Electrokinetic Analysis of Liposome

Composition and Cooperative

Polymer Adsorption

Submitted in partial fulfillment

of the requirements for the degree of

Bachelor of Science in Engineering

Department of Chemical Engineering

Princeton University

James Whitacre

April 28, 2003

Advisor:

Professor Robert K. Prud’homme

ii

I hereby declare that I am the sole author of this thesis.

I authorize Princeton University to lend this thesis to other institutions or individuals for

the purpose of scholarly research.

James Whitacre

April 28, 2003

I further authorize Princeton University to reproduce this thesis by photocopying or by

other means, in total or in part, at the request of other institutions or individuals for the

purpose of scholarly research.

James Whitacre

April 28, 2003

iii

Princeton University requires the signature of all persons using or photocopying this

thesis. Please sign below, provide address, and note date.

iv

Abstract

Liposomes consisting of Phosphatidylglycerol (PG) and Phosphatidylcholine (PC) (9:1,

7:3, 3:7, 1:9, 0.25:9.75, mol:mol) as well as Phosphatidylserine (PS) and PC (7:3, 3:7)

with adsorbed hydrophobically-modified poly(ethylene glycol) polymers HMPEG6k-DP3,

HMPEG12k-DP2.5, and HMPEG35k-DP2.5 were investigated using dynamic light

scattering and electrophoresis. Liposomes containing the lipid 1,2-Dioleoyl-3-

Dimethylammonium-Propane (DODAP) were also studied for pH-sensitive release of an

electrostatically adsorbed, polyvalent diblock copolymer, poly(ethylene oxide) tertiary

amine methacrylate (PEO5k-DMA31). Dynamic light scattering was used to determine

the hydrodynamic radius and polydispersity of the prepared liposomes. Electrophoresis

was used to characterize the zeta potential for a range of lipid vesicles with some

liposomes investigated at varying pH and electric field strength.

All liposomes prepared were roughly 57 nm (+ 6 nm) in hydrodynamic radius with a

polydispersity averaging 0.063 (+ 0.011). Hydrophobically-modified polymers

HMPEG12k-DP2.5 and HMPEG35k-DP2.5 were added at 0.15 mg/m2 (mg polymer per m

2

lipid) to 7:3 PG:PC and 7:3 PS:PC liposomes resulting in a reduction of electrophoretic

mobility of about 86 %. The liposomes maintained stability after adsorption of the

HMPEG polymers as indicated by an increase in hydrodynamic radius without a marked

increase in polydispersity. PG:DODAP (7:3, 9:1) containing liposomes demonstrated

partial charge neutralization when pH was lowered from 7.4 to 5.5. Addition of PEO113-

DMA31 to pH-sensitive liposomes at pH 7.4 was able to shield the surface charge by 96

% however, pH-triggered release of the polymer did not occur when solution was

buffered at pH 5.5. The implications of these results are discussed in the context of drug

and gene delivery applications.

v

Table of Contents

Abstract___________________________________________________ IV

List of Figures and Tables_____________________________________ VI

Introduction________________________________________________ 1

Background________________________________________________ 2

2.1 Classical Liposomes______________________________________ 2

2.2 Polymer-Protected Liposomes________________________________ 5

2.3 The Electric Double Layer__________________________________ 10

Materials and Experimental Methods____________________________ 13

3.1 Materials______________________________________________________ 13

3.2 Liposome Preparation____________________________________________ 13

3.3 Phosphate Assay________________________________________________ 15

3.4 Dynamic Light Scattering_________________________________________ 16

3.5 Electrophoretic Mobility__________________________________________ 17

3.6 Baleux Assay___________________________________________________ 19

Experimental Results _________________________________________20

4.1 Phosphate Assay________________________________________________ 20

4.2 Hydrodynamic Radius___________________________________________ 21

4.3 Current Analysis________________________________________________ 21

4.4 Mobility of Bare Liposomes_______________________________________ 23

4.5 Size and Mobility – HMPEG-Modified Liposomes_____________________ 24

4.6 Mobility – pH-Sensitive Liposomes_________________________________ 27

4.7 Size and Mobility – pH-Sensitive Liposomes with PEO113-DMA31_______ 28

Discussion__________________________________________________30

5.1 Electrophoretic Mobility Error Analysis______________________________ 30

5.2 Electrophoretic Mobility Standardization_____________________________ 32

5.3 pH-Sensitivity of DODAP_________________________________________34

5.4 pH-Sensitive Liposomes with PEO113-DMA31________________________35

vi

5.5 Liposomes Protected with Hydrophobically-Modified Polymers___________36

Conclusions________________________________________________ 38

Recommendations for Future Work______________________________39

References_________________________________________________ 41

Appendix A.1 Derivation of hydrodynamic radius for dynamic light scattering measurements___________________43

Appendix B.1 Derivation of zeta potential from apparent electrophoretic mobility measurements_________________45

Appendix B.2 Method of electrophoretic mobility peak selection__________________________________________49

Appendix C.1 Description of HMPEG polymers_______________________________________________________50

Appendix C.2 HMPEG polymer surface coverage equations______________________________________________51

Appendix D.1 PEO113-DMA31 polymer description and surface coverage information________________________53

Appendix E.1 Lipid and buffer chemical properties_____________________________________________________54

vii

List of Figures

Figure 2.1 Schematic of polar lipids arranged in a unilamellar, bilayer vesicle.

Figure 2.2 Schematic of polar lipids arranged in a micelle

Figure 2.3 Schematic of HMPEG and PE-PEG dissociation

Figure 2.4 Schematic of counter-ion distribution around a charged liposome and

charge potential as a function of distance.

Figure 3.1 Apparent electrophoretic mobility peaks generated by Delsa software

Figure 4.1 Phosphate calibration curve for determination of phospholipid

concentration (Phosphate Assay)

Figure 4.2 Standard deviation in electrophoretic mobility as a function of applied

current for selected liposomes

Figure 4.3 Electrophoretic mobility as a function of applied current for selected

liposomes

Figure 4.4 Zeta potential as a function of % (molar) negatively charged lipid for

selected liposomes

Figure 4.5 Percent change in zeta potential as a function of % Γ * HMPEG coverage

for 7:3 PG:PC and 7:3 PS:PC liposomes

Figure 4.6 Electrophoretic mobility as a function of % Γ * HMPEG coverage for 7:3

PS:PC and 7:3 PG:PC liposomes

Figure 4.7 Change in hydrodynamic radius as a function of % Γ * HMPEG coverage

for 7:3 PG:PC and 7:3 PS:PC liposomes

Figure 4.8 Electrophoretic mobility as a function of pH for liposomes containing

DODAP

Figure 4.9 Electrophoretic mobility as a function of pH for liposomes containing

DODAP and PEO113-DMA31 polymer

Figure 4.10 Change in hydrodynamic radius as a function of pH for liposomes

containing PEO113-DMA31 polymer

Figure 5.1 Normalized electrophoretic mobility as a function of applied current for

selected liposomes

viii

Figure 5.2 Electrophoretic mobility divided by percent charged lipid as a function of

applied current for selected liposomes

Figure 5.3 Electrophoretic mobility as a function of current for a single liposome

system using A) two calibrated cell constants and B) the new standard cell

constant 19

Figure 5.4 Theoretical electrostatic potential as a function of distance from liposome

surface for liposomes with 70% negatively charged lipid compared to blob

sizes and experimental zeta potential for HMPEG12k and HMPEG35k at

1 Γ * coverage.

Figure B1.1 Apparent electrophoretic mobility as a function of cell position

Figure B2.1 Graphics of apparent electrophoretic mobility peak selection of each laser

angle

Figure C1.1 Schematic of geometry and polymer chain density comparing grafted PEG

and hydrophobically-modified polymers containing multiple hydrophobic

anchors

List of Tables

Table 3.1 Lists lipid composition for all liposomes prepared

Table 4.1 Results of phosphate assay listing phospholipid concentration in selected

liposome stock solutions

Table 4.2 Dynamic light scattering results listing hydrodynamic radius and

polydispersity index for all prepared liposomes without polymer

Table 4.3 Electrophoretic mobility and zeta potential for liposomes of varying lipid

composition

Table 4.4 Baleux Assay absorbance calibration curves and assay results for

HMPEG1, HMPEG3, and HMPEG6

Table 4.5 DLS results for 7:3 PG:PC and 7:3 PS:PC liposomes over a range of

HMPEG polymer coverage

Table 5.1 Electrophoretic mobility as a function of current for a single liposome

system using two calibrated cell constants

Table 5.2 Calibrated cell constant and measured conductivity for all electrophoresis

calibrations

Table C2.1 Physical and chemical properties of HMPEG polymers

Table D1.1 Physical properties and values used for calculation of PEO113-DMA31

polymer coverage

Table E1.1 Chemical properties for selected buffer components

Table E2.1 Chemical properties for the lipids used in this study

1

Introduction

Some of the most pressing issues in drug design today involve the engineering of drugs

that can retain activity, exhibit long circulation times, and are of minimal toxicity to non-

target cells in vivo. Research into drug delivery systems such as liposomes has indicated

them as a promising, viable approach to overcoming each of these concerns1.

For years, polymer-protected or “stealth” liposomes have been studied for their role as

potential drug carriers due to their large solution trapping volumes, retention of inner

solution, long circulation times within the body, and the potential to passively target

specific cells. The ability of a long-circulating liposome to preferentially release its

contents within the cell before lysosomal fusion has the potential to dramatically lower

the effective dosage needed while at the same time lower the toxicity for liposome-drug

systems2.

As indicated, the use of liposomes as drug carriers has three main objectives. The first is

to control drug release by increasing the half-life and attaining a linear release rate of the

drug while maintaining drug activity. The second is to decrease the effective drug dosage

or ED50 by delivering the drug to the cell’s cytosol. And finally, the third objective is to

increase the lethal drug dosage by only targeting relevant cells or tissues3. There are

several liposome properties that can influence the way a liposome behaves and interacts

with the body but the background will focus mainly on the issues most relevant to the

experimental research conducted: namely the stability of liposomes and aspects related to

liposome protection and drug release.

1 A. Chonn, P.R. Cullis. Recent advances in liposome technologies and their applications for systemic gene

delivery. Advanced Drug Delivery Reviews 30 (1998) 73-83 Elsevier Scientific Publishers Ireland Ltd.

2 A. Chonn, 73-83

3 D. Lasic, D. Needham. The “Stealth” Liposome: A Protypical Biomaterial. Chemical Reviews 95-8 (1995) 2601-2628

2

Background

2.1 Classical Liposomes

There are several physical properties that make liposomes a good choice for a drug

delivery system. For one, the lipid components are non-toxic, non-immunogenic, and

biodegradable4. Many commonly used lipids occur naturally within the human body

5

meaning their use is pre-approved by the FDA. Liposomes are also a good candidate for

drug delivery because of their retention of inner solute and exclusion of large external

compounds. This is achieved by the properties of the lipid bilayer which acts as a

chemical, mechanical, and electrical barrier for a large range of compounds both inside

and outside the vesicle.6

The most commonly used liposomes are unilamellar vesicles consisting of a spherical

lipid bilayer. Lipids are typically selected so that a lamellar structure represents their

most thermodynamically stable phase in solution. The inner and outer surfaces arrange

themselves so that the polar head group of these lipids, which is naturally hydrophilic, is

exposed to the aqueous solution. These systems typically have diameters ranging from

tens to hundreds of nanometers, depending on lipid composition, and will self assemble

when exposed to a hydrophilic environment7,8

. Liposomes are characterized as small

(SUV) or large unilamellar vesicles (LUV), according to their size.

Fusogenic Properties

Fusion allows the liposome membrane to exchange lipids with other membranes,

sometimes exposing the inner solution to the external environment. This is a critical

aspect of this drug carrier system because it allows for drug release under the right

conditions.

Lipids such as PE are known to promote fusion. For instance, evidence suggests that

rapid aggregation of vesicles containing over 60% of DOPE is partially due to the smaller

hydration layer of these vesicles, which is attributed to the unique properties of this lipid.9

Similarly, PE is inherently unstable when in a lamellar phase. It actually prefers an

inverted hexagonal II phase (non-bilayer phase).10

This preference in forming a non-

bilayer phase acts to destabilize the vesicle and might also encourage fusion events to

occur.11

Recently, liposomes containing 7:3 NC12-DOPE:PC were also shown to be very

fusogenic.12

In this system, the PE lipid is negatively charged as a result from addition of

an acyl chain onto the polar head group. Addition of the hydrophobic chain on the

surface was done in an attempt to promote fusion events better than typical PE lipids. The

liposomes investigated in this work are designed to model the surface charge properties

3

of the system just described. Negatively charged PS is used in place of NC12-DOPE

with later experiments also involving the use of PG in place of the more expensive PS.

Despite the critical importance of fusion for drug release to occur, there are times when

fusogenicity is a major disadvantage. This property will allow fusion between the

liposomes themselves, which can cause pre-mature drug release and can cause the

liposomes to aggregate and fall out of solution. Since this instability is unfavorable for a

drug carrier system, it is important to protect the liposomes from the occurrence of such

events.

One way to lower or eliminate

aggregation is by incorporating

charged lipids into the liposome. For

instance, a negatively charged

liposome surface would help to

lower the frequency of these fusion

events due to the negative-negative

electrostatic charge repulsion. At

high enough concentrations,

negatively charged lipids can

stabilize the liposomes and prevent

flocculation. Unfortunately, a higher

surface charge density also results in

faster clearance from the body. This

is likely due to a quicker recognition

of the liposome by proteins in the

immune system.

www.dadairs.com/liposomes.htm

Figure 1: Structural arrangement of phospholipids in a

unilamellar, bilayer vesicle. The bilayer shell that makes

up the liposome consists of hydrophilic phospholipid

heads (gray spheres), which position themselves so they

are in contact with the aqueous environment of the

solution, inside and outside the vesicle. The hydrocarbon

tails (wavy lines) bury themselves inside the bilayer due

to a hydrophobic affect.

Liposome Removal Once in the blood stream, liposomes quickly accumulate in the liver, kidneys, and spleen

as well as areas of high vascular permeability such as tumors. 13

The RES

(Reticuloendothelial System) in the liver is responsible for most of this liposome

removal14

, which has been attributed to macrophages known as Kumpfer cells15

. Uptake

from these cells increases substantially for liposomes with a large positive surface

charge,16

which is largely why negatively charged lipids are preferred for adding stability

to the lamellar phase.

It is currently believed that liposomal removal by the RES is initiated by opsonins in the

complement system.17,18 The chemical binding of these proteins through opsonification is

the first step in a pathway in which the liposomes are taken up by monocytes and

macrophages and degraded19

. Addition of a polymer layer to the liposome surface has

been shown to dramatically reduce specific protein recognition and prolong circulation

4

times20,21

. It has been suggested repeatedly, but without substantial evidence, that the

polymer acts by sterically inhibiting opsonification.22

A more in-depth discussion of

polymer-protected liposomes will follow in the section 2.2.

