Landscape of finite-temperature equilibrium behaviour of curvature-inducing proteins on a bilayer membrane explored using a linearized elastic free energy model

Using a recently developed multiscale simulation methodology, we describe the equilibrium behaviour of bilayer membranes under the influence of curvature-inducing proteins using a linearized elastic free energy model. In particular, we describe how the cooperativity associated with a multitude of protein–membrane interactions and protein diffusion on a membrane-mediated energy landscape elicits emergent behaviour in the membrane phase. Based on our model simulations, we predict that, depending on the density of membrane-bound proteins and the degree to which a single protein molecule can induce intrinsic mean curvature in the membrane, a range of membrane phase behaviour can be observed including two different modes of vesicle-bud nucleation and repressed membrane undulations. A state diagram as a function of experimentally tunable parameters to classify the underlying states is proposed.     

Low temperature spectroscopy of proteins. Part II: Experiments with single protein complexes

In this part of the review we describe aspects of the physics of proteins at low temperature as they are reflected in the spectra of individual pigment–protein complexes. The focus of this review is on the spectral diffusion of chromophores that are naturally embedded in light-harvesting complexes from purple bacteria. From the spectral diffusion behaviour we can deduce details about the organisation of the energy landscape of the protein and discuss the implications for the motions of the protein in conformational phase space.     

Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule

Previous studies suggest that there are three different jam phases in the cellular automata automaton model with a slow-to-start rule under open boundaries.In the present paper,the dynamics of each free-flow-jam phase transition is studied.By analysing the microscopic behaviour of the traffic flow,we obtain analytical results on the phase transition dynamics.Our results can describe the detailed time evolution of the system during phase transition,while they provide good approximation for the numerical simulation data.These findings can perfectly explain the microscopic mechanism and details of the boundary-triggered phase transition dynamics.     

Diffusion of Myelin Oligodendrocyte Glycoprotein in Living OLN-93 Cells Investigated by Raster-Scanning Image Correlation Spectroscopy (RICS)

Many membrane proteins and lipids are partially confined in substructures ranging from tens of nanometers to micrometers in size. Evidence for heterogeneities in the membrane of oligodendrocytes, i.e. the myelin-producing cells of the central nervous system, is almost exclusively based on detergent methods. However, as application of detergents can alter the membrane phase behaviour, it is important to investigate membrane heterogeneities in living cells. Here, we report on the first investigations of the diffusion behavior of the myelin-specific protein MOG (myelin oligodendrocyte glycoprotein) in OLN-93 as studied by the recently developed RICS (raster-scanning image correlation spectroscopy) technique. We implemented RICS on a standard confocal laser-scanning microscope with one-photon excitation and analog detection. Measurements on FITC-dextran were used to evaluate the performance of the system and the data analysis procedure. Ellen Gielen and Nick Smisdom contributed equally to this work.     

Magnetic islands modelled by a phase-field-crystal approach

Using a minimal model based on the phase-field-crystal formalism, we study the coupling between the density and magnetization in ferromagnetic solids. Analytical calculations for the square phase in two dimensions are presented and the small deformation properties of the system are examined. Furthermore, numerical simulations are conducted to study the influence of an external magnetic field on various phase transitions, the anisotropic properties of the free energy functional, and the scaling behaviour of the growth of the magnetic domains in a crystalline solid. It is shown that the energy of the system can depend on the direction of the magnetic moments, with respect to the crystalline direction. Furthermore, the growth of the magnetic domains in a crystalline solid is studied and is shown that the growth of domains is in agreement with expected behaviour.     

Membrane-mediated interactions of rod-like inclusions

Inclusions embedded in lipid membranes undergo a mediated force, due to the tendency of the membrane to relax its excess of elastic energy. In this paper we determine the exact shape of a two-dimensional vesicle hosting two different inclusions, and we analyse how the inclusion conformation influences the mediated interaction. We find non-trivial equilibrium configurations for the inclusions along the hosting membrane, and we derive the complete phase diagram of the mediated interaction. In particular, we find a non-vanishing mediated force even when the distance between the inclusions is much greater than their size. Our model can be applied to describe the mediated interactions of parallel, elongated inclusions embedded in three-dimensional membranes. Received 22 October 2001 and Received in final form 8 March 2002     

Competition between folding and aggregation in a model for protein solutions

We study the thermodynamic and kinetic consequences of the competition between single-protein folding and protein-protein aggregation using a phenomenological model, in which the proteins can be in the unfolded (U), misfolded (M) or folded (F) states. The phase diagram shows the coexistence between a phase with aggregates of misfolded proteins and a phase of isolated proteins (U or F) in solution. The spinodal at low protein concentrations shows non-monotonic behavior with temperature, with implications for the stability of solutions of folded proteins at low temperatures. We follow the dynamics upon “quenching” from the U-phase (cooling) or the F-phase (heating) to the metastable or unstable part of the phase diagram that results in aggregation. We describe how interesting consequences to the distribution of aggregate size, and growth kinetics arise from the competition between folding and aggregation.     

