The fractal structure of polycation–DNA complexes

$: The fractal structure of polycation–DNA complexes$
1

THE FRACTAL STRUCTURE OF POLYCATION-DNA COMPLEXES

SUPTI SARKAR , LI KIM LEE, STEPHEN L. HART1, HELEN C. HAILES2, SUSANA M. LEVY, ALETHEA TABOR2, PARVIZ AYAZI SHAMLOU3

Department of Biochemical Engineering University College London, Torrington Place, London WC1E 7JE

1 Institute of Child Health, UCL Molecular Immunology Unit, Institute of Child Health, University College London

Medical School, London WC1N 1EH 2 Department of Chemistry, UCL

University College London, Christopher Ingold Laboratories, 20 Gordon Street, London WC1H OAJ

3 Corresponding Author: [email protected]

Keywords: Aggregate, diffusion-limited colloidal aggregation and regime limited colloidal aggregation, DVLO theory, fractal dimensions, gene therapy.

Abstract We use static light scattering to obtain new measurements on the internal structure of

aggregated non-viral delivery vector particles in colloidal suspension. The vector

particles are prepared by charge neutralisation of plasmid DNA by Poly-L-Lysine (PLL-

DNA) and a Lipofectin/integrin-targeting Peptide (LPD). We use established theories of

stability of colloidal particles and fractal concepts to explain the aggregation processes

and demonstrate the existence of a new property (fractal dimension) of the aggregated

vector particles. Aggregation is shown to produce particles with fractal dimensions in

the range between 1.8 and 2.4; the former suggests a loose 3-dimensional structure and

the latter characterises an aggregation process that leads to the formation of particles

with tightly packed structures. We show that the fractal dimension of the vector

particles is sensitive to changes in physico-chemical conditions (ionic strength) of the

buffer solution and propose that fractal dimension may provide a useful means of

monitoring the physical state of non-viral delivery vector particles during preparation

and storage.

Biotechnol. & Appl. Biochem. Immediate Publication. Published on 8 Jul 2004 as manuscript BA20040017

Copyright 2004 Portland Press Ltd.

2

Introduction

DNA vaccination and gene therapy offer significant advantages in the treatment of

many intractable diseases such as different cancers, AIDS and autoimmune diseases

[1,2] but many technical challenges must be overcome before the potential of these

techniques are realised. A major challenge is the need for better delivery systems. Viral

vectors are popular, but there are safety concerns regarding their use [3] and it is

proving difficult to make them in large quantities and sufficient purity [4,5]. DNA

complexes pose fewer problems than viral vectors, but suffer from unacceptably low

transfection efficiencies. Considerable research has been devoted to establishing the

causes of poor transfection and the size of plasmid DNA complexes has been identified

as an important factor. When polycations are mixed with nucleic acids, the ensuing

electrostatic interactions result in the collapse of DNA into a compact structure. Work in

our laboratories [6-8] and elsewhere [9,10] has shown that aggregation of these

compacted DNA-polycation complexes occurs under most physico-chemical conditions,

including physiological conditions. This form of aggregation may play an important

role in cell transfection. We recently reported that the tendency for aggregation of these

systems is governed by their physio-chemical properties and is described by the DLVO

theory [6]. We also described the kinetics of aggregation of these complexes using

Monte Carlo simulations [8]. The properties of aggregates of DNA complex have also

been investigated in numerous studies using a variety of techniques including light

scattering, centrifugation, gel electrophoresis, electron microscopy, X-ray diffraction

and atomic force microscopy [10-14]. However, these techniques provide no

information on the mechanisms of aggregation and give no indication of the

morphology of the resulting aggregates. The spatial distribution of DNA complexes

within the aggregates may vary considerably with time and/or as a result of changes in



3

the physio-chemical and preparation conditions. The three-dimensional structure of the

aggregates may vary from a loosely bound, open structure to a tightly packed, dense

structure. The impact of these structures on transfection efficiency may be significant

but has not been investigated because it has proven difficult to quantify these structures.

The concept of fractals has been used previously to describe the morphology of many

structures resulting from naturally occurring growth processes. The formation of a

fractal structure starts when primary nano-particles or clusters of such particles in a

liquid medium collide continuously to form larger self-similar structures; depending on

the detailed kinetics of the collisions between the particles the final structure may vary

from a 1-dimensional linear structure to a 2- or 3-dimensional branched, porous or solid

structure. Mass fractals are formed in this way and may be characterised by their fractal

dimension, Df, which relates the size (R) to the mass (M) of the structure. Thus:

( ) fD1NR α= (1)

where α is a constant and N is the number of the primary particles in the structure. Df is

typically in the range 1 ≤ Df ≤ 3. Experimental studies combined with theoretical

analysis have identified two physical processes by which mass fractal structures form.

Briefly, reaction-limited colloidal aggregation (RLCA) has been reported to occur at

low particle concentrations and/or low sticking probability where only a small fraction

of encounters between particles leads to aggregation. These conditions lead to the

formation of compact fractal structures with a high value of fractal dimension (Df ≥

2.1). In contrast, diffusion-limited colloidal aggregation (DLCA) occurs at high particle

concentrations. In this case it is hypothesised that all particle-particle collisions cause



4

aggregation, corresponding to a sticking probability of unity. The result is the formation

of loose structures with fractal dimensions close to 1.8 [28].

