑀𝑊 is the Maxwell-Wagner charge relaxation time,

𝜏𝑀𝑊 =𝜀𝑝+𝜀𝑚

𝜎𝑝+2𝜎𝑚 (2.1-22)

The Clausius-Mossotti factor 𝑓𝑐𝑚 can thus be written as:

𝑓𝑐𝑚 = {

𝜎𝑝−𝜎𝑚

𝜎𝑝+2𝜎𝑚= 𝑅𝑒(𝑓𝑐𝑚), 𝑓𝑜𝑟 𝜔𝜏𝑀𝑊 ≪ 1

𝜀𝑝−𝜀𝑚

𝜀𝑝+2𝜀𝑚, 𝑓𝑜𝑟 𝜔𝜏𝑀𝑊 ≫ 1

(2.1-23)

From Eq. 2.1-23, when the applied alternating current (AC) frequency is low (Pethig

2010) (usually referred to below 50 MHz), the Clausius-Mossotti factor can be expressed

as

𝑅𝑒(𝑓𝑐𝑚) = 𝜎𝑝−𝜎𝑚

𝜎𝑝+2𝜎𝑚 (2.1-24)

15

Figure 2.1-4. Schematic representation of particle DEP in an inhomogeneous electric

field. a) positive DEP (p-DEP), particle moves to higher 𝛻𝐸2. b) negative DEP (n-DEP),

particle moves away from higher 𝛻𝐸2. The red arrow represents the direction of the

dipole moment and the movement direction of the particle.

Considering a plot of AC frequency vs. 𝑓𝑐𝑚, when 𝜀𝑝 > 𝜀𝑚 and 𝜎𝑝 < 𝜎𝑚, 𝑓𝑐𝑚 is

negative at low frequencies and n-DEP occurs, whereas at high frequencies, 𝑓𝑐𝑚 is

positive and p-DEP prevails. Conversely, when 𝜀𝑝 < 𝜀𝑚 and 𝜎𝑝 > 𝜎𝑚, 𝑓𝑐𝑚 is positive at

low frequencies and p-DEP prevails, whereas at high frequencies, 𝑓𝑐𝑚 is negative and n-

DEP occurs. The frequency when the switch between p-DEP and n-DEP happens is

termed the crossover frequency (Jones 2005).

2.1.4 Generating Inhomogeneous Electric Fields

As mentioned in 2.1.3, to generate a DEP force, the system requires an

inhomogeneous electric field (�⃑� ). Briefly, to generate the non-uniform electric field in a

microfluidic channel, usually either the size/shape of the electrodes are altered, or the

16

channel's opening size is changed dramatically, or insulator structures (and/or arrays) are

placed in the channel.

DEP devices using electrodes to generate inhomogeneous electric field are often

called electrode-based DEP (eDEP). eDEP devices can be fabricated by photolithography

(Chung et al. 2012), electron-beam evaporation (Zheng, Brody & Burke 2004), chemical

vapor deposition (CVD) (Zheng et al. 2004), etc. The shape of the electrodes include the

following: single pair electrodes (Kuzyk et al. 2008, Linko et al. 2009), quadrupole

electrodes (Chung et al. 2012), castellated electrodes (Kim et al. 2014), triangle pairs

(Holzel et al. 2005), arrays of micro-electrodes (Martinez-Duarte et al. 2013) and

plasmonic nanotip arrays (Schaefer, Kern & Fleischer 2015) etc.

Although these fabrication methods allow for micro/nanoelectrodes generating

high electric fields with low applied voltage, the fabrication is often complicated and

expensive, making large-scale systems less economically feasible (Gallo-Villanueva et al.

2009). Furthermore, electrodes are easily contaminated by bioparticles (Chou et al. 2002,

Cummings, Singh 2003). An alternative is to use insulator-based DEP.

Insulator-based DEP (iDEP), first proposed by Masuda et al. (Masuda, Itagaki &

Kosakada 1988) in the year 1988 and realized by Chou et al. (Chou et al. 2002) in the

year 2002, is a technique where insulating structures are functioning as "obstacles" in the

electric field, which disrupts the homogeneity of the field creating regions of large

electric field gradients adjacent to the insulating structure area (Gallo-Villanueva et al.

2009, Cummings, Singh 2003).

17

Compared to eDEP, iDEP's fabrication process is usually much less complicated

(Shafiee et al. 2009), for example, photolithographic (Gan et al. 2013) methods or etching

(Chou et al. 2002) methods were applied in the process. To improve the gradient of

electric field, methods such as focused ion beam milling (FIBM) (Camacho-Alanis, Gan

& Ros 2012, Nakano, Camacho-Alanis & Ros 2015) have also been used to improve the

efficiency to manipulate samples.

The typical shape of the iDEP device includes placing insulator post arrays in the

microfluidic channel (Chou et al. 2002, Tegenfeldt et al. 2004, Regtmeier et al. 2007b,

Regtmeier et al. 2010, Gallo-Villanueva et al. 2009, Lapizco-Encinas, Rito-Palomares

2007, Gan et al. 2013, Nakano et al. 2012, Nakano et al. 2011), and a sawtooth structured

channel (Staton et al. 2010) etc. Similar insulating structures are created by the corner of

a narrow linkage between channels (Abdallah et al. 2013, Ros et al. 2013), or the

confinement between the sample reservoirs and the channel (Braff, Pignier & Buie 2012,

Dingari, Buie 2014, Patel et al. 2012). By forming a ridge inside the channel, 3D iDEP

(Viefhues et al. 2012, Viefhues et al. 2013, Viefhues, Regtmeier & Anselmetti 2013) is

achieved, which highly increased the electric field near the insulating structure. Further

methods to implement iDEP have also been achieved using nanopipettes (Clarke et al.

2005, Clarke et al. 2007) to create narrow openings.

Further, in addition to the insulating array method, by modifying the post arrays

to a tilted angle, flow through fractionation devices (Beech, Jonsson & Tegenfeldt 2009,

Thomas, Dorfman 2014, Chen, Dorfman 2014b, Chen, Dorfman 2014a) were achieved

18

due to the nonsymmetrical lateral displacement of DEP trapping regions in a microfluidic

system.

However, one typical drawback is it usually requires large voltage potentials

(typically over 1000 𝑉), and a high electric field in conductive biological fluids inside a

microchannel (Sabounchi et al. 2008, Hardt, Schönfeld 2007), always causing high

electric current leading to Joule heating in direct current power supply devices (Shafiee et

al. 2009). This phenomena was detailed in Nakano et al. (Nakano, Luo & Ros 2014). To

avoid Joule heating, an alternating current (AC) power supply is used throughout this

thesis.

2.2 Common Models for DNA Dielectrophoresis

There are several models established regarding the electric double layer (EDL)

surrounding the particles. The dielectric properties are believed to be related to the

movement of the charges in the electric double layer (Midmore, Diggins & Hunter 1989).

The concepts of surface conductance and surface conductivity are used to quantify the

electrical properties. It is believed that the surface conductance is determined by the

movement of the ions in the electric double layer.

Early studies often use latex spheres in their experiments since the bulk

conductivity of the latex particles is negligible and thus the particle conductivity is due to

the charge movement around the spheres (Ermolina, Morgan 2005). Some research

shows that the polarization of the particles is mostly dependent on the surface

conductance (Green, Morgan 1999, Hughes, Morgan & Flynn 1999). But these results

19

only apply to particles in the micrometer range and fail to explain sub-micrometer sized

particles.

One theory used to explain polarization is brought by O'Konski known as

Maxwell-Wagner-O'Konski (MWO) theory (O'Konski 1960). In the MWO model, the

movement of the charge within Stern layer is considered to be dominant and therefore

their model for the particle conductivity is given by:

𝜎𝑝 = 𝜎𝑏 +2𝐾𝑠

𝑎 (2.2-2)

Here, 𝜎𝑝 is the particle conductivity, 𝜎𝑏 is the bulk material of the sphere's

conductivity. 𝐾𝑠 is the surface conductance due to the Stern layer and 𝑎 is the particle

radius. This theory can explain micrometer particles in the high frequency range (Chew

1984, Fixman 1983) where

(𝜆𝐷/𝑎)2𝑒|𝜁𝐹

𝑅𝑇|/2 ≫ 1 (2.2-3)

and with a thin electric double layer when

𝜆𝐷 ≪ 𝑎 (2.2-4)

More specifically:

𝜆𝑑

𝑎≤ 0.1 (2.2-5)

where 𝜆𝑑 is the thickness of the Debye layer, 𝜁 is the zeta potential, 𝐹 is Faraday

constant, 𝑅 is ideal gas constant, and 𝑇 is temperature.

20

However, this model failed to explain a sub-micrometer particle's behavior

(Green, Morgan 1999). In Eq. 2.2-2, the ion transfer in the diffuse layer is not considered.

In a thick double layer, the ion transfer in the diffuse layer is not negligible. Additionally,

the effect of ion migration in the diffuse layer in a low frequency AC field is significant

(Zhao 2011a). Thus, this model cannot explain a thick EDL or low frequency condition,

or even a thin EDL in a low frequency condition (Zhao, Bau 2009, Zhao, Bau 2008,

Saville et al. 2000).

Another model (Dukhin, Deryaguin 1974, Lyklema 1995) brought by Dukhin and

Lyklema (DL theory) and later improved by Hinch (Hinch et al. 1984) and Chew (Chew

1984) not only considered the effect of Stern layer but also the diffuse layer (Kijlstra,

Vanleeuwen & Lyklema 1992). With the modification of their model, the conductivity of

the particle can be written as:

𝜎𝑝 = 𝜎𝑏 +2𝐾𝑠

𝑎+

2𝐾𝐷𝑖𝑓𝑓

𝑎 (2.2-6)

where 𝐾𝐷𝑖𝑓𝑓 is the diffuse layer conductance.

Compared to the MWO theory, DL theory explained the thin double layer EDL in

low frequency. However, the DL model is based on the assumption that the EDL is at

"local equilibrium" (Zhao 2011a), which infers that the total number of the ions inside the

EDL does not change before and after the application of electric field. Reaching

equilibrium needs sufficient time and only low frequencies could provide the time for the

EDL to obtain "local equilibrium". Thus DL theory only applies to the low frequency

condition but is incapable of explaining high frequency conditions.

21

Furthermore, both MWO theory and DL theory assumed that the particle and its

EDL stay relatively stationary on the dipole moment (Zhao, Bau 2008, Zhao 2011a). But

for particles with a thick double layer, the effect of electrophoretic motion of the particle

is significant, and the movement between particle and EDL induced by the response of

particle to the electric field should be taken into consideration. This is the most important

reason that the MWO and DL theories do not fit with the thick double layer case.

A new Poisson-Nernst-Planck (PNP) model is used by Zhao, to explain the thick

EDL case. This model adds the consideration of a particles electrophoretic mobility aside

from the EDL consideration in DL theory. The PNP theory not only explained the dipole

moment of spherical particles (Zhao, Bau 2009), but also explained long cylindrical

particles with an electric field transverse to their axis (Zhao, Bau 2008) and aligned with

the axis (Zhao, Bau 2010).

Zhao's PNP model applied the experimental object from latex particles to DNA.

For short DNA with the size limitation of 150 𝑏𝑝 (Zhao, Bau 2010), they used a nanorod

model and for longer DNA, they applied the PNP model to the long and coiled molecule

considering the DNA as a spherical particle with its radius of gyration as the particle

radius (Zhao 2011b).

However, all the models mentioned above failed to consider the shape change of

DNA molecules along the electric fields and the orientation of the particles, which, in

most cases, complicates the DEP mechanism. DNA particles with defined shape and rigid

structure are called for to facilitate such research.

22

The models mentioned above did not consider the DNA molecules under different

buffer valency. Chapter 7 will compare the DNA molecules trapping behaviors in

different buffer valency, both circular plasmid DNA (λ-DNA) and a rigid DNA structure

(6-helix bundle origami) was used to demonstrate the act of EDL on the DEP behavior.

2.3 DNA Origami Model

In this dissertation, apart from the linear DNA and circular plasmid DNA (λ-

DNA), DNA origamis were used as their defined size and shape as well as mono-size-

distribution. Due to their rigid structure, the elongation of the particle is omitted when an

electric field is applied.

Figure 2.3-1. Schematics of the shape of a) 6HxB DNA and b) Triangle origami. 𝑎, 𝑏 and

𝑐 are the half axis. a) rod-like 6HxB origami with 𝑎 > 𝑏 = 𝑐. 𝑎 = 190 𝑛𝑚, 𝑏 = 𝑐 = 3.5 𝑛𝑚. b) Triangle origami is approximated as an oblated ellipsoid with 𝑎 = 𝑏 = 87 𝑛𝑚, 𝑐 = 1 𝑛𝑚.

Two DNA origami species were selected as their geometry varies significantly.

The distinct structures were described as follows. The 6HxB origami is a cyclic DNA

motif that consists of six DNA double helices where each helix connects to nearby

23

helices to form a hexagonally symmetric tube (Mathieu et al. 2005). The diameter of the

6-helix bundle structure is ~ 7 𝑛𝑚 and the length ~ 380 𝑛𝑚 resembling a rod, as

outlined in Figure 2.3-1a. The 6HxB can thus be treated as a prolate ellipsoid with 𝑎 >

𝑏 = 𝑐, where 𝑎 = 190 𝑛𝑚, 𝑏 = 𝑐 = 3.5 𝑛𝑚. The triangle origami has a length of

130 𝑛𝑚 along its symmetry axis and is 2 𝑛𝑚 high(Rothemund 2006), see Figure 2.3-1b.

Thus, this particle can be approximated as an oblate ellipsoid (𝑎 = 𝑏 > 𝑐, with 𝑎 =

86.7 𝑛𝑚 and 𝑐 = 1 𝑛𝑚) with a and b corresponding to the radius of the circumscribed

circle.