Exploring the dynamics of a class of post-tensioned, moment resisting frames

In this paper, we present an equivalent low-order nonlinear system that describes the dynamics of a generic class of post-tensioned frames. The proposed nonlinear single degree of freedom system is derived from energy considerations. We demonstrate that the equation of motion for the entire, planar, post-tensioned frame is equivalent to the dynamics of a single tied rocking block on an elastic foundation. As validation for this analytical model we present physical tests (1/4 scale) undertaken at Bristol. Quasi-static push-pull-over tests and dynamic frequency sine sweep shake table tests are conducted on the physical model. Comparison of results indicate that the analytical model predicts both quasi-static nonlinear push-over and nonlinear dynamic resonant behaviour very well. Further numerical simulations on the analytical model identify the nonlinear resonant frequency backbone curves for a range of system parameters. We explore catchment basins of both Poincaré phase and system parameter spaces. In addition we describe failure boundaries and system integrity surfaces giving an indication as to likely bounds on forcing amplitudes.     

Organization of membrane-associated proteins in lipid bilayers

Lateral organization of proteins in biomembranes is vitally important to membrane functions such as signal transduction, endocytosis, and membrane trafficking. One of the major goals in current biomembrane science is to reveal the microscopic mechanism of membrane-associated protein organization in biomembranes. Here, we investigate the structural organization of membrane-associated proteins in lipid bilayers by combining self-consistent field theory with density functional theory. The present study can simultaneously take into account the entropy effect of lipids, depletion effect of membrane-associated proteins due to the presence of lipid headgroups as well as the effect of interfacial interaction. By varying the volume fraction of lipids, we examine various effects on protein organization, and reveal that a close-packed crystal structure appears at low lipid volume fractions due to interfacial energy and weak depletion effect, whereas a chain structure with branches occurs at high lipid volume fractions mainly due to strong depletion. The present results may provide some theoretical insight into further experiments on organization of membrane proteins.     

Euler Walk on a Cayley Tree

We describe two possible regimes (dynamic phases) of the Euler walk on a Cayley tree: a condensed phase and a low-density phase. In the condensed phase the area of visited sites grows as a compact domain. In the low-density phase the proportion of visited sites decreases rapidly from one generation of the tree to the next. We describe in detail returns of the walker to the root and growth of the domain of visited sites in the condensed phase. We also investigate the critical behaviour of the model on the line separating the two regimes.     

Minireview: The compact phase in polymers and proteins

Proteins are linear molecules. However, the simple model of a polymer viewed as spheres tethered together does not account for many of the observed characteristics of protein structures. Here we review some recent works tackling this problem. In particular, we will show that there is a growing evidence suggesting that the compact structures of folded proteins are selected in their gross topological features based on geometry and symmetry rather than on sequence consideration. They are poised at the edge of compaction, thus accounting for their flexibility. Different aspects of protein behavior can be rationalized by studying how the energy landscape of a single chain in the marginally compact phase can be modified.     

Adiabatic pumping mechanism for ion motive ATPases

An ion motive ATPase is a membrane protein that pumps ions across the membrane at the expense of the chemical energy of adenosine triphosphate (ATP) hydrolysis. Here we describe how an external electric field, by inducing transitions between several protein configurations, can also power this pump. The underlying mechanism may be very similar to that of a recently constructed adiabatic electron pump [Science 283, 1905 (1999)]].     

Discrete nonlinear Schrödinger equation and polygonal solitons with applications to collapsed proteins

We introduce a novel generalization of the discrete nonlinear Schr?dinger equation. It supports solitons that we utilize to model chiral polymers in the collapsed phase and, in particular, proteins in their native state. As an example we consider the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. We use its backbone as a template to explicitly construct a two-soliton configuration. Each of the two solitons describe well over 7.000 supersecondary structures of folded proteins in the Protein Data Bank with sub-angstrom accuracy suggesting that these solitons are common in nature.     