Endocytic Pathway Liposomes in the optimal size range with diameters between 50nm < D < 250nm, are

mostly able to elude the body’s defense mechanisms and pass through the vasculature

and into cell tissue. From here the liposomes will eventually enter into a nearby cell by

way of endocytosis. Inside the cell, the liposomes are encapsulated by endosomes, which

will interact with lyzosomes shortly thereafter forming a phagolysosome. These vesicles

contain digestive enzymes that, upon fusion with the endosome, will quickly degrade the

endosome’s contents23

. Depending on the properties of the liposome, some of the

vesicles will fuse with the endosomal wall and release the drug into the cell’s cytosol.

This is typically the final destination for many drugs on the market and so finding ways

to improve delivery to the cytosol is a large focus of much research including some of the

work presented in this paper.

The ability to control the fusogenic properties of a liposome by surface charge has been

exploited to create systems that are more likely to fuse under the acidic conditions within

the endosome. The liposomes are designed with lipids that can change their charge in a

way that will neutralize the liposome when it travels from the blood stream to the the

endosomal compartment. The pH sensitivity of these lipids allows the liposome to be

selectively fusogenic after endocytosis. Use of pH-sensitive liposomes have, for

instance, been shown to deliver water-soluble compounds more efficiently than non-pH

sensitive systems24

indicating the effectiveness of this approach.

4 Gregoriadis G., Engineering liposomes for drug delivery: progress and problems. Reviews 13 (1995) 527-

537

5 Lasic D., 2601-2628

6 Lasic D., 2601-2628

7 Avanti Polar Lipids: http://www.avantilipids.com/PreparationOfLiposomes.html

8 Lasic D., 2601-2628 9 Avanti Polar Lipids: http://www.avantilipids.com/PreparationOfLiposomes.html

10 Simoes S., Slepushkin V., Duzgunes N., M. Pedroso de Lima. On the mechanisms of internalization and

intracellular delivery mediated by pH-sensitive liposomes. Biochim. et Biophys. Acta 1515 (2001) 23-37

11 Chonn A., 73-83

12 Auguste D. (unpublished results) 13 Blume G, Cevc C. Liposomes for the sustained drug release in vivo. Biochim. et Biophys. Acta 1029

(1990) 91-97

14 Lasic D., 2601-2628

5

15 Moghimi S. M., Hunter A.C., Murray J.C., Long-Circulating and Target-Specific Nanoparticle Theory

and Practice. Pharmacol. Rev. 53 (2001) 283-318

16 Chonn A., 73-83

17 Huong T. M., Ishida T., Harashima H., Kiwada H. The complement system enhances the clearance of

phosphatidylserine (PS)-liposomes in rat and guinea pig. Int. J. Pharm. 215 (2001) 197-205

18 Ishida T., Kojima H., Harashima H., Kiwada H. Biodistribution of liposomes and C3 fragments

associated with liposomes: evaluation of their relationship. Int. J. Pharm. 205 (2000) 183-93

19

Moghimi S.M., 283-318 20 Slepushkin V. A., Simoes S., Dazini P., Newman M. S., Guo L. S., Pedroso de Lima M. C., Duzgunes

N.. Sterically Stabilized pH-sensitive Liposomes: Intracellular delivery of aqueous contents and prolonged

circulation in vivo. J. Bio. Chem. 272 (1997) 2382–2388,

21 Torchilin V.P., Shtilman M.I., Trubetskoy V.S., Whiteman K., Milstein A.M. Amphiphilic vinyl polymers effectively prolong liposome circulation time in vivo. Biochim Biophys Acta 1195 (1994) 181-4

22 Allen C., Dos Santos N., Gallagher R., Chiu G., Shu Y., Li W.M., Johnstone S.A., Janoff A.S., Mayer

L.D., Webb M.S., Bally M.B., Controlling the Physical Behavior and Biological Performance of Liposome

Formulations through Use of Surface Grafted Poly(ethylene Glycol). Bioscience Reports 22 (2002) 225-

250

23 Gregoriadis G.. 527-537

24 Torchilin, V.P., Zhou, F., and Huang, L. J. Liposome Res. 3 (1993), 201-255

5

2.2 Polymer-Protected Liposomes

One way to increase passive cellular uptake is to inhibit quick removal by the body’s

natural defenses. Currently, the most effective method is to add lipids with covalently

bound PEG polymer to the liposome. And indeed, this method of protection has been

shown to improve circulation half-life for the liposome vesicle.1 It is believed that the

change in liposome properties is due to PEG’s ability to prevent opsonification by serum

proteins.

The original idea for using PEG came from observation of the body’s own long

circulating vesicle, the red blood cell. These cells are able to avoid macrophage

interaction, which is believed to be largely due to oligosaccharide groups on the surface.

This allows them to circulate in the body for an average of 120 days.2

Steric Protection There is mounting evidence that suggests PEG performs this role through steric repulsion

at the membrane surface. It has been shown that PEG has no affect on desorption of

ligands from the liposome surface and it has been proposed that its affect on adsorption is

also negligible.3 Since it’s not competing thermodynamically for binding sites on the

surface, the polymer must be somehow affecting the kinetics of protein adsorption4. But

as a non-reactive, neutral, hydrophilic molecule, PEG is not attracted to the liposome

surface, nor can it bury any hydrophobic sections into the lipid layer. All of these aspects

suggest that its mere presence acts as a steric barrier preventing most large molecules

from direct access to the surface.

This steric protection afforded by PEG is

due to a lateral surface pressure that

increases with higher polymer

concentration. However, as concentrations

of PEG bound to the surface continue to

increase, a micellar lipid-PEG phase

becomes preferred over the lamellar

(liposome) phase resulting from the lateral

pressure caused by PEG.5 Though a

problem for covalently bound polymers,

this should not occur if polymers are

electrostatically bound or hydrophobically

anchored to the surface. Unless the

binding proves to be very strong, the

lateral pressure should cause excess

polymer to simply diffuse off of the

surface before compromising the stability

of the liposome.

http://cwx.prenhall.com/bookbind/pubbooks/

mcmurrygob/medialib/media_portfolio/24.html Figure 2: Hydrophobic lipid tails can bury into

the center of a sphere creating a micelle. If too

much polymer grafted to lipid is in solution, the

lateral surface pressure will destabilize the

lamellar phase and can cause lipids to take on

non-bilayer phases such as micelles.

6

Polymer Coverage Regimes The density of polymer on the liposome surface is broken down into two primary

regimes. At very low concentrations, the polymers are too far apart to interact with each

other. Under these conditions, known as the mushroom regime, the polymer tail is free to

move about in solution and generally occupies a semi-sphere described by the Flory

Radius Rf in Equation 1.

Lmush = Rf = aN3/5

(1)

This radius can also be used to estimate the thickness of the layer, which is equal to the

average extension length of the polymer coil, Lmush. For the mushroom regime, the

thickness is both a function of the monomer size, a, and the degree of polymerization, N.

As the concentration of polymer on the surface increases, the chains begin to come in

contact with one another. This contact prevents a full range of motion for the polymer,

causing it to take on a slightly altered form which is termed, the brush regime.

Lbrush = N*a5/3

/(D2/3

) (2)

For the brush regime, the polymer layer thickness is also a function of the distance D

between polymer attachment points to the liposome surface as indicated in Equation 2.

In order to get a rough estimate of the scale of such a layer relative to the liposome itself,

a quick calculation is provided below. The example we will first consider is a 2 kDa

PEG polymer chain with ethylene glycol monomers estimated at a length of a = 3.5 Å.

Using the molecular weight of ethylene glycol (M.W.EG = 44 g/mol), the number of

monomer units N is found to be about 45 for a 2 kDa PEG chain with a mushroom layer

thickness of about Rf = 3.46 nm. Considering the fact that most liposomes being

investigated for drug delivery applications have diameters of between 100 nm and 200

nm, it becomes evident that this layer can be rather thin.

Determination of polymer coverage regime

The polymer coverage regime can be calculated by measuring the ratio of the area

covered by PEG in an unrestricted mushroom regime APEG nPEG to the total surface area

available ATotal according to Equation 3.

x = APEG nPEG /ATotal (3)

• For x < 1, there is not enough PEG to completely cover the surface meaning that

polymer coverage is in the mushroom regime.

• For x > 1, the polymer takes up more area than is available on the surface suggesting

that the polymers are interacting and are in the brush regime.

• For x ≈ 1, the surface is covered by PEG so that the polymers just touch. This is the

boundary that separates the mushroom regime from the brush regime, which will be

referred to as 1Γ*.

7

PEG Properties PEG is a neutrally charged, crystalline polymer with a high solubility in both aqueous

and organic solvents6. It has an unlimited water solubility which is attributed to it’s good

structural fit with water: water molecules that make up PEG’s hydration shell appear to

orient themselves in a structured manner around the polymer chain.7 One reason that

PEG can sterically inhibit proteins from reaching the liposome surface is attributed to its

large excluded volume, which is at least partially an effect of its high degree of

conformational entropy.8 This means that a relatively small amount of PEG can occupy a

lot of space. As suggested above, this property is believed to be critical to PEG’s ability

to shield the liposome from protein recognition. As the polymer’s chain length increases,

the void fraction also increases meaning that more space will be occupied by solution.

However, the affect of the polymer’s molecular weight must be balanced by the fact that

these larger polymers are only effective at blocking larger macromolecules and

interaction with cells.9

Steric inhibition might not be the only way that PEG protects the liposome from proteins.

For instance, several studies have indicated that PEG shields the surface charge. In fact,

1.5% (moles lipid) of PE-PEG was shown to shield liposome surface charge by 80%.10

Though unable to restrict smaller ions and other compounds from reaching the liposome

surface, PEG can affect transport dynamics of solution within the polymer layer. One

way that this occurs is by expanding the shear plane around the vesicle. The charge

potential felt at this layer is important because it is indicative of the forces other charged

particles will be exposed to when near the vesicle.

Removal Characteristics It has been shown that lamellar lipid vesicles without a polymer layer, or classical

liposomes, have a non-linear rate of removal from the body with a strong dependence on

initial concentration.11

As higher concentrations are administered, the body exhibits a

faster initial rate of removal. This initial phase of liposome removal from the blood

stream has been attributed to the mononuclear phagocyte system (MPS).12

The second

phase of clearance characteristics appears to be almost completely independent on

concentration.13

In contrast, PEG-protected liposomes have clearance characteristics that appear to be

entirely independent of the initial concentration.14, 15

This property is important because it

indicates that circulations times can be significantly influenced by dosage for these

systems. This level of control is not available for classical systems that don’t employ a

polymer layer.

8

Figure 2.3: This figure schematically shows dissociation of (a) PE-PEG, a lipid-linked PEG derivative,

and (b) an HMPEG polymer with three hydrophobic anchors. The hydrophobic anchors are shown in red

and PEG is shown in green. The cooperativity between multiple hydrophobic anchors reduces dissociation

of the polymer from the liposome surface.

Electrostatic Polymers Electrostatic binding is one alternative to grafting PEG to the liposome surface.

Polymers that are electrostatically bound to the liposome surface can have an equilibrium

constant that strongly favors the bound state. Unfortunately, PEG will be at

approximately infinite dilution in the blood stream and so reestablishing equilibrium

forces a steady flux of polymer to desorb from the liposome surface. This desorption

poses a serious challenge for these liposomes to remain in circulation.

One possible way to decrease the rate at which polymer coverage is lost is to develop

polymers with very large Keq values. Polyvalent polymers are known to exhibit very

strong cooperative binding making them a good candidate.

PEO113-DMA31 Based on this reasoning, we investigated a polymer with multiple cationic groups. The

polymer, PEO113-DMA31, is a polyvalent diblock copolymer synthesized by the Armes

group.16

The first number describes the number of ethylene oxide monomers in the PEG

chain. In this case, the polymer has 113 ethylene glycol units, which corresponds to a 5

kDa PEG chain. The second number indicates the average number of tertiary amine

methacrylate groups attached to one end of the polymer. PEO113-DMA31 has 31 of

these cationic groups arranged in a linear fashion, each providing a binding site for the

negatively charged lipids on the liposome surface.

b)

a)

9

Hydrophobically Anchored Polymers Yet another way to bind polymers to the liposome surface is to attach hydrophobic

anchors. The anchor will prefer to be buried within the lipid bilayer because of favorable

interactions with other nonpolar lipid chains. Despite the strong hydrophobic affect, an

equilibrium will still exist between bound and unbound states, meaning polymer would

be lost over time when these liposomes are placed in the body.

Using the same principles of cooperativity applied for the electrostatic polymers, this

study investigated three hydrophobically-modified polymers, each with multiple

hydrophobic anchors (See Figure 3). The anchors are acyl chains, which will bury into

the hydrocarbon interior of the lipid bilayer. The acyl chains are connected to other

hydrophobes by a PEG spacer of varying length (See Appendix 5). By having PEG

attached at two sites, the chain is greatly restricted in conformational structure. Unlike

typical grafted PEG, the polymers in this study will take on a horizontal conformation

and possibly provide a unique form of steric protection.

Polymer Fluidity The mobility of polymer across the liposome surface is another important characteristic

of these systems. For liposomes in a gel phase, the lipids are highly immobile implying

that any covalently bound polymer would also be restricted in movement across the

surface. For liquid phase liposomes, the lipid bilayer is fluid allowing for some

movement though even in this case the movement will be very slow.17

The mobility of electrostatically bound polymers is likely to be much greater than its

covalent counterpart. With a relatively homogeneous surface charge on the liposome, the

polymer has little inhibiting it from migrating around the surface. This can have several

consequences. For one, this will probably result in less restriction on the lateral diffusion

of the lipids on the surface. This also might result in less steric pressure on proteins that

reach the liposome surface.

On the other hand, polyvalent polymers like PEO113-DMA31 might actually have the

smallest amount of mobility due to the cooperative nature of this binding. This should

also be true of the lipids bound to the poly-lysine group on this polymer. The strength of

this binding suggests that these polymers might not only provide longer steric protection,

they might also affect liposome fluidity.

There is very little work that has been done with hydrophobically-anchored polymers that

would indicate the mobility of these polymers. However, it is likely to be largely

dependent on the specific design of the polymer. With a single hydrophobic anchor,

these polymers will probably migrate to a degree that is comparable to PEG-grafted

lipids. With the architecture of HMPEG polymers used in this study, the multiple

anchors are likely to limit overall mobility of each other to a degree that is dictated by the

spacer size connecting them. The PEG spacer might also be able to restrict movement

due to its unique conformation: restriction of PEG at both ends could theoretically allow

it to become physically entangled with other PEG spacers.

