Mark J. Uline

Membrane curvature enables N-Ras lipid anchor sorting to liquid-ordered membrane phases

Trafficking and sorting of membrane-anchored Ras GTPases are regulated by partitioning between distinct membrane domains. Here, in vitro experiments and microscopic molecular theory reveal membrane curvature as a new modulator of N-Ras lipid anchor and palmitoyl chain partitioning. Membrane curvature was essential for enrichment in raft-like liquid-ordered phases; enrichment was driven by relief of lateral pressure upon anchor insertion and most likely affects the localization of lipidated proteins in general.

Phase behavior of lipid bilayers under tension.

Given the proposed importance of membrane tension in regulating cellular functions, we explore the effects of a finite surface tension on phase equilibrium using a molecular theory that captures the quantitative structure of the phase diagram of the tensionless DPPC/DOPC/Cholesterol lipid bilayer. We find that an increase in the surface tension decreases the temperature of the transition from liquid to gel in a pure DPPC system by ∼1.0 K/(mN/m), and decreases the liquid-disordered to liquid-ordered transition at constant chemical potentials by approximately the same amount. Our results quantitatively isolate the role of tension in comparison to other thermodynamic factors, such as pressure, in determining the phase behavior of lipid bilayers.

Interleaflet Coupling and Domain Registry in Phase-Separated Lipid Bilayers

There is clear evidence of an interleaflet coupling in model lipid/cholesterol membranes exhibiting liquid-liquid phase separation. The strength of this coupling is quantified by the mismatch free energy, γ. We calculate it using a molecular mean-field model of a phase-separated lipid/cholesterol bilayer and obtain values that increase as the concentration of saturated lipids in the coexisting phases is increased. These values lie in the range 0.01-0.03 k(B)T/nm(2). We clarify the relationship between the interleaflet coupling and the extent of interleaflet alignment of liquid domains by analyzing a statistical mechanical model of coupled fluctuating domain interfaces. The model is solved exactly using the correspondence between statistical mechanics and quantum mechanics, yielding an expression for the characteristic size of fluctuations out of domain registry. This length scale depends only weakly on the strength of the interleaflet coupling and inevitably is only of the order of nanometers, which explains the experimental result that fluctuations out of domain registry have not been observed by optical microscopy.

Calculating Partition Coefficients of Chain Anchors in Liquid-Ordered and Liquid-Disordered Phases

We calculate partition coefficients of various chain anchors in liquid-ordered and liquid-disordered phases utilizing a theoretical model of a bilayer membrane containing cholesterol, dipalmitoyl phosphatidylcholine, and dioleoylphosphatidylcholine. The partition coefficients are calculated as a function of chain length, degree of saturation, and temperature. Partitioning depends on the difference between the lipid environments of the coexisting phases in which the anchors are embedded. Consequently, the partition coefficient depends on the nature of the anchor, and on the relative compositions of the coexisting phases. We find that saturated anchors prefer the denser liquid-ordered phase, and that the fraction of anchors in the liquid-ordered phase increases with increasing degree of saturation of the anchors. The partition coefficient also depends upon the location of the double bonds. Anchors with double bonds closer to the middle of the chain have a greater effect on partitioning than those near the end. Doubling the number of saturated chains increases the partitioning into the liquid-ordered phase for tails that are nearly as long or longer than those comprising the bilayer. Partitioning of such chains increases with decreasing temperature, indicating that energy considerations dominate entropic ones. In contrast, partitioning of shorter chains increases with increasing temperature, indicating that entropic considerations dominate.

On the generalized equipartition theorem in molecular dynamics ensembles and the microcanonical thermodynamics of small systems

We consider various ensemble averages within the molecular dynamics (MD) ensemble, corresponding to those states sampled during a MD simulation in which the application of periodic boundary conditions imposes a constraint on the momentum of the center of mass. As noted by Shirts et al. [J. Chem. Phys. 125, 164102 (2006)] for an isolated system, we find that the principle of equipartition is not satisfied within such simulations, i.e., the total kinetic energy of the system is not shared equally among all the translational degrees of freedom. Nevertheless, we derive two different versions of Tolmans generalized equipartition theorem, one appropriate for the canonical ensemble and the other relevant to the microcanonical ensemble. In both cases, the breakdown of the principle of equipartition immediately follows from Tolmans result. The translational degrees of freedom are, however, still equivalent, being coupled to the same bulk property in an identical manner. We also show that the temperature of an isolated system is not directly proportional to the average of the total kinetic energy (in contrast to the direct proportionality that arises between the temperature of the external bath and the kinetic energy within the canonical ensemble). Consequently, the system temperature does not appear within Tolmans generalized equipartition theorem for the microcanonical ensemble (unlike the immediate appearance of the temperature of the external bath within the canonical ensemble). Both of these results serve to highlight the flaws in the argument put forth by Hertz [Ann. Phys. 33, 225 (1910); 33, 537 (1910)] for defining the entropy of an isolated system via the integral of the phase space volume. Only the Boltzmann-Planck entropy definition, which connects entropy to the integral of the phase space density, leads to the correct description of the properties of a finite, isolated system. We demonstrate that the use of the integral of the phase space volume leads to unphysical results, indicating that the property of adiabatic invariance has little to do with the behavior of small systems.

