Accessory mutations balance the marginal stability of the HIV-1 protease in drug resistance

The HIV-1 protease is a major target of inhibitor drugs in AIDS therapies. The therapies are impaired by mutations of the HIV-1 protease that can lead to resistance to protease inhibitors. These mutations are classified into major mutations, which usually occur first and clearly reduce the susceptibility to protease inhibitors, and minor, accessory mutations that occur later and individually do not substantially affect the susceptibility to inhibitors. Major mutations are predominantly located in the active site of the HIV-1 protease and can directly interfere with inhibitor binding. Minor mutations, in contrast, are typically located distal to the active site. A central question is how these distal mutations contribute to resistance development. In this article, we present a systematic computational investigation of stability changes caused by major and minor mutations of the HIV-1 protease. As most small single-domain proteins, the HIV-1 protease is only marginally stable. Mutations that destabilize the folded, active state of the protease therefore can shift the conformational equilibrium towards the unfolded, inactive state. We find that the most frequent major mutations destabilize the HIV-1 protease, whereas roughly half of the frequent minor mutations are stabilizing. An analysis of protease sequences from patients in treatment indicates that the stabilizing minor mutations are frequently correlated with destabilizing major mutations, and that highly resistant HIV-1 proteases exhibit significant fractions of stabilizing mutations. Our results thus indicate a central role of minor mutations in balancing the marginal stability of the protease against the destabilization induced by the most frequent major mutation

Interaction of Conical Membrane Inclusions: Effect of Lateral Tension

Considering two rigid conical inclusions embedded in a membrane subject to lateral tension, we study the membrane-mediated interaction between these inclusions that originates from the hat-shaped membrane deformations associated with the cones. At non-vanishing lateral tensions, the interaction is found to depend on the orientation of the cones with respect to the membrane plane. The interaction of inclusions of equal orientation is repulsive at all distances between them, while the inclusions of opposite orientation repel each other at small separations, but attract each other at larger ones. Both the repulsive and attractive forces become stronger with increasing lateral tension. This is different from what has been predicted on the basis of the same static model for the case of vanishing lateral tension. Without tension, the inclusions repel each other at all distances independently of their relative orientation. We conclude that lateral tension may induce the aggregation of conical membrane inclusions.Comment: 10 pages (revtech), 5 figures (postscript

Lateral phase separation of confined membranes

We consider membranes interacting via short, intermediate and long stickers. The effects of the intermediate stickers on the lateral phase separation of the membranes are studied via mean-field approximation. The critical potential depth of the stickers increases in the presence of the intermediate sticker. The lateral phase separation of the membrane thus suppressed by the intermediate stickers. Considering membranes interacting with short and long stickers, the effect of confinement on the phase behavior of the membranes is also investigated analytically

Lateral diffusion of receptor-ligand bonds in membrane adhesion zones: Effect of thermal membrane roughness

The adhesion of cells is mediated by membrane receptors that bind to complementary ligands in apposing cell membranes. It is generally assumed that the lateral diffusion of mobile receptor-ligand bonds in membrane-membrane adhesion zones is slower than the diffusion of unbound receptors and ligands. We find that this slowing down is not only caused by the larger size of the bound receptor-ligand complexes, but also by thermal fluctuations of the membrane shape. We model two adhering membranes as elastic sheets pinned together by receptor-ligand bonds and study the diffusion of the bonds using Monte Carlo simulations. In our model, the fluctuations reduce the bond diffusion constant in planar membranes by a factor close to 2 in the biologically relevant regime of small bond concentrations.Comment: 6 pages, 5 figures; to appear in Europhysics Letter

Segregation of receptor-ligand complexes in cell adhesion zones: Phase diagrams and role of thermal membrane roughness

The adhesion zone of immune cells, the 'immunological synapse', exhibits characteristic domains of receptor-ligand complexes. The domain formation is likely caused by a length difference of the receptor-ligand complexes, and has been investigated in experiments in which T cells adhere to supported membranes with anchored ligands. For supported membranes with two types of anchored ligands, MHCp and ICAM1, that bind to the receptors TCR and LFA1 in the cell membrane, the coexistence of domains of TCR-MHCp and LFA1-ICAM1 complexes in the cell adhesion zone has been observed for a wide range of ligand concentrations and affinities. For supported membranes with long and short ligands that bind to the same cell receptor CD2, in contrast, domain coexistence has been observed for a rather narrow ratio of ligand concentrations. In this article, we determine detailed phase diagrams for cells adhering to supported membranes with a statistical-physical model of cell adhesion. We find a characteristic difference between the adhesion scenarios in which two types of ligands in a supported membrane bind (i) to the same cell receptor or (ii) to two different cell receptors, which helps to explain the experimental observations. Our phase diagrams fully include thermal shape fluctuations of the cell membranes on nanometer scales, which lead to a critical point for the domain formation and to a cooperative binding of the receptors and ligands.Comment: 23 pages, 6 figure