1 Lasic, D., and Martin, F., (eds) Stealth Liposomes, CRC Press Inc., Boca Raton, FL (1995)

10

2 Moghimi S.M., 283-318

3 Allen C., 225-250

4 Allen C., 225-250

5 Allen C., 225-250

6 Allen C., 225-250

7 Allen C., 225-250 8 Allen C., 225-250

9 Janoff A. (Ed.) “Liposomes: Rational Design” Needham D. Surface Chemistry of the Sterically

Stabilized PEG-Liposome. Marcel Dekker. New York (1999)

10 Allen C., 225-250

11 Janoff A. (Ed.) “Liposomes: Rational Design” Allen T. and Stuart D. Liposome Pharmacokinetics

Marcel Dekker. New York (1999)

12 Janoff A. (Ed.) Liposomes: Rational Design Allen and Stuart (author of section)

13 Janoff A. (Ed.) Liposomes: Rational Design Allen and Stuart (author of section)

14 Janoff A. (Ed.) Liposomes: Rational Design Allen and Stuart (author of section)

15 Gregoriadis G., 527-537

16 Armes S. P. University of Sussex (Falmer, U.K.)

17 Yaroslavov A.A. Reversibility of structural rearrangements in the negative vesicular membrane upon

electrostatic adsorption/desorption of the polycation. Biochimica et Biophysica Acta 1560 (2002) 14-24

10

2.3 The Electric Double Layer

Description The net negative charge at a liposome’s surface will attract cations and exclude anions

creating an ion concentration gradient around the liposome. This concentration gradient

also results in a chemical potential gradient that will oppose the buildup of counter

charges at the liposome surface. The opposition to this ion buildup naturally follows

from the local decrease in entropy that results from ordering of ions around the liposome.

Hence, a balance is established between the electrostatic attraction of counter-ions to the

liposome surface and the force that compels these ions to diffuse toward a location of

lower ion concentration.

The ions that accumulate near the liposome surface partially cancel the surface charge, to

a degree that is dependent on the distance from the surface and the solution ionic

strength. This charge cancellation can effectively lower the stability that this surface

charge supplies. Within a thin layer surrounding the liposome, also known as the Stern

Layer, ions will become tightly bound to the surface and can be considered immobile.

As seen in Figure 2.4, this layer is even thinner than the hydrodynamic plane of shear or

slipping plane and consists mostly of ions that are directly bound to the surface.

Inside the slipping plane, ions will only

be affected by diffusion and

electrostatics meaning that most ions

within this layer will largely remain

unaffected by convective transport

processes.

Zeta Potential

To obtain a more accurate description of

the liposomes stability in the presence of

ionic species, it is helpful to measure the

actual repelling force afforded by the

charged lipids. With ions accumulating

inside the slipping plane, measuring the

force at this interface will likely give the

most accurate description of the

vesicle’s stability. The most common

way of describing the electrostatic force

is by determining the electrical potential

between the bulk solution and the plane

of shear, otherwise known as the zeta

potential ζζζζ. This value is directly related

to the colloidal stability and hence is an

important property of liposomes.

(Lab Biophysik am Forschungszentrum Borstel )i

Figure 2.4: Counter-ions accumulate around the

charged surface of a liposome. The electrical

potential drops off with increasing distance from the

charged surface. At the shear plane, this potential is

known as the zeta potential.

Diffuse

Phase

Negatively Charged Liposome

Plane of Shear

11

The zeta potential is, to a first approximation, proportional to the surface charge at the

plane of shear. Both zeta potential and electrophoretic mobility are strongly influenced

by the properties of the solution such as salt concentration, pH, viscosity, and

temperature. The zeta potential is not only a function of ion concentration, but is also

strongly dependent on ionic valency. For instance, a divalent ionic species such as

calcium will have a much greater attraction to the liposome surface than monovalent

species such as sodium. Along with its antibacterial properties,ii EDTA complexes with

multi-valent ions, which is a primary reason that this compound is included in all

liposome solutions (See Materials and Methods).

Theoretical Model Following derivations by Debra Auguste,

iii the theoretical electrostatic potential Ψ was

calculated as a function of position based on assumptions made by Guoy and Chapman

(Equation 4). The model treats the liposome surface as an infinite plane with a

homogeneous charge density and assumes ions in solution are point charges. It also

assumes that the solvent only affects the electrostatic potential through its dielectric

constant.

−−

−+=Ψ

]exp[1

]exp[1ln

2

x

x

ze

kT

κγ

κγ (4)

In this equation electrostatic potential is given as a function of distance from the liposome

surface x, where k is Boltzman’s constant, T is temperature, z is ionic valence, and e is

the charge of an electron. κ is the Debye-Huckel parameter, which can be found using

Equation 5.iv

2/1

222

=

kT

zne

ro

o

εε

κ (5)

The Debye-Huckel parameter is also a function of the dielectric constant of the solution εr

as well as the permittivity of free space εo.

Gamma γ is a dimensionless parameter that will vary depending on the potential at the

surface Ψo, where x= 0 (Equation 6). Ψo can be found through its relation to the surface

charge density σ as shown in Equation 7.v

+

Ψ

−

Ψ

=

12

exp

12

exp

kT

ze

kT

ze

o

o

γ (6)

12

( )

Ψ

=

kT

zedkTn

o

oo

2sinh8

2/1εσ (7)

Surface charge density can also be calculated using Equation B1.18, which removes the

last degree of freedom in this system of equations allowing one to solve for Equation 4.

These equations will be useful in assessing how zeta potential is expected to vary with

the amount of charged lipid on the surface. They will also allow us to estimate how the

sensitivity of electrostatic potential to radial distance near the Debye length will vary

with surface charge. Furthermore, these equations will provide a model for better

understanding how the zeta potential can change in the presence of adsorbed polymer.

i Laborgruppe Biophysik am Forschungszentrum Borstel Zentrum für Medizin und Biowissenschaften

Parkallee 10, 23845 Borstel, Deutschland Methods: Zeta Potential and Particle Size Measurements

http://www.fz-borstel.de/biophysik/

ii Vaara M. Agents that increase the permeability of the outer membrane. Microbiol Rev 56 (1992) 395-

411

iii Auguste D. Surface-Modified Liposomes: Hydrophobic and Electrostatic Association of PEG

Conjugates. Dept. Chem. Eng. Princeton University (Unpublished Results) iv Auguste D. v Auguste D.

13

3 Materials and Methods

1.1 Materials

1,2, Dioleoyl-Glycero-3 [Phospho-RAC-(1-Glycerol)] (Mw = 797.04), L-a-

Phosphatidylserine (Brain) (Mw = 810.03), 1,2-Dioleoyl-sn-Glycero-3-Phosphocholine

(Mw = 786.12), and 1,2-Dioleoyl-3-Dimethylammonium-Propane (Mw = 648.06) were

purchased from Avanti Polar Lipids (Alabaster, AL). Poly(PEG6k-lysine-stearylamide)

(HMPEG1: Mw = 42,000, Mn = 18,000, DP = 3), Poly(PEG12k-lysine-stearylamide)

(HMPEG3: Mw = 48,000, Mn = 29,000, DP = 2.5), and Poly(PEG35k-lysine-stearylamide)

(HMPEG6: Mw = 138,000, Mn = 86,000, DP = 2.5) were prepared by the Kohn group at

Rutgers University (Piscataway, NJ). The polyvalent diblock copolymer PEO113-

DMA31 was prepared by the Armes group at University of Sussex (Falmer, U.K.).i

TES (N-[Tris(hydroxymethyl)methyl]-2-aminoethanesulfonic acid), NaCl, and NaOH

were obtained from Aldrich Chemical Company (Milwaukee, WI). EDTA

(Ethylenediaminetetraacetic acid) and Phosphorus standard solution were obtained from

Sigma (St. Louis, MO). Sodium Citrate was obtained from Mallinckrodt (Paris, KT).

Conductivity standard for electrophoretic calibrations was obtained from Fischer

Scientific (Middletown, VA). The pH of solutions was measured using an Accumet pH

meter 50 (Fischer).

3.2 Liposome Preparation

Liposomes were prepared by a freeze-thaw extrusion technique using a large range of

lipid compositions as outlined in Table 3.1. This technique is popularly used due to the

efficiency, high trapping volume, and technical simplicity compared to other techniques

such as reverse phase evaporation, sonication, and methods involving detergent removal.ii

Table 3.1 is a summary of lipid composition for each of the liposomes used in this

research. Under relevant conditions, Phosphatidylserine (PS) and Phosphatidylglycerol

(PG) are negatively charged and Phosphatidylcholine (PC) is neutrally charged. 1,2-

Dioleoyl-3-Dimethylammonium-Propane (DODAP) has a pKa that allows it to change

from neutral to positively charged under the acidic conditions such as are present in the

endosome of a cell. More information is provided for each of these lipids in Table E1.2

in the Appendix.

14

Table 3.1: Lists lipid ratios of all liposomes prepared.

Composition (mol:mol) Lipid Ratio

PS:PC 7:3

PS:PC 3:7

PG:PC 9:1

PG:PC 7:3

PG:PC 3:7

PG:PC 1:9

PG:PC 0.25:9.75

PG:DODAP 9:1

PG:DODAP 7:3

PC:DODAP 7:3

Lipids dissolved in an organic solvent (chloroform) are mixed in the desired ratio with

most stock solutions prepared at 50 µmoles of total lipid. For instance, with chloroform

solutions of 25 mg lipid/ ml chloroform, a 7:3 PS:PC (mol:mol) stock solution will

require 1.134 ml of PS chloroform solution and 0.472 ml of PC chloroform solution.

After being mixed, the lipid solution is put under vacuum for 24 hrs in a dessicator to

slowly remove all solvent. This process steadily decreases the hydrophobic environment

of the solution causing the hydrophobic lipid tails to arrange into multiple bilayer sheets.

1 to 2 ml of an aqueous buffer solution (150 mM NaCl, 10 mM TES, 0.1 mM EDTA)

was then added to the lipid thereby further increasing the hydrophilic environment and

causing the lipid bilayer sheets to swell and self-enclose into multilamellar vesicles upon

agitationiii

. The buffer was designed to mimic physiological conditions including salt

concentration by NaCl and pH which was adjusted to 7.4 using NaOH. EDTA was added

to remove divalent ions in solution in order to minimize flocculation and TES (N-Tris-

(Hydroxymethyl) Methyl-2 Amino Ethane Sulfonic Acid) was used to buffer the solution

against changes in pH. It is important to maintain the temperature of the hydrating

solution (buffer) above the gel phase transition temperature (Tc) for any lipid contained in

the liposome formulation throughout the hydration process.iv For these particular lipids,

it is fine to leave the samples in a refrigerator, however, most solutions were kept at room

temperature during the entire process. Only for liposomes containing DODAP, where the

freeze-thaw process was postponed for a day or more, were these solutions kept in a

refrigerator.

In order to create stable, large, unilamellar vesicles with substantial trapping volumes, a

freeze thaw, extrusion method was performed. This process involved submerging each 1

to 2 ml sample, held in 5ml cryogenic tubes, in a liquid nitrogen filled dewar for about 30

seconds or until the solution was completely solidified. The sample was then allowed to

completely melt under luke-warm water with intermittent periods of vigorous shaking.

Mixing was done to assist establishment of thermal equilibrium and prevent local

temperature spikes above the desirable temperature range. The rapid phase transition

helped to minimize membrane fouling during the following extrusion process.v

15

Prior to extrusion, the extruder was dismantled, rinsed with 70:30 ethanol:water (vol:vol),

and dried using Kimwipes. After reassembling the extruder, nitrogen was sent through at

low pressure (~50 psi) to remove any remaining ethanol. About 12 ml of buffer solution

was also sent through the extruder in 3 ml doses to further rinse the apparatus. Each

solution was then extruded ten times by pressure (150-300 psi) through a double

membrane polycarbonate filter (pore size = 2E-7 m, diameter = 2.5E-4 m). Pressure was

typically kept at 150 psi to minimize loss of sample from spraying. Higher pressures

were only used when needed to induce flow through the filter, which typically was the

case for the first 2 to 3 extrusions. Again, this process should occur at temperatures

above the gel phase transition temperature for all lipids contained in the liposome

formulation.

3.3 Phosphate Assay

In order to accurately characterize the prepared liposome solutions, it was necessary to

determine a more exact measurement of lipid concentration. This was accomplished with

a phosphate assay, developed by Fiske and Subbarowvi

, which resulted in an accurate

spectroscopic measurement of phosphate content (moles). The procedure used follows a

modified version of the assay outlined by Paul Meersvii

of the Liposome Company.

Ashing

Four samples were prepared for each liposome solution by diluting 10 µL of stock

solution (25 mM) with 112.5 µL of buffer. From this dilution, 10 µL was placed into

four test tubes representing the four samples for each liposome solution. These test tubes

were then placed in a ventilated heating block (T = 200 °C) to remove all solvent. After

the solvent had evaporated, the temperature was kept constant as sulfuric acid (200 µL,

10%) was added to each of the samples, which were then left to sit for one hour.

Hydrogen peroxide (50 µL, 30%) was then added to each sample, which acted to degrade

the organic material. The test tubes were kept in the heating mantle for an additional 40

minutes to decompose the hydrogen peroxide.

Assay The samples were then removed from the mantle and allowed to cool to room

temperature. De-ionized water (480 µL) was added by washing the sides of each test

tube after which, the samples were vortexed. A color reagent (0.5 mL) was added to each

sample which was then vortexed and placed in a water bath (45 °C) for 20 minutes. The

color reagent consisted of a 1:2:7 volume ratio of aqueous ammonium molybdate (5%),

freshly prepared ascorbic acid (10%, w/v), and de-ionized water.

16

3.4 Dynamic Light Scattering

The average radius of the prepared liposomes was determined by dynamic light scattering

(DLS) for each of the prepared liposomes. These measurements looked at fluctuations in

light intensity (λ = 532 nm) reflected at a 90° angle over time (100 s) for each sample in

order to determine the size distribution and shape of particles in solution. This was done

through the use of an autocorrelation function for the light intensity, which found the

average particle hydrodynamic radius R and polydispersity index P.D.I. of particles in

solution from the second order viral equation. The third and further terms in the series

describe the skew in the distribution of particle diameters but were neglected because

they are relatively small. Samples were diluted with buffer solution in order to obtain

readings in an optimal frequency range (50-500 kHz) and analyzed by DLS for the each

of the liposome solutions.

