Sergei I. Mukhin

Analytical approach to thermodynamics of bolalipid membranes.

Abstract We consider a model of bilayer lipid membrane with bola-lipids. The bola-lipid is modeled by linking tails of the hydrophobic chains in the opposite monolayers within bilayer as a first approximation. A number of thermodynamical characteristics are calculated analytically and compared with the ones of a regular membrane without chains linkage. Pronounced difference between lateral pressure profiles at the layers interface for linked and regular bilayer models is found. In the linked case, the lateral pressure mid-plane peak disappears, while the free energy per chain increases. We have also calculated distribution of the orientaional order parameter of linked chains across the bilayer, and found it is in contrast with the usual lipids case.

Spectral properties of the t-J model in the presence of hole-phonon interaction

We examine the effects of electron-phonon interaction on the dynamics of the charge carriers doped in two-dimensional (2D) Heisenberg antiferromagnet. The {ital t}-{ital J} model Hamiltonian with a Fr{umlt o}hlich term which couples the holes to a dispersionless (optical) phonon mode is considered for low doping concentration. The evolution of the spectral density function, the density of states, and the momentum distribution function of the holes with an increase of the hole-phonon coupling constant {ital g} is studied numerically. As the coupling to a phonon mode increases the quasiparticle spectral weight decreases and a {open_quote}{open_quote}phonon satellite{close_quote}{close_quote} feature close to the quasiparticle peak becomes more pronounced. Furthermore, strong electron-phonon coupling smears the multimagnon resonances ({open_quote}{open_quote}string states{close_quote}{close_quote}) in the incoherent part of the spectral function. The jump in the momentum distribution function at the Fermi surface is reduced without changing the hole pocket volume, thereby providing a numerical verification of Luttinger theorem for this strongly interacting system. The vertex corrections due to electron-phonon interaction are negligible in spite of the fact that the ratio of the phonon frequency to the effective bandwidth is not small. {copyright} {ital 1996 The American Physical Society.}

Microscopic Model and Analytic Derivation of Area Per Molecule for DPPC-Cholesterol Bilayers

An area per molecule dependence on components concentration for DPPC-Cholesterol bilayers is calculated analytically using a microscopic model in a biologically relevant concentration range. DPPC lipid is modeled as flexible string with finite bending rigidity [1,2]. Cholesterol molecule is modeled as rigid rod of finite thickness [3]. Surface tension at hydrophobic interface is linear combination of “partial tensions” of bilayer components. The models three important parameters are: surface tension at hydrophobic interface for pure DPPC membrane, bending rigidity of DPPC lipid, extrapolated surface tension at hydrophobic interface for cholesterol membrane. These parameters are chosen by nearly perfect fitting agreement of our theoretical curve with molecular dynamics simulations data [4] for these two-component bilayers. The molecular chains order parameter dependence on coordinate for 40% cholesterol - 60% DPPC membrane, measurable in NMR experiments, is calculated analytically and compared with molecular dynamics simulation data [5]. The order parameter calculation allows for DPPC tilt angle. The model parameters found by fitting the MD data are used further to calculate lateral pressure distribution and coefficient of thermal area expansion. The microscopic model allows one to study other thermodynamic coefficients and diffusion phenomena in multi-component bilayers. 1.Mukhin S.I., S. Baoukina, Analytical derivation of thermodynamic characteristics of lipid bilayer from a flexible string model. Phys. Rev. E. 71: 061918 (2005). 2.Mukhin S.I., B.B. Kheyfets, Analytical approach to thermodynamics of bolalipid membranes. Phys. Rev. E. 82: 051901 (2010). 3.Mukhin S.I., B.B. Kheyfets, Pore formation phase diagrams for lipid membranes. JETP Lett. 99: 358-362 (2014). 4. Edholm O., J.F. Nagle. Areas of Molecules in Membranes Consisting of Mixtures. Biophys. J. 89: 1827-1832 (2005). 5. Hofsass C., Lindahl E., and Edholm O. Molecular Dynamics Simulations of Phospholipid Bilayers with Cholesterol. Biophys. J. 84: 2192-2206 (2003).

Analytical Derivation of Thermodynamic Properties of Bolalipid Membrabe

A model of bilayer lipid membrane with bola-lipids is studied. The bola-lipid is modeled by linking tails of the hydrophobic chains in the opposite monolayers within bilayer. We use for analytical derivations a flexible string model of hydrocarbon chain (Mukhin, Baoukina 2005) with modified condition at the linked chains ends. Calculated lateral pressure profiles are asymmetrical due to different concentrations of the U-shaped bolalipids in the opposite monolayers, Fig. 1, and orientational order parameters for linked and regular chains differ significantly at the monolayers interface, Fig. 2.View Large Image | View Hi-Res Image | Download PowerPoint SlideView Large Image | View Hi-Res Image | Download PowerPoint Slide

Analytical derivation of thermodynamic properties of bilayer membrane with interdigitation

We consider a model of bilayer lipid membrane with interdigitation, in which the lipid tails of the opposite monolayers interpenetrate. The interdigitation is modeled by linking tails of the hydrophobic chains in the opposite monolayers within bilayer as a first approximation. This model corresponds to the types of interdigitation that are not related with the areal “hydrophobic” dilation of the membrane. A number of essential thermodynamical characteristics are calculated analytically and compared with the ones of a regular bilayer membrane without interdigitation. Important difference between lateral pressure profiles at the layers interface for linked and regular bilayer models is found. In the linked case, the lateral pressure mid-plane peak disappears, while the entropy decreases and the free energy per chain increases. Within our model we found that in case of elongation of the chains inside a nucleus of, e.g., liquid-condensed phase, homogeneous interdigitation would be more costly for the membrane’s free energy than energy of the hydrophobic mismatch between the elongated chains and the liquid-expanded surrounding. Nonetheless, an inhomogeneous interdigitation along the nucleus boundary may occur inside a “belt” of a width that varies approximately with the hydrophobic mismatch amplitude.

Lateral Pressure Profile In Membrane With Lipids Interdigitation: Analytical Derivation

We derive analytically thermodynamic characteristics of a lipid bilayer membrane with interdigitation: lipid tails of the opposite monolayers interpenetrate. To allow for interdigitation, our microscopic model of bilayer treats lipids as semi-flexible chains with tails linked across the mid-plane of the membrane. We found striking difference between lateral pressure profiles for linked and not linked chains in the vicinity of the monolayers interface, see figure. Lateral pressure mid-plane peak disappears in the linked-tails case, while the free energy per chain increases by amount ΔFint∼6kBT (per chain) . This is purely entropic contribution to the free energy due to linking of the opposite chains. From this we deduced critical pressure capable of forcing interdigitation to a depth of a single lipid-chain CH2-CH2 segment of a volume Δv∼70A3 : Pint= ΔFint / Δv ∼3.5MPa, in good agreement with experiment in DPPC bilayer (Chemistry Letters. Vol. 37 (2008) , p.604, Nobutake Tamai et al.). We also studied geometric constraints imposed by the balance between the interdigitation free energy increase ΔFint and energy of the hydrophobic mismatch in case of a liquid-condensed domain embedded in the liquid-expanded surrounding during e.g. the liquid-gel phase transition.View Large Image | View Hi-Res Image | Download PowerPoint Slide