Kirill Katsov

Biological and synthetic membranes: What can be learned from a coarse-grained description?

We discuss the role coarse-grained models play in the investigation of the structure and thermodynamics of bilayer membranes, and we place them in the context of alternative approaches. Because they reduce the degrees of freedom and employ simple and soft effective potentials, coarse-grained models can provide rather direct insight into collective phenomena in membranes on large time and length scales. We present a summary of recent progress in this rapidly evolving field, and pay special attention to model development and computational techniques. Applications of coarse-grained models to changes of the membrane topology are illustrated with studies of membrane fusion utilizing simulations and self-consistent field theory.

Field Theoretic Study of Bilayer Membrane Fusion. I. Hemifusion Mechanism

Self-consistent field theory is used to determine structural and energetic properties of metastable intermediates and unstable transition states involved in the standard stalk mechanism of bilayer membrane fusion. A microscopic model of flexible amphiphilic chains dissolved in hydrophilic solvent is employed to describe these self-assembled structures. We find that the barrier to formation of the initial stalk is much smaller than previously estimated by phenomenological theories. Therefore its creation it is not the rate-limiting process. The relevant barrier is associated with the rather limited radial expansion of the stalk into a hemifusion diaphragm. It is strongly affected by the architecture of the amphiphile, decreasing as the effective spontaneous curvature of the amphiphile is made more negative. It is also reduced when the tension is increased. At high tension the fusion pore, created when a hole forms in the hemifusion diaphragm, expands without bound. At very low membrane tension, small fusion pores can be trapped in a flickering metastable state. Successful fusion is severely limited by the architecture of the lipids. If the effective spontaneous curvature is not sufficiently negative, fusion does not occur because metastable stalks, whose existence is a seemingly necessary prerequisite, do not form at all. However if the spontaneous curvature is too negative, stalks are so stable that fusion does not occur because the system is unstable either to a phase of stable radial stalks, or to an inverted-hexagonal phase induced by stable linear stalks. Our results on the architecture and tension needed for successful fusion are summarized in a phase diagram.

A New Mechanism of Model Membrane Fusion Determined from Monte Carlo Simulation

We have carried out extensive Monte Carlo simulations of the fusion of tense apposed bilayers formed by amphiphilic molecules within the framework of a coarse-grained lattice model. The fusion pathway differs from the usual stalk mechanism. Stalks do form between the apposed bilayers, but rather than expand radially to form an axial-symmetric hemifusion diaphragm of the trans leaves of both bilayers, they promote in their vicinity the nucleation of small holes in the bilayers. Two subsequent paths are observed. 1) The stalk encircles a hole in one bilayer creating a diaphragm comprised of both leaves of the other intact bilayer, which ruptures to complete the fusion pore. 2) Before the stalk can encircle a hole in one bilayer, a second hole forms in the other bilayer, and the stalk aligns and encircles them both to complete the fusion pore. Both pathways give rise to mixing between the cis and trans leaves of the bilayer and allow for transient leakage.

Field Theoretic Study of Bilayer Membrane Fusion: II. Mechanism of a Stalk-Hole Complex

We use self-consistent field theory to determine structural and energetic properties of intermediates and transition states involved in bilayer membrane fusion. In particular, we extend our original calculations from those of the standard hemifusion mechanism, which was studied in detail in the first article of this series, to consider a possible alternative to it. This mechanism involves non-axial stalk expansion, in contrast to the axially symmetric evolution postulated in the classical mechanism. Elongation of the initial stalk facilitates the nucleation of holes and leads to destabilization of the fusing membranes via the formation of a stalk-hole complex. We study properties of this complex in detail, and show how transient leakage during fusion, previously predicted and recently observed in experiment, should vary with lipid architecture and tension. We also show that the barrier to fusion in the alternative mechanism is lower than that of the standard mechanism by a few k(B)T over most of the relevant region of system parameters, so that this alternative mechanism is a viable alternative to the standard pathway. We emphasize that any mechanism, such as this alternative one, which affects, even modestly, the line tension of a hole in a membrane, affects greatly the ability of that membrane to undergo fusion.

New mechanism of membrane fusion

We have carried out Monte Carlo simulation of the fusion of bilayers of single chain amphiphiles which show phase behavior similar to that of biological lipids. The fusion mechanism we observe is very different from the “stalk” hypothesis. Stalks do form on the first stage of fusion, but they do not grow radially to form a single bilayer diaphragm. Instead, stalk formation destabilizes the membranes and results in hole formation in the vicinity of the stalks. When holes in each bilayer nucleate spontaneously next to the same stalk, an incomplete fusion pore is formed. The fusion process is completed by propagation of the initial connection, the stalk, along the edges of the aligned holes.

