Design Design of Bio-Chips from of Bio-Chips from

TheoryTheoryand Multiscaleand Multiscale

SimulationSimulation

Prominent TechnologiesProminent Technologies

DNA and Peptide/protein

DNA & Protein MicroarraysDNA & Protein Microarrays

are useful for a variety of tasks

• Genetic analysis• Disease detection• Synthetic Biology• Computing

What tools are required?What tools are required?

• $1000 Genome at birth

• $100 Diagnostic exam

• Proteome at birth?

• Universal standards

Problems in Surface Mounted Problems in Surface Mounted technologies: Microarrays, Next-gen technologies: Microarrays, Next-gen

……Cross platform comparisons

• Controls• Validation• Data bases for comparisons

Nearly impossible due differences in the physics and chemistry at the surface

A Central Theoretical A Central Theoretical Issue:Issue:

Binding (recognition) is different in the presence of a surface than in homogeneous solution.

The surface determines:

Polarization fields

Ionic screening layers

Ultimately: Device response

Salt Water

Prepared Hard Surface

--

-- -

--

- - --- - --

-- -

--

--

--- - -

-- -

GCTA

AT

CGGC

AT

Probes

Targets- ---

-------

T

TT A A

A

CC C

G G G

G

5nm

---

- - --

- --

-

-

--

-

Materials, Preparation Materials, Preparation and Size Matterand Size Matter

• DNA prep

10 μm to bulk solid

10nm

100nm

What length scales are What length scales are required?required?

• Solid Substrate Roughness

• Linkers

• Surface Probes

• Targets

• Solution Correlations

ChemistryChemistry

Na Cl .1 to .8 M

ProbeTarget

Simulations and Theories of Bio ChipsSet up must include

• Substrate (Au, Si, SiO2 …)• Electrostatic fields• Surface modifications• Spacers (organic)• Probe and Target Bio (DNA or peptide) strands• Salt and lots of Water• Force field, …

Wong & Pettitt CPL 326, 193 (2000)Wong & Pettitt TCA 106, 233 (2001)Wong & Pettitt Biopoly 73, 570 (2004)Pettitt, Vainrub, Wong NATO ASI (2005)Qamhieh, Wong Lynch Pettitt IJNAM (2009)

Simulate a simple classical force fieldSimulate a simple classical force field

Model the interactions between atoms• Bonds - 2 body term

– harmonic, Hooke's law spring

• Angles - 3 body term

• Dihedrals - 4 body term

bonds

eb rrK 2)(

angles

eK 2)(

torsions

nK )cos(1 Source: http://www.ch.embnet.org/MD_tutorial/

Nonbonded Terms• 2 body terms

• van der Waals (short range) & Coulomb (long range)

• Coulomb interaction consumes > 90% computing timeEwald Sum electrostatics to mimic condensed phase

screening• Periodic Boundary Conditions

r

qq

rrji

atomsofpairsNonbonded

ijijij

612

4

Electrostatic Forces Dominate Behavior

F = ma or

With a classical Molecular Mechanics potential, V(r)

These potentials have only numerical solutions.

t must be small, 10-15s

rmrV )(

)(0)()()()( 32!2

1 tttrttrtrttr

Correlations• Neither Vertical nor Flat on surface

(tilt)

• Nonuniform Structures

• Linker/spacer effects

Wong & Pettitt CPL 326, 193 (2000)Wong & Pettitt TCA 106, 233 (2001)

ImplicationsImplications• Colloidal behavior affects

– synthesis / fabrication – and binding

• Tilt restricts possible geometries of pairing

• Affinity and specificity

G & G

Forces: Surface and SolutionForces: Surface and Solution

±±±±

±

Water

+[salt]

Substrate

–– – ––– –

––

–

–

––––

–

– ––

–

–

–

–

–

–––––

– –

–

––

––

±±±±±±±

±±

±

TheoryTheoryCalculate the free energy difference of

hybridization between that in solution and on a surface

Gsol-hybrid -Gsur-hybrid= Gss-att-Gdup-att

Target + Probe Target : Probe

Target + Probe:Surface Target :Probe:Surface

Gsol-hybrid

Gsur-hybrid

Gdup-attachGss-attach

TheoryTheoryTo get the work to form a single duplex on the

surface we need:

•ΔGsol which we can take from thermodynamic tables: solution reference state (John Santa-Lucia).