Structure factor of a lamellar smectic phase with inclusions

Motivated by numerous X-ray scattering studies of lamellar phases with membrane proteins, amphiphilic peptides, polymers, or other inclusions, we have determined the modifications of the classical Caillé law for a smectic phase as a function of the nature and concentration of inclusions added to it. Besides a fundamental interest on the behavior of fluctuating systems with inclusions, a precise characterization of the action of a given protein on a lipid membrane (anchoring, swelling, stiffening ...) is of direct biological interest and could be probed by way of X-ray measurements. As a first step we consider three different couplings involving local pinching (or swelling), stiffening or curvature of the membrane. In the first two cases we predict that independent inclusions induce a simple renormalization of the bending and compression moduli of the smectic phase. The X-ray experiments may also be used to probe correlations between inclusions. Finally we show that asymmetric coupling (such as a local curvature of the membrane) results in a modification of the usual Caillé law. Received 10 March 2000 and Received in final form 30 August 2000     

Symmetrical adhesion of two cylindrical colloids to a tubular membrane

With the full treatment of the Helfrich model we theoretically study the symmetrical adhesion of two cylindrical colloids to a tubular membrane. The adhesion of the rigid cylinders with different radius from the membrane tube surface can produce both shallow wrapping with relatively small wrapping angle and deep wrapping with big wrapping angle. These significant structural behaviors can be obtained by analyzing the system energy. A second order adhesion transition from the desorbed to weakly adhered states is found, and a first order phase transition where the cylindrical colloids undergo an abrupt transition from weakly adhered to strongly adhered states can be obtained as well.     

Thermodynamics of the HMF model with a magnetic field

We study the thermodynamics of the Hamiltonian mean field (HMF) model with an external potential playing the role of a “magnetic field”. If we consider only fully stable states, the caloric curve does not present any phase transition. However, if we take into account metastable states (for a restricted class of perturbations), we find a very rich phenomenology. In particular, the caloric curve displays a region of negative specific heat in the microcanonical ensemble in which the temperature decreases as the energy increases. This leads to ensembles inequivalence and to zeroth order phase transitions similar to the “gravothermal catastrophe” and to the “isothermal collapse” of self-gravitating systems. In the present case, they correspond to the reorganization of the system from an “anti-aligned” phase (magnetization pointing in the direction opposite to the magnetic field) to an “aligned” phase (magnetization pointing in the same direction as the magnetic field). We also find that the magnetic susceptibility can be negative in the microcanonical ensemble so that the magnetization decreases as the magnetic field increases. The magnetic curves can take various shapes depending on the values of energy or temperature. We describe first order phase transitions and hysteretic cycles involving positive or negative susceptibilities. We also show that this model exhibits gaps in the magnetization at fixed energy, resulting in ergodicity breaking.     

Energetic variational approaches in modeling vesicle and fluid interactions

In this paper, we establish a hydrodynamic system to study vesicle deformations under external flow fields. The system is in the Eulerian formulation, involving the coupling of the incompressible flow system and a phase field equation. The phase field mixing energy can be viewed as a physical approximation/regularization of the Helfrich energy for an elastic membrane. We derive a self-consistent system of equations describing the dynamic evolution of vesicles immersed in an incompressible, Newtonian fluid, using an energetic variational approach. Numerical simulations of the membrane deformations in flow fields can be conducted based on the developed model.     

tBid蛋白引发磷脂膜透化过程的研究

Bid蛋白是仅有BH3结构域的Bcl-2家族蛋白,在溶酶体膜透化以及线粒体外膜透化引发的细胞凋亡过程中起着非常重要的调控作用,但是Bid蛋白与生物膜之间的相互作用导致脂膜透化的确切机制尚不十分清楚.本文利用激光扫描共聚焦显微成像技术及基于氧化石墨烯表面诱导荧光衰逝的单分子荧光技术,分别从单囊泡及单分子水平对tBid蛋白与磷脂膜之间的相互作用进行了系统的研究.结果表明,tBid蛋白在膜上聚集后可引起脂膜的透化,且脂膜透化的发生源于聚集体中一些tBid蛋白更深入地插入了脂膜中.     

Thermodynamics of small systems embedded in a reservoir: a detailed analysis of finite size effects

We present a detailed study on the finite size scaling behaviour of thermodynamic properties for small systems of particles embedded in a reservoir. Previously, we derived that the leading finite size effects of thermodynamic properties for small systems scale with the inverse of the linear length of the small system, and we showed how this can be used to describe systems in the thermodynamic limit [Chem. Phys. Lett. 504, 199 (2011)]. This approach takes into account an effective surface energy, as a result of the non-periodic boundaries of the small embedded system. Deviations from the linear behaviour occur when the small system becomes very small, i.e. smaller than three times the particle diameter in each direction. At this scale, so-called nook- and corner effects will become important. In this work, we present a detailed analysis to explain this behaviour. In addition, we present a model for the finite size scaling when the size of the small system is of the same order of magnitude as the reservoir. The developed theory is validated using molecular simulations of systems containing Lennard-Jones and WCA particles, and leads to significant improvements over our previous approach. Our approach eventually leads to an efficient method to compute the thermodynamic factor of macroscopic systems from finite size scaling, which is for example required for converting Fick and Maxwell–Stefan transport diffusivities.