In biotechnology, many growth processes including growth of filamentous micro-

organisms and microbial colonies have been shown to have fractal properties [34]. For

example, it has been demonstrated that the fractal dimensions of bacterial colonies and

the branching ability of filamentous micro-organisms are sensitive to changes in

nutrient concentration. Other examples of fractal aggregation include aggregation of

particles with adsorbed antibody fragments, coagulation of waste water sludge and

many non-biological systems [15-19].

To our knowledge, however, no study has been reported in the literature on the fractal

properties of non-viral vector delivery systems. In the present investigation we

hypothesis that the aggregation of DNA complexes leads to the formation of fractal

structures and provide new experimental data to test the hypothesis. We measure the

fractal dimension of aggregates of DNA complexes using static light scattering (SLS)

and demonstrate that the fractal dimension provides insight into the spatial distribution

of DNA complexes within the aggregate. We show that the fractal dimension of these

aggregates are sensitive to changes in physico-chemical properties of the system and

recommend that fractal methods may be used as a new tool for monitoring the quality of

gene delivery vectors during preparation and storage.



5

Materials and methods

Reagents and plasmid DNA

All solutions were prepared from deionised Milli-Q water (resistivity ≈18.2 MΩ.cm)

(Millipore Ltd, Bedford, MA, USA) and filtered with 0.22 µm pore size Millipore

syringe filters to remove particulates. HEPES (N-[2-hydroxyethyl]piperazine-N’-[2-

ethanesulfonic acid]) (Sigma-Aldrich, Poole, Dorset, UK) was dissolved in deionised

water and the pH was adjusted as required, by adding NaOH.

Experiments were performed with a 6.9 kb plasmid, pSVβ (Promega Corp., Madison,

WI, USA). The plasmid was transformed and propagated in Escherichia coli DH5α

(Gibco Life Technologies, Gaithersburg, MD, USA) and purified using a Qiagen Kit

(West Sussex, UK). Plasmid purity was analysed by spectrophotometry and gave an

absorbance ratio ( )280260 A/A of 1.8 [20]. Further details are given elsewhere [21].

Experiments were carried out with two different condensing agents. Most experiments

were performed using the Lipofectin-integrin-targetting Peptide-DNA (LPD) vector

particles described fully elsewhere [22-25]. The LPD particles were prepared at a

0.75:4:1 (L:P:D) weight ratio, corresponding to a charge ratio of +7 (ratio of positive

equivalents of the cationic groups to negative charge equivalents of the nucleic acid).

Experiments were performed at different electrolyte concentrations ranging from 20

mM to 1 M NaCl.

Limited tests were also performed with the condensing agent, poly-L-lysine, PLL,

(MW≈25,250, Sigma, Poole, Doorset, UK) and used without further purification or



6

modification. Purified plasmid was resuspended at a concentration of 25 µg/ml in 20

mM HEPES pH 7.2 and mixed with an equal volume of PLL (31.67 µg/ml in 20 mM

HEPES pH 7.2) to form PLL/DNA complexes at a molar charge ratio of 2.0. NaCl was

added to the buffer solution to give ionic strengths of 20, 40, 80 100, 150, 250, 750 or

1000 mM.

There is no reported measurement of fractal dimensions for gene delivery particles

described in the present study. Therefore, to provide comparative data we also

performed a series of initial tests with latex particles (Duke Scientific, CA, USA). The

latex particles were purchased originally in a surfactant-stabilised state as standard

calibration particles (220 nm ± 5 nm) for the particle-sizing instrument. The particles

were suspended in either 250 mM or 1 M NaCl pH 3.0 solutions for static light

scattering studies.

Dynamic light scattering measurements

The stability of the vector particles in solution was evaluated by measuring the particle

size as a function of time. Size measurements were carried out by dynamic light

scattering (DLS), using a Malvern Zetasizer 3000 (Malvern Instruments Ltd, Malvern,

Worcester, UK) equipped with a 10 mW, HeNe laser operating at 633 nm wavelength

and 90° scattering angle. The method of measurement and analysis of data have been

previously described [6-8].

Static light scattering measurements

Fractal properties of the vector particles were obtained from static light scattering

measurements using a Malvern 4800 computer controlled spectrophotometer (Autosizer



7

4800, Malvern Instruments Ltd, Worcestershire, UK. The light source used was a 50

mW 532 nm Uniphase Micro Green laser. The scattered light was collected by an

avalanche photodiode detector positioned at angle θ relative to the forward direction of

the incident beam. All experiments were performed at the constant temperature of 25°C.

