Mechanochemical coupling of lipid organization and protein function through membrane thickness deformations.

Cell membranes are composed of a great variety of protein and lipid species with distinct unperturbed hydrophobic thicknesses. To achieve hydrophobic matching, the lipid bilayer tends to deform around membrane proteins so as to match the protein hydrophobic thickness at bilayer-protein interfaces. Such protein-induced distortions of the lipid bilayer hydrophobic thickness incur a substantial energy cost that depends critically on the bilayer-protein hydrophobic mismatch, while distinct conformational states of membrane proteins often show distinct hydrophobic thicknesses. As a result, hydrophobic interactions between membrane proteins and lipids can yield a rich interplay of lipid-protein organization and transitions in protein conformational state. We combine here the membrane elasticity theory of protein-induced lipid bilayer thickness deformations with the Landau-Ginzburg theory of lipid domain formation to systematically explore the coupling between local lipid organization, lipid and protein hydrophobic thickness, and protein-induced lipid bilayer thickness deformations in membranes with heterogeneous lipid composition. We allow for a purely mechanical coupling of lipid and protein composition through the energetics of protein-induced lipid bilayer thickness deformations as well as a chemical coupling driven by preferential interactions between particular lipid and protein species. We find that the resulting lipid-protein organization can endow membrane proteins with diverse and controlled mechanical environments that, via protein-induced lipid bilayer thickness deformations, can strongly influence protein function. The theoretical approach employed here provides a general framework for the quantitative prediction of how membrane thickness deformations influence the joint organization and function of lipids and proteins in cell membranes.

Stochastic self-assembly of reaction-diffusion patterns in synaptic membranes.

Synaptic receptor and scaffold molecules self-assemble into membrane protein domains, which play an important role in signal transmission across chemical synapses. Experiment and theory have shown that the formation of receptor-scaffold domains of the characteristic size observed in nerve cells can be understood from the receptor and scaffold reaction and diffusion processes suggested by experiments. We employ here kinetic Monte Carlo (KMC) simulations to explore the self-assembly of synaptic receptor-scaffold domains in a stochastic lattice model of receptor and scaffold reaction-diffusion dynamics. For reaction and diffusion rates within the ranges of values suggested by experiments we find, in agreement with previous mean-field calculations, self-assembly of receptor-scaffold domains of a size similar to that observed in experiments. Comparisons between the results of our KMC simulations and mean-field solutions suggest that the intrinsic noise associated with receptor and scaffold reaction and diffusion processes accelerates the self-assembly of receptor-scaffold domains, and confers increased robustness to domain formation. In agreement with experimental observations, our KMC simulations yield a prevalence of scaffolds over receptors in receptor-scaffold domains. Our KMC simulations show that receptor and scaffold reaction-diffusion dynamics can inherently give rise to plasticity in the overall properties of receptor-scaffold domains, which may be utilized by nerve cells to regulate the receptor number at chemical synapses.

Symmetry of membrane protein polyhedra with heterogeneous protein size.

In experiments on membrane protein polyhedral nanoparticles (MPPNs) [Basta et al., Proc. Natl. Acad. Sci. USA 111, 670 (2014)PNASA60027-842410.1073/pnas.1321936111], it has been observed that membrane proteins and lipids can self-assemble into closed lipid bilayer vesicles with a polyhedral arrangement of membrane proteins. In particular, MPPNs formed from the mechanosensitive channel of small conductance (MscS) were found to have the symmetry of the snub cube-a chiral, Archimedean solid-with one MscS protein located at each one of the 24 vertices of the snub cube. It is currently unknown whether MPPNs with heterogeneous protein composition maintain a high degree of symmetry. Inspired by previous work on viral capsid symmetry, we employ here computational modeling to study the symmetry of MPPNs with heterogeneous protein size. We focus on MPPNs formed from MscS proteins, which can exist in closed or open conformational states with distinct sizes. We find that, as an increasing number of closed-state MscS proteins transitions to the open conformational state of MscS, the minimum-energy MscS arrangement in MPPNs follows a strikingly regular pattern, with the dominant MPPN symmetry always being provided by the snub cube. Our results suggest that MPPNs with heterogeneous protein size can be highly symmetric, with a well-defined polyhedral ordering of membrane proteins of different sizes.