Sample Preparation Each sample was diluted with buffer solution to a lipid concentration of about 1.7 mM,

which corresponded to the lower end of the optimal frequency range. This dilution was

primarily chosen for its efficient use of sample. Liposome samples containing adsorbed

polymer were at a lipid concentration of 1 mM or less, however, the frequency for these

samples was about an order of magnitude higher than that of the bare liposomes.

In order to minimize errors in laser diffraction, the 12 mm test tubes were inspected for

scratches and blown with N2 to remove dust. Each tube was then rinsed with methanol

and blown dry with N2 prior to sample addition. To ensure that the laser beam passed

through the solution, each sample volume was at least 1ml. The outside of each tube was

blown again with N2 before measurements were taken.

DLS Operations

The water bath, set at T = 25 °C, was turned on first so that thermal equilibrium could be

reached with the octanol bath, which would house the test tube. The test tube was also

left in the octanol bath for about four minutes prior to measurements in order to allow

thermal equilibrium to be established. The laser was plugged in, with the beam blocked

while not in use, and allowed to warm up for ten minutes. The power for the DLS can be

switched on as well as for the auto-correlator. This piece of equipment, performs an

analysis of the time autocorrelation function of scattered light (See Appendix A.1). The

reflection angle of light being observed should be set to 90°, the wavelength set to λ =

532 nm, and the aperture size set to 100 µm. Voltage was turned on directly before each

measurement and was turned off immediately thereafter.

DLS Software

Data analysis was performed on a PC computer with the ALV 5000

software program.

The refractive index and viscosity of water were used in lieu of precise values for the

buffer solution. Errors in the size measurement are linear with error in the values for

viscosity and refractive index, and are therefore expected to be less than 0.1%. The

program was setup to auto-scale the data with a measurement duration of 5 s and a total

runtime of 100 s.

17

3.5 Zeta Potential Measurements

Electrophoretic Light Scattering The electrophoresis experiments were performed with a Coulter

® DELSA 440 (Langley

Ford Instruments, Division of Coulter Electronics: Amherst, MA). This instrument

determines the particle velocity in response to an applied electric field by laser Doppler

Velocimetry, which takes advantage of the frequency shift of light scattering off of the

particle’s surface. This is the well-known Doppler shift, which occurs whenever light is

emitting from a source that is moving relative to the position of the measuring device.

Cell Loading:

Each sample was loaded into the same 1 ml platinum cell with a 5 ml flat-tipped syringe.

Prior to loading, the cell was rinsed with 3-5 cc of ultra de-ionized water three times for

each of the 3 cell entry tubes. After vigorously shaking out as much water as possible, 3

ml of buffer solution was sent through the cell to ensure each sample maintained its salt

concentration. Great care was taken to ensure that no bubbles were in the cell reservoirs

or in the cell channel. In the reservoir, bubbles can greatly affect the electric field

through the channel while bubbles inside the channel can dramatically affect the velocity

profile that is being measured. Once the cell is loaded with sample, the outside of the cell

was dried with nitrogen and the glass was buffed with Fischer lens paper to minimize

light scattering from the glass wall.

Calibration:

The cell constant was calibrated with Fisher conductivity standard at conductivity= 1015

milliSeimens/cm. An accurate measurement of the solution’s conductivity is important

because it relates the resistivity to the geometry of cell.

Delsa Operational Conditions:

All measurements were taken at 25 ˚C (+ 0.2) using four laser beam angles (8.9º, 17.6º,

26.3º, 35.2º). The electrophoretic mobility was measured for each sample at seven

positions across the cell channel with a corresponding run time of 60 s, frequency of

500Hz, current of 10 mA, and a single measurement voltage time of 2.5 s with a 0.5 s

relaxation period (unless otherwise indicated). Initial tests were performed by varying

concentration, run time, frequency, and applied current in order to maximize the signal to

error ratio.

Cell Alignment:

In order to obtain accurate measurements of electrophoretic mobility across the entire

chamber, it is important that the cell’s position inside the DELSA is known with high

accuracy. A rough measurement of the cell chamber’s bottom is first obtained manually

by lowering the cell until the laser starts to dim as seen through an attached microscope.

For moderately refractive solutions, it should be easy to view the laser as it passes

through the solution. The reset button for the cell bottom is depressed and fine-tuning is

then done using highly accurate motors controlled with the Delsa software. The cell is

first lowered ten microns and then raised by increments of two microns. This method

allowed for easy detection of the minimum intensity averaged over all the laser angles,

18

which corresponded to the location of the cell wall. Once the wall position is found, the

external micrometer was zeroed which is used later in the calculations to obtain a more

accurate estimate of electrophoretic mobility.

Figure 3.1: Figures A and B above are taken from actual apparent electrophoretic mobility measurements

for liposome solution 0.25:9.75 PG:PC (1 mM lipid in buffer solution) at cell position x = 0.77 mm, I = 10

mA, pH = 7.4 and T = 25 ˚C. Shown here is an apparent electrophoretic mobility measurement with the y

axis representing relative photo detection intensity for laser angles 8.9º (---), 17.6º (---), 26.3º (---), and

35.2º (---). This particular measurement has very little noise as seen in Figure A and the peaks almost

superimpose at high resolution as shown in Figure B.

Electrophoretic Measurements

Prior to measurements, it is important to check the cell constant and light intensity

detector levels. The cell constant should be around 19 and the light intensity detected

from the four laser angles should average to about 4 V to minimize measurement error.

At this point, electrophoretic measurements can be taken across the cell. First the cell

was moved using the software to the first position. After rechecking the cell temperature,

the current, frequency, and run-time were set and measurements were performed. This

produced a graph of electrophoretic mobility versus intensity for each of the laser angles

as shown in Figure 3.1. A very clear peak was found in almost every case, which was

selected by boxing in the area on the screen. After defining the peak representing the

liposomes, the computer calculated the electrophoretic mobility and standard deviation

for each laser angle.

A) B)

19

3.6 Baleux Assay

Prior to the addition of hydrophobically-modified PEG (HMPEG) to liposome solutions,

it was necessary to obtain an accurate measurement of HMPEG concentration in the

solutions prepared. These concentrations were quantified using an assay developed by

Baleuxviii

, where 25µL of color reagent (40mM I2, 120mM KI) was added for each ml of

HMPEG solution. These samples for each polymer were prepared by diluting 1 ml of

stock solutions (1mg/ml HMPEG/buffer solution) with 4 ml of buffer solution

corresponding to the optimal adsorption range for the spectrometer being used

(1.0>OD>0.1).

After coloring reagent was added, each sample sat for exactly five minutes before the

optical density was measured at λ=500nm in a 2 ml cuvette. The optical density was very

sensitive to the time of measurement so it was very important to make this measurement

after the same time span observed during calibration procedures. Sample concentrations

were calculated using calibration curves developed by Debra Augusteix. For some

unknown reason, the OD was different when 5 ml cuvettes were used so all

measurements using the larger cuvette volume were disregarded.

i Vamvakaki M., Billingham N., and Armes S. Synthesis of Controlled Structure Water-Soluble Diblock

Copolymers via Oxyanionic Polymerization. Macromolecules 32 (1999) 2088-2090 ii Hope, M.J. et al. Generation of Multilamellar and Unilamellar Phospholipid Vesicles. Chemistry and

Physics of Lipids, 40 (1986) 89-107 Elsevier Scientific Publishers Ireland Ltd.

iii J.A Zasakzinski, E. Kisak, C. Evans. Complex vesicle-based structures. Current Opinion in Colloid and

Interface Science 6 (2001) 85-90 Elsevier Scientific Publishers Ireland Ltd.

iv Avanti Polar Lipids: http://www.avantilipids.com/PreparationOfLiposomes.html

v Avanti Polar Lipids: http://www.avantilipids.com/PreparationOfLiposomes.html vi Fiske, C. H.; Subbarow, Y. The Colorimetric Determination of Phosphorous. J. Biol. Chem. 66 (1925) 375-400 vii Meers, P. Phosphate Assays (e-mail). Outline of procedure for colorimetric determination of

phosphorous. PMEERS@LIPO.COM. viii

Baleux, B., Analytical Chemistry: Colorimetric Determination of Non-Ionic Polyoxyethylene

Surfactants Using I2 and KI Solution, C.R. Acad. Sci. Ser. C 279 (1972) 1617-1620.

Procedure translated by Yuri Dancik (ChemE '00) ix Auguste D. (unpublished results)

20

4 Results

4.1 Phosphate Assay Results

Electrophoretic mobility and, to a lesser extent, hydrodynamic radius were influenced by

the lipid concentration for each sample analyzed. In order to take consistent

measurements using the same lipid concentration, an accurate assessment of phospholipid

concentration was performed for each of the stock liposome solutions listed in Table 4.1.

Figure 4.1: Depicts total phosphate content as a function of optical density (OD) for standard

solutions at λ=820 nm. Standard solutions consisted of two samples of phosphate standard

(0.65 mM) at 0, 5, 10, 20, 50 (nmoles).

Table 4.1: Lists experimentally determined (Column

2) and Calculated (Column 3), stock solution

phospholipid concentrations for each of the lipid

compositions listed. Concentration values are averaged over assay results for four samples.

Lipid

Composition

Assay

Concentration

(mM)

Calculated

Concentration

(mM)

3:7 PS:PC 44.5 50

7:3 PS:PC 38.5 50

7:3 PG:PC 26.7 25

9:1 PG:PC 23.9 25

7:3 PG:DODAP 15.7 17.5

9:1 PG:DODAP 26.4 22.5

Colorimetric absorbance (λ=820 nm) was measured against blank solutions and

correlated to a standard solution (Figure 4.1) to obtain the experimentally measured

phosphate content. With a single phosphate group per lipid, this allowed for an accurate

measurement of lipid concentration for each of the prepared solutions as shown in Table

4.1. The standard deviation between the assay results and experimental preparation had

an average value of 3.0mM. Surprisingly, the optical density of these samples was

dependent on the size of the cuvette being used. Samples measured in 4 ml cuvettes had

a significantly larger OD than those measured in 2 ml cuvettes. Only results obtained

using 2 ml cuvettes are shown in Figure 4.1 and Table 4.1.

The lipid DODAP does not contain a phosphate group, which made an accurate

assessment of lipid concentration difficult for these samples. In order to determine these

concentrations, it was assumed that the lipid ratio measured during preparation was

accurate. It was also assumed that there was little or no preferential membrane fouling

associated with DODAP. Based on these assumptions, the lipid concentration values

(Table 4.1) for 7:3 PG:DODAP and 9:1 PG:DODAP were multiplied by 10/7 and 10/9

respectively, corresponding to the ratio of total lipid to phospholipid in each sample.

y = 37.915x

R2 = 0.9944

0

10

20

30

40

50

0 0.5 1 1.5OD

Ph

osp

ho

rou

s (

nm

ole

s)

21

4.2 Dynamic Light Scattering (DLS) Table 4.2: Listed is the experimental R and P.D.I. for each of the liposomes prepared as

measured by DLS for solutions buffered at

pH= 7.4, T= 25 °C. Results were calculated

based on the second order virial equation.

Lipid Composition R (nm) P.D.I

9:1 PG:DODAP 59 0.064

7:3 PG:DODAP 52 0.056

9:1 PG:PC 53 0.087

7:3 PG:PC 45 0.063

3:7 PG:PC 55 0.054

1:9 PG:PC 57 0.051

0.25:9.75 PG:PC 65 0.071

7:3 PS:PC 61 0.054

3:7 PS:PC 64 0.063

The hydrodynamic radius R of each of these

liposomes is within the empirically

determined optimal range for liposome

retention in vivo. 1

The Polydispersity Index

P.D.I. for each liposome solution is under

10%, suggesting that the vesicle size is fairly

mono-disperse. This index is another

important indicator of liposome retention in

vivo since it describes the range of vesicle

sizes in the prepared solution. Together, these

results indicate that the method of preparation

is well suited to create the type of liposomes

desired in this study.

It is also interesting to note that each liposome solution listed above was stable for at least

a month as indicated by electrophoretic mobility tests and the DLS tests shown here.

This indicates that very little surface charge is needed under the conditions of these

experiments to stabilize the liposomes.

4.3 Zeta Potential Analysis

To determine how PS, PG, and PC affect the electrokinetic behavior of liposomes, a

select group of liposome compositions were studied by electrophoresis. These liposomes

covered a wide range of concentrations of PS and PG in order to select optimum

experimental conditions. These preliminary experiments determined optimal operating

parameters for electric field oscillation frequency, current, and measurement time.

Optimization was based on minimizing the standard deviation for light scattering

intensity corresponding to apparent electrophoretic mobility.

All solutions were diluted to 1 mM lipid concentration, which was proved high enough to

provide adequate light scattering while minimizing interactions between liposomes and

conserving sample. A run time of 60 s was chosen due to the relatively small amount of

error associated with this time span. Run times of two minutes caused heating of the cell

during the experiment, which also resulted in a larger standard deviation.

Frequency Analysis

Lowering the frequency from 1000 Hz to 500 Hz caused the standard deviation to

decrease for some of the liposome samples. It also had a slight affect on the resolution of

the peak in that there were occasionally smaller peaks tapering off from the main peak.

Halving the frequency again to 250 Hz helped to improve the standard deviation even

more for some solutions but decreased resolution so much that some liposome solutions

could not be measured at this frequency. For consistency in measurements, it was

decided to conduct all future mobility measurements at a frequency of 500 Hz.

22

0

0.1

0.2

0.3

0.4

0.5

0 5 10 15 20 25

Current (mA)

S.D

.

Figure 4.2: This graph shows standard deviations in peak light intensity as a function of applied current for 7:3 PS:PC (�), 3:7 PS:PC (�), 1:9 PG:PC (�) and 0.25:9.75 PG:PC (�) liposome solutions at

pH=7.4, T=25 °C. Since standard deviation was also a function of mobility, the values were all standardized using the same process discussed for comparison of mobilities: (See Discussion).

Current Analysis As shown in Figure 4.2, the standard deviation was strongly dependent on current for I <

5 mA but independent of surface charge. Similarly, electrophoretic mobility was also a

function of current at I < 5 mA (Figure 4.3).

0

1

2

3

4

5

6

0 5 10 15 20 25

Current (mA)

Mo

bilit

y (µ

m/s

)/(V

/cm

)

Figure 4.3: This graph shows experimental µe at varying applied currents for 7:3 PS:PC (�), 3:7 PS:PC (�), 1:9 PG:PC (�), and 0.25:9.75 PG:PC (�) liposome solutions at pH = 7.4, T = 25 ˚C. The mobilities

were adjusted based on a cell constant of 19 (See Discussion)

For some liposome solutions, the electrophoretic mobility peak would split into two twin

peaks where the average of these peaks was the mobility found at I = 10 mA. This also

had a negative impact on the standard deviation so it was decided to conduct all future

measurements at a current of 10 mA.