Homogeneous nucleation and growth in simple fluids. I. Fundamental issues and free energy surfaces of bubble and droplet formation

The free energy of forming a droplet and a bubble with a given particle number n and volume v within the pure-component Lennard-Jones supercooled vapor and superheated liquid, respectively, are further explored using density-functional theory. Similar to what was found previously [M. J. Uline and D. S. Corti, Phys. Rev. Lett. 99, 076102 (2007); M. J. Uline and D. S. Corti, J. Chem. Phys. 129, 234507 (2008)], the limits of stability again appear within both free energy surfaces evaluated at two other metastability conditions, one closer to the binodal and one closer to the spinodal. Furthermore, an ad hoc bond connectivity criterion is also applied in an attempt, however approximately, to eliminate certain configurational redundancies that arise from the chosen droplet and bubble definitions. What results are free energy surfaces describing the formation of equilibrium embryos that should be an improved representation of the fluctuations that are relevant to those nonequilibrium embryos seen in an actual nucleation event. Finally, we discuss in some detail the use of the (n,v) reaction coordinate within the framework of an equilibrium-based theory and its relation to other descriptions of nucleation.

A mechanical argument for the differential performance of coronary artery grafts

Coronary artery bypass grafting (CABG) acutely disturbs the homeostatic state of the transplanted vessel making retention of graft patency dependent on chronic remodeling processes. The time course and extent to which remodeling restores vessel homeostasis will depend, in part, on the nature and magnitude of the mechanical disturbances induced upon transplantation. In this investigation, biaxial mechanical testing and histology were performed on the porcine left anterior descending artery (LAD) and analogs of common autografts, including the internal thoracic artery (ITA), radial artery (RA), great saphenous vein (GSV) and lateral saphenous vein (LSV). Experimental data were used to quantify the parameters of a structure-based constitutive model enabling prediction of the acute vessel mechanical response pre-transplantation and under coronary loading conditions. A novel metric Ξ was developed to quantify mechanical differences between each graft vessel in situ and the LAD in situ, while a second metric Ω compares the graft vessels in situ to their state under coronary loading. The relative values of these metrics among candidate autograft sources are consistent with vessel-specific variations in CABG clinical success rates with the ITA as the superior and GSV the inferior graft choices based on mechanical performance. This approach can be used to evaluate other candidate tissues for grafting or to aid in the development of synthetic and tissue engineered alternatives.

Effects of the salt concentration on charge regulation in tethered polyacid monolayers.

Charge regulation in polyacid monolayers attached at one end to a planar surface is studied theoretically. The polyacid layers are designed to mimic single-stranded DNA monolayers. The effects of the local pH and salt concentration on the protonation states of the polyacid layer are studied using a molecular mean-field theory that includes a microscopic description of the conformations of the polyacid molecule along with electrostatic interactions, acid-base equilibrium, and excluded volume interactions. We predict that, in the case of a monovalent salt, NaCl, the amount of proton binding increases dramatically for high surface coverage of polyacid and low bulk salt concentration. When the polyelectrolyte is almost completely charge neutralized by bound protons, there is an expulsion of sodium from the layer. We show that the degree of protonation can go all the way from 0% to 100% when the bulk pH is kept fixed at 7 by changing the surface coverage of polyacid and the bulk salt concentration. The effects of increasing protonation and the expulsion of the cations from the monolayer are reduced when sodium ions are replaced by divalent magnesium ions. Our theoretical results concur with X-ray photoelectron spectroscopy studies of ssDNA monolayers on gold.

Activated instability of homogeneous droplet nucleation and growth

For the pure-component supercooled Lennard-Jones vapor, the free energy of forming a droplet with a given particle number and volume is calculated using density-functional theory. In contrast to what was noted in previous studies, the free energy surface beyond the pseudosaddle point no longer exhibits a valley but rather channels the nuclei toward a locus of instabilities, initiating an unstable growth phase. Similar to a previous study of bubble formation in superheated liquids [M. J. Uline and D. S. Corti, Phys. Rev. Lett. 99, 076102 (2007)], a new picture of homogeneous droplet nucleation and growth emerges.

Mode specific elastic constants for the gel, liquid-ordered, and liquid-disordered phases of DPPC/DOPC/cholesterol model lipid bilayers.

Using microscopic molecular theory, we determine the bending and saddle-splay constants of three-component lipid bilayers. The membrane contains cholesterol, dipalmitoyl-phosphatidylcholine (DPPC) and dioleoylphosphatidylcholine (DOPC) and the predictions of the theory have been shown to qualitatively reproduce phase diagrams of giant unilamellar vesicles (GUVs) of the same three components. The bending and saddle-splay constants were calculated for the gel, liquid-ordered (lo) and liquid-disordered (ld) phases. By proper expansion of the free energy, the molecular theory enables us to determine the effects of the mode of membrane bending deformation on the value of the elastic constants for different phases. In particular, we refer to the ability of the molecules to arrange the composition between the two monolayers upon deformation. The bending and saddle-splay constants obtained from the free energy expansion can be expressed in terms of moments of the local lateral pressures and their derivatives, all evaluated for a symmetric planar bilayer. The effect of blocked vs. free exchange of lipids across the two monolayers on the values of the bending constant is as high as 50 k(B)Tin the ld phase to as high as 200 k(B)T in the lo phase. These results show that one must strongly consider the mode of deformation in determining the mechanical properties of lipid bilayers. We discuss how the different contributions to the lateral pressures affect the values of the elastic constants, including the effects of the cholesterol concentration and temperature on the membrane elastic constants. We also calculate the equilibrium binding concentrations of lipid tail anchors as a function of membrane curvature by explicitly determining the chemical potential difference of species across a curved bilayer. Our results are in excellent agreement with recent experimental results.