In the first approximation, the DEP migration is described similar to a compact

particle considered an ellipsoid surrounded by counterions and the DEP force for at low

frequency (𝜔 < 15000 Hz in all experiments) is epressed as (Clarke et al. 2007, Lei, Lo

2011):

𝐹 𝐷𝐸𝑃 =4

3𝜋𝑎𝑏𝑐𝜀𝑚 (

𝜎𝑝−𝜎𝑚

𝑍𝜎𝑝+(1−𝑍)𝜎𝑚) ∇�⃑� 2 (2.3-1)

Here, 𝜎𝑝 and 𝜎𝑚 denote the particle and medium conductivity, respectively, 𝑎, 𝑏 and 𝑐

are the radii of the ellipsoid along the 3 major axes, 𝑍 is the depolarization factor and �⃑�

the electric field. Assuming that in this model 𝜎𝑝 denotes the sum of the contributions

arising from condensed and diffuse counterions near the DNA species. The

dielectrophoretic migration gives a particle velocity, �⃑� 𝐷𝐸𝑃, arising from the balance of

𝐹 𝐷𝐸𝑃 and the drag force expressed as (Kwon et al. 2008, Baylon-Cardiel et al. 2009):

e p em

24

�⃑� 𝐷𝐸𝑃 = −𝐹 𝐷𝐸𝑃

𝑓 (2.3-2)

where 𝑓 is the friction factor. For an ellipsoid, 𝑓 is given by (Probstein 2003):

𝑓 = 6𝜋𝜂2

𝑆 (2.3-3)

where 𝜂 is the medium viscosity and 2/𝑆 is the mean translational coefficient. When

introducing the DEP mobility, 𝜇𝐷𝐸𝑃, via

�⃑� 𝐷𝐸𝑃 = −𝜇𝐷𝐸𝑃∇�⃑� 2 (2.3-4)

Combining Eq. 2.3-1 to 2.3-4 𝜇𝐷𝐸𝑃 for an ellipsoid particle can be derivative as:

𝜇𝐷𝐸𝑃 =4

3𝜋𝑎𝑏𝑐𝜀𝑚 (

𝜎𝑝−𝜎𝑚

𝑍𝜎𝑝+(1−𝑍)𝜎𝑚)

1

𝑓 (2.3-5)

The polarizability of the particle 𝛼, can then be determined, using the following

expression 𝜇𝐷𝐸𝑃 via 𝜇𝐷𝐸𝑃 =α

2𝑓 (2.3-6).

For the polarization factor 𝑍 and a shape factor 𝑆 for the two distinctive types of

origamis are as follows, related equations and calculated parameters summarized in Table

2.3-1.

6HxB Origami

As shown in Figure 2.3-1, the 6HxB can be treated as a prolate ellipsoid with

𝑎 > 𝑏 = 𝑐, where 𝑎 = 190 𝑛𝑚, 𝑏 = 𝑐 = 3.5 𝑛𝑚. In the case of a prolate ellipsoid,

𝑍∥ is (Lei, Lo 2011, Cruz, Garcia-Diego 1998):

25

𝑍∥ =𝑏𝑐

2𝑎2𝑒3 [𝑙𝑛 (1+𝑒

1−𝑒) − 2𝑒] (2.3-7)

where 𝑒 corresponds to the eccentricity:

𝑒 = √1 −𝑏𝑐

𝑎2 (2.3-8)

Further, for a prolate ellipsoid 𝑆 amounts in (Probstein 2003):

𝑆 = 21

√𝑎2−𝑏2ln

𝑎+√𝑎2−𝑏2

𝑏 (2.3-9)

Using equation 2.3-3, 2.3-5 and 2.3-9, we can calculate 𝜇𝐷𝐸𝑃 for the 6HxB origami in

parallel orientation.

For a perpendicular orientation of the 6HxB with respect to the electric field 𝑍 changes to

𝑍⊥:

𝑍⊥ =1

1−𝛾2 −𝛾−2

4(1−𝛾−2)−1.5 ln [1+(1−𝛾−2)

0.5

1−(1−𝛾−2)0.5] (2.3-10)

where 𝛾 =𝑎

𝑏

Triangle Origami

In the case of an oblate particle, 𝑍∥ parallel to the electric field is expressed as:

𝑍∥ = (−𝛾2

2𝑀) + (

𝜋𝛾

4𝑀1.5) − (𝛾

2𝑀1.5) arctan (𝛾2

𝑀)0.5

(2.3-11)

where 𝛾 =𝑐

𝑎 and 𝑀 = 1 − 𝛾2.

26

Note that 𝑆 for an oblate ellipsoid is given as:

𝑆 =2

√𝑎2−𝑐2tan−1 √𝑎2−𝑐2

𝑐 (2.3-12)

Using Eq. 2.3-3, 2.3-5, 2.3-11 and 2.3-12, 𝜇𝐷𝐸𝑃 for the triangle origami can now be

calculated.

Furthermore, a polarization perpendicular to the plane of the triangle origami is considered.

𝑍⊥ is then given as (Rivette, Baygents 1996):

𝑍⊥ = (1

𝑀) + (

𝜋𝛾

2𝑀1.5) − (𝛾

𝑀1.5) arctan (𝛾2

𝑀)0.5

(2.3-13)

27

28

CHAPTER 3

3. MATERIALS, METHODS AND INSTRUMENTAL

3.1 Chemicals

Si wafers were purchased from University Wafer (USA). Negative photoresist

SU-8 2007 and developer were from Microchem (USA). Sylgand 184 and curing agent

for preparing Poly(dimethylsiloxane) (PDMS) was purchased from Dow Corning

Corporation (USA). Potassium phosphate monobasic, sodium phosphate dibasic,

tris(hydroxymethyl)aminomethane (Tris), ethylenediaminetetraacetic acid (EDTA),

magnesium acetate, acetone, isopropanol, 2-mercaptoethanol and acetic acid were

purchased from Sigma-Aldrich (USA). Ethanol was purchased from KOPTEC (USA)

and Silane-3400 (Poly(ethyleneoxy)di(triethoxy)-silane, 𝑀𝑊 = 3400) from Laysan Bio

(USA). YOYO-1 iodide was purchased from Life Technologies (USA). Limbda DNA is

purchased from Invitrogen (USA). Glass slides were obtained from Electron Microscopy

Sciences (USA) and Pt wire from Alfa Aesar (USA). Ultrapure water is obtained from a

Synergy purification system (Millipore, USA).

3.2 Origami Synthesis and Characterization

The synthesis method is the same with Gan’s previous publication (Gan et al.

2013). DNA origamis were synthesized using circular M13mp18 virus DNA as the

scaffold and tailored complementary short strand DNA fragments (staple strands) direct

the scaffold into desired shapes. 10-fold excess of staple strands was mixed with the

scaffold in TAE-Mg buffer (40 𝑚𝑀 Tris 𝑝𝐻 = 7.5, 1 𝑚𝑀 EDTA, 12.5 𝑚𝑀 Mg(OAc)2,

29

20 𝑚𝑀 acetic acid) and annealed reducing the temperature from 95 ℃ to 20 ℃. The

DNA origamis were then purified with agarose gel electrophoresis and extracted via a

DNA freeze squeeze column (Bio-Rad, USA). All polarizability determination

experiments were performed with gel purified DNA origami. To characterize the DNA

origamis sample were deposited on mica, incubated until dried and rinsed with ultrapure

water followed by ethanol. Atomic Force Microscopy (AFM) imaging with intermittent

contact mode was performed with a MFP-3D instrument from Asylum Research (USA).

3.3 Microchip Fabrication

First, a SU-8 structure was created on a Si wafer through photolithography as

previously described (Duong et al. 2003) serving as the master for PDMS molding, as

shown in Figure 3.3-1. Briefly, a thin layer of SU-8 was spincoated on a Si wafer and

exposed to UV light through a photomask (Photosciences, USA) and developed.

Subsequently, the PDMS pre-polymer and agent were mixed thoroughly, cast on the

master wafer and then cured in 80 ℃ for 4 ℎ. After lift-off, reservoir holes were manually

punched at each end of the structured channel. PDMS and glass slides were cleaned with

acetone, isopropanol and ultrapure water and blow-dried with N2. The PDMS channel

and a glass slide (PDMS spin-coated glass slide in Chapter 7, detailed in Chapter 3.4)

were then treated with an oxygen plasma using a plasma cleaner (PDC-001 Harrick

Plasma, Harrick, USA) and the device was sealed by superimposing the two surfaces.

30

Figure 3.3-1. a) A thin layer (~10 𝜇𝑚) of SU-8 (brown) was spin-coated on a Si wafer

(dark gray), followed by exposure to UV light trough a chrome on soda-lime photomask

with desired pattern (shallow gray). b) After exposure and a soft baking procedure, the

unexposed SU-8 were removed with developing solution. After hard baking procedure,

the inverted structure of photoresist is on the wafer. c) Casting PDMS on master wafer to

make PDMS mold (shallow blue). d) Lift-off procedure to get desired structure. e) punch

reservoir holes. f) Oxygen plasma seal the structure from e) to a clean glass slides

(PDMS spin coated glass for method in Chapter3.4.2).

3.4 Channel Incubation

The method development for channel incubation is shown in Appendix A.

3.4.1 In Sodium/Potassium Phosphate Buffer System

This method is used in Chapter 5 and Chapter 6. Briefly, Newly assembled

microchips were incubated over night with a freshly prepared solution of 10 𝑚𝑀 Silane-

3400 in 5 𝑚𝑀 phosphate buffer 𝑝𝐻 = 8.3. The channel is then rinsed with 5 𝑚𝑀

phosphate buffer before experiment.

31

3.4.2 In Phosphate Buffer System Containing Magnesium

In Chapter 7, a buffer contains magnesium (~5 𝑚𝑀 KH2PO4/K2HPO4 and

~5 𝑚𝑀 MgCl2) is used and the channel incubation method is adjusted accordingly. Chip

assembly procedures were exactly the same, only the glass slide is spin coated with 1: 5

(curing agent: pre-polymer) PDMS. Newly assembled chips were incubated with a

freshly prepared solution of 0.04 % (w/w) Silane-3400 in 9: 1 (v/v) ethanol -water 𝑝𝐻 =

5.0 for 30 𝑚𝑖𝑛. The incubation buffer is then exchanged with the experiment buffer

(~ 5 𝑚𝑀 KH2PO4/K2HPO4 and ~ 5 𝑚𝑀 MgCl2, 𝑝𝐻 = 7.0, conductivity (𝜎)

~ 0.20 𝑆/𝑚) by a pressure pump at least 3 times, giving at least 30 𝑚𝑖𝑛 between each

run, letting the channel fully recover for aqueous ambient before the experiment start.

3.5 Constructing the Voltage-Supply Instrument and the Software Programming

The application of the whole set-up is to control the voltages applied to the four

reservoirs from the cross-shaped injection chip as shown in Figure3.6-1b (see Chapter

3.6), while recording the time elapsed from the moment the sample plug leaves the

injection point to the moment the sample reaches the detection point. In this set-up, the

critical points are to control the four channels of voltage simultaneously and the time

synchronization between voltage control and automatic data recording.

There are 2 generations of the instrument. For each generation, LabVIEW

program were written correspondingly according to the each hardware construction.

32

3.5.1 Generation 1

In Generation 1, the hardware to control the high voltages are iseg High Voltage

Power Supply T3DP 030 405 EPU (iseg Spezialelektronik GmbH, Germany), (later

abbreviated as iseg power supply), containing three channels and each provides voltages

up to 3000 𝑉, and NI USB 6343 X series DAQ (National Instrument, USA) (abbreviated

as USB box), only providing up to ±10 𝑉, which needed a high voltage amplifier

Matsusada AMT-3B20 (Matsusada Precision, Inc., Japan) (abbreviated as AMT),

amplifying voltage to ±3000 𝑉.

3.5-1. A schematics of the control LabVIEW program from Generation 1. The computer

sent signal to both iseg power supply and USB box almost simultaneously. While iseg

power supply used VISA to control, USB box used DAQ control. For iseg power supply

specifically, the read-in and read out of voltage from Channel A, B and C are in a queue,

which carried out as a loop over time.

The schematics of the control program of this set-up is shown in Figure 3.5-1. In

this set-up, three channels are controlled by iseg power supply and one channel is

33

controlled by USB box combined with AMT. iseg power supply is controlled by Virtual

Instrument Software Architecture (VISA), which can be placed in Labview platform. The

USB box can be controlled in LabVIEW directly when using a plug-in NIDAQ961f1

(National Instruments, USA), (later abbreviated as DAQ). However, the iseg power

supply could only execute commands single-threadedly, which means only one voltage

reading could be taken into and read out from its RAM at one instant. In order to control

all three channels' voltages, the program was written to input and output voltages from

three channels in a loop, and the loop command was run repeatedly to insure that the

voltages of the three channels were carried out almost instantly.

Ideally, the response of all three iseg power supply channels controlled by VISA

and the USB box channel controlled by DAQ should be instantaneous. However, a slight

time delay between the different set-ups occurred and as the time of running the program

increased, the time delay cannot be omitted. Moreover, the iseg power supply hardware

cannot ensure stable high voltage larger than 500 𝑉, and to switch the polarity of the

voltages from iseg power supply, an additional equipment is needed. Switching the

polarity of the power took approximate 1 s, which is highly unfavorable in the condition

when time synchronization is strictly required. A second generation of set-up was needed

to consider this.

3.5.2 Generation 2

The second generation of the set-up considered the importance of time

consistency and accuracy, thus, all the voltages were controlled by the USB box. The set-

34

up of the hardware is as follows: The USB box controls all four channels of voltages (up

to ±10 𝑉), three of which were connected to Ultravolt High Voltage Power Supply

(Ultravolt, USA) (later abbreviated as Ultravolt), providing voltage up to ±5000 𝑉, and

serving as a voltage amplifier; and one of the channels was connected to AMT as

mentioned in 3.5.1. In this case, the time limit of the voltage control is only limited to the

speed of the computer, which promised the voltage control for all channels to happen

simultaneously. The schematics of voltage control is shown in Figure 3.5-2.

Figure 3.5-2. Schematics of the voltage control for Generation 2. Compare to Figure 3.5-

1 from Generation 1, the time delay between Channel 1, 2 and 3 (Ultravolt C 1, Ultravolt

C 2 and Ultravolt C 3) are omitted, thus giving a better time control.

Generation 2 also incorporated the photon multiplier (HAMAMATSU H9319-11,

Japan) into the LabVIEW program, to later record the time the injection peak appeared

(detailed in Chapter 6). To integrate the photon multiplier in the program and realize the

time synchronization, the time is started to record as soon as the voltage applying step

started (𝑡 = 0). The program is designed to take the recording of photon multiplier at a

35

specific step (Step 3), in the beginning of Step 3, the starting time for photon multiplier

is recorded (𝑡 = 𝑡0), and from this time point, the corresponding time and photon counts

were recorded in a txt file. At the end of Step 3 (𝑡 = 𝑡1), both time and photon counts

stopped recording until the next run.