23

4.4 Electrophoretic Mobility of Bare Liposomes

Table 4.3: Lists experimentally determined electrophoretic mobility for each liposome sample. Zeta potential was calculated using Equation B1.14.

Lipid Composition

% Negatively Charged Lipid

Mobility (µm/s)/(V/cm)

Zeta Potential (mV)

9:1 PG:DODAP 90 3.7 46

7:3 PG:DODAP 70 3.6 47

7:3 DODAP:PC 70 0.01 0.1

9:1 PG:PC 90 3.8 49

7:3 PG:PC 70 3.4 44

1:9 PG:PC 10 0.95 12

0.25:9.75 PG:PC 2.5 0.5 6

7:3 PS:PC 70 3.0 38

3:7 PS:PC 30 2.0 26

The zeta potential for all liposome compositions demonstrated a strong dependence on

the amount of charged lipid present as seen in Figure 4.4. The zeta potential also varied

with the specific negatively charged lipid being used as well as what neutrally charged

lipid was present.

0

10

20

30

40

50

60

0 20 40 60 80 100

% Charged Lipid

Ze

ta P

ote

nti

al (m

V)

Figure 4.4: This graph shows Zeta Potential calculated from electrophoretic mobility using Equation

B1.14 for DODAP:PC (7:3, �), PG:PC (0.25:9.75, 1:9, 7:3, 9:1,�), PG:DODAP (7:3, 9:1, �), and PS:PC (3:7, 7:3, �) liposomes at pH=7.4, T= 25 ˚C.

In the case of PG:PC liposomes, zeta potential had a second order dependence on the

percent of lipid that was PG (%PG) as listed in Equation 8.

ζ = -0.0036[%PG]2 + 0.8249[%PG] + 4.0736 (8)

R2 = 1.0000

24

1 Ogihara-Umeda I, Sasaki T, Kojima S, Nishigori H. Optimal radiolabeled liposomes for tumor imaging.

J Nucl Med 37.2 (1996) 326-332

24

4.5 Liposomes Protected with Hydrophobically-Modified Polymers

Baleux Assay Prior to the addition of hydrophobically modified PEG (HMPEG) to liposome solutions,

it was decided to obtain an accurate measurement of HMPEG concentration in solution.

These concentrations were quantified using an assay developed by Baleux1 and

calibration curves for this assay (Table 4.4, columns 2 & 3) developed by Debra

Auguste.2

Table 4.4: Baleux Assay results are based on calibration curves given in Column 2. Column 3 lists the R2

values for the calibration experiments. The reported values for HMPEG concentration in Column 3 are

averaged over three samples. These results are compared to HMPEG solutions (*), recently prepared by

Debra Auguste. Each of the samples in the assay were prepared to produce a concentration of 5 mg/L.

Polymer d[OD]/d[Cp] R2 Cp (mg/L) Standard

Deviation

Expected Cp

(mg/L)

HMPEG6k-DP3 0.038 0.987 13.1 0.51 5

HMPEG6k-DP3* 0.038 0.987 13.9 0.70 5

HMPEG12k-DP2.5 0.054 0.996 7.79 0.40 5

HMPEG12k-DP2.5* 0.054 0.996 10.43 0.53 5

HMPEG35k-DP2.5 0.049 0.976 10.8 0.58 5

HMPEG35k-DP2.5* 0.049 0.976 9.43 0.55 5

Experimentally determined concentrations were roughly double the expected values for

each of the samples listed above. It is highly unlikely that the preparation of HMPEG

solutions on separate occasions by separate researchers would result in the same

magnitude of measurement error. It is possible the assay was not performed correctly or

the calibration curves used do not apply to the spectrometer used. Regardless of the

source of error, it was decided that the accuracy of the solution concentrations, based on

similarities between the two sets of solutions tested, was sufficient for meaningful data to

be drawn from further testing that employed these solutions. Therefore, the polymer

concentrations intended during preparation were used for future measurements instead of

the concentrations found in this assay.

Electrophoretic Mobility

The influence of hydrophobically-modified polymer on liposome zeta potential was

measured at several concentrations using electrophoresis. As can be seen in Figure 4.5,

mobility was not strongly dependent on the degree of polymer coverage. Coverage of

1Γ* (See Appendix C2) corresponds to maximum single layer mushroom regime

coverage. The functional dependence of mobility on degree of polymer coverage appears

roughly similar for each of the HMPEG polymers employed. It is interesting to note that

even at levels of ¼ Γ* coverage, HMPEG35k and HMPEG12k dramatically lowered the

zeta potential of the vesicle by 85% and 87%, respectively (Figure 4.5).

25

0.1

0.3

0.5

0.7

0.9

0 0.5 1% Γ*

Mo

bilit

y (µ

m/s

)/(V

/cm

)

Figure 4.5: Graph (A) shows the mobility as a function of % Γ * for liposome solutions 7:3 PG:PC or 7:3

PS:PC protected with HMPEG6k (�), 12k (�), and 35k (�) at pH =7.4, T= 25 ˚C. Mobilities were

modified using a cell constant of 19 (See Discussion). HMPEG surface coverage information can be found

in Appendix C2. Graph (B) shows percent change in zeta potential due to adsorbed HMPEG polymer as a

function of polymer coverage.

The primary difference between the polymers is in the size of the PEG spacer:

HMPEG12k has a 12k spacer while HMPEG35k has a 35k spacer. These two polymers

had a very similar Γ* value, meaning the total mass of polymer on the surface at 1 Γ*

coverage was almost identical (See Table C2.1). Since even the degree of polymerization

of the polymer, as measured by number of hydrophobic anchors per polymer chain, is

similar between HMPEG12k and HMPEG35k (Table C2.1), it seems that the only

significant variable, PEG chain length, is not affecting the degree of surface charge

shielding for the range of conditions being considered.

Hydrodynamic Radius 7:3 PG:PC and 7:3 PS:PC liposomes with varying degrees of hydrophobically-modified

HMPEG polymer coverage were measured by dynamic light scattering in order to

determine the size and polydispersity of these vesicles. Liposome solutions containing

HMPEG6k aggregated before these measurements could be taken.

The size of liposomes with adsorbed HMPEG polymer was found to vary significantly

with both PEG spacer size and polymer concentration. Unfortunately these tests were not

repeated making it hard to estimate the accuracy of these results. Dynamic light

scattering measurements were repeated for other bare liposomes with results varying on

the order of nanometers (not shown).

At 0.25 Γ* coverage, HMPEG35k actually has a smaller impact on the hydrodynamic

radius than HMPEG12k at the same surface coverage (Figure 4.8), despite the fact that

the PEG spacer size for HMPEG35k is roughly double the size for HMPEG12k.

80

85

90

95

0 0.2 0.4 0.6 0.8 1

%∆

in

ζ (

mV

)A) B)

26

0

10

20

30

40

0 0.5 1 1.5

% Γ*

Ch

an

ge in

R (

nm

)

Figure 4.7: This graphs shows change in liposome hydrodynamic radius as a function of % Γ* surface

coverage for HMPEG12k (�)and HMPEG35k(�). Results were calculated using the values for R listed in

Table 4.5. The change in hydrodynamic radius with no polymer added (�) is also marked here for clarity.

Sources of Error

Though the small P.D.I. (Table 4.5) indicates that aggregation is not occurring for

liposomes that are in the presence of HMPEG, the time between adding the polymer and

measuring the hydrodynamic radius was not consistent between tests and may play a

factor in these results. Studies have shown that even negatively charged liposomes

(without polymer) can gradually increase in size over time3, which may account for the

values stated in Table 4.5.

Table 4.5: DLS Results for 7:3 PG:PC and 7:3 PS:PC containing HMPEG polymer

Lipid Composition Polymer Time (wks) % Γ* R (nm) P.D.I.

7:3 PS:PC HMPEG35k-DP2.5 1 0.25 64 0.04

7:3 PS:PC HMPEG35k-DP2.5 1 1 96 0.07

7:3 PS:PC HMPEG12k-DP2.5 1 0.25 77 0.06

7:3 PG:PC HMPEG12k-DP2.5 5 1 71 0.04

7:3 PG:PC HMPEG35k-DP2.5 7 0.29 97 0.09

7:3 PG:PC none 0 0 45 0.06

7:3 PS:PC none 0 0 61 0.05

1 Baleux, B., "Analytical Chemistry: Colorimetric Determination of Non-Ionic Polyoxyethylene Surfactants

Using I2 and KI Solution," C.R. Acad. Sci. Ser. C 279 (1972) 1617-1620. 2 Debra Auguste (unpublished results) 3 M. Roy, M. Gallardo, and J. Estelrich. Influence of Size on Electrokinetic Behavior of

Phosphatidylserine and Phosphatidylethanolamine Lipid Vesicles. Journal of Colloid and Interface Science. 206 (1998) 512-517

27

4.6 pH-Sensitive Liposomes

Electrophoretic Mobility A pH-sensitive liposomes system was developed consisting of negatively charged PG and

titratable DODAP. Sensitivity to pH changes was due to addition of the lipid DODAP, which

has a pKa of approximately 6.7.

-4

-3

-2

-1

0

1

2

5 6 7 8

pH

Mo

bilit

y (µ

m/s

)/(V

/cm

)

Figure 4.8: shows standard mobility as a function of solution pH for liposome compositions 7:3 PG:DODAP (�),

9:1 PG:DODAP (�), and 3:7 DODAP:PC (�) liposomes at lipid concentrations of 1mM and T = 25 ˚C. Mobilities

were standardized by methods outlined in the Discussion Section.

Each of the liposomes prepared with DODAP demonstrated a change in mobility by pH shift. In

order to get a better sense of how much DODAP could influence the surface charge, liposomes

were made with a lipid composition of 3:7 DODAP:PC. At pH = 7.4, these liposomes had a

mobility that was approximately zero {µe = 9E-3 (µm/s)/(V/cm)} as was expected since both PC

and DODAP are expected to be neutral at this pH. The mobility jumped to µe = 1.0

(µm/s)/(V/cm) when 3:7 DODAP:PC was prepared in a solution buffered at pH = 5.5.

As seen in Figure 4.8, 7:3 PG:DODAP and 9:1 PG:DODAP liposomes were also prepared at pH

= 5.5 and pH = 7.4. The 7:3 PG:DODAP had a larger mobility than 9:1 PG:DODAP at pH =

7.4 { µe = -3.66 + 0.05 (µm/s) /(V/cm), µe = -3.56 + 0.02 (µm/s)/(V/cm)}and at pH = 5.5 { µe = -

2.71 (µm/s)/(V/cm) , µe = -2.53 (µm/s)/(V/cm)}. This peculiar result could certainly be

accounted for through sources of error, however it was repeated at pH = 7.4 with almost the

same results.

The change in mobility due to pH shift for 7:3 PG:DODAP, 9:1 PG:DODAP, and 7:3

PC:DODAP was 0.95, 1.03, and 1.00 (µm/s)/(V/cm), respectively, which demonstrates a nearly

identical change. These results are surprising considering these samples were not all prepared

with the same lipid mole % of DODAP.

28

4.7 pH-Sensitive Liposomes with PEO113-DMA31

The charge shielding affects of PEO113-DMA31 were also investigated by electrophoresis for

7:3 PG:DODAP and 9:1 PG:DODAP liposomes at varying pH. These experiments were

conducted in hope that the pH-sensitivity of these liposomes would be enough to remove

PEO113-DMA31 from the surface.

Solutions were prepared by adding 150% of the polymer needed to fully cover the vesicle

surface. The binding constant is unknown but assumed to be overwhelmingly in favor of the

bound state. Polymer was added in excess, meaning that surface coverage was probably greater

than 1Γ*.

Mobility was reduced by roughly 50% for 7:3 PG:DODAP (with PEO113-DMA31) and by 43%

for 9:1 PG:DODAP (with PEO113-DMA31) when pH was shifted from 7.4 to 5.5. However, the

changes in absolute mobility were at a negligible 0.08 (µm/s)/(V/cm) for both liposome systems

(Figure 4.9).

At pH = 7.4, adding PEO113-DMA31 to 7:3 PG:DODAP and 9:1 PG:DODAP liposomes was

found to reduce the mobility by 96% and 95%, respectively. However, at pH = 5.5, the charge

of these liposomes was still being shielding by roughly 97% as shown in Figure 4.9. This

indicates that much of the polymer was remaining on the vesicle surface, even as DODAP was

becoming positively charged.

-4

-3

-2

-1

0

1

2

3

5 6 7 8

pH

Mo

bilit

y (µ

m/s

)/(V

/cm

)

Figure 4.9: Graph (A) shows standard mobility as a function of solution pH for liposome compositions 7:3

PG:DODAP (�) and 9:1 PG:DODAP (�) containing 1.5 Γ* of PEO113-DMA31 and 7:3 PG:DODAP (�) and 9:1

PG:DODAP (�) without polymer at T = 25 ˚C. Mobilities were standardized by methods outlined in the Discussion Section. Graph (B) is a close up view of compositions 7:3 PG:DODAP (�) and 9:1 PG:DODAP (�) liposomes

with PEO113-DMA31 polymer.

A) B)

-0.2

-0.1

0

5 6 7

29

Hydrodynamic Radius To confirm that polymer was still bound to the surface at acidic pH, the hydrodynamic radius

and polydispersity of these liposomes were measured using dynamic light scattering. The

positive values for change in hydrodynamic radius (Figure 4.10) indicate that the polymer is

indeed still bound to the surface in acidic conditions where DODAP is positively charged.

0

10

20

30

40

5 6 7 8pH

Ch

an

ge

in

Ra

diu

s (

nm

)

Figure 4.10: This graph shows the change in hydrodynamic radius due to the addition of 1.5 Γ* PEO113-DMA31,

as measured by DLS, for 7:3 PG:DODAP (�) and 9:1 PG:DODAP (�) liposomes at pH 5.5 and 7.4 .

Interestingly, the change in R due to the polymer actually increases significantly from pH = 7.4

to pH = 5.5 by 160% and 140% for 9:1 PG:DODAP and 7:3 PG:DODAP, respectively. The

polydispersity index was less than ten percent for all samples, indicating that aggregation was

not occurring during any of the tests with or without PEO113-DMA31 polymer.

30

5 Discussion

5.1 Electrophoretic Mobility Error Analysis

Resolution The improved resolution observed at larger current is likely a reflection of sources of

error that become negligible at higher particle velocities. At higher currents, the velocity

of the liposomes resulting from the electric field will increase while Brownian motion,

which adds noise to these measurements and is dependent on temperature, will remain

constant. To correct for this, the particle diffusion coefficient is also taken into account

by the DELSA, allowing for a calculation of error associated with diffusion to be largely

removed from the final mobility values.