Regulation of membrane proteins through local heterogeneity in lipid bilayer thickness.

Cell membranes show an intricate organization of lipids and membrane proteins into domains with distinct composition and hydrophobic thickness. Using mechanosensitive ion channels as a model system, we employ the membrane elasticity theory of lipid-protein interactions together with the Landau-Ginzburg theory of lipid domain formation to quantify protein-induced lipid bilayer thickness deformations in lipid bilayers with heterogeneous hydrophobic thickness. We show that protein-induced lipid bilayer thickness deformations yield, without any assumptions about preferential interactions between particular lipid and protein species, organization of lipids and membrane proteins according to their preferred hydrophobic thickness, and couple the conformational states of membrane proteins to the local membrane composition. Our calculations suggest that protein-induced lipid bilayer thickness deformations endow proteins in cell membranes with diverse and controlled mechanical environments that, in turn, allow targeted regulation of membrane proteins.

Supramolecular organization of membrane proteins with anisotropic hydrophobic thickness.

Experiments have revealed that membrane proteins often self-assemble into locally ordered clusters. Such membrane protein lattices can play key roles in the functional organization of cell membranes. Membrane protein organization can be driven, at least in part, by bilayer-mediated elastic interactions between membrane proteins. For membrane proteins with anisotropic hydrophobic thickness, bilayer-mediated protein interactions are inherently directional. Here we establish general relations between anisotropy in membrane protein hydrophobic thickness and supramolecular membrane protein organization. We show that protein symmetry is distinctively reflected in the energy landscape of bilayer-mediated protein interactions, favoring characteristic lattice architectures of membrane protein clusters. We find that, in the presence of thermal fluctuations, anisotropy in protein hydrophobic thickness can induce membrane proteins to form mesh-like structures dividing the membrane into compartments. Our results help to elucidate the physical principles and mechanisms underlying the functional organization of cell membranes.

Do Anti-TNF Agents Increase the Risk of Inflammatory Bowel Disease Evolution in Patients with Ankylosing Spondylitis? Real Life Data.

OBJECTIVE: The aim of this study was to determine whether there is any association with anti-tumor necrosis factor (TNF) agent administration and development of new-onset inflammatory bowel disease (IBD) in ankylosing spondylitis (AS) patients. METHODS: Records of the patients who met 1984 modified New York criteria for AS between 1998 and 2016 at Rheumatology Department were evaluated retrospectively and data about the patients, IBD properties and medication were obtained. RESULTS: Among 420 patients, 310 were male, the average age was 42.9 ± 1.3 years, average disease duration was 16.7 ± 10.4 years. Anti-TNF agents were in use by 154 patients, 52 patients were receiving etanercept (ETN), infliximab (INF), adalimumab (ADA), and golimumab (GO) treatments were ongoing in 50, 41, and 11 patients, respectively. New-onset IBD developed in 10 patients; 3 from the group treated with non-anti-TNF drugs (1.1%) and 7 from the group treated with anti-TNF agents (4.5%) (p = 0.042). No significant difference was detected between three anti-TNF agent forms in relation with the risk of IBD onset. In AS patients, existence of familial AS (OR 4.69 (95%CI 1.28-17.19, p = 0.020) and anti-TNF agent treatment (OR 4.17 (95%CI 1.06-16.38, p = 0.041) were independent risk factors for new-onset IBD development. CONCLUSION: Despite the increased risk of new-onset IBD development during the course of AS, paradoxical response to anti-TNF drugs must also be considered as a source that triggers onset of IBD.

Directed Supramolecular Organization of N-BAR Proteins through Regulation of H0 Membrane Immersion Depth.