•ΔGatt from a consideration of the surface effects (chemistry and physics)

Coarse graining DNA Coarse graining DNA electrostatic fieldelectrostatic field

(Poisson-Boltzmann(Poisson-Boltzmann)

Vainrub, Pettitt, Chem. Phys. Lett. 323 160 (2000)

Ambia-Garrido, Pettitt, Comp Phys Com 3, 1117 (2008)

J. Ambia-Garrido

The ions and water penetrate the grooves.The ions and water penetrate the grooves.

Na+

Cl-

H2O

Feig & Pettitt BJ 77, 1769 (1999)

A Simple Model

• Ion permeable, 20 Å sphere over a plane/surface– 8 bp in aqueous saline solution over a surface

• Linear Poisson-Boltzmann has an

analytic solution

h

DNA - Vainrub and Pettitt, CPL ’00Ellipse - Garrido and Pettitt, CPC, 08

The shift of the dissociation free energy or temperature for an immobilized 8 base pair

oligonucleotide duplex at 0.01M NaCl as a function of the distance from a charged dielectric surface

q=0 or 0.36e-/nm2

S

HTm

linker

Vainrub and Pettitt, CPL ’00Vainrub and Pettitt, Biopoly ’03

Surface at a constant potential for a metal coated substrate @ .01 M NaCl

Vainrub and Pettitt, CPL ’00Vainrub and Pettitt, Biopoly ’03

Response to E-fieldsResponse to E-fieldsSalt and Substrate Material Effects on 8-bp DNA

Vainrub & Pettitt, Biopoly 2004

Finite Concentration and CoverageFinite Concentration and Coverage 

outside the sphere and plane,

inside the sphere,

|r =a+ = |r =a- , r |r =a+ = r |r =a- on the sphere,

|z =0+ = |r =0- , z |z =0+ - r |z =0- = - on the plane.

 

h

Different from O & K

Vainrub and Pettitt, Biopolymers 2003Vainrub & Pettitt et al , NATO Sci , 2005

Coulomb Blockage Dominates Coulomb Blockage Dominates Optimum DNA spacingOptimum DNA spacing

High negative charge density repels target

surface binding

Langmuir

On Chip

Target Conc

Bin

ding

Probe surface density

RT

wn

RT

STH

θ

θ TPPP000

ZZZC

(exp

1exp

hybridization efficiency θ (0 θ 1) target concentration C0 Vainrub &Pettitt, PRE (2002) Vainrub &Pettitt, JACS (2003)

Experimental Isotherm for perfectly Experimental Isotherm for perfectly matched lengthsmatched lengths

Explains some experiments:• Low on-array hybridization efficiency on glass (Guo et al 1994, Shchepinov et al 1995)• Broadening and down-temperature shift of melting curve (Forman et al 1998, Lu et al

2002)• Surface probe density effects (Peterson et al 2001, Steel et al 1998, Watterson 2000)

0 5x1012 1x1013 2x1013-15

-14

-13

-12

-11

ln[(

1-

)C/]

(1+)Np

0.0

0.2

0.4

0.6

0.8

1.0

200 250 300 350

Parameter:[(V

d-V

p)/RT

0]*qp

*Np

12 10 8 6 4 2 1 0

Temperature (K)

Hyb

rid

iza

tion

eff

icie

ncy

Melting curve temperature and widthMelting curve temperature and width Analytic wrt surface probe density (coverage)

*1012 nP probes/cm2

TmTm - Tm

W + W W In solutionTm = S – R ln C)

W = 4RTm2/

On-array: Isotherms

m

p2

0

p2

m

T3

2 W

n3wZ H2

n3wZ T

dA20 /dT20

duplex

Critical for SNP detection design Pettitt et al NATO Sci 206, 381 (2005)