However, at lower currents, the velocity in the direction of the electric field becomes

comparable to the diffusive term, which may be causing the large uncertainties in the

corrected mobilities. This may account for the fact that the particle velocity standard

deviation at a given cell position shrank in the presence of a larger electric field resulting

in the improvement in resolution seen in Figure 4.2.

Mobility

The dependence of mobility on current might be unrelated to the dependence of standard

deviation on current. For highly fluid liposomes, such as those under investigation, it is

possible that electrostatically charged lipids could migrate to align themselves into a

more energetically favorable position when in a strong electric field. Similarly, it is also

possible that counter-ions within the shear plane will also become polarized by this field.

1

10

0.1 1 10 100

Current (mA)

No

rma

lize

d M

ob

ilit

y

Figure 5.1: Shown is a Log-Log plot of normalized electrophoretic mobility versus applied electric current

for 7:3 PS:PC (�), 3:7 PS:PC (�), 1:9 PG:PC (�), and 0.25:9.75 (�) liposome solutions at pH=7.4, T=

25 ˚C. Results were standardized for a cell constant of 19 and normalized by the mobility at high current.

31

If such an alignment were to take place, it would be apposed by an increasing

electrostatic repulsion due to charge localization within the vesicle. The repulsive force

between individual charged lipids would be very large at shorter distances suggesting that

little charge migration or change in mobility should occur for densely charged surfaces

like that of the 7:3 PS:PC vesicles. Figure 5.1 was created in order to properly gauge

whether current is having the same affect on each of the liposome solutions. By

normalizing the mobility, it becomes clear that sensitivity to current does depend on the

amount of charged lipid contained in the liposomes. Considering the standard deviation

in mobility is independent of surface charge (Figure 4.2), the results for each of the

liposome solutions in Figure 5.1 would need to superimpose in order for this source of

error to completely account for changes in mobility with changing current.

It also appears that the error in mobility at lower currents (compared to higher currents) is

strongly dependent on the ratio of charged to neutral lipid suggesting the surface charge

is playing a role in these observations. Figure 5.2 seems to indicate that, though the

surface charge is playing a role, the degree to which this charged is shielded may also be

important.

Charge Shielding

Using the electrophoretic mobility results, it may also be possible to get a sense of how a

particle’s surface charge density will be masked by counter-ions in solution. Figure 5.2

indicates the affects of charge shielding on the particle’s mobility. If shielding did not

take place or took place to the same degree regardless of particle surface charge, the data

from each of the liposome compositions listed would be expected to superimpose at high

currents where mobility is independent of current.

0

10

20

30

40

50

0 5 10 15

Current (mA)

Mo

bilit

y/ %

Ch

arg

ed

Lip

id

Figure 5.2: This graph shows the mobility per unit charge as a function of current for 7:3 PS:PC (�), 3:7

PS:PC (�), 1:9 PG:PC (�), and 0.25:9.75 PG:PC (�) liposome solutions at pH=7.4, T = 25 ˚C.

A lower shielding of surface charge should also mean a greater sensitivity to the applied

electric field, which could at least partially account for the greater sensitivity to current

for low charge density liposome such as 0.25:9.75 PG:PC.

32

5.2 Electrophoretic Mobility Standardization

Use of the DELSA was fraught with calibration issues. Though the same cell was used

during all electrophoresis experiments, the cell constant obtained during calibration of the

machine fluctuated in value from about 14 to 20. The cell constant, largely dictated by

the geometry of the cell, is important because it is proportional to the measured effective

conductivity. This conductivity is related to the electric field strength through Ohm’s law

which in turn, is related to mobility through Equation B1.2. This means that the cell

constant that is calibrated will be directly proportional to the measured electrophoretic

mobility.

The same conductivity standard was being used for each calibration and no bubbles were

observed during cell loading of this standard, making the obvious sources of error

unlikely suspects. Though the cell was flushed with an amount of conductivity standard

over ten times the volumetric size of the cell, it was decided that the most likely reason

for fluctuations in calibrated cell constant was due to dilution affects from solutions

(typically de-ionized water) that had previously occupied the cell. Flushing the cell

slowly and shaking out the fluid after each time the cell was completely full appeared to

provide more accurate and consistent calibrations. Such a technique proved more

effective than excessive flushing of the cell at high pressure. From this observation, it is

likely that there were pockets of fluid or low pressure areas in the cell that were allowing

some of the original fluid to remain in the cell even after several flushes.

With substantial fluctuations in calibrated cell constant for each set of electrophoresis

experiments, it was impossible to obtain consistent mobility values on different days for a

given liposome solution. Table 5.1: This is a summary of the results for two electrophoretic mobility tests conducted for 7:3 PS:PC

over a range of currents at pH=7.4, T= 25 °C.

Test A 7:3 PS:PC Conductivity=13.4 Cell constant =17.9646 Date: 3/27/2003

Current (mA)

µe

(µm/s) /(V/cm) Test B 7:3 PS:PC Conductivity=8.7 Cell constant = 11.657 Date: 2/11/2003

Current (mA)

µe

(µm/s) /(V/cm)

2.8 -3.2 2.8 -1.88

5.6 -2.87 5.6 -1.86

10 -2.85 11.2 -1.78

22.4 -2.89 22.4 -1.81

It was noticed that the ratio of conductivities between the two runs was equal to the ratio

of the cell constants (8.7/13.4=11.657/17.965). This suggested that the relationship

between cell constant and conductivity was linear, largely independent of calibration, and

could be exploited to accurately compare the two DELSA runs as demonstrated in Figure

5.3.

Each of the tests summarized in Figure 5.3 were conducted on different days with very

distinct cell constant calibrations. Based on the linearity of conductivity and cell

constant, the mobilities for the first set of measurements, denoted in blue diamonds, were

multiplied by a correction factor.

33

2

3

4

5

6

7

0 5 10 15 20 25

Current (mA)

Mo

bilit

y (µ

m/s

)/(V

/cm

)

Figure 5.3: Graph (A) shows mobility as a function of current for 7:3 PS:PC liposomes calibrated with cell

constant = 18.0 (�) and cell constant = 11.7 (�) at pH = 7.4, T = 25 ˚C. The mobilities shown in (A)

were recalibrated used a cell constant of 19. Graph (B) shows unmodified mobilities based on original

calibrations

For example, the mobilities in Table 5.2 were multiplied by a correction factor of 19/(old

cell constant), which corresponded to the ratio of a new universal cell constant 19 to that

of the cell constant used to obtain the mobility value. Clearly the two sets of data now

overlap suggesting that the experimental results were repeatable and moreover, that the

other samples could be compared. Repeating this standardization process on other

liposome compositions confirmed the validity and accuracy of this method.

In order to obtain consistent measurements that could be analyzed over the range of

liposome compositions employed, it was necessary to prove that this standardization

process could be used to compare all samples based on a single cell constant. Though the

relationship between conductivity and the cell constant was clearly linear, it might also be

a function of the liposome composition being used in which case the comparison between

samples of different composition would be highly inaccurate. Though the liposome

surface charge varied between samples, the lipids were purposefully very dilute in the

solution so that this variation in charged lipid content would have a negligible affect on

the solution conductivity.

Table 5.2: This table lists the conductivity of several different samples along with the cell constant that

was calibrated prior to the measurement and the ratio of conductivity to cell constant Q.

Sample Date Conductivity (mS/cm) Cell Constant Q

7:3 PS:PC 2/11/2003 8.7 11.7 0.75

7:3 PS:PC 3/27/2003 13.4 18.0 0.75

3:7 PS:PC 12/20/2002 15.2 19.9 0.76

3:7 PS:PC 2/11/2003 8.6 11.7 0.74

0.25:9.75 PG:PC 4/1/2003 16.0 20.4 0.78

1:9 PG:PC 4/1/2003 15.5 20.4 0.76

7:3 PG:DODAP 4/3/2003 14.4 19.0 0.76

9:1 PG:DODAP 4/3/2003 14.5 19.0 0.76

1

2

3

4

0 5 10 15 20 25

34

The results in Table 5.2 are an attempt to justify comparisons between liposome solutions

of varying composition based on the relationship between cell constant and solution

conductivity. The last column Q in Table 5.2 represents the ratio of conductivity to cell

constant. This ratio is fairly consistent among all samples suggesting the conductivities

were all roughly the same (14.4 + 0.4). Furthermore, the variation in this ratio shows no

relationship to the concentration of charged lipid present. This not only demonstrates that

this control (solution conductivity) was maintained, but also indicates that all samples can

be adjusted to a universal cell constant in order to compare the different samples.

pH affect on Conductivity pH was found to have a noticeable affect on solution conductivity. Solutions at pH = 7.4

had a conductivity to cell constant ratio of 0.76 (S.D. = 7 E-3) while solutions at pH = 5.5

had a ratio of 0.91 (S.D. = 5 E-3). This is not surprising since both buffers were prepared

with the same salt concentration, but obviously at different pH, which also affects

conductivity. Since conductivity is directly related to the calculated mobility, this

disparity will alter the mobility of acidic solutions by as much as 20%.

In order to compare the mobility results shown in Figure 4.8 and Figure 4.9, the

standardization process was revised to account for both changes in cell constant and

solution conductivity. This was accomplished by multiplying all mobilities (already

modified using the method discussed above) by Q/Qo, where Qo = 0.75 is the average

conductivity to cell constant ratio for solutions buffered at pH = 7.4. This essentially

corrects each mobility based on a universal conductivity instead of a universal cell

constant.

5.3 pH-sensitivity of DODAP

Compared to liposomes with a similar charged lipid composition such as 3:7 PS:PC

liposomes (µe = -2.0 (µm/s)/(V/cm) at pH = 7.4), the mobility of 3:7 DODAP:PC at pH =

5.5 was rather low with the absolute mobility being roughly half that of 3:7 PS:PC. It is

likely that the large discrepancy between these values is principally due to the extent to

which DODAP is positively charged at pH = 5.5. The pKa of DODAP is close enough to

the solution pH to significantly reduce the average charge of these lipids.

The sensitivity to pH conditions for liposomes containing DODAP was also surprisingly

not affected by the other lipids contained in the liposome. In fact, the change in mobility

between 7:3 PG:DODAP and 3:7 DODAP:PC was nearly identical suggesting that a pH-

sensitive liposome could be created based on these results that completely neutralized its

average surface charge under acidic conditions. More generally, it indicates the design

flexibility and the potential of this liposome system.

35

Sources of Error: pH Gradients The process by which the pH was changed from pH = 7.4 (pH in the stock solution) to

pH = 5.5 in samples might have been problematic. pH gradients will develop across the

lipid bilayer in liposome systems where the external solution is replaced by another

solution of a different pH. The existence of such a gradient could significantly affect pH

sensitivity of the liposome.

Phayre reports a rapid loss of the pH gradient 3 hrs after changing pH1, which is slightly

less than the approximate 4.5 hour period between preparation and mobility

measurements conducted in this study. The method of preparation was also one where a

rapid change in pH took place in the external solution, which can dramatically reduce

liposome stability. This, however, did not seem to be a serious issue for these liposomes

based on the low polydispersity that was measured.

5.4 pH-Sensitive Liposomes with PEO113-DMA31

Previous work with polyvalent polymers has indicated that the favorable interaction

between these polymers and oppositely charged lipids can cause lipid segregation on the

vesicle surface.2 It is possible that the observed increase in hydrodynamic radius under

acidic conditions (Figure 4.10) is from lipid segregation on the liposome surface due to

the favorable interaction between the polyvalent polymer and PG.

It is also interesting to note that the increase in hydrodynamic radius for 7:3 PG:DODAP

is roughly double that of 9:1 PG:DODAP at both pH = 7.4 and 5.5 (Figure 4.10). This

might indicate that lipid segregation is already occurring at pH = 7.4.

Lipid segregation should increase the binding strength between the negatively charged

lipids and the polyvalent polymer. Furthermore segregation of lipids would decrease the

electrostatic repulsion between protonated DODAP lipids and PEO113-DMA31. This

would effectively reduce the sensitivity of polymer desorption from the presence of

DODAP under acidic conditions.

It has also been shown that polyvalent species are able to cause lipid migration across the

lipid bilayer.3 With charge neutralization on the surface (due to polymer adsorption), the

electrostatic repulsion of PG lipids on the inner bilayer might cause a mass flux of this

lipid toward the less negatively charged outer surface. For similar reasons this may force

protonated DODAP lipids to prefer the inner layer of the liposome under acidic

conditions. This type of electrostatically-induced lipid migration across the bilayer could

account for the similarity in pH-sensitivity between 7:3 PG:DODAP and 9:1

PG:DODAP.

36

5.5 Liposomes Protected with Hydrophobically-Modified Polymers

Surface Charge Shielding To get a better understanding of how the HMPEG polymers were affecting the zeta

potential of the liposomes, the zeta potential for HMPEG12k and HMPEG35k polymers

adsorbed at 1Γ* coverage were compared to theoretical electrostatic potential in Figure

5.4. Also shown in this graph is the average blob diameter Z (Appendix C2), which had

previously been determined by Debra Auguste to be 12.8 nm and 7.5 nm for HMPEG35k

and HMPEG12k, respectively.4 The blob diameter was used here instead of

hydrodynamic radius because the former is based upon flow around the particle while the

latter considers full polymer extension length. The shear plane is dependent on flow

characteristics around the liposome and not on liposome size making the blob length an

important property for this discussion.

0

1

2

3

4

5

0 5 10 15

Distance from surface (nm)

Po

ten

tial

(mV

)

Figure 5.4: Graph (A) shows theoretical electrostatic potential in black calculated from Equation 4 as a

function of distance from the liposome surface for liposomes with 70% negatively charged lipid without

polymer. Vertical lines represent the average blob diameter and horizontal are experimental zeta potential

for HMPEG12k (blue) and HMPEG35k (red) polymers at 1Γ* coverage. Graph (B) shows theoretical

electrostatic potential (black) on a logarithmic scale along with zeta potential for HMPEG12k (blue),

HMPEG35k (red), and 7:3 PG:PC without polymer.

It is interesting to note that the theoretical electrostatic potential changes very little at the

distance of these two blob lengths. The shear plane of these particles clearly has not

extended that far assuming the theoretical model is accurate to an order of magnitude

indicating that the blob length is not a good indicator of the polymer’s influence on the

shear plane.

1

10

100

0 1 2 3 4

A) B)

37

With the number of hydrophobic anchors on the surface very similar between these two

polymers, the density of PEG should become more and more similar as one gets closer to

the liposome surface. After taking this into account, along with the log-linear

dependence of zeta potential on the distance of the shear plane, it is not surprising that the

values between HMPEG12k and HMPEG35k were so similar. The functionality between

electrostatic potential and distance also helps to explain why there was very little

dependence on the concentration of polymer adsorbed to the surface.