The spectrometer was calibrated by performing angular measurements of intensity on

toluene. The toluene count rate was taken at 30°, 90° and 150°, to ensure that the count

rate at 90° was half that at 30° and 150°. In our experiments, angular scans were

performed from θ = 12° to 100°, with a measurement made every 4° (23 steps) for an

acquisition time of 10 seconds (sample acquisition time ≥ 230 seconds) for PLL-DNA

and 10°- 30° for LPD and latex particles (31 steps) The intensity measurements were

repeated at different times following sample preparation. The ability to measure the

intensity of scattered light at angles less than 20o on a goniometer system will depend

on the degree of flare that the laser produces as it enters the cuvette. The refractive

index difference between the glass of the vat and the liquid contained in the vat will

exasperate this situation. To reduce this flare, toluene can be used in the vat. However,

if the system is very well aligned and the vat and fluid used in the vat is exceptionally

clean, there is no reason why measurements made at angles lower than 20o cannot be

performed (Malvern Instruments – private communication). The way to validate the

suitability of the system for measurements at such forward angles is to perform angle

scans with a suitable solvent such as toluene. If the system is well aligned and clean, the

standard angle scan will produce a flat response. This measurement was always

performed in our experiments prior to measurements of the samples to ensure that the

system was suitable for data collection .



8

The theory of light scattering to determine the fractal dimension has been reviewed in

several publications [26,27] and therefore only a brief description is given here. In the

experiments, the scattered intensity I(q) from the randomly oriented particles in

suspension is measured as a function of the scattering angle, θ. The magnitude of the

scattered vector, q, measured in reciprocal length, is given by:

λθπ /2)sin(4 nq = (2)

where n is the refractive index of the solution (1.33) and λ the incident wavelength of

the light in a vacuum (532 nm). The scattered intensity I(q) may be described as the

product of the form factor, P(q) which is the scattered intensity function of the

elementary (scatterer) particles of radius a and the structure function, S(q), which

accounts for the scattered intensity arising from the spatial distribution of the scatterer

particles within the aggregate, having a characteristics maximum length l. Thus:

)()()( qPqSqI ∝ (3)

In the intermediate regime of the wave number, which is of interest to this study, i.e. in

the range l-1 < q < a-1, the form factor P(q) is assumed to be constant and independent of

fractal dimension [35] Importantly, in this regime, theoretical consideration leads to the

following mathematical statement between the structure function S(q) and the wave

number (q) [36][37]Thus:

fDqqS −∝)( (4)



9

Therefore, in the intermediate regime, letting P(q)=1.0 and using equations 3 and 4,

leads to the following relationship [15, 26]:

fDqqSI(q) −∝∝ )( (5)

According to Equation 5, a plot of the scattered intensity (photoncounts), I(q), or the

form factor, S(q), vs. the wave number, q on log-log coordinates would be expected to

yield a straight line with a negative slope equal to the fractal dimension. In the

discussion that follows we have used the I(q) vs q plots to present our results [36][37].

To ensure accuracy of results, the angular range 12° ≤ θ ≤ 68° was chosen for

determination of the fractal dimenison in the experiments with PLL-DNA (0.2 < qa <

1) and 10o ≤ θ ≤ 30o (0.1 < qa < 1) in experiments involving the latex particles and LPD.

Measurements of fractal dimension were initiated when the average aggregate size

exceeded ten times the size of the initial particle size in order to ensure accuracy of data.

Zeta potential measurements

Zeta potentials were measured using laser Doppler velocimetry in a Malvern Zetasizer

3000 (Malvern Instruments Ltd). After the initial particle sizing period, typically

between two and three hours, the sample was diluted further with the relevant buffer to

maintain an acceptable photomultiplier signal. In these measurements the lipopolyplex

(LPD) DNA concentration was approximately 20 µg/ml. The zeta potential was

averaged from 10 measurements.



10

Results and Discussion

Measurements of DNA of various sizes have been reported previously,in our

laboratories, we have studied the factors that influence the size and size distribution of

DNA complexes under different physico-chemical conditions for nearly a decade using

static and dynamic light scattering as well as atomic force microscopy [6][8][38]. These

studies demonstrate that the presence of a negatively charged condensing agent, such as

the poly-L-lysine or the Lipofectin, cause the DNA molecule to collapse on itself

forming a condensed structure in association with the components in the condensing

reagent, it has been suggested that the reduction in the size of the DNA molecule

facilitates its transport across cell-wall membrane, and the complex structure, formed

through binding of the DNA and the components in the condensing agent, has been

implicated in the cellular trafficking processes that lead to transfection. However,

charge neutralization renders the condensed DNA molecules susceptible to aggregation,

the rate and extent of aggregation are critically controlled by the buffer conditions (ionic

strength and pH). There is as yet no consensus of opinion on the precise molecular

mechanisms by which the components in the condensing agent interact (associate) with

the DNA molecules, although a number of hypothesis has been suggested [39]. The

elucidation of the molecular association mechanisms is beyond the scope of our paper,

which is intended to be a contribution on the fractal properties of the aggregates, which

are formed as a result of collision between the elementary units (scatterer particles) of

condensed DNA. In this respect, an important parameter is the size of the elementary

(scatterer) particles, but in our experiments with PLL-DNA and LPD systems, the

definition of a scatterer particle size presented two practical difficulties. The first

difficulty stemmed from the rapidly aggregating nature of the condensed DNA particles



11

in most buffers, which made it difficult to establish the precise size of the scatterer

particles at t=0, which is taken to represent the time at the end of DNA condensation

process and prior to the start of aggregation. The second difficulty was related to the

inability of the static light scattering technique to detect the size of the uncondensed

DNA molecules prior to condensation. These challenges and our approaches to

resolving them are considered first before discussing the results of the fractal

experiments

The static light scattering technique employed in the present study, was not able to

detect the (uncondensed) DNA molecules in solution. It has been reported previously

that the loose structure of the (uncondensed) DNA molecule does not allow sufficient

light scattering to facilitate such measurements [40-43]. Also, the peptide (Poly-L-

Lysine) solution on its own did not produce any detectable measurements [39]. Size and

scattering intensity I(q) became detectable only upon condensation of the DNA.