The program is designed to perform continuous runs when all the voltage

parameters were set and did not required a change. But after several tests, the missed

synchronization between voltage control and the multiplier was found due to the

hardware of the photon multiplier causing a slight time delay each time, which could be

omitted during the same run. After several runs, the total time extended and the errors

added up so the time delay could not be negligible any more. In this case, the time 𝑡 =

𝑡0 and 𝑡 = 𝑡1 recorded from photon multiplier were not the real time t0 and t1, but to

note, 𝑡0 and 𝑡1 were still in the same run, so the time difference was still in a tolerable

time scale. A simple solution is to add another 2 lines in the recorded data to track the

specific number of runs and steps each recorded point corresponded to, so the error

between each run wouldn't affect the overall timing. Since in the experiment the needed

precise timing was the time difference with Step 3, the method worked well.

Generation 2 set-up also compiled a CCD camera (Quantum 512SC,

Photometrics, USA) in the program. Similarly to the photon multiplier, the camera is

triggered at the third step of the program. When the third step starts, the program sent a

series of Transistor-transistor logic (TTL) signals to the camera, each signal triggered an

image recording to the camera, thus the complete recording of step 3 can be recorded by

36

the camera. The time and frequency of the TTL signals were adjustable. Since the time

between each picture recording is known and the starting trigger time is simultaneous

when the third step started, the exact time of recording is also deducible.

3.6 Detection

DNA samples (6HxB origami and triangle origami were used in Chapter 5 and

Chapter 6, λ-DNA and 6HxB were used in Chapter 7) were diluted to a concentration of

40 − 100 𝑝𝑀 (100 𝑝𝑀 for 6HxB and triangle origami, 40 𝑝𝑀 for λ-DNA) in the

detection buffer of sodium/potassium phosphate (Chapter 5 and Chapter 6: 5 𝑚𝑀

sodium/potassium phosphate buffer, 𝑝𝐻 ~ 8.3, conductivity ~ 0.1 𝑆/𝑚) or magnesium

containing potassium phosphate buffer (Chapter 7: 5 𝑚𝑀 KH2PO4/K2HPO4 and 5 𝑚𝑀

MgCl2 for experiment group 10 𝑚𝑀 KH2PO4/K2HPO4 for control group). Both mono-

valent buffer (potassium buffer) and di-valent buffer (Mg2+ containing buffer) resulted in

a 𝑝𝐻 ~7.0 and conductivity ~ 0.2 𝑆/𝑚, and contained (0.2 % v/v) 2-mercaptoethanol,

and a ratio of YOYO-1 to base pairs of 1: 20.

Reservoir holes were punched on a PDMS slab to increase the volume of the chip

reservoirs and served as a sample holder. Platinum wires were attached to the reservoir

holes on the sample holder. For Chapter 5 and Chapter 7, each reservoir was filled with

~40 𝐿 of sample solution (Shown in Figure 3.6-1a). For Chapter 6 specifically, sample

was filled in Reservoir A (Shown in Figure 3.6-1b) and all other reservoirs were filled

with fresh buffer. The chip was held with a stage (PRIOR ProScan II, PRIOR scientific,

USA) under a microscope (IX 71, Olympus, USA) (for Chapter 6, the stage was used for

37

visual inspection and to determine migration distances). All the platinum wires were

wired to the power supply set-up mentioned in 3.5.

Figure 3.6-1. a) iDEP device consists of a linear microchannel molded with PDMS with a

cross section of 10 × 80 μm, in which post arrays with elliptic bases were integrated along

the entire microchannel length of ~ 1 𝑐𝑚 . Diameters for the oval posts are 10.5 and

11.6 𝜇𝑚 along the short and long axis, respectively, and the separation between the posts

is 2.1 𝜇𝑚. The lower zoom-in shows a three-dimentional representation of a section of the

post array in the microfluidic channel (not to scale). Applied AC potential is along black

arrows. b) Schematics of the microfluidic device used to determine DNA origami

polarizabilities. Channels linked to reservoirs A, B and C are 1.7 cm long, and the channel

linked to reservoir D containing the post array is 2 𝑐𝑚 long. All the channels are 100 µ𝑚

wide and 10 µ𝑚 deep. The distance between intersection and detection point is L. The

zoom of the long channel shows a section of the post array (not to scale) The diameter of

the posts is 10 µ𝑚, and the distance between posts within a row is 2.5 µ𝑚, the distance

between the rows (in flow direction) is 6.6 µ𝑚 . The blue arrow corresponds to the

migration.

For Chapter 5 and 7, AC voltages were applied along the straight channel filled

with DNA sample (Shown in Figure 3.6-1a). The fluorescence intensity is observed with

an inverted microscope (IX 71, Olympus, USA) equipped with a fluorescence filter set

suitable for YOYO-1 (exciter ET 470/40x, dichroic T495 LP, emitter ET 525/50m,

38

Olympus, USA). A CCD camera (Quantum 512SC, Photometrics, USA) was used for

image data acquisition. Data analysis was performed with ImageJ freeware (1.47b)

(Anonymous 2015).

For Chapter 6 (Shown in Figure 3.6-1b), DC voltages were applied to the

reservoirs to induce a pinched electrokinetic injection. Specifically, three reservoirs

(Reservoir A, C and D from Figure 3.6-1b) were filled with phosphate buffer (as detailed

at the beginning of Chapter 3.6), and the fourth reservoir was filled with ~250 𝑝𝑀

6HxB/triangle origami sample prepared with aforementioned buffer. The chip was held

with a stage (PRIOR ProScan II, PRIOR scientific, USA) on an optical microscope (IX

71, Olympus, USA) to record the positions. Voltages are applied to the reservoirs to

control the injection.

Specifically, to determine the electrophoretic mobility for 6HxB and triangle

origami, a cross-shaped device is used. The dimension for the device is exactly the same

with the device shown in Figure 3.6-1b, only without post arrays in Channel D. Two

steps were required to induce electrokinetic injection. First, 0 𝑉, 150 𝑉, 500 𝑉 and 100 𝑉

DC voltages were applied to Reservoir A, B, C and D respectively and sample was

loaded from Reservoir A to C. Next, 150 𝑉, 0 𝑉, 150 𝑉 and 500 𝑉 DC voltages were

applied to Reservoir A, B, C and D respectively so a pinched flow of sample from the

intersection is injected to Channel D. The injected plug was detected by a photomultiplier

(HAMAMATSU H9319-11, Japan) at a specific channels and the detection point is

defined as 𝐿. 𝐿 was measured for each channel and varied by ~0.2 𝑚𝑚 for each

experiment. As described in Chapter 3.5, a LabVIEW program synchronized the

39

photomultiplier and the voltage control. When the second step (pinched sample plug

injected into channel D) started, the photomultiplier started to record the intensity at the

detection position. An electropherogram of the intensity (number of photons) via time

was plotted. An example of the electropherogram is shown in Figure SI C-4 from

Appendix C. The migration time is defined as the time when the intensity reached the

maximum. Through this experiment, the electrophoretic mobilities for 6HxB and triangle

origami can be determined. The results of the electrophroretic mobilities are shown in

Chapter 6.2-1.

For the determination of the polarizabilities for the two origami species (Chapter

6), a device with post array in channel D is used, as depicted in Figure 3.6-1b. Pinched

electrokinetic injections were also performed. First, a DC-only pinched injection

condition is applied (conditions as described above). Next, using the same DC injection

conditions, in the second step described in the last paragraph, an AC signal was overlaid

to reservoir D in addition (See Figure 3.6-1b). With DC only, the migration time is

recorded as 𝑡0, while with an AC overlay, the migration time is recorded as 𝑡. Each AC

condition (or DC only) were recorded five times. Different AC conditions were

performed on each chip. The applied AC voltage varied from 600 𝑉 to 1400 𝑉 at 200 𝐻𝑧

for 6HxB and 1400 𝑉 to 1800 𝑉 at 300 𝐻𝑧 for the triangle origami. The resulting times

were used to correlate 𝑙𝑛𝜏 (detailed in Chapter 6) with the amplitude of the applied 𝑈𝐴𝐶

signal.

40

3.7 Data process

For Chapter 5, data analysis was performed with ImageJ. The trapping length,

𝐿𝑡𝑟𝑎𝑝, was found by drawing a straight line in the 𝑦-direction at the point in the 𝑥-

direction where the concentration was at the maximum. Subsequently the 𝑦-coordinates

at which the concentration was decreased to 50 % of the maximum concentration was

used to define the trapping length (𝐿𝑡𝑟𝑎𝑝). This procedure was applied to both the

numerical simulation data as well as to the recorded fluorescence intensity from

experiments. 𝐿𝑡𝑟𝑎𝑝 in numerical simulations was determined at the 20th period for each

frequency. Experimentally, 𝐿𝑡𝑟𝑎𝑝 was determined from the average of 60 frames. A total

of five trapping regions for experiments and three trapping regions for simulations around

the iDEP posts were analyzed for each frequency.

41

CHAPTER 4

4. NUMERICAL MODELING

4.1 Introduction

COMSOL Multiphysics is a multipurpose software platform for simulating

physics-based problems. The software provides numbers of modules to satisfy different

physical environments, such as pressure acoustics, alternating current/direct current

physics, fluid flow, heat transfer and structural mechanics. By applying a single module

or combining multiple modules, a numerical model can be established mimicking the

experimental conditions. In the software, numerical solvers with different algorithms can

be employed to perform simulations for a stationary or time-dependent study, which

provides valuable information for designing experiments and elucidating experimental

results.

4.2 Multiphysics Model Set-up

To simulate the DNA molecules' behavior in the microfluidic channels, COMSOL

Multiphysics (Version 4.3b-5.0) was used.

A desired geometry can be either directly drawn in the program or exported from

AutoCAD software as .dxf format file. In this thesis, a two-dimensional (2D) geometry is

often used. A three-dimensional (3D) geometry can be created by defining a workplane

(the 2D geometry) and extruding the plane in a desired thickness. The materials used for

the geometry can be chosen from the materials library or defined as necessary. Various

42

parameters such as density, permittivity, conductivity, viscosity etc. that are the physical

properties from the geometry and later used in the simulations are defined in this section.

Mesh: Mesh enables the discretization of the geometry into small units of simple

shapes, referred to as elements, which was used in the approximations in the simulation

study. The quality and the resolution of the mesh element directly affects the accuracy of

the simulation results. The finer the mesh is, the more accurate the simulation is, but the

longer time it takes. In most of the study, "extremely fine" mesh was used while in some

big structures "extra fine" was used.

To build a multiphysics model, the physics has to be chosen to claim the initial

states and input corresponding equations applied in simulations. In this thesis, one or

more physics from electric currents, creeping flow and transport of diluted species were

used.

Electric currents (ec): In this physics, the boundary conditions from the geometry

is defined as insulator, electric potential or ground. When defined as insulator, the

boundary condition specifies no current flows across the boundary, which is often the

case in the insulator based microfluidic channel. Electric potential and ground are the

initial conditions when at the boundary, a specific potential or ground (potential equal to

0) is applied.

Laminar flow (spf): This physics defines the flow type inside the geometry

(microfluidic channel), as in this case, incompressible Navier-Stokes flow (Batchelor

1967). The inlet and out of the fluid are defined as "open boundary" to indicate no

43

pressure is applied to the channel and the initial velocity of the fluid is zero. At the

channel walls, a "no slip" condition is applied, as described from Chapter 2.1. And the

driving force for the solution is only electroosmotic force and for the DNA dispersed in

the solution, electrophoresis is also applied due to the negative charge nature.

Transport of diluted species (tds): This physics is used to define the initial state

and physical conditions applied to the dispersed species (DNA) in the solution. e.g. The

sample does not pass the walls, so "no flux" condition is applied. At the inlet and outlet

of the fluid, "inflow" and "outflow" conditions are applied to specify the initial

concentration of the species at the boundary and the initial concentration of the whole

flow area can also be defined in this physics. The DNA sample in this channel

experiences diffusion and dielectrophoretic force, which are inserted in this physics with

convection-diffusion model detailed in Chapter 4.2.

After setting up geometry, materials, physics and mesh, solvers and algorithms

can be chosen according to the necessity and then study can be carried out for the

simulation. Chapter 4.3 will talk about time dependent solver specifically.

4.3 Convection-Diffusion Model

To model DNA transport (in Chapter 5), a convention-diffusion model is employed,

which has been previously used for protein (Nakano et al. 2011), DNA (Martinez-Duarte

et al. 2013) and nanoparticle DEP (Cummings, Singh 2003) accounting for DNA origami

electrophoresis, electroosmotic flow, dielectrophoresis and diffusion. No pressure drop is

accounted for in this model. The total flux 𝑗 is then expressed as:

44

𝑗 = −𝐷∇𝑐 + 𝑐(�⃑� 𝐸𝑃 + �⃑� 𝐸𝑂𝐹 + �⃑� 𝐷𝐸𝑃) (4.2-1)

where 𝐷 is the diffusion coefficient, c is the sample concentration, �⃑� 𝐸𝑃 is the

electrophoretic velocity and �⃑� 𝐸𝑂𝐹 the electroosmotic velocity. COMSOL Multiphysics is

used to model the electric field in the channel and subsequently solve for the concentration

distribution. The electric field in the simulation is adapted to experimental conditions. The

diffusion coefficient was estimated at room temperature using 𝐷 = 𝑘𝑇/𝑓, with the mean

friction factors (Probstein 2003), and, the Boltzman constant, 𝑘, and the temperature, 𝑇.

An electrophoretic mobility, 𝜇𝐸𝑃 , of −3.5 × 10−8 𝑚2/𝑉𝑠 is used to account for the

origami electrophoresis as previously reported for dsDNA (Regtmeier et al. 2007b) while

an electroosmotic mobility, 𝜇𝐸𝑂𝐹 of 2.2 × 10−8 𝑚2/𝑉𝑠 was determined with the current

monitoring method (Hellmich et al. 2005) described in Chapter 2.1 (data not shown). The

DEP mobility is calculated by applying Eq. 2.3-4 from Chapter 2.3.

In the very first study, equation 4.2-1 is solved in steady state:

𝜕𝑐

𝜕𝑡∇𝑗 = 0 (4.2-2)

To solve this model, electric currents, Laminar flow and transport of diluted species

physics as mentioned in 4.1, were used to simulate the electric field distribution,

electrokinetic component, and sample concentration respectively.

4.4 Time Dependent Study

In the DNA trapping experiment (Chapter 5), alternating current (AC) voltages

with a sine waveform were applied and time-dependent study is needed for the simulation

45

of the electric field change via time and the DNA concentration profile change as a

consequence. A sinusoidal AC component for the electric field is introduced for solving

the creeping flow module and transport of diluted species module in the time dependent

solver.

