Estimation of the parameters of the Smoluchowski equation describing the occurrence of pores in a bilayer lipid membrane
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THE EUROPEAN PHYSICAL JOURNAL E
Regular Article
Estimation of the parameters of the Smoluchowski equation describing the occurrence of pores in a bilayer lipid membrane under soft poration A.A. Anosov1,3,a , E.Yu. Smirnova1 , E.D. Ryleeva1 , I.A. Gligonov1 , E.A. Korepanova1,2 , and A.A. Sharakshane3 1 2 3
I.M. Sechenov First Moscow State Medical University (Sechenov University), Moscow, Russia Pirogov Russian National Research Medical University, Moscow, Russia Kotelnikov Institute of Radioengineering and Electronics of RAS, Moscow, Russia Received 9 March 2020 / Received in final form 17 August 2020 / Accepted 22 September 2020 Published online: 6 October 2020 c EDP Sciences / Societ` a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. The conductive lipid pores occurring in planar bilayer membranes are known to manifest themselves experimentally as current fluctuations. Reliable recording of such fluctuations during phase transitions, as well as in membranes with various additives (for example, SDS), allows one to determine the characteristics of hypothetical hydrophilic pores, namely, their number, sizes, lifetimes, and duration of time intervals between pores. Because, in contrast with electroporation, the emergence of pores in a membrane does not require high voltages, this process is called soft poration. Studying the characteristics of pores under soft poration allows us to estimate the parameters of the Smoluchowski equation and compare them with the corresponding parameters used to describe electroporation. In this work, the experimental characteristics of current fluctuations in the membrane with the addition of SDS to the bulk solution were used to estimate the parameters of the Smoluchowski equation: the pore edge tension, the energy of the hydrophobic pore/hydrophilic pore barrier, the coefficient of pore diffusion in the radius space, the initial distribution density of the number of pores, and the attempt rate density of the lipids in a membrane. The obtained estimates are close to the parameter values used in studies of electroporation.
1 Introduction The increase in the lipid bilayer permeability in response to the application of electric field [1], under phase transitions [2] or with the addition of detergents [3,4] is usually associated with the formation of conductive lipid pores. Lipid pores can be investigated experimentally by registering the current fluctuations in planar bilayer lipid membranes [4–6] or by observing the leakage of fluorescent markers from the liposomes [7]. The molecular mechanisms of the formation of conductive pores under electroporation are studied by the methods of molecular dynamics [8]. To analyze the evolution of such pores, the Smoluchowski equation is used which describes the diffusion of pores in the radius space [9]. This model assumes that both hydrophobic and hydrophilic pores can exist in a membrane. The electric field reduces the potential barrier between them thus facilitating the formation of hydrophilic pores. We propose
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