Considering the rapidly aggregating nature of the condensed DNA particles we devised

controlled experiments to establish the size of the scatterer particles. In the case of

DNA-PLL system, we previously showed [6][7]that mixing of the DNA and PLL in

distilled water induced DNA condensation, but did not cause aggregation. In all other

buffers, condensation was followed by rapid aggregation. We therefore used

measurements in water to define a nominal (notional) “scatterer” size of 50 nm (data

not shown) for the DNA-PLL particles. In the case of the Lipofectin-(integrin-

targeting) Peptide-DNA (LPD) system, Figure 1a indicates a mean scatterer size of

150nm, the size distributions, which are shown as function of time, confirm that in

distilled water DNA condensation occurs without aggregation. Interestingly, as shown

in this figure 1b, prior to mixing with the DNA solution, the Lipofectin particles had a



12

bimodal size distribution with two peak sizes at 400 nm and 1300nm. However,

immediately after mixing with a solution containing the DNA-Peptide, the large particle

size fractions of Lipofectin disappeared as the Lipofectin (DOPE and DOTMA)

components associated/interacted with the DNA-Peptide molecules to form the

condensed particles (Figure 1a). Taken together, the controlled experiments involving

the condensation (but not aggregation) of DNA-PLL and Lipofectin-Peptide-DNA in

distilled water suggest that the scatterer size is system specific, and, additionally, these

observations indicate that unlike fractal experiments involving mono-size model (latex)

particles, condensed DNA scatterer particles exhibit a size distribution, which is

expected to impact the aggregation process, although it is not at yet possible to quantify

the effect.

The rapid aggregation of condensed DNA (scatterer) particles in most buffers

necessitated the use of a special experimental procedure in order to capture the dynamic

size distribution of the particles during aggregation. To achieve this, measurements

were carried out in-situ, by filling the sample cell of the instrument with the DNA

solution first, followed by adding a predetermined amount of the condensing agent

(poly-L-lysine or Lipofectin) while collecting data throughout the procedure. As

explained previously, our control experiments consisted of carrying out the same

experiments in distilled water (where condensation occurred in the absence of

aggregation) to obtain the scatterer size.

Figures 2a and 2b show the variation of the scattered intensity, I(q), of light with q,

with time as a parameter. The data refer to experiments with the LPD, PLL-DNA and

latex particles. The scattering vector, q, was calculated from Equation 2 with n = 1.33



13

(for water) and λ = 532 nm. For clarity of presentation only some of the data points are

shown. The conditions of the experiments always satisfied the basic requirements of the

Rayleigh-Debye model but for accuracy the calculations were confined to data in the

range 12° < θ < 68° corresponding to 0.2 < qa < 1.0 for PLL-DNA and 10O ≤ θ ≤ 30O for

LPD and latex, where the radius, a, of the scatterer within the aggregates was taken to

be 50 nm (PLL-DNA) and 150 nm (LPD). In the case of PLL_DNA and LPD systems.

the plots indicate show the cut-off point at q=1/l, below which the scattered intensity

I(q) becomes independent of wave number (q). Critically, in the range (q)l ≥1.0 and

(q)a ≤ 1.0, which is the scattering range for a mass fractal [37], a power-law

relationship a single gradient (-Df) adequately describe the measurements.. There is no

evidence of any secondary aggregation, which have been reported to occur in some

systems when primary aggregates collide to form larger entities. Such a phenomenon

has been reported to lead to two or more sub-regions in the intermediate regime, each

with a fractal dimension [44]. Based on the power-law relationship, fDqI(q) −∝ , in the

intermediate regime, we applied linear regression analysis to the data points in Figure 2.

The results gave a fractal dimension, Df, of 1.92 for LPD complexes at a salt

concentration of 100mM and 2.20 for buffers at physiological salt concentrations

between 100 and 150 mM in the case of PLL-DNA. Theoretical considerations based on

statistical physics of diffusion-limited colloidal aggregation (DLCA) and reaction-

limited colloidal aggregation (RLCA) suggest that the PLL-DNA complexes aggregated

in the RLCA regime, for which a theoretical mass fractal dimension, Df, of 2.1 ± 0.1 has

been cited [28] and confirmed by computer simulations [29]. In the absence of any

previous data, we performed experiments with latex particles aggregating under RLCA

conditions (Df = 2.2). These are also shown in Figure 2b. It is interesting to note

however that while the latex particles took nearly 9 days to produce aggregates with



14

measurable fractal properties, the aggregation of PLL-DNA particles was completed

within about one hour.