Specifically, a steady state study was first generated as described in Chapter 4.1

and 4.2 at time 𝑡 = 0 𝑠, to solve electric currents (ec) module, and then a time-

dependent study was built with the start time, time step interval and end time. To note, in

the time dependent study, the electric field changed via time. Namely, in creeping flow

module and transport of diluted species module, the electric field is set up as

�⃑� = �⃑� 0𝑠𝑖𝑛 (2𝜋𝑓𝑡) (4.3-1)

where �⃑� is the electric field in time dependent study and �⃑� 0 is the electric field solved

from the steady state study, 𝑓 is the AC frequency and 𝑡 is the time elapse. Generally in

the simulation, the time was set up as 20 periods of the application of the AC voltages,

and the step was 1/8 of one AC period. e.g. When simulating 60 Hz AC, the time would

be 1s

60× 20 = 0.33 s and the step interval would be

1s

60×

1

8= 0.0021 s. Proper solvers,

numbers of iterations and tolerance were selected to approach the results.

4.5 Electric Field Calculation

COMSOL Multiphysics was used to model the electric field in the channel with the

electric currents (ec) module (Chapter 6). All the channel walls were considered electric

insulators with Neumann boundary condition and the potentials applied were adapted to

46

experimental conditions. From these calculations |�⃑� 𝑔𝑎𝑝| (mean electric field in the

dielectrophoretic trap) and |�⃑� 𝑚𝑖𝑑| (electric field in the space between two rows of posts

where no appreciable dielectrophoresis acts) were extracted.

47

CHAPTER 5

5. DEP MANIPULATIONS OF DNA ORIGAMIS

5.1 Introduction

Insulator-based dielectrophoresis (iDEP) provides an efficient and matrix-free

approach for manipulation of micro-and nanometer-sized objects. In order to exploit iDEP

for DNA nanoassemblies, a detailed understanding of the underlying polarization and

dielectrophoretic migration is essential. Here, we explore the dielectrophoretic behavior of

6-helix bundle (6HxB) and triangle DNA origamis with identical sequence but large

topological difference and reveal distinct iDEP trapping behavior in low frequency AC

electric fields. In particular, both DNA origami show a characteristic frequency

dependence of the iDEP trapping and moreover, the trapping of triangle origami required

larger applied electric fields. To further elucidate the observed DEP migration and trapping,

polarizability models were discussed for the two species according to their structural

difference. The experimental observations were further complemented by numerical

simulations revealing a considerable contribution of the electrophoretic transport of the

DNA origami species in the DEP trapping regions. The numerical model showed

reasonable agreement with experiments at lower frequency, however at higher frequency,

the experimentally observed extension of the iDEP trapping regions deviated considerably.

Our study demonstrates for the first time to the best of our knowledge that DNA origami

species can be successfully trapped and manipulated by iDEP and reveals a distinctive DEP

behavior of the two origami species. The experimentally observed trapping regimes will

48

facilitate future exploration of DNA origami manipulation and assembly and will also be

useful to exploit future analytical applications of these nanoassemblies with iDEP.

5.2 Results and Discussion

5.2.1 iDEP Trapping of 6HxB and Triangle Origami

Figure 5.2-1. a) Top: The 6-helix bundle origami is schematically depicted. Bottom: A

representative AFM image of DNA origami adsorbed on a mica surface. b) Top: The

triangle origami is schematically depicted. Bottom: A representative AFM image of

triangle origami adsorbed on a mica surface.

As descripted in Chapter 2, although originated from the same ssDNA scaffold,

the geometry of the two DNA origami species varies significantly (see Figure 5.2-1).

iDEP experiments were conducted at varying frequency, electric field strengths and

conductivity. Early electrode-based DEP experiments showed positive DEP (p-DEP)

49

trapping for origami species (Kuzyk et al. 2008, Linko et al. 2009). In this study, both

origami species showed positive iDEP trapping at characteristic applied frequencies and

electric fields. The experimental method is detailed in Chapter 3.6. Figure 5.2-2

summarizes these trapping regions for the two species. The 6HxB bundle DNA showed

iDEP trapping at applied potentials of 500 − 2100 𝑉 at a conductivity of 0.1 𝑆/𝑚.

Interestingly, DEP trapping occurred in varying frequency ranges. At the lowest applied

potential of 500 𝑉, the frequency range under which trapping was observed ranged from

60 − 500 𝐻𝑧. At 1500 𝑉 the trapping frequency range increased to 150 − 2500 𝐻𝑧 and

reached a span of 200 𝐻𝑧 to 15 𝑘𝐻𝑧 for an applied electric field of 2100 𝑉.

Figure 5.2-2. Schematic representation of the experimentally observed frequency range

under which DEP trapping occurs with a medium conductivity of 0.1 𝑆/𝑚. The applied

electric field for the 6HxB varied; however, for the triangle species, iDEP trapping could

only observed at 2100 𝑉.

The iDEP behavior of the triangle DNA origami was distinctively different from

the 6HxB. iDEP trapping was only observed at 2100 V at a conductivity of 0.1 𝑆/𝑐𝑚.

The frequency range under which iDEP trapping occurred under these conditions

50

spanned a range from 300 − 1500 𝐻𝑧. Other conductivities were tested, but distinctive

iDEP trapping could not be observed for the two DNA species at higher buffer

conductivity.

5.2.2 Extension of the Trapping Area

Figure 5.2-3. a) and b) Snapshots of DEP trapping in the insulator-based post array for

six-helix bundle (6HxB) for two exemplary frequencies (𝑎 = 60 𝐻𝑧, 𝑏 = 400 𝐻𝑧) at

500 V as obtained from fluorescence video microscopy. c) and d) Snapshots of DEP

trapping in the insulator-based post array for triangle origami for two exemplary

frequencies (𝑐 = 300 𝐻𝑧, 𝑑 = 1000 𝐻𝑧)

For both DNA origami species, a decrease in the trapping area around the

insulating posts was observed with increasing frequency. Figure 5.2-3 shows this effect

exemplarily for the 6HxB and the triangle origami for two frequencies. Similar results

were also observed by previous work on electrodes (Asbury, Diercks & van den Engh

51

2002, Bakewell et al. 1998) and near insulator structures (Chou et al. 2002). To quantify

this effect a trapping length 𝐿𝑡𝑟𝑎𝑝 is defined corresponding to the extension of the

dielectrophoretic trap along the longitudinal direction in the microchannel. 𝐿𝑡𝑟𝑎𝑝 was

measured as described in the methods section (Chapter 3.6) for a distinctive frequency

range and applied potential for the two origami species experimentally and compared to

numerical simulations.

For numerical modeling of the frequency dependent variations in the trapping

area around the insulating posts, a convection-diffusion model was used as detailed in

Chapter 4.3. In Figure 5.2-4, the distribution of the concentration region around the

insulating posts is shown in several snapshots within one period of the sinusoidal AC

signal at 60 Hz and 500 V. An interesting phenomenon that was not captured in the

experimental study was revealed with this time dependent study (detailed in Chapter 4.4).

Depending on the specific time point within one period, the maximum of the

concentration changes, i.e. the trapping area, shifts along the outline of the insulator post.

As shown in Figure 5.2-4, the concentration profile in the trapping region centers in the

DEP trap for maximum amplitudes (both ‘middle’ positions in Figure 5.2-4) and slides

up and down in between. The concentration profile is centered in the ‘middle’ positions,

since the largest DEP force acts.

These numerical results indicate that the theoretical model captures changes in the

actual trapping area with a resolution of 2 𝑚𝑠 corresponding to the length of the time steps

of the simulation. Note that the experimental observation of DNA origami trapping

52

required a minimum of 200 𝑚𝑠 of exposure time. Hence, the detailed migration in the

trapping area within one period could not be resolved experimentally.

Figure 5.2-4. Time-dependent concentration profiles as obtained from numerical

simulations for the time steps of 1/4 periods computed for 60 Hz and 500 𝑉/𝑐𝑚 for the

case of 6HxB. The shift of the trapping zone (from top to bottom and back) is clearly

apparent with a centered trapping zone for maximum amplitude. The color code refers to

the concentration of DNA species normalized to the initial concentration.

As mentioned above, a decrease in the trapping area is experimentally observed

with higher frequency. To further investigate this effect, 𝐿𝑡𝑟𝑎𝑝 was quantified from both

the experimental data and numerical simulations at frequencies from 60 to 500 𝐻𝑧 (at

500 𝑉) and from 300 to 1500 𝐻𝑧 (at 2100 𝑉) for 6HxB and triangle origami,

respectively. Figure 5.5-1 compare experimentally obtained 𝐿𝑡𝑟𝑎𝑝 values with the

simulation data. First, the same trend was observed for both 6HxB and triangle origami

for the experimental and simulation data: the larger the frequency, the smaller is the

trapping area. For example, for 6HxB origami, at a frequency of 60 Hz 𝐿𝑡𝑟𝑎𝑝 results in

12.3 ± 0.8 µ𝑚 (experimental) and 10.2 ± 0.4 µ𝑚 (simulation), while at a frequency of

400 Hz 𝐿𝑡𝑟𝑎𝑝 reduces to 8.5 ± 0.5 µ𝑚 (experimental) and 7.3 ± 0.6 µ𝑚 (simulation). At

53

intermediate low frequencies 𝐿𝑡𝑟𝑎𝑝 increases linearly with decreasing frequency for both

origami species. This trend levels however off at small frequencies in simulations and a

characteristic minimum for 𝐿𝑡𝑟𝑎𝑝 is observed at higher frequencies experimentally.

5.2.3 Origami Migration Behavior in iDEP Traps

Numerical simulations as shown in Figure 5.2-4 indicated that the DNA origami

migrates periodically in the iDEP trap. Figure 5.2-5 shows the concentration profile of

DNA without a DEP component and with only a DEP component. This further confirmed

that the variations in trapping position are indeed due to electrophoresis. The migration in

the iDEP trap is thus investigated by determining 𝐿𝑡𝑟𝑎𝑝 and considering electrophoresis

of the DNA species in the iDEP trap. The influence of the electrophoretic transport on

𝐿𝑡𝑟𝑎𝑝 is reflected in the time 𝑡ℎ𝑎𝑙𝑓 a DNA origami needs to migrate electrophoretically

along 𝐿𝑡𝑟𝑎𝑝 in one half period. This time relates to the electrophoretic mobility and the

applied electric field as follows:

𝐿𝑡𝑟𝑎𝑝 = 𝜇𝐸𝑃|�⃑� |𝑡ℎ𝑎𝑙𝑓 (5.2-1)

The changes in 𝐿𝑡𝑟𝑎𝑝 were accessed for various frequencies when 𝜇𝐸𝑃 is known. For

example, for 6HxB at 300 𝐻𝑧, 𝑡ℎ𝑎𝑙𝑓 amounts in 1.67 𝑚𝑠 resulting in an 𝐿𝑡𝑟𝑎𝑝 of 7.6 ±

0.5 µ𝑚 according to simulations. 𝐿𝑡𝑟𝑎𝑝 decreases linearly as expected with increasing

frequency. This trend is observed for both origami species in the high and intermediate

frequency regimes in the simulations (see Figure 5.2-6).

54

Figure 5.2-5. Simulation of normalized concentration profile with only electrokinesis a)

and with only DEP b), both of them were after 20 periods of AC. a) Concentration profile

with only electrophoresis and electroosmosis in upper most and lower most case. To

note, the concentration does not significantly increase, compared to Figure 5.2-4. b)

Concentration profile with the effect of dielectrophoresis only. The concentration

increased around the trapping area, but shifting of the maximum concentration is not

observed.

Both origami species however deviate from this linear relationship at lower

frequencies. Below approximately 80 𝐻𝑧, 𝐿𝑡𝑟𝑎𝑝 ceases to increase. This limitation can be

attributed to the fact that the origami electrophoretic migration velocity is sufficiently

large so the molecule can explore the entire trapping region by migration. However,

𝐿𝑡𝑟𝑎𝑝 can not be extended further due to the limitations in the DEP trapping strength. In

other words, the DEP force confines the origami in a defined region in the proximity of

the insulating posts, however electrophoresis in this region is still permitted (within

dimensions of 𝐿𝑡𝑟𝑎𝑝).

The experimental data support this migration behavior at the lower and

intermediate frequencies, however 𝐿𝑡𝑟𝑎𝑝 shows a minimum at ~ 250 𝐻𝑧 for the 6HxB

and ~ 1000 𝐻𝑧 for the triangle origami. This characteristic frequency dependence

55

indicates a change in the dielectrophoretic trapping strength and thus 𝐿𝑡𝑟𝑎𝑝. Note that

Yokokawa et al. (Yokokawa et al. 2010) and Martinez-Duarte et al. (Martinez-Duarte et

al. 2013) reported a crossover of positive to negative DEP for 𝜆-DNA at ~ 75 −

100 𝑘𝐻𝑧. Since the DEP strength decreases before the crossover frequency is reached, it

could be that the characteristic minimum in 𝐿𝑡𝑟𝑎𝑝 found experimentally is related to

changes in 𝛼 and thus the DEP trapping strength of the two DNA origamis. This change

in DEP strength could also originate from changes in the polarization orientation as

discussed below. Experimentally 𝐿𝑡𝑟𝑎𝑝 does not saturate at lower frequencies, indicating

that the magnitude of the DEP mobility could be over-estimated or that the electrokinetic

component could be under-estimated in the simulations.

Figure 5.2-6. a) 𝐿𝑡𝑟𝑎𝑝 is plotted versus applied frequency for the 6HxB origami as

obtained from experiments (diamonds) and numerical simulations (squares) in a range

from 60 to 500 Hz. b) Ltrap is plotted versus applied frequency for the triangle origami as

obtained from experiments (dots) and numerical simulations (squares) in a range from

300 to 1500 Hz. Error bars represent the standard deviation.

56

5.4 iDEP trapping strength of the two origami species

Figure 5.2-2 indicates that larger electric fields are necessary to trap the triangle

origami DNA in comparison to the 6HxB. In fact, significant trapping for the triangle

origami was only observed above 2100 𝑉. This can be attributed to a stronger

polarization of 6HxB DEP forces acting on it. Furthermore, the 6HxB shows a wider

frequency range for trapping which shifts towards higher frequencies up to 15 𝑘𝐻𝑧 for an

applied potential of 2100 𝑉 in accordance with experiments previously reported under

similar conditions for DNA (Martinez-Duarte et al. 2013, Yokokawa et al. 2010). The

polarization parallel to �⃑� is further considered, as pointed out by several authors

(Schlagberger, Netz 2008, Manning 2009); thus, estimated 𝜇𝐷𝐸𝑃 and 𝛼 amount in similar

magnitudes for the two origamis (see Table 2.3-1). Hence, one would expect similar

electric fields necessary for iDEP trapping of the two species, which is contrasted by the

experimental observations. The reason for this discrepancy may originate in differences

in the polarization orientation of the two origami species. For example, Table 2.3-1

indicates that in the extreme case of perpendicular orientation of polarization both 𝜇𝐷𝐸𝑃

and 𝛼 result in two orders of magnitude smaller values than compared to the parallel

orientation. A (partial) polarization perpendicular to the electric field may be the cause

for the higher �⃑� necessary for trapping.