Indirect interactions of membrane-adsorbed cylinders

Biological and biomimetic membranes often contain aggregates of embedded or adsorbed macromolecules. In this article, the indirect interactions of cylindrical objects adhering to a planar membrane are considered theoretically. The adhesion of the cylinders causes a local perturbation of the equilibrium membrane shape, which leads to membrane-mediated interactions. For a planar membrane under lateral tension, the interaction is repulsive for a pair of cylinders adhering to the same side of the membrane, and attractive for cylinders adhering at opposite membrane sides. For a membrane in an external harmonic potential, the interaction of adsorbed cylinders is always attractive and increases if forces perpendicular to the membrane act on the cylinders.Comment: 9 pages, 8 figures; typos correcte

Random pinning limits the size of membrane adhesion domains

Theoretical models describing specific adhesion of membranes predict (for certain parameters) a macroscopic phase separation of bonds into adhesion domains. We show that this behavior is fundamentally altered if the membrane is pinned randomly due to, e.g., proteins that anchor the membrane to the cytoskeleton. Perturbations which locally restrict membrane height fluctuations induce quenched disorder of the random-field type. This rigorously prevents the formation of macroscopic adhesion domains following the Imry-Ma argument [Y. Imry and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1975)]. Our prediction of random-field disorder follows from analytical calculations, and is strikingly confirmed in large-scale Monte Carlo simulations. These simulations are based on an efficient composite Monte Carlo move, whereby membrane height and bond degrees of freedom are updated simultaneously in a single move. The application of this move should prove rewarding for other systems also.Comment: revised and extended versio

Effective free energy for pinned membranes

We consider membranes adhered through specific receptor-ligand bonds. Thermal undulations of the membrane induce effective interactions between adhesion sites. We derive an upper bound to the free energy that is independent of interaction details. To lowest order in a systematic expansion we obtain two-body interactions which allow to map the free energy onto a lattice gas with constant density. The induced interactions alone are not strong enough to lead to a condensation of individual adhesion sites. A measure of the thermal roughness is shown to depend on the inverse square root of the density of adhesion sites, which is in good agreement with previous computer simulations.Comment: to appear as a Rapid Communication in Phys. Rev.

Adhesion of surfaces via particle adsorption: Exact results for a lattice of fluid columns

We present here exact results for a one-dimensional gas, or fluid, of hard-sphere particles with attractive boundaries. The particles, which can exchange with a bulk reservoir, mediate an interaction between the boundaries. A two-dimensional lattice of such one-dimensional gas `columns' represents a discrete approximation of a three-dimensional gas of particles between two surfaces. The effective particle-mediated interaction potential of the boundaries, or surfaces, is calculated from the grand-canonical partition function of the one-dimensional gas of particles, which is an extension of the well-studied Tonks gas. The effective interaction potential exhibits two minima. The first minimum at boundary contact reflects depletion interactions, while the second minimum at separations close to the particle diameter results from a single adsorbed particle that crosslinks the two boundaries. The second minimum is the global minimum for sufficiently large binding energies of the particles. Interestingly, the effective adhesion energy corresponding to this minimum is maximal at intermediate concentrations of the particles.Comment: to appear in Journal of Statistical Mechanics: Theory and Experimen

Phi-values in protein folding kinetics have energetic and structural components

Phi-values are experimental measures of how the kinetics of protein folding is changed by single-site mutations. Phi-values measure energetic quantities, but are often interpreted in terms of the structures of the transition state ensemble. Here we describe a simple analytical model of the folding kinetics in terms of the formation of protein substructures. The model shows that Phi-values have both structural and energetic components. In addition, it provides a natural and general interpretation of "nonclassical" Phi-values (i.e., less than zero, or greater than one). The model reproduces the Phi-values for 20 single-residue mutations in the alpha-helix of the protein CI2, including several nonclassical Phi-values, in good agreement with experiments.Comment: 15 pages, 3 figures, 1 tabl