Phase separation of saturated and mono-unsaturated lipids as determined from a microscopic model

A molecular model is proposed of a bilayer consisting of fully saturated dipalmitoylphosphatidylcholine (DPPC) and mono-unsaturated dioleoylphosphatidylcholine (DOPC). The model not only encompasses the constant density within the hydrophobic core of the bilayer, but also the tendency of chain segments to align. It is solved within self-consistent field theory. A model bilayer of DPPC undergoes a main-chain transition to a gel phase, while a bilayer of DOPC does not do so above zero degrees centigrade because of the double bond which disrupts order. We examine structural and thermodynamic properties of these membranes and find our results in reasonable accord with experiment. In particular, order-parameter profiles are in good agreement with NMR experiments. A phase diagram is obtained for mixtures of these lipids in a membrane at zero tension. The system undergoes phase separation below the main-chain transition temperature of the saturated lipid. Extensions to the ternary DPPC, DOPC, and cholesterol system are outlined.

Roles of Repulsive and Attractive Forces in Determining the Structure of Nonuniform Liquids: Generalized Mean Field Theory

The structure of a nonuniform Lennard-Jones (LJ) liquid near a hard wall is approximated by that of a reference fluid with repulsive intermolecular forces in a self-consistently determined external mean field incorporating the effects of attractive forces. We calculate the reference fluid structure by first determining the response to the slowly varying part of the field alone, followed by the response to the harshly repulsive part. Both steps can be carried out very accurately, as confirmed by Monte Carlo simulations, and good agreement with the structure of the full LJ fluid is found. [S0031-9007(98)07606-6] PACS numbers: 61.20.Gy, 68.10.Cr, 68.45.Gd Dense liquids have highly nontrivial density correlations arising because the harshly repulsive molecular cores cannot overlap [1 ‐ 3]. Because of the constantly changing molecular arrangements, such correlations play a much more fundamental role in liquids than they do in other condensed phases such as glasses and solids, which sample only a few basic configurations. Indeed, a model with only repulsive intermolecular forces [2] can give a surprisingly accurate description of the full density correlations seen in a uniform dense simple liquid like Ar because the vector sum of the longer ranged attractive forces on a given particle essentially cancels [1] in most typical configurations. Nonuniform liquids present a greater and qualitatively different challenge, since even the averaged effects of attractive forces clearly do not cancel [4]. We discuss here an example where both attractive and repulsive forces can greatly influence the liquid’s structure: a LennardJones (LJ) fluid next to a hard wall. We obtain accurate numerical results using a physically suggestive generalized mean field description of the attractive forces [5]. We consider first the effects of these slowly varying forces on the liquid’s structure before taking account of the response to the rapidly varying (hard-core-like) part of the external field. This treatment of attractive interactions is quite different from that used in conventional integral equation and density functional methods [6], and we believe it offers important conceptual and computational advantages.

Molecular theory of hydrophobic mismatch between lipids and peptides

Effects of the mismatch between the hydrophobic length d, of transmembrane alpha helices of integral proteins and the hydrophobic thickness, Dh, of the membranes they span are studied theoretically utilizing a microscopic model of lipids. In particular, we examine the dependence of the period of a lamellar phase on the hydrophobic length and volume fraction of a rigid, integral, peptide. We find that the period decreases when a short peptide, such that d Dh, is inserted. The effect is due to the replacement of extensible lipid tails by rigid peptide. As the peptide length is increased, the lamellar period continues to increase, but at a slower rate, and can eventually decrease. The amount of peptide which fails to incorporate and span the membrane increases with the magnitude of the hydrophobic mismatch |d−Dh|. We explicate these behaviors which are all in accord with experiment. Predictions are made for t...

Theory of T junctions and symmetric tilt grain boundaries in pure and mixed polymer systems

We apply self-consistent-field theory to T junctions and symmetric tilt grain boundaries in block copolymer systems with and without the addition of homopolymer. We find that, in the absence of homopolymer, T junctions have a larger free energy per unit area than that of the symmetric tilt junctions with which they compete except for a range of angles between about 100° and 130°. With the addition of homopolymer, this range increases. These results are quite consistent with experiment. As the angle between grains increases towards 180°, the T junction undergoes a morphological change somewhat similar to that which occurs in symmetric tilt grain boundaries. At the onset of this change, the free energy per unit area decreases markedly.

Intermolecular forces and the structure of uniform and nonuniform fluids

We discuss the ramifications of Widoms idea that attractive intermolecular forces essentially cancel in dense uniform liquids. This idea was used directly in the WCA theory of uniform liquids, where the structure of the liquid is approximated by that of a simpler reference fluid with purely repulsive intermolecular forces. To take account of the unbalanced attractive forces found in nonuniform fluids, Weeks, Selinger, and Broughton (WSB) developed a new method where the structure is related to that of a nonuniform reference fluid in an external field chosen to yield a self-consistent description of correlations induced by the repulsive forces and a mean field treatment of the attractive forces. Using simulations, we provide a quantitative test of the accuracy of both methods for the uniform fluid at different points in the phase diagram by relating correlation functions in the uniform fluid to those in a nonuniform fluid with a particle fixed at the origin. We find that at high densities the WSB approach can correct most of the small errors in the structure of the WCA reference fluid. At lower densities the WSB method provides a considerable improvement over the WCA theory. A simplified version of the WSB method is presented that is of comparable accuracy.