Therefore, this scenario is considered in more detail. Noted that unusual

polarization perpendicular to the applied electric field has been observed previously with

polyelectrolytes (Lachenmayer, Oppermann 2002) and rod-like viruses (Kang, Dhont 2008,

57

Kramer et al. 1992), where this phenomenon is referred to ‘anomalous birefringence’

(Schlagberger, Netz 2008). Several theoretical models have been proposed for the

mechanism of this anomalous alignment (perpendicular to �⃑� ), however none explains an

universal case (Schlagberger, Netz 2008). Generally, these unusual polarizations occurred

at low ionic strengths, low frequencies, small �⃑� and high concentrations. However,

perpendicular orientations were also predicted to occur for high electric fields and low

concentrations for more flexible rods (Schlagberger, Netz 2008). Several factors have been

identified giving rise to perpendicular orientation. Particle-particle interactions between

the charged colloids in distances of the polarized double layer are considered to be relevant

(Kang, Dhont 2008), and additional hydrodynamic (Schlagberger, Netz 2008) and

electroosmotic (Kang, Dhont 2008, Saintillan, Darve & Shaqfeh 2006) effects were

proposed causing the unusual polarization effects.

It seems likely that the 6HxB could act similar to a virus particle of comparable size

and therefore orient perpendicular to the electric field to some extent, which would

decrease its polarizability. This would result in higher electric fields necessary for trapping

(compared to the triangle origami), and is in contrast to the experimental observations in

this chapter. A similar effect could hold for the triangle origami species. However, there is

no other experimental observation reported substantiating a perpendicular orientation of

the much smaller, oblate triangle origami. A presumable much faster rotational component

of the triangle origami might counteract such perpendicular orientation, but a (partially)

perpendicular orientation cannot be excluded to explain the reduced polarization and

consequently larger trapping electric fields for the triangle origami.

58

Next, the influence of particle-particle interactions is considered in the iDEP trap.

Note that the 6HxB is 380 nm in length and the space between adjacent insulating posts

forming an iDEP trap measures ~ 3µm. Since trapping occurs, a concentration of origami

species in the iDEP trap arises, which might lead to considerable steric hindrances in the

iDEP trap. Additionally, alignment of several 6HxB rods or aggregation might favor lower

trapping electric fields. This would be in accordance with Solanen et al. (Salonen et al.

2007) who report an increase in DEP forces when particle aggregation of charged

nanoparticles occurs. Polarization effects occurring at the ends of the charged rod arising

from ionic diffusion and convection may additionally favor such alignment. (Zhao, Bau

2010) These factors may favor DNA origami aggregation causing smaller electric fields

necessary for trapping the 6HxB, and could explain the experimental observations.

Such origami-origami interactions in the iDEP trap are fully reversible, as the iDEP

trap is ‘emptied’ by diffusion of the origami species out of the iDEP trap when �⃑� is turned

off. Lastly, noted that the larger observed polarizability of the 6HxB could originate from

the specific counterion distribution of the 6HxB. In fact, the ionic contribution from the

inner core of the 6HxB might give rise to an overall improved polarization in contrast to

current theoretical models. Summarizing, the observed trapping behavior cannot be

sufficiently explained with an orientation of the two origami species parallel to the electric

field. Additional contributions from (partial) perpendicular alignment, particle-particle

interactions in the iDEP trap or polarization effects due to the distinct DNA origami

geometry represent factors likely influencing the observed origami iDEP behavior.

59

5.2.4 Trapping Conditions for 6HxB Dimer

6HxB origami is easy to form dimers (Rothemund 2006) through π-π interactions.

As shown in Figure 5.2-7. Through gel purification, the dimer could be separated out and

DEP experiment is carried out to determine the trapping condition.

Figure 5.2-7. a) Gel image of the 6HxB origami. The monomer, dimer and single

stranded staples were shown in the image. b) AFM image of the 6HxB DNA origami.

A similar trapping profile is shown in Figure 5.2-8. As shown from the image, as

the frequency increases, the trapping area decreases and the intensity increases. However,

for 6HxB dimer specifically, the trapping was observed only under comparatively high

salt concentration. In this experiment, the buffer contained 10 𝑚𝑀 sodium and potassium

phosphate buffer and 50 𝑚𝑀 of sodium chloride, with 𝑝𝐻 of 8.3 and conductivity of

0.7 𝑆/𝑚. However in this condition, the 6HxB monomer does not get trapped.

Theoretically, 6HxB dimer should have a larger polarizability in a same conductivity

condition, but as from calculation, is not significantly larger than its monomer. For

60

example, at conductivity of 0.1 𝑆/𝑚, the polarizability for 6HxB monomer is 2.603 ×

10−30 𝐹𝑚2, and for 6HxB dimer is 6.240 × 10−30 𝐹𝑚2, in the same magnitude. At

conductivity 0.7 S/m, the polarizability for 6HxB dimer is 8.901 × 10−31𝐹𝑚2, for its

monomer, for the same polarizability, the conductivity should be around 0.3 𝑆/𝑚.

However, no trapping for 6HxB monomer is observed at such high conductivity.

Figure 5.2-8. 6HxB dimer trapping. Voltage were applied in perpendicular direction. a)

6HxB dimer trapping at 500 𝑉 60 𝐻𝑧. b) 6𝐻𝑥𝐵 dimer trapping at 500 𝑉 200 𝐻𝑧.

One argument for the high conductivity trapping of the 6HxB dimer is the

difference between the ion cloud distributions between two distinct concentration buffers,

as for low concentration buffers, the thickness of the EDL often plays a role. Another

speculation is that the 6HxB dimers might not maintain the rigidity and the persistence

length might be shorter than the length of 6HxB dimer (760 nm). The explanation

remains to be discovered. To note, using a device with similar channel and post

dimensions, dimer trapping is also observed, see Appendix B.

61

5.3 Section Summary

In this contribution, DEP manipulation of the 380 𝑛𝑚 long 6HxB as well as the

triangle DNA origami with a size as low as 130 𝑛𝑚 employing iDEP is successfully

demonstrated. The two investigated DNA origamis showed distinct differences in

trapping electric field and frequency. Trapping of the two species was only observed at a

medium conductivity of 0.1 𝑆/𝑚, while higher conductivity did not demonstrate iDEP

trapping at the tested frequency ranges. The triangle DNA origami required a higher

applied electric field for trapping and corresponding electric field gradients for iDEP

trapping. This was in contrast to model calculations adapted from classical DEP theory

for ellipsoids, which resulted in a similar polarizability and 𝜇𝐷𝐸𝑃 for the two origami

species. Considerations on perpendicular orientation of the rod like 6HxB as previously

described in the literature did not support the larger electric fields required for the triangle

origami trapping. Therefore, it is demonstrated that additional effects need to be

considered to fully understand the DEP behavior of DNA based nanoassemblies. Other

contributions from particle-particle interactions in the iDEP trap or variations in the

counter ion distribution due to the specific topology of the DNA origami could be

responsible for the here presented experimental observations.

The frequency dependence on the dielectrophoretic trapping behavior for both

species was furthermore studied in numerical simulations revealing electrophoretic

migration of both origami species in the DEP trapping regions. The numerical model

presented was in good agreement with experiments in the intermediate frequency range

as tested experimentally. At high frequencies, the experimental observations indicate a

62

minimum in 𝐿𝑡𝑟𝑎𝑝, which we attribute to frequency dependent changes in the polarization

behavior of the two origami species. The tested experimental trapping conditions and

adaptation of the numerical model to DNA origami species will allow careful design and

optimization of analytical applications of DNA origami in the future such as micro- and

nanoscale stearing and nanoassembly but also separation, concentration and fractionation

applications.

63

CHAPTER 6

6. DETERMINATION OF THE POLARIZABILITY OF DNA ORIGAMIS

6.1 Introduction

During the past decade, various methods for the synthesis of self-assembled

nanoassemblies such as artificial DNA structures have developed. Two-dimensional

(2D) and three-dimensional (3D) structures such as 2D stars (He et al. 2006), circular

structures (Han et al. 2011) as well as 3D rods (Mathieu et al. 2005), cubes (Chen,

Seeman 1991, Kuzuya, Komiyama 2009), spheres (Han et al. 2011) and other hollow

structures (Han et al. 2011, Ke et al. 2009) were successfully synthezised. Transportation

and manipulation of such nanostructures for precise positioning into specific micro- and

nano-environments is essential for their application in nanotechnology such as DNA

computing (Li et al. 2013), biosensing (Pinheiro et al. 2011), DNA photonics (Kukolka et

al. 2006), and drug delivery (Liu et al. 2012). Thus, understanding the physical properties

fundamental to the DNA nanoassembly migration mechanisms is essential for designing

and developing tools for their optimized application.

The selectivity of migration mechanisms for these applications greatly depends on

the intrinsic molecular properties of the various DNA origamis. Dielectrophoresis (DEP)

of DNA origamis has been of interest due to the possibility of trapping and controlled

positioning in electric field gradients (Tuukkanen et al. 2006, Tuukkanen et al. 2007)

DEP refers to the migration of a polarizable particle in a non-uniform electric field (�⃑� )

(Pohl 1978, Jones 2005) in response to an induced dipole moment. For a given aqueous

64

medium, the dielectrophoretic properties of the object depend on the bulk particle

properties but also the polarization of the interface with the surrounding medium. This in

turn is influenced by particle characteristics (Chen et al. 2009) such as size, shape,

deformability, charge, charge density, and the electric double layer (EDL) (Midmore,

Diggins & Hunter 1989).

In addition, the migration and positioning properties exploited in DEP can also be

employed for separation and fractionation. Separation of particles by DEP can be

achieved by a bulk transport component, overlaying dielectrophoretic trapping which can

be pictured similar to a chromatographic process. DC induced transport in combination

with AC dielectrophoresis is one possibility to achieve separation induced through DEP.

Ajdari and Prost proposed the theoretical framework for this dielectrophoretic separation

process in 1991 (Ajdari, Prost 1991) based on DNA length dependent polarizabilities in

combination with electrokinetic transport. Experimental approaches followed, such as by

Washizu’s group proposing the idea of DEP chromatography using a pressure driven bulk

transport device with an array of electrodes (Sano et al. 2002, Kawabata, Washizu 2001)

to induce dielectrophoresis. Regtmeier et al. (Regtmeier et al. 2007b) proposed an

insulator-based approach to separate DNA which could be applied to linear DNA in a

size range of several thousand to ~ 160 kbp (Regtmeier et al. 2007b) and for supercoiled

DNA (Regtmeier et al. 2010) also capable of separating DNA topoisomers (Regtmeier et

al. 2010) .

Insulator-based dielectrophoresis (iDEP) could also be employed for the

quantitative determination of DNA polarizabilities. Following Ajdari and Prost’s model

65

(Ajdari, Prost 1991), the migration process through an insulating post array can be

described by electrophoretic migration intermitted by dielectrophoretic trapping. DNA

molecules thus have to overcome potential barriers during migration though the periodic

iDEP post array. The escape process can be described according to a Kamer’s rate model

exhibiting a distinctive rate of escape relating to the trapping time. As previously shown,

this theoretical framework can also be employed for the quantitiative determination of

particle or biomolecule polarizabilties (Regtmeier et al. 2010, Regtmeier et al. 2007b).

Here, we apply this concept for the determination of DNA origami polarizabilities

(Regtmeier et al. 2007b) in a microfluidic chip employing iDEP. This approach allowed

to determine the polarizabilities of two DNA origami species with distinct geometries

(six-helix bundle and triangle origami) originating from the same ssDNA scaffold. Our

study reveals distinct differences in the migration behavior of the two origami species

through the microfluidic potential landscape which we relate to the intrinsic physical

properties of the two DNA origamis. Furthermore, it reveals the orientation of the DNA

origami assemblies and the influence of this process in the migration mechanism as well

as the fundamental properties contributing to the migration process. The content of this

chapter is submitted to Analytical Chemistry.

6.2 Results and Discussion

6.2.1 Determination of Origami Polarizabilities

The method employed to determine the origami polarizability followed a

previously reported method determining the migration time of DNA species through a post

array subject to an overlay of DC and AC potentials (Regtmeier et al. 2010). The DC

66

component induces an electrokinetic migration which is combined with dielectrophoresis

at each row of posts in the array. Figure 3.6-1b represents the employed microdevice in

which the cross of microchannels serves as the injector and the long channel contains the

array of posts in which the overall migration time for a defined distance is recorded.

Without posts, the DNA is subject to electrokinetic migration, based on the acting

electroosmostic flow and electrophoretic characteristics of the DNA origami. The

electrophoretic mobilities for 6HxB and triangle origami were determined as 5.0 (± 0.5) ×

10−8 𝑚2/𝑉𝑠 and 5.0 (± 0.8) × 10−8 𝑚2/𝑉𝑠 respectively with pinched injection

experiment (method described in Chapter 3.6). Once an additional AC potential of

amplitude 𝑈𝐴𝐶 is applied, dielectrophoretic forces are induced retarding the origami

migration. The DNA origami species show positive DEP which was previously determined

for 6HxB and the triangle origami under similar experimental conditions (Gan et al. 2013).

Figure 6.2-1. Schematics of potential landscape for DNA origami migration through one

dielectrophoretic trap. The blue arrow shows the x-axis, corresponding to the migration.

67

The escape process out of the dielectrophoretic trap can be characterized via a

Kramer’s rate model. Ajdari and Prost (Ajdari, Prost 1991) adapted this escape process for

the electrophoretic migration of DNA species through a potential landscape periodically

interrupted with potential wells induced through dielectrophoresis. This model has been

adapted to the migration of natural DNA and is used here for DNA origami, as

schematically depicted in Figure 6.2-1.