Many membrane remodeling events rely on the ability of curvature-generating N-BAR membrane proteins to organize into distinctive supramolecular configurations. Experiments have revealed a conformational switch in N-BAR proteins resulting in vesicular or tubular membrane shapes, with shallow membrane immersion of the H0 amphipathic helices of N-BAR proteins on vesicles but deep H0 immersion on tubes. We develop here a minimal elastic model of the local thinning of the lipid bilayer resulting from H0 immersion. Our model predicts that the observed conformational switch in N-BAR proteins produces a corresponding switch in the bilayer-mediated N-BAR interactions due to the H0 helices. In agreement with experiments, we find that bilayer-mediated H0 interactions oppose N-BAR multimerization for the shallow H0 membrane immersion depths measured on vesicles, but promote self-assembly of supramolecular N-BAR chains for the increased H0 membrane immersion depths measured on tubes. Finally, we consider the possibility that bilayer-mediated H0 interactions might contribute to the concerted structural reorganization of N-BAR proteins suggested by experiments. Our results indicate that the membrane immersion depth of amphipathic protein helices may provide a general molecular control parameter for membrane organization.

Searching for empirical evidence on traffic equilibrium.

Cities around the world are inundated by cars and suffer traffic congestion that results in excess delays, reduced safety and environmental pollution. The interplay between road infrastructure and travel choices defines the level and the spatio-temporal extent of congestion. Given the existing infrastructure, understanding how the route choice decisions are made and how travellers interact with each other is a crucial first step in mitigating traffic congestion. This is a problem with fundamental importance, as it has implications for other limited supply systems where agents compete for resources and reach an equilibrium. Here, we observe the route choice decisions and the traffic conditions through an extensive data set of GPS trajectories. We compare the actual paths followed by travellers to those implied by equilibrium conditions (i) at a microscopic scale, where we focus on individual path similarities, and (ii) at a macroscopic scale, where we perform network-level comparison of the traffic loads. We present that non-cooperative or selfish equilibrium replicates the actual traffic (to a certain extent) at the macroscopic scale, while the majority of individual decisions cannot be reproduced by neither selfish nor cooperative equilibrium models.

Stochastic lattice model of synaptic membrane protein domains.

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

Distribution of randomly diffusing particles in inhomogeneous media.

Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct particle hopping rates. Starting from the master equations (MEs) governing diffusion in inhomogeneous media we derive here, for arbitrary spatial dimensions, the deterministic lattice equations (DLEs) specifying the average particle number at each lattice site for randomly diffusing particles in inhomogeneous media. We consider the case of free (Fickian) diffusion with no steric constraints on the maximum particle number per lattice site as well as the case of diffusion under steric constraints imposing a maximum particle concentration. We find, for both transient and asymptotic regimes, excellent agreement between the DLEs and kinetic Monte Carlo simulations of the MEs. The DLEs provide a computationally efficient method for predicting the (average) distribution of randomly diffusing particles in inhomogeneous media, with the number of DLEs associated with a given system being independent of the number of particles in the system. From the DLEs we obtain general analytic expressions for the steady-state particle distributions for free diffusion and, in special cases, diffusion under steric constraints in inhomogeneous media. We find that, in the steady state of the system, the average fraction of particles in a given domain is independent of most system properties, such as the arrangement and shape of domains, and only depends on the number of lattice sites in each domain, the particle hopping rates, the number of distinct particle species in the system, and the total number of particles of each particle species in the system. Our results provide general insights into the role of spatially inhomogeneous particle hopping rates in setting the particle distributions in inhomogeneous media.

Symmetry and Size of Membrane Protein Polyhedral Nanoparticles.

In recent experiments [T. Basta et al., Proc. Natl. Acad. Sci. U.S.A. 111, 670 (2014)] lipids and membrane proteins were observed to self-assemble into membrane protein polyhedral nanoparticles (MPPNs) with a well-defined polyhedral protein arrangement and characteristic size. We develop a model of MPPN self-assembly in which the preferred symmetry and size of MPPNs emerge from the interplay of protein-induced lipid bilayer deformations, topological defects in protein packing, and thermal effects. With all model parameters determined directly from experiments, our model correctly predicts the observed symmetry and size of MPPNs. Our model suggests how key lipid and protein properties can be modified to produce a range of MPPN symmetries and sizes in experiments.