Strength and linearity of hybridization signalStrength and linearity of hybridization signal

109

1010

1011

1012

10-2 10-1 100 101 102 103 104

0.186421

Target concentration (*exp[G0/RT

0] Moles)

Hyb

rid

s d

en

sity

(1

/cm

2 )

0 5x1012 1x1013

0

2x1010

Probe density (1/cm2)

x1012

Vainrub and Pettitt JACS (2003); ibid Biopolymers, (2004)

Peak of sensitivityPeak of sensitivity

0.0 2.0x1012 4.0x10120.0

0.2

0.4

0.6

0.8

1.0

T = 360 K

T = 340 K

T = 334 K

T = 332 K

T = 330 K

Nor

mal

ized

hyb

ridiz

atio

n si

gnal

Probe surface density (cm-2)

2P

pwZ

RTn

Vainrub and Pettitt, JACS (2003)

Linear range of hybridizationLinear range of hybridization

10-4

10-3

10-2

10-1

100

10-13 10-11 1x10-9 1x10-7 1x10-5 1x10-3

4

4

4

43

3

3

2

3

2

2

21

1

1

1

Target concentration (mol/L)

Hyb

ridiz

atio

n ef

ficie

ncy

RT

ZwnSTH

RT

θZZwn

RTθ

RTθθZZwnδ

PP

TPPTPP

200

2

exp

1exp)1(

)1(

Non-linear error is below

RT

ZZZwn

RT

STH

θ

θ

VN

SnC

TPPP00

A

P0

(expexp

1

Beyond the linear range use the on-array binding isotherm

Probe vs. Target lengths often Probe vs. Target lengths often mismatch in various waysmismatch in various ways

vs.. . .

Longer sequences are the expectedLonger sequences are the expectedand require true mesoscale models

Perfect pairing Pairing w/ an overhangGarrido Vainrub &Pettitt CPC ‘10

To Accommodate To Accommodate Longer Sequences and Longer Sequences and Secondary Structure Secondary Structure

Near a SurfaceNear a Surface

Mesoscale:Mesoscale: Allow for variations

inLinker chemistry

Over-hangUnder-hangon probes

and targetsin all combinations.

Parameterize ssDNA as well as dsDNA.

Garrido Vainrub &Pettitt JPCM submitted

DNA Entropic contributionsDNA Entropic contributions

• Sample with Monte-Carlo

• via Meirovitch (hypothetical scan)

• via Quasi Harmonic

• Correlations of sequence mismatch with physical corrections

• Data mining for equilibrium thermodynamics

ΔG

ΔG

Information vs efficiencyInformation vs efficiency

• ssDNA has the same spatial average as dsDNA but not fluctuations.

• Longer strands have more information 4n.– Kinetic problem

• Shorter strands pair more efficiently.– Kinetic balance

High Salt is Far Beyond Analytic High Salt is Far Beyond Analytic PB (Mean Field) ElectrostaticsPB (Mean Field) Electrostatics

Gouy-Chapman ~1910 Double layer at charged interfaces.

How good is this?

Add all the atoms via integral equations in 3D (renorm.- HNC)

Solvent and ion charge densities

HNC-IEMF-PB

w/ Ions

H2Oε=80

Charge-Charge correlationsCharge-Charge correlations

• Multi Layer effects not Bilayer

• Dominate at interfaces

• Determine the thermodynamics

• Change the kinetics

To design for To design for Affinity and SpecificityAffinity and Specificity

Coverage and Surface effects•Use Electric fields

– Effects of DNA with poly cations

•Use surface effects– Layered hard materials

•Use quantitative theories – Explicit polymer entropy

– Non m.f. coverage and electrostatics

Arnold VainrubClem Wong

Joaquin Ambia-GarridoJesse Howard

Khawla QamhiehAlex Micu

Keck Center for Computational BiologyMike Hogan, Lian Gao,

Rosina Georgiadis,Yuri Fofanov

Thanks to NIH, NASA, DOE, Welch Foundation, ARP&SDSC, PNNL, PSC, NCI, MSI