The potential barrier caused by a dielectric trap can be expressed as (Ajdari, Prost

1991):

𝜏 =1

𝐷∙ (

𝑘𝑇

𝑞𝐸)2

exp (∆𝑊𝐷𝐸𝑃

𝑘𝑇) (6.2-1)

where 𝜏 is the mean trapping or escape time, ∆𝑊𝐷𝐸𝑃 is the potential barrier, and k and 𝑇

are Boltzmann constant and temperature, respectively. 𝐷 is the diffusion coefficient, q is

the effective charge or proportinallity factor between the exerted force due to

electrophoresis and �⃑� is the electric field. ∆𝑊𝐷𝐸𝑃 relates to the depth of the potential well

induced through dielectrophoresis:

∆𝑊𝐷𝐸𝑃 =1

2𝛼�⃑� 2 (6.2-2)

Thus, by combining 6.2-1 and 6.2-2, a relation between the trapping time and the

polarizability can be established. Experimentally, the trapping time were obtained at

various 𝑈𝐴𝐶2 values and then the polarizability can be retrieved through the following

relation:

68

𝑙𝑛𝜏 = 𝛾 + 𝑐𝛼𝑈𝐴𝐶2 /𝑘𝑇 (6.2-3)

where const. and c are constants. 𝛾 can be expressed as:

𝛾 = ln (1

𝐷) + 2 ln (

𝑘𝐵𝑇

𝑞𝐸) (6.2-4)

The measurement of the migration time though the post array with N number of rows at a

specific AC amplitude and DC offset allows to determine 𝜏:

𝜏 = (𝑡 − 𝑡0)/𝑁 (6.2-5)

where 𝑡 relates to the total time recorded and 𝑡0 corresponds to the electrokinetic

migration time under DC conditions along 𝐿, when no AC induced dielectrophoresis

occurs. Moreover, 𝑐 in Eq. 4 can be expressed as (Regtmeier et al. 2007a):

𝑐 =1

2

|�⃑� 𝑔𝑎𝑝|2

𝑈𝐴𝐶2 (1 −

|�⃑� 𝑚𝑖𝑑|2

|�⃑� 𝑔𝑎𝑝|2 ) (6.2-6)

Solving for the electric field in the microdevice using COMSOL (see Chapter 4.5), the

constant 𝑐 was determined in a geometry matching the experimental conditions and

potentials applied. It resulted in 886.42 𝑚−2.

With this theoretical framework, the overall migration time t for various AC and

DC conditions for the two origami species was measured and the trapping time 𝜏 was

calculated. The measurement method applied and data analysis process was detailed in

Chapter 3.6. The resulting plot of 𝑙𝑛 𝜏 vs 𝑈𝐴𝐶 is shown in Figure 6.2-2 for the 6HxB and

the triangle origami. 𝛼 was determined according to Eq. 3 from the slope of the linear

69

regression lines, as shown in Figures 6.2-2a and b. They resulted in 2.44 (± 0.32) ×

10−30 𝐹 𝑚2 for the 6HxB species and 3.63 (± 0.35) × 10−30 𝐹 𝑚2 for the triangle

origami. These values were significant in the 95% confidence interval. Note that the

polarizability of the 6HxB is in close agreement to the previously estimated polarizability

using a prolate model (Gan et al. 2013) resulting in 𝛼6𝐻𝑥𝐵,𝑚𝑜𝑑𝑒𝑙 of 2.60 × 10−30 𝐹 𝑚2.

On the other hand, 𝛼𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 results in a value in between the parallel and perpendicular

orientation, as compared to the previous estimations based on the two extreme

orientations (Gan et al. 2013). Thus the orientation of the two DNA origami during the

migration process through the potential landscape are discussed in the following section.

Figure 6.2-2. a) lnτ versus the square of the AC voltages for a) 6HxB origami observed

from 400 𝑉 to 1200 𝑉 at 200 𝐻𝑧 and b) triangle origami observed from 1400 V to

1800 V at 300 𝐻𝑧. The lines represent linear regression lines.

70

6.2.2 Orientation of the Origami Species

The 6HxB origami has a diameter of ~ 7 𝑛𝑚 and a length ~ 380 𝑛𝑚 resembling

a rod, as outlined in Figure 2.3-1a (Mathieu et al. 2005, Gan et al. 2013) (See Chapter 2).

Due to this rod-like shape for 6HxB origami, an orientation parallel to the electric field

was assumed (Zhao, Bau 2010, Schlagberger, Netz 2008). The dielectrophoretic force,

𝐹 𝐷𝐸𝑃, acting on an origami species can be approximated by considering it as an ellipsoid

and is given by (Clarke et al. 2007, Lei, Lo 2011, Gan et al. 2013):

𝐹 𝐷𝐸𝑃 =1

2𝛼∇�⃑� 2 (6.2-7)

with

𝛼 =8

3𝜋𝑎𝑏𝑐𝜀𝑚

𝜎𝑝−𝜎𝑚

𝑍𝜎𝑝+(1−𝑍)𝜎𝑚 (6.2-8)

where, 𝜎𝑝 and 𝜎𝑚 denote the particle and medium conductivity, respectively, 𝜀𝑚

is the permittivity of the medium, 𝑎, 𝑏 and 𝑐 are the lengths of the 3 major axes, 𝑍 is the

depolarization factor and �⃑� the electric field. Thus a prolate particle for the rod-like

6HxB origami is assumed with 𝑎 > 𝑏 = 𝑐, where 𝑎 = 190 𝑛𝑚, 𝑏 = 𝑐 = 3.5 𝑛𝑚,

resulting in the parallel depolarization factor 𝑍∥ of 1.252 × 10−3 (Gan et al. 2013).

Considering Eq. 8 with a medium conductivity of 0.1 𝑆/𝑚, the 𝜎𝑝 for the 6HxB origami

resulted in 22.8 (±3.8) 𝑆/𝑚 . This is in excellent agreement with the previously reported

value of 23.5 (±3.2) 𝑆/𝑚 by Clarke et al. for DNA (Clarke et al. 2007).

em

71

The dimensions of the triangle origami and its approximation as an oblate

ellipsoid are shown in Figure 2.3-1 b. In Gan’s work(Gan et al. 2013), it was indicated

that the polarizability of the triangle origami modeled as an oblate ellipsoid results from

an orientation in between the extremes of parallel and perpendicular orientation. Based

on the experimentally determined magnitude of 𝛼𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 reported in this work,

information was gained about the orientation of the triangle origami during the escape

process.

Figure 6.2-3. a) Schematics of the triangle origami orientation with respect to the

electric field �⃑� . b) The alignment of 6HxB DNA (blue rods) and triangle origami (blue

triangle) against the electric field streamlines (red) in a set of post arrays. Black lines

outline the posts. The blue arrow indicates the flow direction. The 6HxB origami orients

parallel to the electric field �⃑� along the migration direction. The angle θ is indicated with

dashed lines showing the orientation of the triangle origami with respect to �⃑� . The sizes

of the origamis are not to the scale.

72

Assuming the orthogonal coordinates are 𝑥, 𝑦 and 𝑧 aligns with the triangle

origami’s semi-principal axes 𝑎 ,𝑏 and 𝑐 respectively (as shown in Figure 2.3-1) and the

angles between 𝑥, 𝑦, 𝑧 and �⃑� are 𝜃, 𝜑 and 𝛽. The orientation of the triangle origami can

be calculated from the vector and geometry relations, as shown next.

The DEP force is given by Eq. 6.2-7, where 𝐹 𝐷𝐸𝑃 originates from contributions of

all three directions:

∇�⃑� 2 =𝜕�⃑� 2

𝜕𝑥+

𝜕�⃑� 2

𝜕𝑦+

𝜕�⃑� 2

𝜕𝑧 (6.2-9)

∇�⃑� 2 = 2�⃑� ∙𝜕�⃑�

𝜕𝑥+ 2�⃑� ∙

𝜕�⃑�

𝜕𝑦+ 2�⃑� ∙

𝜕�⃑�

𝜕𝑧= 2�⃑� ∙ (

𝜕�⃑�

𝜕𝑥+

𝜕�⃑�

𝜕𝑦+

𝜕�⃑�

𝜕𝑧) = 2�⃑� ∙ ∇�⃑� (6.2-10)

From Eq. 6.2-7 and Eq. 6.2-8 follows:

𝐹 𝐷𝐸𝑃 =1

2𝛼∇�⃑� 2 =

1

2𝛼 ∙ 2�⃑� ∙ ∇�⃑� = 𝛼 ∙ �⃑� ∙ ∇�⃑� (6.2-11)

and from Eq. 6.2-9:

𝐹 𝐷𝐸𝑃 = 𝛼 ∙ �⃑� ∙ (𝜕�⃑�

𝜕𝑥+

𝜕�⃑�

𝜕𝑦+

𝜕�⃑�

𝜕𝑧) (6.2-12)

Since the angle between 𝑥, 𝑦, 𝑧 and �⃑� are 𝜃, 𝜑 and 𝛽, respectively,

𝜕�⃑�

𝜕𝑥= |�⃑� |𝑐𝑜𝑠𝜃 (6.2-13)

𝜕�⃑�

𝜕𝑦= |�⃑� |𝑐𝑜𝑠𝜑 (6.2-14)

73

𝜕�⃑�

𝜕𝑧= |�⃑� |𝑐𝑜𝑠𝛽 (6.2-15)

From Eq. 6.2-12, Eq. 6.2-13, Eq. 6.2-14 and Eq. 6.2-15 follows:

𝐹 𝐷𝐸𝑃 = 𝛼 ∙ �⃑� ∙ |�⃑� | ∙ (𝑐𝑜𝑠𝜃 + 𝑐𝑜𝑠𝜑 + 𝑐𝑜𝑠𝛽) (6.2-16)

Similar to Eq. 6.2-11, by analyzing the 𝑥, 𝑦 and 𝑧 components respectively,

𝐹 𝑥 =1

2𝛼𝑥∇�⃑� 𝑥

2 =1

2𝛼𝑥 ∙ 2�⃑� 𝑥 ∙ ∇�⃑� 𝑥 = 𝛼𝑥 ∙ �⃑� 𝑥 ∙ ∇�⃑� 𝑥 = 𝛼𝑥 ∙ �⃑� 𝑥 ∙

𝜕�⃑� 𝑥𝜕𝑥

= 𝛼𝑥 ∙ �⃑� 𝑥 ∙𝜕�⃑�

𝜕𝑥=

𝛼𝑥 ∙ �⃑� 𝑥 ∙ |�⃑� |𝑐𝑜𝑠𝜃 = 𝛼𝑥 ∙ (�⃑� ∙ 𝑐𝑜𝑠𝜃) ∙ |�⃑� |𝑐𝑜𝑠𝜃 = 𝛼𝑥 ∙ �⃑� ∙ |�⃑� |𝑐𝑜𝑠2𝜃 (6.2-17)

𝐹 𝑦 = 𝛼𝑦 ∙ �⃑� ∙ |�⃑� |𝑐𝑜𝑠2𝜑 (6.2-18)

𝐹 𝑧 = 𝛼𝑧 ∙ �⃑� ∙ |�⃑� |𝑐𝑜𝑠2𝛽 (6.2-19)

where 𝛼𝑥, 𝛼𝑦, and 𝛼𝑧are the polarizability along 𝑥, 𝑦 and 𝑧 direction respectively. The

DEP force arises from contributions of all three directions, thus:

𝐹 𝐷𝐸𝑃 = 𝐹 𝑥 + 𝐹 𝑦 + 𝐹 𝑧 (6.2-20)

and

|𝐹 𝐷𝐸𝑃|2 = |𝐹 𝑥|

2 + |𝐹 𝑦|2 + |𝐹 𝑧|

2 (6.2-21)

Substituting Eq. 6.2-16, Eq. 6.2-17, Eq. 6.2-18 and Eq. 6.2-19 into Eq. 6.2-21,

𝛼2 ∙ (𝑐𝑜𝑠𝜃 + 𝑐𝑜𝑠𝜑 + 𝑐𝑜𝑠𝛽)2 = 𝛼𝑥2 ∙ 𝑐𝑜𝑠4𝜃 + 𝛼𝑦

2 ∙ 𝑐𝑜𝑠4𝜑 + 𝛼𝑧2 ∙ 𝑐𝑜𝑠4𝛽 (6.2-22)

74

For triangle origami, the 𝑥 and 𝑧-axes are parallel to the long axis, whereas the 𝑦 axis is

perpendicular to long axis of the origami:

𝛼𝑥 = 𝛼∥, 𝛼𝑦 = 𝛼⊥, 𝛼𝑧 = 𝛼∥ and 𝛽 = 𝜃

Due to the geometric symmetry of the particle one can write:

𝑐𝑜𝑠𝛽 = 𝑐𝑜𝑠𝜃 = 𝑐𝑜𝑠𝜋

4∙ 𝑐𝑜𝑠 (

𝜋

2− 𝜑) =

√2

2𝑠𝑖𝑛𝜑 (6.2-23)

Furthermore, similar to 6HxB DNA, due to triangle origami’s oblate ellipsoid shape (Gan

et al. 2013), the polarizability of the oblate ellipsoid is given by Eq. 6.2-8. Thus an oblate

particle is assumed for the triangle origami with 𝑎 = 𝑏 > 𝑐 (as detailed in Chapter 2),

where 𝑎 = 𝑏 = 86.7 𝑛𝑚, 𝑐 = 1 𝑛𝑚. Considering 𝑍∥ is the depolarization factor for the

long axis of the origami parallel to the electric field and the 𝑍⊥ is the depolarization

factor for the long axis of the origami perpendicular to the electric field (Gan et al. 2013)

detailed in Table 2.3-1, the polarizability for long axis parallel to the electric field and

perpendicular to the electric field can thus be expressed as:

𝛼∥ =8

3𝜋𝑎𝑏𝑐𝜀𝑚

𝜎𝑝−𝜎𝑚

𝑍∥ 𝜎𝑝+(1−𝑍∥ )𝜎𝑚 (6.2-24)

and

𝛼⊥ =8

3𝜋𝑎𝑏𝑐𝜀𝑚

𝜎𝑝−𝜎𝑚

𝑍⊥ 𝜎𝑝+(1−𝑍⊥ )𝜎𝑚 (6.2-25)

Combining Eq. 6.2-23, Eq. 6.2-24 and Eq. 6.2-25 into Eq. S 6.2-22, results in the

following equation:

75

𝛼2(2 − cos2θ + 2√2cosθ√1 − cos2θ) = (8πabc

3εm)

2

(σp−σm

Z∥σp+(1−Z∥)σm)2cos4θ +

1

2∙

(8πabc

3εm)

2

(σp−σm

Z⊥σp+(1−Z⊥)σm)2(1 − cos2θ)2 (6.2-26)

With the dimensions of the triangle origami species, the polarizability from the

experiment (3.63 × 10−30 𝐹 ∙ 𝑚2), a medium conductivity of 0.1 𝑆/𝑚, the particle

conductivity of 6HxB origami of 22.8 𝑆/𝑚 and the medium permittivity for water at

20 ℃ (7.089 × 10−10 𝐹/𝑚), Eq. 6.2-26 can be solved resulting in the orientations as

listed in Table 6.2-1, where the errors are derived from the errors associate with the

experimentally determined polarizabilities.

solution I II

θ (˚) 59.4 (± 0.9) 69.3 (± 0.2)

φ (˚) 46.1 (±1.7) 30.0 (± 0.3)

Table 6.2-1: Solutions for the calculated orientation angle of the triangle origami (for a

definition of the angles, see Figure 6.2-3a.