However, we would expect that the polymer with the larger PEG spacer would have a

higher density of PEG near the surface and hence extend the shear plane to a greater

extent. This was not the case as seen in the mobility results of Figure 4.5. This seems to

suggest that the conformation of the PEG spacer will depend on the size of the spacer. In

other words, the 12k PEG spacer is able arrange itself so that it is more densely packed

near the surface than the 35k PEG spacer.

Unique Properties of a Multi-Loop Architecture Previous work conducted by Debra Auguste

5 found that with the presence of excess

polymer, HMPEG12k was able to reduce complement protein binding by an incredible

93% for 7:3 NC12DOPE/DOPC liposomes yet HMPEG35k only reduced binding by

about 55%. However, reduction in mobility caused by the adsorption of these two

polymers was nearly identical over the range of coverage studied. This suggests that the

charge shielding affects of these polymers are not indicative of their ability to prevent

protein absorption.

The charge shielding effect of any neutral polymer is believed to be largely due to

expansion of the shear plane surrounding the liposome. The shear plane is probably most

affected by polymer chain density near the surface, while steric pressure and protein

protection are also likely to be dependent on the range of motion afforded to these

polymers as well as the homogeneity of surface coverage.

The lack of correlation between charge coverage and protein absorption between

HMPEG12k and HMPEG35k may reflect the type and range of movement available to

the PEG spacers in these polymers. These polymers are very unique in that the majority

of PEG chains are bound at two points to the liposome surface. If the tension (due to

Brownian motion) between these two anchors were to increase, it would force the PEG

chain into a position that is largely parallel with the lipid surface. This not only places

the polymer, on average, closer to the surface, it may also provide new and better

protection due to a radial pressure. Furthermore, restricting the movement of PEG at

both of its ends should make this polymer a stronger steric barrier.

Larger spacers are likely to allow for a less restricted conformation of the PEG as well as

more mobility of the hydrophobic anchors. Over time, the random migration of the

hydrophobes might cause larger PEG chains to become entangled resulting in a very

heterogeneous surface coverage. Entanglement is possible for polymers with this

architecture because the PEG chain is restricted in movement at both ends and because

the anchors are free to move around in the bilayer.

38

1 A. Phayre, H. Farfano, and M. Hayes. Effects of pH Gradients on Liposomal Charge States Examined by

Capillary Electrophoresis. 18 (2002) 6499-6503

2 A. Yaroslavov. 14-24 3 A. Yaroslavov. 14-24 4 Debra Auguste (unpublished results) 5 Debra Auguste (unpublished results)

38

6 Conclusions

Bare Liposomes The electrophoretic mobility of liposomes was found to be not only dependent on the

amount of charged lipid but also on the specific lipid providing that charge. Mobility

also depended on what neutral lipids were present in the liposome. The mobility of

PG:PC liposomes was found to have a second order dependence on the amount of PG.

pH-Sensitive Liposomes Liposomes containing the lipid DODAP were shown to be sensitive to changes in pH

conditions similar to the differences between the blood stream and endosomal

compartments within a cell. Stability of the liposome was dependent on the amount of

DODAP in the liposome for PG:DODAP systems with the minimum PG:DODAP ratio

being around 7:3 PG:DODAP. This placed a limit on the study of pH-sensitive

liposomes containing only the lipids PG and DODAP.

PEO113-DMA31

Though PEO113-DMA31 did not come off by the small changes in the average lipid

charge density, it is likely that this could occur in the presence of a larger DODAP:PG

ratio (see Recommendations). Furthermore, this polymer provided over 95% surface

charge shielding for both 7:3 PG:DODAP and 9:1 PG:DODAP liposomes at both pH

conditions tested. In fact, this polymer shielded the liposome surface charge to such an

extent that the mobility was less than half that of the mobility for 0.25:9.75 PG:PC

liposomes: the lowest mole % of negatively charged lipid that was prepared and tested.

The observed increase in hydrodynamic radius when pH was changed from pH = 7.4 to

pH = 5.5 for 7:3 PG:DODAP and 9:1 PG:DODAP liposomes containing PEO113-

DMA31 polymer was also an interesting result. In light of electrophoretic mobility

results showing the mobility actually decreased from this shift in pH, it seems very likely

that lipid segregation was taking place. The substantially larger hydrodynamic radius for

7:3 PG:DODAP containing PEO113-DMA31 (compared to 9:1 PG:DODAP) also lends

support to the claim that lipid segregation was occurring on the surface.

HMPEG Polymers Each of the polymers shielded the surface charge by about the same degree with a

relatively small dependence on polymer concentration. Few results were obtained for

HMPEG6k because of aggregation problems, however, it appeared to have similar affects

on mobility.

Liposome size dependence on polymer concentration was very unique between

HMPEG12k and HMPEG35k. Assuming these results are accurate, this may indicate

that the polymer conformation cannot be treated as static and will vary dramatically with

polymer concentration on the liposome surface along with the size of the PEG spacer.

39

7 Recommendations for Future Research

Current Analysis There are many rather straightforward ways in which one could further explore whether,

and to what degree, lipid migration occurs within liposomes exposed to an electric field.

The most obvious next step would be to look at the mobility of standard mobility latex

particles at varying currents. These particles are solid thereby making the charges

immobile. If the mobility was strongly dependent on current then additional experiments

would be needed using latex particles of different, standardized mobilities with an

analysis similar to that shown in Figure 5.1. Assuming these results supported the claim

that lipid migration was occurring, addition work could also be done using the liposomes

developed in this work.

The experimental conditions in this study were set so that the electric field is generated

for 2.5 s upon which time a relaxation period of 0.5 s occurs where no field is being

applied and after which, the field is regenerated in the opposite direction. Even if lipid

migration would occur under these conditions at these time scales, the relaxation period

would ultimately diminish the time averaged lipid segregation and with it, the ability to

measure such an occurrence. Keep in mind, however, that these settings will also affect

temperature control as well as the velocity profile across the cell. For these reasons, I

would first suggest incrementally decreasing the relaxation period and comparing

sensitivity to current at different relaxation periods. It might be necessary to also

decrease the total runtime in order to minimize possible heating within the cell. A small

relaxation period should allow lipid migration to develop and remain in a segregated state

within the liposome during the entire measurement process.

Hydrodynamic Radius I strongly suggest that any future work adhere to a strict time period between preparation

of liposomes and DLS measurements. If liposomes with polymers absorbed to the

surface are used, then you should concurrently run DLS tests for liposomes of the same

lipid composition without polymer (regardless of previous measurements for these

liposomes). These two rules should account for any changes in liposome size over time.

DODAP

One of the biggest challenges encountered was preparation of the pH sensitive liposomes

containing DODAP. When PG:DODAP liposomes were prepared, the vesicles would

quickly aggregate when 30% (lipid) or more of DODAP was added. However, this did

not prove to be a problem for PC:DODAP liposomes. Liposomes were then prepared

consisting of 4:3:3 DODAP:PC:PG with no aggregation occurring, however, this lipid

composition was not characterized by DLS or electrophoresis. It is the opinion of this

author that the addition of PC will enable the mobility to be more sensitive to changes in

pH due to a significant reduction in the PG to DODAP ratio. It would be interesting to

40

further pursue this line of thought in search of a PG:DODAP liposome that was more

sensitive to changes in pH with regards to surface charge and stability.

Many of the mobility and hydrodynamic radius results for liposomes containing DODAP

were unexpected. For example, pH-sensitivity that was dependent on the presence of

DODAP but not on the amount of this DODAP between 10-30% (molar) DODAP. The

radius of these vesicles, however, appeared to be pH-sensitive to a degree that was

influenced by the amount of DODAP present. These experiments are, to my knowledge,

the first tests conducted on liposomes containing DODAP and a negatively charged lipid

making these peculiar results both strange and exciting.

In addition, I feel that it is important that future developments in this work look to exploit

the pH gradients created from the preparation process outlined in this work. This is likely

to more closely model the changing conditions experienced during endocytosis of the

liposome and hence the results obtained would be more relevant for drug delivery

applications.

PEO113-DMA31

The mobility results with PEO113-DMA31 also suggest that there were too many

cationic charges on the polymer to allow it to easily desorb from changes in pH. In light

of potential limits on the amount of DODAP that can be incorporated into the liposome, I

would suggest investigating polymers with a smaller polyvalent group. Armes group also

synthesized PEO45-DMA5 and PEO45-DMA20, both of which should bind less tightly

to the liposome surface. Though the PEG chain is less than half the size of that being

investigated, these affects should be small compared to charge neutralization from

electrostatic binding.

For protection from protein adsorption, it is also very important to minimize the amount

of lipid segregation on the liposome surface. This may prove difficult when attempting

to also increase pH-sensitivity of the liposome. This difficulty could be overcome by

integrating physical aspects between the two classes of polymer studied in this work.

Specifically, I propose the use of a polyvalent polymer that makes use of the multi-loop

architecture of the HMPEG polymers.

43

Appendix A.1

Dynamic Light Scattering Data Analysis

The following is a brief derivation of the governing equations used by the computer

software to calculate the radius and polydispersity based on the data obtained. This

discussion will closely follow the work of Barbara Frisken.1 The main goal of this

discussion is to indicate what physical properties are relevant to the measurements in this

experiment.

Light emitted from a laser beam passes through the solution and reflects off of the

liposomes where it is then detected at a specific reflection angle. The data is analyzed

through use of the normalized time autocorrelation function of the intensity of light

scattered, in this case at 90 degrees, which is defined by Equation A1.12

[ ]

2

)2(

)(

)(

tI

tttIg

∆+

= (A1.1)

In this equation I(t) and I(t+∆t) are the intensity of scattered light at time t and t + ∆t,

respectively. Alternately, this function can also be expressed by the field-field time

autocorrelation function, g(1)

( τ) by Equation A1.2 and Equation A1.3.3

g(2)

(τ) = B + β[g(1)

(τ)]2 (A1.2)

)(*)(

)(*)()()1(

tEtE

tEtEg

τ

τ

+

= (A1.3)

E(t) and E*(t + τ) are the scattered electric fields at time t and t + τ, respectively. The

baseline, B, represents the value of g(2)

(τ) at long times which can be estimated as 1. β is

a parameter that will depend on the geometry of the experimental setup.

Monodisperse Particle Systems Assuming the particles are monodisperse, g

(1)(τ) will take the form of Equation A1.4,

with the decay rate Γ, defined by Equation A1.5.4

g(1)

(τ)= exp(-Γτ) (A1.4)

Γ=Dq2. (A1.5)

D is the particle diffusion coefficient and q is the scattering wave vector which is defined

by Equation A1.6.5

44

=

2sin

4

0

θ

λ

πnq (A1.6)

n is the refractive index of the solvent, λ0 is the laser’s wavelength and θ is the scattering

angle. The particle diffusion coefficient can be used to obtain hydrodynamic radius R of

the particles through the use of the Stokes-Einstein equation, shown here as Equation

A1.7. The hydrodynamic radius is also dependent upon the temperature T, viscosity η,

and Boltzmann’s constant kB.

D

TkR B

πη6= (A1.7)

Polydisperse Particle Systems

When the assumption of a monodisperse system is not used, g(1)

(τ) must be integrated

over all decay rates as shown in Equation A1.8.6

∫∞

ΓΓ−Γ=0

)1()exp()()( dGg ττ (A1.8)

where G(Γ) is normalized as shown in Equation A1.9.7

∫∞

=ΓΓ0

1)( dG (A1.9)

After careful manipulation using the method of cumulants, g(1)

(τ) can be rewritten as

Equation A1.10.8

+−+Γ−= ...

!3!21)exp()(

3322)1(τ

µτ

µττg (A1.10)

and plugged back into Equation A1.2 to get

2

3322)2(...

!3!21)2exp()(

+−+Γ−+= τ

µτ

µτβτ Bg (A1.11)

The Γ term is the first cumulant and represents an average over the distribution of decay

rates. After simple manipulation of Equations A1.5 and A1.7, Γ can be plugged in to

solve for the average hydrodynamic radius, shown in Equation A1.129

Γ

=26 q

TkR B

πη

(A1.12)

The second cumulant µ2/2 corresponds to the polydispersity index (PDI) of the particles

and the third cumulant µ3/6 corresponds to the asymmetry of the particles. The third

cumulant and additional terms in the series are generally not included for PDI < 10%

since these higher order terms can introduce more uncertainty into the calculated values.

45

1 Frisken B. Revisiting the method of cumulants for the analysis of dynamic light-scattering data. Applied

Optics 40 (2001) 4087-4091

2 Frisken B 3 Frisken B 4 Frisken B 5 Frisken B 6 Frisken B 7 Frisken B 8 Frisken B 9 Frisken B

45

Appendix B.1

Electrophoresis and Zeta Potential

One way to determine the zeta potential is to measure the velocity of a liposome in the

presence of an electric field. Electro-kinetic mobility can often be measured accurately

which is related to the potential at the shear plane by Equation B1.6. The basic

instrumental setup consists of a quartz chamber containing the buffered sample solution

with two reservoirs of solution at either end of the chamber. Two electrodes are

positioned in axial alignment with the chamber and a high voltage power source supplies

the electric field. The following derivations of zeta potential by electrophoresis will

follow a review by Yan Xu.1

Depending on the charge, ions will migrate toward one of the electrodes generating the

electric field. This phenomenon is known as electrophoresis. The force from the electric

field, which is proportional to the field strength E and effective particle charge q, causes

all charged particles in solution to accelerate. These ions quickly reach a steady state

velocity due to an apposing frictional force. This force is proportional to the ion velocity,

ve and a frictional coefficient f, as is seen in Equation B1.1:

qE = f ve (B1.1)

The electrophoretic mobility of the charged particle, µe, is then given by:

qE/ f = ve = µeE (B1.2)

where f is a function of the hydrodynamic radius r of the particle and the solution

viscosity η as shown in Equation B1.3.

f = 6πηr (B1.3)

Rearrangement of Equation B1.2 and Equation B1.3 results in an electrophoretic mobility

that decreases as the hydrodynamic radius of the particle increases:

µe = q/6πηr (B1.4)

Electro-osmotic Flow The quartz at the wall-solution interface will be negatively charged as SiO2

-. Cations

from solution will accumulate near this surface in a fashion similar to the electric double

layer discussed in the introduction of charged liposomes. Ions that are present in the

diffuse phase at this surface will migrate toward the cathode at the end of the chamber

creating electro-osmotic flow. This phenomenon is very similar to the electrophoresis

described above as seen in Equation B1.5, which relates the electro-osmotic velocity veo

to the electro-osmotic mobility µ eo.

46

veo = µeo E (B1.5)

The electro-osmotic mobility is a function of the dielectric constant εr of the solution, the

permittivity of free space εo, the zeta potential at the wall, ζ, and the viscosity, η, as

shown in Equation B1.6.