It is notable that the fractal dimension of aggregates of the PLL-DNA particles

remained effectively unchanged despite the fact that the aggregate size distribution

shifted continuously towards larger sizes throughout the period of measurement, as

shown in Figure 3. Taken together, these observations support the view that the addition

of poly-L-lysine rapidly induces condensation of the plasmid DNA by charge

neutralisation [30]. The decrease in the repulsive interaction force due to the electrical

double layers of the complexes, caused by the electrolyte in the medium, resulted in the

aggregation of the self-assembled complexes over a period of about one hour, forming

fairly compact structures, characteristic of aggregation in the RLCA regime. A constant

fractal dimension that was unaffected over time is evidence of little restructuring of the

aggregates. To our surprise, the fractal dimension of the PLL-DNA aggregates also

remained unaffected by minor changes (between 50 mM and 150 mM NaCl) in salt

concentration (data not shown). Similar results were obtained for the LPD particles, but,

crucially, we noted a change in fractal dimension for extreme values of electrolyte

concentration, as shown in Figure 4. For electrolyte concentrations of 750 mM and 1000

mM, the fractal dimension increased to 2.1 and 2.4 respectively, indicating more

compact structures. In contrast, we obtained a fractal value of 1.7 for aggregation

occurring at an electrolyte concentration of 40 mM, indicating the formation of loose

structures, as expected for growth in the DLCA regime, for which a theoretical value of

fractal dimension of 1.8 has been reported [28, 31].



15

The data in Figure 5 show the change in the average sizes of the LPD aggregates as a

function of time for different electrolyte concentrations. Examination of the data

indicate that aggregation slows down at both low and high electrolyte concentrations.

Crucially, aggregation rate is at its maximum for an electrolyte concentration of 150

mM corresponding to physiological conditions. The energy plots for the different

systems shown in Figure 6 confirm that at the extremes of electrolyte concentrations,

the energy barrier increases reflecting the changes in the zeta potential of the system

(Figure 7). The increase in the energy barrier reduces the aggregation rate as seen in the

plots in Figure 5 for the extreme electrolyte concentration (40 mM NaCl). These results

may be explained via the concepts of the critical coagulation concentration (ccc) and the

critical stabilisation concentration (csc), both of which have found application in the

analysis of aggregation data for biological and non-biological systems. As the

electrolyte concentration is increased, the electrical double layer surrounding the

particles diminishes reducing the electrostatic repulsive force between the colliding

particles. Theoretically, the electrolyte concentration at which the double layer force

becomes zero corresponds to the critical coagulation constant (ccc). The impact of

electrolyte concentration on the stability of the particles and the ccc for a particular

system may be determined in terms of the stability ratio, W. According to the DLVO

theory, an increase in electrolyte concentration leads to a reduction in the sticking

probability following collision between particles. As result, only a fraction, 1/W, of the

encounters between particles lead to a permanent contact. The stability ratio, W, may be

obtained in a number of ways [32] a useful equation for its estimation is the Reerink and

Overbeek approximation [33], given by:



https://www.researchgate.net/publication/284300284_Introduction_to_Colloid_and_Surface_Chemistry?el=1_x_8&enrichId=rgreq-1a57760ca6bbe4c8b821bae7838fcbca-XXX&enrichSource=Y292ZXJQYWdlOzg0Njc2MTA7QVM6OTk0MjY5MjQyMzY4MTFAMTQwMDcxNjYzNDc4Mg==

16

W≈

TK

Va B

maxexp21κ

(7)

where κ = [ ]NaCl3.288 nm-1is the Debye-Hückel parameter (e.g. 1.27 × 10-9 for 150

mM NaCl), a is the radius of a primary particle (i.e. 150 nm for the LPD system), KB is

Boltzmann’s constant (1.38 × 10-23 J/K) and T is the absolute temperature (taken to be

298 K).

The energy barrier, Vmax, determined when dV/dH = 0, is obtained from Figure 6. Figure

8 shows the stability ratio (W) as a function of electrolyte concentration. As the salt

concentration is increased the colloidal stability decreases, as shown by a decrease in

the value of W until a minimum is reached that corresponds to the ccc. Interestingly,

beyond the ccc value (80-150 mM), the stability ratio increases with further increase in

the electrolyte concentration. This type of behaviour is contrary to what may be

expected from the DLVO theory but has been reported previously for proteins and other

systems. This form of stabilisation has been explained in terms of an additional

(hydration) force in the DLVO theory . It has been shown that under certain conditions

(high salt concentrations) the presence of water close to a hydrophilic surface causes the

formation of hydrated ions, which are adsorbed on the surface. The resulting thin layers

of adsorbed water molecules and ions (hydrated ions) cause repulsion between colliding

particles at close distances. It is hypothesised [19] that hydrophilic moieties on the

surfaces of protein (and peptide) molecules may induce the formation of hydrated ions

in solutions causing the observed anomalous behaviour of the particles in high salt

concentration aqueous buffers [19]. However, our current theoretical understanding of

the impact of key controlling factors on the strength of these hydration forces is limited,



17

particularly for practical systems such as the non-viral gene delivery particles of interest

in this study. In the absence of this information it is recommended that the stability

profiles shown in Figure 8 are determined experimentally as described in this study.

