Electrostatic interaction effects on the size distribution of self-assembled giant unilamellar vesicles

Mohammad Abu Sayem Karal, Marzuk Ahmed, Victor Levadny, Marina Belaya, Md. Kabir Ahamed, Mostafizur Rahman, and Md. Mostofa Shakil

Phys. Rev. E 101, 012404 – Published 9 January 2020

Abstract

The influence of electrostatic conditions (salt concentration of the solution and vesicle surface charge density) on the size distribution of self-assembled giant unilamellar vesicles (GUVs) is considered. The membranes of GUVs are synthesized by a mixture of dioleoylphosphatidylglycerol and dioleoylphosphatidylcholine in a physiological buffer using the natural swelling method. The experimental results are presented in the form of a set of histograms. The log-normal distribution is used for statistical treatment of results. It is obtained that the decrease of salt concentration and the increase of vesicle surface charge density of the membranes increase the average size of the GUV population. To explain the experimental results, a theory using the Helmholtz free energy of the system describing the GUV vesiculation is developed. The size distribution histograms and average size of GUVs under various conditions are fitted with the proposed theory. It is shown that the variation of the bending modulus due to changing of electrostatic parameters of the system is the main factor causing a change in the average size of GUVs.

Received 23 June 2019

DOI:https://doi.org/10.1103/PhysRevE.101.012404

Physics Subject Headings (PhySH)

Electrical properties of membranes Membrane assembly Vesicles

Giant vesicles

Phase contrast optical microscopy

Physics of Living SystemsPolymers & Soft Matter

Authors & Affiliations

Mohammad Abu Sayem Karal ^1,*,†, Marzuk Ahmed^1,*, Victor Levadny^2,*, Marina Belaya ³, Md. Kabir Ahamed ¹, Mostafizur Rahman¹, and Md. Mostofa Shakil ¹

¹Department of Physics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
²Theoretical Problem Center of Physico-Chemical Pharmacology, Russian Academy of Sciences, Moscow 117977, Russia
³Department of Mathematics of Russian State University for the Humanities, Moscow GSP-3 125993, Russia

^*These authors contributed equally to this work.
^†Author to whom correspondence should be addressed: asayem221@phy.buet.ac.bd

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Vol. 101, Iss. 1 — January 2020

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Images

Figure 1
Effects of salt concentration on the size distribution of GUVs containing $X = 0.4$ . (a) Phase contrast image and (b) size distribution histogram at $C = 12 mM$ . (c) Phase contrast image and (d) size distribution histogram at $C = 312 mM$ . The bar in the images corresponds to 50 μm. Here $N$ is the number of observed GUVs. The dotted lines show the best-fitting curves corresponding to Eq. (1). The parameters are (b) $μ = 2.89$ and $σ = 0.46$ and (d) $μ = 2.26$ and $σ = 0.38$ . The values of $R^{2}$ for the fitted curves are (b) 0.94 and (d) 0.95. The solid lines show the theoretical curves corresponding to Eq. (9). The fitting parameters are (b) $K_{ben} = 36.0 k_{B} T$ , $D_{freq} = 9.5 μ m$ , and $L = 1240$ and (d) $K_{ben} = 16.0 k_{B} T$ , $D_{freq} = 6.8 μ m$ , and $L = 1061$ . The values of $R^{2}$ are (b) 0.66 and (d) 0.75.
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Figure 2
Average size of GUVs containing $X = 0.4$ at various $C$ obtained from histograms in accordance with Eq. (2). Average values and standard errors of the size for each $C$ were determined from two independent experiments using 300–400 GUVs for each experiment. The solid line shows the theoretical curve corresponding to Eq. (14) with Eq. (15) using $D_{freq 0} = 12.0 μ m$ , $K_{ben 0} = 17.0 k_{B} T$ , and $γ = 2 m M^{3 / 2}$ .
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Figure 3
Effects of DOPG molar fraction on size distribution of DOPG and DOPC GUVs at $C = 162 mM$ . (a) Phase contrast image and (b) size distribution histogram of the GUV suspension for $X = 0.1$ . (c) Phase contrast image and (d) size distribution histogram of the GUV suspension for $X = 0.9$ . The bar in the images corresponds to 50 μm. Here $N$ is the number of observed GUVs. The dotted lines show the best-fitting curves corresponding to Eq. (1). The parameters are (b) $μ = 2.34$ and $σ = 0.34$ and (d) $μ = 2.81$ and $σ = 0.39$ . The values of $R^{2}$ are (b) 0.90 and (d) 0.97. The solid lines show the theoretical curves corresponding to Eq. (9). The other parameters are (b) $K_{ben} = 18.0 k_{B} T$ , $D_{freq} = 7.0 μ m$ , and $L = 1209$ and (d) $K_{ben} = 30.0 k_{B} T$ , $D_{freq} = 11.0 μ m$ , and $L = 1094$ . The values of $R^{2}$ are (b) 0.67 and (d) 0.84.
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Figure 4
Average size of DOPG and DOPC GUVs for various $X$ at $C = 162 mM$ obtained from histograms in accordance with Eq. (2). Average values and standard errors of the sizes for each $X$ were determined from two independent experiments using 300–350 GUVs for each experiment. The solid line shows the theoretical curve corresponding to Eq. (14) with Eq. (15) using $D_{freq 0} = 10.5 μ m$ , $K_{ben 0} = 17.0 k_{B} T$ , and $γ = 2 m M^{3 / 2}$ .
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Figure 5
Relationship between the average size $D_{ave}$ [obtained from histograms in accordance with Eq. (2)] and the bending modulus of the GUV bilayer $K_{ben}$ [obtained from histograms in accordance with Eq. (9)]. (a) Effects of $C$ on $D_{ave}$ and $K_{ben}$ for $X = 0.4$ . (b) Effects of $X$ on $D_{ave}$ and $K_{ben}$ at $C = 162 mM$ . Average values and standard errors were determined from two independent experiments.
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Physical Review E

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