Monod-Wyman-Changeux Analysis of Ligand-Gated Ion Channel Mutants

We present a framework for computing the gating properties of ligand-gated ion channel mutants using the Monod-Wyman-Changeux (MWC) model of allostery. We derive simple analytic formulas for key functional properties such as the leakiness, dynamic range, half-maximal effective concentration, and effective Hill coefficient, and explore the full spectrum of phenotypes that are accessible through mutations. Specifically, we consider mutations in the channel pore of nicotinic acetylcholine receptor (nAChR) and the ligand binding domain of a cyclic nucleotide-gated (CNG) ion channel, demonstrating how each mutation can be characterized as only affecting a subset of the biophysical parameters. In addition, we show how the unifying perspective offered by the MWC model allows us, perhaps surprisingly, to collapse the plethora of dose-response data from different classes of ion channels into a universal family of curves

Modelling diffusion in crystals under high internal stress gradients

Diffusion of vacancies and impurities in metals is important in many processes occurring in structural materials. This diffusion often takes place in the presence of spatially rapidly varying stresses. Diffusion under stress is frequently modelled by local approximations to the vacancy formation and diffusion activation enthalpies which are linear in the stress, in order to account for its dependence on the local stress state and its gradient. Here, more accurate local approximations to the vacancy formation and diffusion activation enthalpies, and the simulation methods needed to implement them, are introduced. The accuracy of both these approximations and the linear approximations are assessed via comparison to full atomistic studies for the problem of vacancies around a Lomer dislocation in Aluminium. Results show that the local and linear approximations for the vacancy formation enthalpy and diffusion activation enthalpy are accurate to within 0.05 eV outside a radius of about 13 Å (local) and 17 Å (linear) from the centre of the dislocation core or, more generally, for a strain gradient of roughly up to 6 × 10^6 m^-1 and 3 × 10^6 m^-1, respectively. These results provide a basis for the development of multiscale models of diffusion under highly non-uniform stress

Quasicontinuum representations of atomic-scale mechanics: From proteins to dislocations

Computation is one of the centerpieces of both the physical and biological sciences. A key thrust in computational science is the explicit mechanistic simulation of the spatiotemporal evolution of materials ranging from macromolecules to intermetallic alloys. However, our ability to simulate such systems is in the end always limited in both the spatial extent of the systems that are considered, as well as the duration of the time that can be simulated. As a result, a variety of efforts have been put forth that aim to finesse these challenges in both space and time through new techniques in which constraint is exploited to reduce the overall computational burden. The aim of this review is to describe in general terms some of the key ideas that have been set forth in both the materials and biological setting and to speculate on future developments along these lines. We begin by developing general ideas on the exploitation of constraint as a systematic tool for degree of freedom thinning. These ideas are then applied to case studies ranging from the plastic deformation of solids to the interactions of proteins and DNA

Membrane mechanics as a probe of ion-channel gating mechanisms

The details of conformational changes undergone by transmembrane ion channels in response to stimuli, such as electric fields and membrane tension, remain controversial. We approach this problem by considering how the conformational changes impose deformations in the lipid bilayer. We focus on the role of bilayer deformations in the context of voltage-gated channels because we hypothesize that such deformations are relevant in this case as well as for channels that are explicitly mechanosensitive. As a result of protein conformational changes, we predict that the lipid bilayer suffers deformations with a characteristic free-energy scale of 10kBT. This free energy is comparable to the voltage-dependent part of the total gating energy, and we argue that these deformations could play an important role in the overall free-energy budget of gating. As a result, channel activity will depend upon mechanical membrane parameters such as tension and leaflet thickness. We further argue that the membrane deformation around any channel can be divided into three generic classes of deformation that exhibit different mechanosensitive properties. Finally, we provide the theoretical framework that relates conformational changes during gating to tension and leaflet thickness dependence in the critical gating voltage. This line of investigation suggests experiments that could discern the dominant deformation imposed upon the membrane as a result of channel gating, thus providing clues as to the channel deformation induced by the stimulus