Conclusion

We have provided new measurements on the aggregation processes that cause

instability of condensed colloidal plasmid particles in suspension. The particles were

prepared by charge neutralisation of plasmid DNA using two different cationic agents,

poly-L-lysine with a molecular weight of 25,250 and a patented Lipofectin-integrin-

targetting peptide mixture. We have used dynamic light scattering to measure the

kinetics of aggregation and static light scattering to quantify the internal structure of the

aggregats. We have observed the existence of fractal aggregates and measured the

fractal dimension under both slow and rapid aggregation conditions. The fractal

dimension of these aggregates change from about 1.8, indicating a loose and open

morphology, to nearly 2.4 suggesting a tightly packed 3-dimensional structure.

Interestingly, we have observed that the fractal dimension is sensitive to changes in the

ionic strength of the buffer solution and our measurements of fractal dimension of the

aggregates over several weeks to months have found little evidence of restructuring over

the time. These results are consistent with established theories of colloidal stability and

fractal concepts, but we have observed a few anomalies. The dependency of aggregation

of the condensed particles on ionic strength followed the expected trend from theory for

salt (NaCl) concentrations between 40 mM and 250 mM. In this regime, the rate of

aggregation increased with increasing ionic strength. However, as ionic strength was

increased beyond 250 mM the aggregation slowed which was unexpected. Crucially,



18

these measurements indicate that aggregation is most rapid for ionic strengths between

80 mM and 200 mM which covers the physiological condition of 150 mM.

Acknowledgements

We would like to thank Mike Kaszuba and Stephen Ward-Smith from Malvern

Instruments (UK) for their expertise in particle sizing, and Aloke Dey-Chowdhury and

Susie Barker (Institute of Child Health) for help in plasmid fermentation.



19

References

1. Anderson,W.F. (1998) Nature 392, (Suppl) 25-30.

2. Crystal,R.G. (1995). Science 270, 404-410.

3. Mountain,A. (2000) Trends in Biotechnology 18, 119-128.

4. Lotfian, P., Levy, M.S., Coffin, R., Ward J., Ayazi Shamlou, P. (2003)

Biotechnology Progress 19, 209-215.

5. Lotfian, P., Levy, M.S., Coffin, R., Ward J., Ayazi Shamlou, P. (2003)

6. Lee,L.K., Mount, C.N., Ayazi Shamlou, P. (2001) Chemical Engineering Science

56, 3163-3172.

7. Mount, C.N., Lee, L.K., Yasin, A., Fearn, T., Scott, A., Ayazi Shamlou, P. (2003)

Biotechnology and Applied Biochemistry 37, 225-234

8. Sarkar.S., Zhang, H., Levy, M.S., Hart, S.L., Hailes, H.C., Tabor, A.B., Ayazi

Shamlou, P. (2003) Biotechnology and Applied Biochemistry 38, 95-102.

9. Rolland, A.P. (1998) Critical Reviews and Therapy in Drug Carrier Systems 15,

143-198

10. Zelphati, O., Nguyen, C., Ferrari, M., Felgner, M., Tsai, J., Felgner, P.L.(1998)

Gene Therapy 5, 1272-1282

11. Ferrari, M.E., Nguyen, C.M., Zelphati, O., Tsai, Y., and Felgner, P.L. (1998)

Human Gene Therapy 9, 341-351.

12. Kreiss, P., Cameron, B., Rangara, R., Mailhe, P., Aguerre-Charriol, O., Airiau,

M., Scherman, D., Crouzet, J., and Pitard, B. (1999) Nucleic Acids Research 27,

3792-2798

13. White, R.E., Wade-Martins, R., Hart, S.L., Frampton, J., Huey, B., Desai-Mehta,

A., Cerosaletti, K.M., Concannon, P., James, M.R. (2003) Journal of Gene Medicine

5, 883-892.



20

14. Wolfert, M.A. and L.W.Seymour. (1996) Gene Therapy 3, 269-273

15. Amal,R. and Raper, J.A. (1993) Particle & Particle Systems Characterisation

10, 239-245.

16. Ayazi Shamlou, P., Stavrinides, S., and Titchener-Hooker, N.J. (1996)

Bioprocess Engineering 14, 237-243.

17. Bohr,H., Kühle, K., Sørensen, A.H., and Bohr, J. (1997) Zeitschrift Für Physik

D 40, 513-515.

18. Magazu, S., Maisano, G., and Mallamace, F. (1989) Physical Review A 39,

4195-4200.

19. Molina-Bolívar, J.A., Galisteo-González, F., and Hidalgo-Álvarez, F. (1998)

Journal of Colloid and Interface Science 298, 445-454.

20. Ayazi Shamlou, P. (2003) Biotechnology and Applied Biochemistry 37, 207-

218

21. Levy, M.S., Collins, I.J., Tsai, J.T., Ayazi Shamlou,P., Ward, J.M., and Dunnill,

P. (2000) Journal of Biotechnology 76, 197-205.

22. Hart, S,L., Arancibia-Carcamo, C,V., Wolfert, M, A., Mailhos, C., O'Reilly, N,

J., Ali, R,R., Coutelle, C., George, A, J.T., Harbottle, R., Knight, A,M., Larkin,

D. F, P., Levinsky, R, J., Seymour, L, W., Thrasher, A, J., Kinnon, C., (1998)

Human Gene Therapy 9 575-585.