Bilayer-thickness-mediated interactions between integral membrane proteins.

Hydrophobic thickness mismatch between integral membrane proteins and the surrounding lipid bilayer can produce lipid bilayer thickness deformations. Experiment and theory have shown that protein-induced lipid bilayer thickness deformations can yield energetically favorable bilayer-mediated interactions between integral membrane proteins, and large-scale organization of integral membrane proteins into protein clusters in cell membranes. Within the continuum elasticity theory of membranes, the energy cost of protein-induced bilayer thickness deformations can be captured by considering compression and expansion of the bilayer hydrophobic core, membrane tension, and bilayer bending, resulting in biharmonic equilibrium equations describing the shape of lipid bilayers for a given set of bilayer-protein boundary conditions. Here we develop a combined analytic and numerical methodology for the solution of the equilibrium elastic equations associated with protein-induced lipid bilayer deformations. Our methodology allows accurate prediction of thickness-mediated protein interactions for arbitrary protein symmetries at arbitrary protein separations and relative orientations. We provide exact analytic solutions for cylindrical integral membrane proteins with constant and varying hydrophobic thickness, and develop perturbative analytic solutions for noncylindrical protein shapes. We complement these analytic solutions, and assess their accuracy, by developing both finite element and finite difference numerical solution schemes. We provide error estimates of our numerical solution schemes and systematically assess their convergence properties. Taken together, the work presented here puts into place an analytic and numerical framework which allows calculation of bilayer-mediated elastic interactions between integral membrane proteins for the complicated protein shapes suggested by structural biology and at the small protein separations most relevant for the crowded membrane environments provided by living cells.

Architecture and Function of Mechanosensitive Membrane Protein Lattices.

Experiments have revealed that membrane proteins can form two-dimensional clusters with regular translational and orientational protein arrangements, which may allow cells to modulate protein function. However, the physical mechanisms yielding supramolecular organization and collective function of membrane proteins remain largely unknown. Here we show that bilayer-mediated elastic interactions between membrane proteins can yield regular and distinctive lattice architectures of protein clusters, and may provide a link between lattice architecture and lattice function. Using the mechanosensitive channel of large conductance (MscL) as a model system, we obtain relations between the shape of MscL and the supramolecular architecture of MscL lattices. We predict that the tetrameric and pentameric MscL symmetries observed in previous structural studies yield distinct lattice architectures of MscL clusters and that, in turn, these distinct MscL lattice architectures yield distinct lattice activation barriers. Our results suggest general physical mechanisms linking protein symmetry, the lattice architecture of membrane protein clusters, and the collective function of membrane protein lattices.

Confotronic dynamics of tubular filaments.

Tubular lattices are ubiquitous in nature and technology. Microtubules and nanotubes of all kinds act as important pillars of biological cells and the man-made nano-world. We show that when prestress is introduced in such structures, localized conformational quasiparticles emerge and govern the collective shape dynamics of the lattice. When coupled via cooperative interactions these quasiparticles form larger-scale quasipolymer superstructures exhibiting collective dynamic modes and giving rise to a hallmark behavior radically different from semiflexible beams.

Dipoles in thin sheets.

A flat elastic sheet may contain pointlike conical singularities that carry a metrical "charge" of Gaussian curvature. Adding such elementary defects to a sheet allows one to make many shapes, in a manner broadly analogous to the familiar multipole construction in electrostatics. However, here the underlying field theory is non-linear, and superposition of intrinsic defects is non-trivial as it must respect the immersion of the resulting surface in three dimensions. We consider a "charge-neutral" dipole composed of two conical singularities of opposite sign. Unlike the relatively simple electrostatic case, here there are two distinct stable minima and an infinity of unstable equilibria. We determine the shapes of the minima and evaluate their energies in the thin-sheet regime where bending dominates over stretching. Our predictions are in surprisingly good agreement with experiments on paper sheets.