µeo = εoεrζ / 4πη (B1.6)

The zeta potential at the cell wall-solution interface is dependant upon both the ionic

nature of the solution as well as characteristics of the charged surface. Low pH

conditions can decrease electro-osmosis simply due to the pKa of SiO2H, which is

responsible for the charged surface. A solution with a strong ionic strength can also

lower electro-osmotic flow due to the loss of a discrete double layer.

Data Analysis

The apparent mobility µapp is the actual mobility of the liposome measured in the cell and

is simply the sum of the electrophoretic mobility and electro-osmotic mobility.

µapp = µ e + µeo (B1.7)

The apparent velocity, υapp, is similarly dependent on the electric field strength and µapp.

υapp = µappE (B1.8)

-7

-6

-5

-4

-3

-2

-1

0

0.0 0.2 0.4 0.6 0.8 1.0

cell position (mm)

ap

pa

ren

t m

ob

ilit

y

(µm

/s)/

(V/c

m)

Figure B1.1: This graph depicts apparent electrophoretic mobility measurements taken across the cell for

laser angles 8.9º (�), 17.6º (�), 26.3º (�), and 35.2º (�). A second order polynomial data fit is used to

model this profile across the chamber.

47

Through use of Equation B1.8, an apparent electrophoretic mobility can be found for

each of the positions across the cell as shown graphically in Figure B1.1. The profile of

mobility can be modeled using a second order polynomial function of position x. Based

on the linear relationship shown in Equation B1.8, µapp can also be modeled this way as is

demonstrated in Figure B1.1. For clarity, the general form of this equation is given in

Equation B1.9, where a,b, and c are constant coefficients.

µapp = ax2 + bx +c (B1.9)

There are two positions (due to symmetry) across the cell where the electro-osmotic flow

is zero, which is know as the stationary layer xo. Without electro-osmosis occurring at

these points, Equation B1.7 simplifies so that the apparent electrophoretic mobility µapp

becomes the electrophoretic mobility µe. The position of the stationary layer can be

calculated using Equation B1.10

xo = hexp + 0.34(2hactual) (B1.10)

where 2hactual is the total distance between the cell walls and hexp is the experimentally

determined cell center. The experimental cell center will be located where the maximum

apparent electrophoretic mobility is measured across the cell. This can be calculated by

taking the derivative of Equation B1.10 with respect to position x and setting this equal to

zero as shown in Equation B1.11 and B1.12.

bax

e+==

∂

∂

exph20µ

(B1.11)

hexp = -b/2a (B1.12)

With these equations, the electrophoretic mobility of the liposomes can be found at the

stationary layer xo.

µe = a(xo)2 +b xo + c (B1.13)

Zeta Potential Calculation Once the electrophoretic mobility is calculated, the zeta potential can be found based on

assumptions made in the Guoy-Chapman Theory. Their model’s main assumptions are

that 1) the liposome surface can be estimated as an infinite plane with a uniform or

smeared charge and 2) that all ions in the diffuse layer can be treated as point charges.

With these assumptions, ζ can be related to µe using Equation B1.14

or

e

εε

ηµζ = (B1.14)

48

where εr is the dielectric constant of the solution, which was estimated to be that of water

(78.36) and εo is the permittivity of free space (8.85E-12 C2 /N m

2).

Theoretical Models The electrophoretic mobility can also be easily estimated using theoretical models

assuming the particle size is large relative to the Dubye-Huckel screening distance, 1/κ.

This term is the exponential decay distance of the countercharge ion distribution around

the particle. For particles that are large relative to 1/κ, such as the liposomes in this work,

µe can be estimated as:

µe = σ /ηκ (B1.17)

where η is the viscosity of solution (0.00089 kg/m s) and σ is the surface charge density

of the particle (coulombs/cm2).

σ = Ze/4 π r2 (B1.18)

The surface charge density can be found if the particle radius r and the total number of

charges on the surface Z are known by using Equation B1.18. Z can be found by

multiplying the total number of lipids on the surface (4 π r2 / 70Å

2) by the fraction of

lipids that are negatively charged.

1 Xu Y. Tutorial. The Chemical Educator: http://journals.springer-ny.com/chedr Springer-Verlag Vol.

1.21 (1996)

49

Appendix B.2

Apparent Electrophoretic Mobility Peak Determination Figure B2.1 is included here to give an indication of how peaks were chosen for analysis

based on the photon intensity data collected. As seen in the graphs below, this step in

data analysis is critical because it demonstrates how standard deviation and to a certain

extent the calculated mobility are dependent on the method of peak selection.

Figure B2.1: These graphs are measurements taken from 1:9 PG:PC (I = 2.8 mA, pH = 7.4, T = 25 °C) for

laser angles 8.9º (---), 17.6º (---), 26.3º (---), and 35.2º (---). The boxed in area on each figure is the

collected data that was chosen by the experimenter for data analysis by the DELSA software.

These particular peaks were chosen because they are good representations of what these

peaks consistently looked like for all data collected with these tests. Some of the laser

angles, particularly the larger angles, did not have well defined peaks which made it

sometimes difficult to decide how much of the data, represented by the gray boxes,

should be considered during peak analysis. Laser angle 35.2 was especially difficult in

that it often had multiple peaks as seen in Figure B2.1 (b) as well as shoulders where one

side of the graph was sloped much less than the other side.

(a) (b)

(c) (d)

50

Z

Appendix C.1

Poly(PEG(6k, 12k, 35k)-lysine-stearylamide) HMPEG

O

O

O

O

OOOOOOOOOOOO

OOOOOOOOOOOO

HO

O

O

O

O

O

O

O

OOOOOOOOOOOO

OOOOOOOOOOOO

HO O

O

O

O

O

O

OOOOOOOOOOOO

OOOOOOOOOOOO

O

O

O

O

O

O

O

O

OOOOOO

O

OOOOOO

OHO

O

O

O

O

O

O

O

OO

O

O

OOOOOOOOOOOO

OOOOOOOOOOO

a). DSPE-PEG5k b). Multi-loop PEG polymer

Figure C1.1. Diagram of (a) a covalently bound PEG to a lipid and (b) a hydrophobically-modified PEG

associating with a lipid membrane (Used by permission from Debra Auguste).

Description

HMPEG architecture: The HMPEG polymers are described as a “strictly alternating

comb associative copolymer derived from PEG and an amphiphilic derivative of L-

lysine.”1 The PEG polymer connects the hydrophobic anchors that will be buried in the

nonpolar interior of the lipid bilayer.

The primary difference between the three HMPEGs studied is in the size of the PEG

spacer connecting the hydrophobic anchors. HMPEG6k, HMPEG12k, HMPEG35k have

PEG spacers lengths averaging 6k, 12k, and 35k, respectively. HMPEG6k has an

average number of hydrophobic anchors per polymer Dp of 3, while HMPEG12k and

HMPEG35k are Dp= 2.5. Each of the polymers also has roughly the same polydispersity

(see Appendix C.2)

The size of the spacer has been shown to be critical to solubility, binding to lipid bilayers

and to complement protein absorption.2 For instance, HMPEG was found to aggregate

rather quickly at concentrations of 1Γ* though it took several days for aggregation to

occur at ¼ Γ * (results not shown). This is most likely due to the small 6k PEG spacer

separating the hydrophobic anchors. A smaller spacer will bring the hydrophobic groups

on a single polymer in closer proximity (on average) when free in solution, which may

help initiate aggregation.

As demonstrated schematically in Figure C1.1, the size of the spacer can also have an

affect on the polymer density near the liposome surface. Spacers that link together two

hydrophobic anchors will have a restricted range of movement, forcing the polymer

density to be much more concentrated near the surface when compared to a grafted PEG

of similar molecular weight. The spacer also restricts the movement of the anchors in a

way that is dependent upon the spacer’s size. Though this aspect is unlikely to influence

charge shielding, it will probably have an affect on protein absorption and the

effectiveness of the polymer in drug delivery applications.

51

1 Heitz C., Pendharkar S., Prud’homme R. K., Kohn J. A New Strictly Alternating Comblike Amphiphilic

Polymer Based on PEG. 1. Synthesis and Associative Behavior of a Low Molecular Weight Sample.

Macromolecules. 32-20 (1999) 6652-6657

2 Auguste D. (unpublished results)

51

Appendix C.2

Hydrophobically Modified-PEG Surface Coverage Calculations

In order to understand the screening affects of the polymers being used, it was important

to prepare liposomes with a well-defined polymer coverage. To accomplish this task, it is

important to obtain accurate knowledge of the partitioning between polymer bound to the

liposome surface and polymer free in solution at equilibrium. Information about this

binding constant was taken from work conducted by Debra Auguste (unpublished results)

and is summarized in Table C2.1 below.

Table C2.1: List of physical and chemical properties for HMPEG polymers used in this research.1

Polymer Nb Z, (Ǻ) MW,

kDa

Polymer Area,

x 1017

m2

Γ*,

mg/m2

Γhm*,

hydrophobe mol%

Keq (mg/m2)

/(mg/ml)

HMPEG6k-DP3 4 50 42 7.9 0.88 0.89 6.1 + 0.8

HMPEG12k-DP2.5 3 75 48 13.3 0.60 0.40 1.9 + 0.1

HMPEG35k-DP2.5 3 128 138 38.8 0.59 0.14 4.3 + 0.5

The space taken up by each PEG spacer can be estimated as a spherical blob as shown

schematically in Figure C1.1. Table C2.1 lists the average number of blobs Nb and the

average diameter Z of these blobs.

Γ (mg polymer/m2 lipid) is the surface coverage of polymer on the liposome and is

related to the concentration of polymer free in solution Cp by:

Γ = Keq Cp (C2.1)

where Keq is the equilibrium binding constant between HMPEG to fusogenic liposomes.

Γ will be a function of the total surface area of lipids exposed to the surface B and the

amount of polymer bound to that surface Ms (g) by:

Γ = 1000 Ms/B (C2.2)

B can be estimated from the concentration of lipid by calculating the total number of

lipids exposed to the surface and multiplying that by the average surface area of each

lipid, as shown in Equation C2.3.

B = ½ V CLipid NA SLipid (C2.3)

In the above equation, ½ represents the approximate amount of lipids that will be exposed

to the external environment for unilamellar vesicles, V is the volume of the solution,

CLipid is the total concentration of lipid, NA is Avogadro’s Number, and SLipid is the

surface area for a single lipid (70 Å2).

52

The amount of polymer bound to the surface Ms can be found by:

Ms = x B Mw / (Spolymer NA) (C2.4)

where Mw is the molecular weight of the polymer, Spolymer is the area that a single

polymer will occupy on the lipid surface, and x is the degree of coverage that is obtained.

x =1 corresponds to the onset of brush coverage of the polymer, which corresponds to a

polymer concentration denoted as 1C*. The surface coverage at this concentration is

denoted as Γ*, as listed in Column 6 of Table C2.1.

Hence the total mass of polymer MT needed for 1Γ * coverage can be found by adding

the total polymer on the liposome surface with that free in solution as:

MT = VCp + Ms

= 1000VMs/ (Keq B) + Ms (C2.5)

The total number of polymer hydrophobes anchored into the liposome surface Γ*hm is

also listed in Table C2.1. This value can be obtained by multiplying the number of

anchors (DP-#) for a specific polymer by the number of polymers on the surface Ms and

multiplying the result by 100 to put in terms of percentage. For instance, HMPEG6k will

have Γ*hm= 100 (3 Ms).

1 Auguste D. (unpublished results)

53

Appendix D.1

PEO113-DMA31 Polymer Surface Coverage Calculations

Included below is a derivation of the equations needed for preparation of liposomes

containing PEO113-DMA31 at concentrations corresponding to 1 Γ* surface coverage.

The mass of polymer Mpolymer needed for 1 Γ* coverage is given by:

Mpolymer = (MW Npolymer)/NA (D1.1)

where MW is the polymer

molecular weight, Npolymer is the

total number of polymer anchors

needed to cover the liposome

surface, and NA is Avogadro’s

number. Npolymer can be found by

dividing the total liposome

surface area accessible to

polymer SL by the surface area of

a single polymer anchor Sp as

shown in Equation D1.2.

Table D1.1: Physical Properties of PEO113-DMA31 polymer

and calculated values for Equations D1.1 to D1.4 based on a

3 ml liposome sample at 1 mM lipid concentration.

Polymer PEO113-DMA31

Number of tertiary amine

methacrylate groups per polymer

31

Surface area of each tertiary amine

methacrylate group (Ǻ2)

82

Mpolymer (mg) 0.410

Npolymer (*1/6.02E23) 4.15E-8

Sp (m2) 2.53E-17

Polymer MW (g/mol) 9867

Slipid (Ǻ2) 70

Lipid Cp (mol/L) 1E-3

V (L) 3E-3

Npolymer = SL/Sp (D1.2)

SL= ½ VCpNASlipid (D1.3)

The outer liposome surface area is calculated from Equation D1.3 where V is volume, Cp

is lipid concentration, and Slipid is the surface area of a single lipid. The equation is then

divided by two to account for only having half of the lipids accessible to polymer due to

the bilayer structure.

The polymer PEO113-DMA31 electrostatically binds to the liposome surface by a linear

tail of 31 tertiary amine methacrylate groups. Each charged group has a surface area of

about 82 Ǻ2, making the total surface area Sp for each polymer roughly:

Sp = 31* 82 (D1.4)

54

Appendix E.1

Lipid and Buffer Information

Table E1.1: Chemical property information for selected buffer components.

Compound Molecular Formula Mw CAS #

TES C6H15NO6S 229.3 7365-44-8

EDTA C10H16N2O8 292.2 60-00-4

N-[Tris(hydroxymethyl)methyl]-2-aminoethanesulfonic acid (TES)

www.sigmaaldrich.com

Ethylenediaminetetraacetic acid (EDTA)

www.sigmaaldrich.com

Table E2.1: Chemical properties for each of the lipids used in this study. pKa

values outside the relevant pH range are marked with an asterisks. Compound Net

Charge at pH=7.4

pKa M.W. (g/mol)

Chemical Formula CAS #

PS -1 * 810.03 C24H47NO9PNa 51826-99-4

DOPC 0 * 786.12 C44H84NO8P 4235-95-4

DOPG -1 * 797.04 C42H78O10PNa 67254-28-8

DODAP 0 6.7 648.06 C41H77NO4 No CAS #

55

1,2-Dioleoyl-sn-Glycero-3-Phosphocholine (DOPC)

L-α-Phosphatidylserine (Brain PS)

1,2-Dioleoyl-Glycero-3-[Phospho-rac-(1-glycerol)] (DOPG)

1,2-Dioleoyl-3-Dimethylammonium-Propane (DODAP)