23. Hart, S.L. (1999) Current Opinions in Molecular Therapeutics 1(2) 197-203

24. Pedroso de Lima, M, C., Simoes, S., Pires, Pedro., Faneca, H., Duzgunes, N.

(2001) Advanced Drug Delivery Reviews 47, 277-294.

25. Lee, L.K., Siapati, E., Jenkins, R.G., McAnulty, R.J., Hart, S.L., Ayazi

Shamlou, P. (2003) Medical Science Monitor 9 (1) 54-61.



21

26. Schmidt, P.W. (1989) The Fractal Approach to Heterogeneous Chemistry:

Surfaces, Colloids, Polymers. Avnir, D. editor. John Wiley & Sons Ltd., New

York. 67-79.

27. Sorensen,C.M. (2001) Aerosol Science and Technology 35 648-687.

28. Lin,M.Y., Lindsay, H.M., Weitz, D.A., Ball, R.C., Klein, R., and Meakin, P.

(1989) Proceedings of the Royal Society of London A 423 71-87.

29. Ball, R.C., Weitz, D.A., Witten, T.A., Leyvraz, F. (1987) Physical Review

Letters 58 274-277

30. Bloomfield,V.A. (1996) Current Opinion in Structural Biology 6 334-341

31. Meakin,P. (1988) Advances in Colloid and Interface Science 28 249-331

32. Shaw, D.J., (1992) Colloid and Surface Chemistry. Butterworth-Heinemann,

Oxford.210-233.

33. Reerink, H, Overbeek, J. Th. G. (1954) Discuss. Faraday. Soc., 18, 74-84.

34. Großkinsky, S., Timme, M., Naundorf, B. (2002) Physical Review Letters, 88,

245501-1- 245501-4.

35. Yates, P., Yan Yao-de., Jameson, G.J., Biggs, S.(2001) 6th World Congress of

Chemical Engineering.

36. Tirado-Mirando, M., Schmitt, A., Callejas-Fernández, J., Fernández-Barbero,

A. (2000) Colloids and Surfaces, A: Physiochemical and Engineering Aspects

162, 67-73.

37. Tang, S., Preece, J.M., McFarlane, C.M., Zhang, Z. (1999) Colloids and

Surface A: Physiochemical and Engineering Aspects 157, 185-192.

38. Hart, S. L., Arancibia-Cárcamo C. V., Wolfert M. A., Mailhos, C., O'Reilly, N.

J., Ali R, R., Coutelle, C, George, A. J. T., Harbottle R.P., Knight A. M., Larkin





22

D. F. P., Levinsky R. J., Seymour L. W., Thrasher, A. J., Kinnon, C. (1998)

Human Gene Therapy. 9, 575-585

39. Lai, E., van Zanten, J.H., (2001) Biophysical Journal, 80, 864-873.

40. Lyubchenko, Y.L., Shlyakhtenko, L.S. (1997), Proc. Natl. Acad. Sci. USA, 94,

496-501

41. Hansma, H.G., Golan, R., Hsieh, W., Lollo, C.P., Mullen-Ley, P., Kwoh, D.

(1998) Nucleic Acids Research, 26, 2481-2487s.

42. Rybenkov, V.V., Vologodskii, A.V., Cozzarelli, N.R. (1997) Journal of

Molecular Biology, 267, 299-311.

43. Bloomfield, V.A., Crothers, D.M., Tinoco, Jr, I., (editors) Shape of Nucleic

Acid in Solution Structures (2000), 386-388, University Science Books,

Sausalito, CA.

44. Thill, A., Moustier, S., Aziz, J., Wiesner, M.R., Bottero, J.Y. (2001) Journal of

Colloid and Interface Science, 243, 171-182.



23

Table 1 The total energy of interaction, VT, between the particles was obtained by summing the van der Waals attractive potential, VA, and the repulsive double layer electrostatic potential, VR. [10,27]

+++

+++

++++

++−=

yxxyxxxyx

yxxyxy

xxyxyAVA 2

2

22 ln212

, where x = (H/a1+a2) and y

=a1/a2, A is the Hamaker constant, assumed to have a value of 5 × 10-21 J. H is the separation distance between the surfaces of two spherical particles of radii a1 and a2. The electrical double-layer repulsion force calculated from the following expression [10]:

( )[ ]H

zeaaTKaaV B

R κγγπε

−+

= exp6422

21

2122

21 , where ε is the permittivity of the medium, KB the

Boltzmann constant, T the absolute temperature (stated elsewhere), κ the Debye-Hückel reciprocal length has a value of 2.4×109 m-1 and e is the elementary charge (stated elsewhere).The dimensionless

functions,γ1 and γ2, of the zeta potentials ζ1 and ζ2, respectively, are given by [ ][ ] 12/exp

12/exp+−

=kTzekTze

i ζζγ



24

Table 1

pH 7.0

ε (F/m) 6.95E-10

κ(m-1) 1.27E+09

A (J) 5.00E-21

KB (J/K) 1.38E-23

Electrolyte concentration

(mM)

Zeta potential, ξ (mV)

γ1 γ2

40 34.4 0.323 80 22.8 0.218 100 20.6 0.198 150 15.0 0.145 250 22.9 0.219 750 23.1 0.221 1000 27.6 0.262



25

Fig. 1a Particle size distributions of LPD complexes at a charge ratio of 7.0 in distilled

water, pH 7.4, as a function of time after preparation 240 sec (♦), 1800 sec (),

3600sec (), 10800 sec (∗). Measurements were taking using dynamic light

scattering measurements at 90o. Data shown is taken from an average of three

differing samples. Figure 1b shows a bimodial distribution of lipofectin in its

storage buffer (filtered water) at 150 sec after preparation.