Unlike 6HxB’s long axis parallel to the electric field, the triangle origami shows a

larger angle between the long axis and �⃑� . Although the triangle origami has the same

scaffold as the 6HxB origami, this analysis shows that the distinct geometry of the two

DNA nanoassemblies affects the orientation of the two species during the escape process.

Based on this analysis, the orientation of the triangle and 6HxB origami during migration

76

through the dielectrophoretic trap around two insulating posts are indicated in Figure 6.2-

3b.

6.2.3 Comparison between 6HxB and Triangle Origami Polarizability

The determined polarizability for the two origami species allows the comparison

with current models on dielectrophoresis of DNA and nanoparticles. It is generally

considered that under low frequency AC conditions, the DEP behavior of a particle is

affected by the dielectric properties of the bulk composition of the particle and the charge

distribution of the condensed and the diffuse layer around it (Lyklema 1995, Zhao, Bau

2010, Ermolina, Milner & Morgan 2006, Lei, Lo 2011, Dukhin, Deryaguin 1974,

O'Konski 1960) . For sub-µm particles, the electrical double layer is large compared to

the volume of the particle, and its properties can dominate the dielectrophoretic

properties (Green, Morgan 1999). The charge density on the surface of a nanoparticle

affects the charge distribution in the adjacent condensed and diffuse layer. Experimental

data on latex particles has illustrated that the dominance of charge movement in the

condensed layer can affect the DEP behavior to a higher extent than in the diffuse layer

(Green, Morgan 1999, Hughes, Morgan & Flynn 1999, Ermolina, Morgan 2005) and is

largely dependent on the surface charge density (Ermolina, Milner & Morgan 2006).

The surface charge density of the 6HxB origami and triangle origami can be

compared. They both share the same total charge since they are based on the same

scaffold and immersed in the same medium. The surface areas of the two species are

different, however, due to their distinctive shapes. Considering the 6HxB as a hollow

cylinder with an inner diameter of 2 𝑛𝑚, outer diameter of 7 𝑛𝑚 and length of 380 𝑛𝑚

77

(see Figure 2.3-1a), and the triangle origami as a hollow prism with inner side length of

~ 80 𝑛𝑚, outer side length of 150 𝑛𝑚 and a height of 2 𝑛𝑚 (see Figure 2.3-1b), the

surface area of the 6HxB is 1.08 × 104 𝑛𝑚2 and the surface area of triangle origami is

1.56 × 104 𝑛𝑚2. Thus the charge density of 6HxB is ~ 40% larger than for the triangle

origami.

These considerations are in agreement with the experimentally determined

polarizabilities in this work (𝛼6𝐻𝑥𝐵 < 𝛼𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 ) and suggest that the DNA origami

species behave like colloidal nanoparticles where the polarizability is largely influenced

by the surface charge density (Ermolina, Milner & Morgan 2006). It is further interesting

to note that the magnitude of 𝛼 of the two origami species is about one order of

magnitude smaller than reported for similarly sized linear DNA (Regtmeier et al. 2007a,

Zhou, Sheng & Harrison 2014) or supercoiled DNA (Regtmeier et al. 2010). This could

be attributed to the compact packing of the double stranded DNA in the case of the

origamis compared to free-draining linear DNA or supercoiled DNA with hydrodynamic

radii in the order of ~1µ𝑚 (Washizu, Kurosawa 1990, Regtmeier et al. 2010).

6.2.4 Influence of Diffusion on the Escape Process

As mentioned above, the elution time delay of the particle is due to the

characteristics of the migration through the post array and the escape rate out of the

dielectrophoretic trap. While the polarizability of the origami species was obtained from

the slopes as indicated in Figure 6.2-1 according to Ajdari and Prost’s model (Ajdari,

Prost 1991), the extrapolated intercepts with the y-axis (𝛾) provide information of the

78

exponential prefactor in Eq. 6.2-4. This term results from the diffusive and

electrophoretic contributions to the escape process. The intercept for 6HxB and triangle

origami occur at 𝑙𝑛 𝜏 of −5.29 and −6.78, respectively. Relating this to 𝛾 for the two

origami species the ratio of their diffusion coefficients were calculated, assuming

temperature, charge and electric field are the same for 6HxB and triangle origami. The

ratio between the diffusion coefficients 𝐷𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒/𝐷6𝐻𝑥𝐵 resulted in 4.4.

This finding may be explained with the orientation of the origami species in the

dielectrophoretic trap during the escape process. It is postulated that the larger diffusion

coefficient of the 6HxB origami originates from the parallel alignment with respect to the

electric field in the dielectrophoretic trap causing a faster diffusion in direction towards

the potential barrier and thus migration direction. For the triangle origami in contrary,

slower diffusion reduces the attempt frequency out of the trap reducing the trapping time.

The above mentioned analysis now allows us to describe the differences of the

migration through the post array for the two origami species considering the migration

through a potential landscape as indicated in Figure 6.2-1. Interestingly, a larger AC

amplitude is needed to trap the triangle origami species in accordance to our previous

findings (Gan et al. 2013). As shown in Figure 6.2-1 the determination of the triangle

origami escape times can only be accomplished under AC amplitudes of 1400 𝑉 to

1800 𝑉. This might seem contradictory to the determined polarizabilities (𝛼6𝐻𝑥𝐵 <

𝛼𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 ), however becomes plausible when the entire escape process is considered. The

analysis of the intercept 𝛾 reveals, that the diffusion characteristics play an important role

79

in the migration process and ultimately contribute to the differences in the migration of

the origami species through the post array as probed here.

6.3 Section Summary

In this contribution, the polarizability of two DNA origami structures were

successfully measured, based on their migration through a potential landscape exhibiting

dielectrophoretic potential barriers. Based on the theoretical model describing the

migration and escape process from the dielectrophoretic trap, this study reveals that the

6HxB DNA with rod-like geometry exhibits a larger polarizability than the triangle

origami although both originate from the same scaffold. From the parallel orientation of

the 6HxB origami with respect to the electric field, the conductivity of the DNA origami

could be determined in excellent agreement with previously reported data on linear

dsDNA. This allowed further to estimate the orientation of the triangle origami during the

escape from the dielectrophoretic potential barrier which revealed orientation with an

acute angle. In addition, the detailed analysis of the escape process allowed to relate the

diffusion characteristics of the two origami species to the observed escape process from

the dielectrophoretic potential barrier. It is postulated that this work provides important

fundamentals to exploit the dielectrophoretic properties of DNA and other

nanoassemblies which is important for nanotechnological applications of DNA origamis

requiring controlled migration or trapping.

80

CHAPTER 7

7. EFFECT OF BUFFER VALENCY IN DEP TRAPPING

7.1 Introduction

Chapter 2.2 discussed common models for DNA polarization and

dielectrophoresis. The electric double layer (EDL) surrounding the particles takes an

important role in the DNA DEP behavior. Many models have be established such as

Maxwell-Wagner-O'Konski (MWO) theory (O'Konski 1960), Dukhin and Lyklema (DL)

theory) or Poisson-Nernst-Planck (PNP) theory (Zhao, Bau 2010, Zhao, Bau 2009, Zhao,

Bau 2008), to modify the polarization in the EDL. However, the established theories are

still under debate especially on the subject of DNA length and frequency dependence

(Henning, Bier & Hoelzel 2010, Zhao 2011b) and the detailed role of the distribution of

counterions and valency.

Although not yet applied to the DEP behavior of DNA, the study of counterion

distribution along a DNA molecule can be related back to 1978, when Manning G. S.

developed the counterion condensation (CC) theory (Manning 1978), describing the

partial neutralization of the charges around DNA as a function of DNA conformation and

counterion valence. Briefly, theoretical models have been proposed such as based on the

Poisson-Boltzmann (PB) equation (Gouy 1910, Chapman 1913), Monte Carlo (MC)

methods (Metropolis et al. 1953), integral equation theory (IET) (Gonzaleztovar,

Lozadacassou 1989), fundamental measure theory (FMT) (Rosenfeld 1989, Rosenfeld

1990, Rosenfeld 1993), modified fundamental measure theory (MFMT) (Yu, Wu 2002,

Yu, Wu & Gao 2004), reference functional density (RFD) theory (Gillespie, Nonner &

81

Eisenberg 2002). Various geometries of DNA models including cylinder (Manning 1978,

Lyubartsev, Nordenskiold 1995, Mills, Anderson & Record 1985, Vlachy, Haymet 1986,

Ni, Anderson & Record 1999, Le Bret, Zimm 1984a, Le Bret, Zimm 1984b), helical

polyion (Korolev et al. 1999a, Korolev et al. 1999b), groove (Montoro, Abascal 1995)

and all-atom (Pack, Wong & Lamm 1999) were used to understand the microscopic

structure of the EDL around DNA (Wang et al. 2005). These methods and models

utilized the CC theory and elucidate the counterion counterion condensation and

neutralization of DNA backbone. The development of the CC theory facilitate the

quantitative interpretations of highly salt-valency-dependent conformational and binding

equilibriums of DNA.

Experimentally, light-scattering (Wilson, Bloomfield 1979) has proved that in a

DNA spermidine aqueous mixture, the presence of Mg2+ decreased the DNA collapse

concentration compared to the sole presence of Na+. X-ray scattering experiments (Das et

al. 2003) proved that the "heavier" counterions (Rb+ compared to Na+ and Sr2+ compared

to Mg2+ ) tended to have a smaller screening length. Moreover, higher valence cations

tended to neutralize the DNA more efficiently, while counterions with the same valence

were interchangeable. The thickness of the condensed monovalent counterion layer was

roughly twice that of the divalent atmosphere. A small-angle X-ray scattering study

(SAXS) (Andresen et al. 2008) proved that trivalent counterions bind to the DNA more

tightly than monovalent ions.

Experimentally DEP hasn’t been used as a tool to study the valency of counterion

behavior around DNA molecules. With the established models describing the counterion

82

binding of DNA as well as the established DEP models, further understanding of the

physical principles of the DEP mechanism regarding valency dependence of counterions

in the EDL can be achieved. This chapter presents an experimental study of two DNA

species (λ-DNA and 6HxB origami) in the presence of mono-valent and di-valent buffer.

The results can provide valuable experimental information elucidating the role of the

EDL in the DNA DEP mechanism.

7.2 Results and Discussion

7.2.1 p-DEP and n-DEP for Monovalent and Divalent Buffer

A numerical simulation (detailed in Chapter 4) of ∇�⃑� 2 for the insulator device is

shown in Figure 7.3-1a where the highest ∇�⃑� 2 (red) appears above and below the posts

where p-DEP should occur. The lowest ∇�⃑� 2 (dark blue) appears to the left and right of

the posts, where n-DEP should be prevalent.

Experiments were performed with λ-DNA in potassium phosphate buffer with

magnesium chloride added. The control experiment was performed with λ-DNA in

potassium phosphate buffer. The experimental methods are detailed in Chapter 3.6. The

conductivity of both buffers were adjusted to 0.2 𝑆/𝑚. AC voltage was applied across the

channel of post arrays with a frequency of 5 𝐻𝑧 to 40 𝑘𝐻𝑧.

In the experiment, the buffer containing magnesium shows n-DEP, as shown in

Figure 7.2-1b, and n-DEP is only shown when the AC voltage is above 2000 𝑉 and

between 40 ~ 100 𝐻𝑧. While the control experiment with only potassium phosphate

buffer shows p-DEP, as shown in Figure 7.2-1c, the lower threshold of the AC voltage

83

was ~100 𝑉 and the highest applied voltage was 3000 𝑉 (the limitation of the

instrumentation). Similar to the observations discussed in Chapter 5, the frequency range

varies with the applied voltage.

Figure 7.2-1. a) Numerical simulation for 𝛻�⃑� 2 in the microfluidic device. b) n-DEP

trapping of λ-DNA in phosphate buffer with MgCl2 with AC voltage 2000 𝑉, 60 𝐻𝑧. c) p-

DEP trapping of λ-DNA in potassium phosphate buffer with AC voltage 2000 V, 60 Hz.

"p" and "n" indicates positive DEP (p-DEP) trapping area and negative DEP (n-DEP)

trapping area.

One possible explanation for the resulting n-DEP behavior is that the di-valent

counterions (Mg2+) neutralized the negative charge of the DNA (Wilson, Bloomfield

1979) more efficiently, thus decreased the overall conductivity of the DNA origami. In

Wilson’s study, the presence of Mg2+ caused 89 − 90% neutralization of the phosphate

charges on the DNA while Na+ reduced the phosphate charge by 76%. Since the

conductivity is due to the sum of contributions of all the charge carriers in the system

(Bordi, Cametti & Colby 2004), in this case the DNA molecule with the presence of

Mg2+ has more charge neutralization resulting in a lower surface conductivity. When the

particle conductivity was smaller than the solvent conductivity, n-DEP was observed.

84

Figure 7.2-2. n-DEP trapping for 6HxB in phosphate buffer with MgCl2.

Moreover, a weak n-DEP trapping for 6HxB origami is also observed with

magnesium buffer (~5 𝑚𝑀 KH2PO4/K2HPO4 and ~5 𝑚𝑀 MgCl2), when 2000 𝑉 and

40 𝐻𝑧 AC voltage is applied, as shown in Figure 7.2-2. As detailed in Chapter 2, the

6HxB origami is a cyclic DNA motif that consists of six DNA double helices, where each

helix connects to nearby helices to form a hexagonally symmetric tube (Mathieu et al.

2005). On the other hand, λ-DNA is a dsDNA which is loosely coiled in solution.

Compared to λ-DNA, 6HxB is a more condensed structure which can lead to less surface

area, so less counterions can neutralize the phosphate charges on the DNA molecules. As

a result, a decrease in surface conductivity of 6HxB is less significant than that of λ-

DNA, and thus results in weaker n-DEP trapping.