Fig. 2a Fractal dimension of LPD particles at pH 7.2 in 100mM NaCl. LPD system for

various time points of 14 min (◊), 22 min(), 28 min () and 35 min(x). Fig.

2b Influence of salt concentration on the fractal dimension of latex particles at

pH 3.0, 250 mM NaCl (◊) and poly-L-lysine/plasmid DNA (PLL/DNA) at pH

7.0, for various time points of 5-150 min(closed symbols). Both systems present

exhibit aggregation in the RLCA regime. Insets show the time taken for the

measured aggregate to form in each instance.

Fig. 3. Particle size distributions of PLL/DNA complexes at a charge ratio of 2.0 in 20

mM HEPES, pH 7.2, 150mM NaCl, as a function of time after preparation. Size

distributions were determined as mean of diameter based on the intensity of

scattered light at 90o. The data shown was obtained from a single representative

sample.

Fig .4. The fractal dimension (Df ) of Lipofectin/integrin-targeting peptide/DNA (LPD)

aggregates as a function of electrolyte concentration (mM). Data is given for the

final Df of the system.

Fig. 5. Size distribution of LPD complexes as a function of time for varying electrolyte

concentrations at pH 7.0: 20 mM (), 40 mM (), 80 mM (), 100 mM (×), 150

mM (*), 250 mM (), 750 mM (+), and 1 M (-). All measurements were taken

using DLS.

Fig. 6. Influence of buffer conditions on the dimensionless total energy of interaction

between two spherical particles of a monomer hydrodynamic radius of 150 nm,



26

as a function of the distance H (nm) between their surfaces; data generated using

the DVLO theory of colloidal interactions.

Fig. 7. Dependence of electrolyte concentration on the LPD system zeta potential. All

systems were at pH 7.0. The zeta potential is calculated from the electrophoretic

mobility of the particles in the buffer.

Fig. 8. Experimental dependence of stability ratio (W) on electrolyte concentration.

Stability values were determined from the Reerink and Overbeek approximation.



27

Figure 1

0

5

10

15

20

1 10 100 1000 10000

size (nm)

% p

opul

atio

n

0

10

20

30

40

50

0 500 1000 1500 2000 2500 3000 3500

size (nm)

% p

opul

atio

n

A

B



28

Figure 2

100

1000

10000

0.001 0.01 0.1

q (nm-1)

Sca

tterin

g In

tens

ity, I

10

100

1000

10000

0.0010 0.0100 0.1000 q (nm-1)

Rel

ativ

e sc

atte

ring

Inte

nsity

, I

si

1MN Cl

250 MN Cl

si

1MN Cl

250 MN Cl

500nm50nm

5 minutes

Rel

ativ

e Sc

atte

ring In

tens

ity

9 days

Rel

ativ

e Sc

atte

ring In

tens

ity

200nm 2000nm

A

B



29

Figure 3

0

5

10

10 100 1000 10000 100000

Log mean diameter (nm)

Inte

nsity

%

3 min9 min18 min34 min64 min98 min



30

Figure 4

1.00

1.50

2.00

2.50

3.00

0 200 400 600 800 1000 1200

Electrolyte concentration (mM)

dF



31

Figure 5

0

1000

2000

0 250 500 750 1000

Time (sec)

Siz

e (n

m)



32

Figure 6

-100

-60

-20

20

60

100

0 1 2 3

H (nm)

Pot

entia

l Ene

rgy

of In

tera

ctio

n V

T /kT

40mM

80mM, 100mM ,

150mM

750mM

1000mM

150 mM



33

Figure 7

-40

-30

-20

-10

00 200 400 600 800 1000 1200


Zeta

pot

entia

l (m

V)



34

Figure 8

-10

0

10

20

30

0 200 400 600 800 1000 1200


log

W



35

Notation

a1, a2 radii of primary particles 1 and 2, m A Hamaker constant, J c ionic concentration, M DH particle hydrodynamic diameter, m e charge on electron (1.6 × 10-19 C) H separation distance between two primary particles, m K Boltzmann constant (1.381×10-23 J/K) T absolute temperature, K VA, VR,VT interaction energies (van der Waals’ attraction, electrical repulsion and

total interaction), J x dimensionless (=(H/a1+a2)) y dimensionless (=a1/a2) z valence (charge number) of ionic species Df fractal deimension q wave vector W stability ratio Greek Letters

γ1 γ2 dimensionless functions of zeta potential ζ1,ζ2 zeta potentials of particles 1 and 2 ε permittivity, dimensionless κ Debye-Hückel parameter µ dynamic viscosity of liquid, kg/ms λ incident wavelength of light in a vacuum θ scattering angle



The fractal structure of polycation–DNA complexes

Documents

Transcript of The fractal structure of polycation–DNA complexes