85

7.3 Section Summary

This chapter applied mono-valent and di-valent buffer in the study of DEP

manipulation of natural form DNA (λ-DNA) and artificial form DNA (6HxB). With the

addition of magnesium, the n-DEP trapping of DNA molecules was observed for both

species. The switching between p-DEP to n-DEP is elucidated. Di-valent counterions

neutralize the phosphate charge on DNA more efficiently than mono-valent counterions.

The neutralization caused the decrease of the overall conductivity, which led to negative

trapping. The current theoretical DEP models for DNA applying DL theory are

underdeveloped and still being debated (Henning, Bier & Hoelzel 2010, Zhao 2011b). So

far, no systematic studies have been carried out for a DNA DEP model applied to a multi-

valent solvent system. From the experimental observations discussed here, the buffer

valency clearly shows distinct effects on DNA DEP. The research method provides

valuable experimental information for the study of the role of the EDL in the DNA DEP

mechanism.

86

8. CONCLUSIONS

In summary, iDEP devices were successfully fabricated to manipulate DNA

molecules and test their polarizabilities. An instrumental setup was built and the

corresponding operating programs developed to control and manipulate the applied

voltage of multiple microfluidic channels and simultaneously monitor the sample

fluorescence via a CCD camera or a photomultiplier.

Two self-assembled DNA species with the same scaffold but large topological

differences showed distinct iDEP trapping behavior in low frequency AC electric fields,

with numerical simulations in agreement with the experimental results. The

polarizabilities of the two species were tested by measuring the migration times through a

potential landscape exhibiting dielectrophoretic barriers. The resulting migration times

correlate to the depth of the dielectrophoretic potential barrier and the escape

characteristics of the origiamis according to an adapted Kramer’s rate model. This study

reveals that the 6HxB DNA with rod-like geometry exhibits a larger polarizability than

the triangle origami, although both originate from the same scaffold. From the parallel

orientation of the 6HxB origami with respect to the electric field, the conductivity of the

DNA origami could be determined in excellent agreement with previously reported data

on linear dsDNA. This allowed for the estimation of the orientation of the triangle

origami during the escape from the dielectrophoretic potential barrier, which revealed an

orientation with an acute angle.

Magnesium was added to potassium phosphate buffer to study the effect of buffer

valency on DEP behavior. With the same conductivity and 𝑝𝐻, λ-DNA in a buffer

87

containing magnesium showed n-DEP while p-DEP was observed in a buffer without

magnesium. This is likely due to be the electric double layer around the DNA being

affected by the di-valent buffer and thus showed distinctive DEP behaviors.

The tested experimental trapping conditions and adaptation of the numerical

model to DNA origami species and λ-DNA will allow careful design and optimization of

analytical applications of DNA and DNA assemblies and which can be utilized for

separation, concentration and fractionation. Further improvements include optimization

of the instrumentation as well as the microfluidic device to realize iDEP separation of

DNA species and the study of crossover frequency by accurately adjusting the buffer

composition and conductivity.

88

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102

APPENDIX A

A CHANNEL INCUBATION METHOD DEVELOPMENT

103

Channel Incubation Method Development

This appendix is a supplementary for the channel incubation methods mentioned in

Chapter 3.

Figure SI A-1. λ-DNA is electrophoretically pumped into the channel through DC

voltage. a) As the time increased, more DNA particles got adsorbed onto the channel

walls as shown in the red circle. 𝑡 = 0 𝑠 is defined as when the recording started. b) is

the result of a) after 30 𝑠, during the time scale, photobleaching also happened. Both a)

and b) were using incubation method described in 3. 4. 1 while c) is using the method

from 3. 4. 2. After DC voltage is off, DNA particles can be clearly observed in c).

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In sodium/potassium phosphate buffer system

Phosphate buffer is commonly used in biological samples. A method for

phosphate buffer with monovalent metal is developed to reduce DNA molecules’

adsorption on PDMS surface and electroosmotic flow inside the channel. Newly

assembled microchips were incubated over night with a freshly prepared solution of

10 𝑚𝑀 Silane-3400 in 5 𝑚𝑀 phosphate buffer 𝑝𝐻 = 8.3. The channel is then rinsed

with 5 𝑚𝑀 phosphate buffer. This method reduced the electroosmotic flow from µEOF =

2.9 × 10−8 𝑚2/𝑉𝑠 as in literature (Hellmich et al. 2005) to 2.2 × 10−8 𝑚2/𝑉𝑠 as from

the electroosmotic test experiments through method (Hellmich et al. 2005) as described

in Chapter 2.1.

In phosphate buffer system containing magnesium

Chapter 7 discussed the possibility of divalent/multivalent metal affecting the

composition of EDL around DNA particle, resulting the change of the DEP behavior of

biomolecules. In Chapter 7 specifically, buffer contains magnesium

(~5 𝑚𝑀 KH2PO4/K2HPO4 and ~5 𝑚𝑀 MgCl2) is used. Mg(II) is known for increasing

the attachment of DNA on surface so the method described in 3.4.1 is not sufficient. An

effective method applies to Mg(II) phosphate buffer system is needed. The new

incubation method is as follows: Chip assembly procedure were exactly the same, only

the glass slide is spin coated with 1: 5 (curing agent: pre-polymer) PDMS. Newly

assembled chips were incubated with a freshly prepared solution of 0.04 % (w/w) Silane-

3400 in 9: 1 (v/v) ethanol -water 𝑝𝐻 = 5.0 for 30 𝑚𝑖𝑛. And then the incubation buffer

105

is exchanged with pressure pump with the experiment buffer (~5 𝑚𝑀 KH2PO4/K2HPO4

and ~5 𝑚𝑀 MgCl2, 𝑝𝐻 = 7.0, conductivity 𝜎 ~ 0.20 𝑆/𝑚) for at least 3 times, giving

at least 30 𝑚𝑖𝑛 between each time, letting the channel fully recovered for aqueous

ambient before the experiment start.

For the magnesium buffer system, the contrast of incubation method 3.4.1 and

3.4.2 are shown in Figure SI A-1. For the aforementioned method, DNA tended to

adsorbed onto the channel walls and few particles could be observed inside the channel.

On the contrary, by using the later method, most particles stayed inside the channel and

the number of the particles stick on channel walls dramatically decreased.

To note, this incubation method does not decrease the electroosmotic flow, on the

contrary, the electroosmotic mobility after incubation is around 5.0 × 10−8 𝑚2/𝑉𝑠,

larger than the electrophoretic mobility of λ-DNA 𝜇𝐸𝑃 = 3.5 × 10−8 𝑚2/𝑉𝑠, causing the

flow direction of DNA from high electric potential to low electric potential. This is also

observed in the experiments.

106

APPENDIX B

B DEP MANIPULATION OF 6HxB DIMER

107

DEP Manipulation of 6HxB Dimer

Similar to Figure 3.6-1a, the device for manipulating 6HxB dimer consists of a

linear microchannel molded with PDMS with a cross section of 10 × 100 µm, in which

post arrays with elliptic bases were integrated along the entire microchannel length of

1 𝑐𝑚. Diameters for the oval posts are 8 µm and 6 µm along the long and short axis,

respectively, and the separation between the posts are 7.4 µm and 15 µm in horizontal

and perpendicular directions. As shown in Figure SI B-1, the numerical simulations of

∇E⃑⃑ 2 and E⃑⃑ were performed with COMSOL Multiphysics 4.3b, with the procedure

described in Chapter 4.2. With applying 500 𝑉 along a 1 𝑐𝑚 channel, the highest

gradient of the ∇E⃑⃑ 2 can reach 1015 𝑉2/𝑚3, which is the same magnitude with the device

for 6HxB monomer manipulation (3.8 × 1015 𝑉2/𝑚3) described in Chapter 5.

Figure SI B-1. Numerical simulation for alternative device for 6HxB dimer trapping. The

scale bar (white) is 10 𝜇𝑚.

Figure 5.2-7b shows the AFM characterization of 6HxB dimer. The diameter of

the particle is ~ 7 𝑛𝑚 and the length ~ 760 𝑛𝑚 resembling a rod. The experiments were

108

performed with the procedure described in Chapter 3.4.1, 3.6 and 3.7. Specifically, the

buffer used in both the incubation solution (Chapter 3.4.1) and the particle manipulation

experiment (Chapter 3.6), contained 10 𝑚𝑀 sodium and potassium phosphate buffer and

50 𝑚𝑀 of sodium chloride, resulting 𝑝𝐻 of 8.3 and conductivity of 0.7 𝑆/𝑚. As detailed

in Chapter 3.6, an AC voltage with an amplitude of 500 𝑉 was applied along the channel

filled with 6HxB dimer sample, with frequency from 5 𝐻𝑧 to 50 𝑘𝐻𝑧. DEP trapping was

observed from 60 𝐻𝑧 to 500 𝐻𝑧.

Figure SI B-2. Experimental results (a and c) and numerical simulation (b and d) for

6HxB dimer in the alternative device. Scale bar (white) is 10 𝜇𝑚. Red circle marked the

position of a post. a) and b) were performed at 500 𝑉 60 𝐻𝑧, while c) and d) were

performed at 500 𝑉 200 𝐻𝑧. For b and d specifically, the results showed the

accumulated concentration profile at the 20th period after the AC voltage is applied.

Similar to 6HxB monomer results, a decrease in the trapping area around the

insulating posts was observed with increasing frequency. Figure SI B-2a, c shows this

effect exemplarily for the 6HxB dimer for two frequencies. To further explore the

phenomena, the numerical study of the concentration profiles with corresponding

frequencies were also performed with COMSOL Multiphysics 4.3b, as detailed in

Chapter 4.3 and 4.4. Specifically, the DEP mobility for 6HxB dimer was calculated by

109

applying Eq. 2.3-4 from Chapter 2.3. With the adjustment to the dimensions of 6HxB

dimer and the conductivity of buffer, the DEP mobility resulted 3.34 × 10−22 𝑚4 ∙ 𝑉−2 ∙

𝑠−1. All the other parameters were detailed in Chapter 4.3.

As detailed in Chapter 4.4, the concentration profile was plotted at the 20th period

with an application of the AC voltage. Specifically, a gray scale color table was selected

and the snapshots of concentration profile at 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8 and the

end of the 20𝑡ℎ period were exported as image sequence in jpg format. The eight images

throughout the 20𝑡ℎ AC period from the image sequence were then overlaid and

compiled into one image with the Z project module in ImageJ freeware 1.47b. The results

were shown in Figure SI B-2b and d, with the applied conditions corresponding to Figure

SI B-2a and c respectively.

110

APPENDIX C

C DEVELOPMENT FOR INJECTION DEVICE

111

SI-6.1 Development of the Injection Device

This appendix is the development of the injection device for Chapter 6. The

experiment is performed in a cross-shaped channel through pinched injection

(Wenclawiak, Puschl 2006) electrokinetically, to record the sample plug from the

injection point (cross section of the chip) to detection point. In the detection channel,

insulator posts arrays creates electric field gradients where DEP takes place, with

schematics shown in Figure 3.6-1a.

Figure SI C-1. Examples of the contamination of channel due to hydrodynamic

resistance. Red lines outline the channel walls. Red arrows show the flow direction. Up,

left, down and right directions connects to Reservoir A, B, C and D (as shown in Figure

3.6-1a) respectively. In all experiments, a same amount (20 𝜇𝐿) of sample/buffer was

filled in reseavoir A, B, C and D. a) without any voltage applied, the sample

contaminated Channel B. b) and c) the loading step when the contamination happened.

In the first design, the post array increased the hydrodynamic resistance in the

detection channel by more than 10 times as oppose to an empty channel of the same

length without post arrays. As a result, if the other three control channel (Channel A, B

and C) does not have enough length, there is a high chance for the back flow to

112

contaminate the channels (or even reservoirs), which is unfavorable for the experiment.

Especially for the pinched injection, Reservoir B has to contain fresh buffer all the time.

An example of the back flow is shown in Figure SI C-1 while the length of Channel B is

3 𝑚𝑚 and the length of Channel D is 10 𝑚𝑚 (The minimum length for the detection

channel can be only down to 10 𝑚𝑚 with the limit of the detection device).

Figure SI C-2. Schematics of the calculation of hydrodynamic resistances. Channel walls

and post walls are outlined in black. Flow direction is from left to right. From the

estimated calculation, the posts were simplified as square shape, as circled in red dashed

square. The resistance are circled in dark blue dashed squares.

Figure SI C-1a shows without voltage applied, the contamination due to the

hydrodynamic force. In the loading step, when the sample was supposed to only fill from

Reservoir A to Reservoir C, while other channels were supposed to fill with only buffer.

But in the actual loading steps, contaminations were shown as Figure SI C-1b and c. It

113

took a long procedure of applying voltages to clean the channel, and once the voltages

were off, the contamination happened almost simultaneously. A solution for this problem

is to design a chip with comparable hydrodynamic resistance at all four channels.

To calculate the hydrodynamic resistance, the channel posts was estimated as

square and all the resistance can be simplified as square shaped resistance as shown in

Figure SI C-2.

The calculation for the hydrodynamic resistance can be simplified with a series of

hydrodynamics in squared shape structures, given as (Tanyeri et al. 2011, Bruus 2008):

𝑅 =12𝜂𝐿

1−0.63ℎ

𝑤

∙1

ℎ3𝑤 (S C-1)

with the serial connection of the resistance as

𝑅𝑠𝑒𝑟𝑖𝑎𝑙 = ∑𝑅𝑖 (S C-2)

and parallel connection of the resistance as

1

𝑅𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙= ∑

1

𝑅𝑗 (S C-3)

The total resistance of channel with post area and without post area can be simply

calculated out. With an estimation of the empty channel resistance should be larger than

1/10 of the post area resistance, if the length of the post area is designed to be 2 𝑐𝑚, the

length of the empty channel should be at least 1.6 𝑐𝑚.

114

With the new design, the pinched injection can be easily carried out as shown in Figure

SI C-3, and no contamination is seen when voltage is off.

Figure SI C-3. A successful example of pinched injection with newly designed device. a)

Sample loading procedure, as Step 1 described in Figure 6.2-1. b) and c) are subsequent

injection step (Step 2) as described and c) follows b). The red arrows show the flow

direction and white arrow shows the location of the sample plug (in c) the sample plug is

downstream and did not show in the image).

An example of electropherogram from pinched injection is shown in Figure SI C-

4.

Figure SI C-4. An example of electropherogram from pinched injection.

115

APPENDIX D

D COPYRIGHT PERMISSIONS

116

117