arXiv subjects

Thomas R. Weikl

Publications and source records attributed to Thomas R. Weikl.

At least 19 recordsLinked to original sources

arXiv2024

Membrane-mediated interactions between arc-shaped particles strongly depend on membrane curvature

Besides direct molecular interactions, proteins and nanoparticles embedded in or adsorbed to membranes experience indirect interactions that are mediated by the membranes. These membrane-mediated interactions arise from the membrane curvature induced by the particles and can lead to assemblies of particles that generate highly curved spherical or tubular membranes shapes, but have mainly been quantified for planar or weakly curved membranes. In this article, we systematically investigate the membrane-mediated interactions of arc-shaped particles adsorbed to a variety of tubular and spherical membrane shapes with coarse-grained modelling and simulations. We determine both the pairwise interaction free energy, with includes entropic contributions due to rotational entropy loss at close particle distances, and the pairwise interaction energy without entropic components from particle distributions observed in the simulations. For membrane shapes with small curvature, the membrane-mediated interaction free energies of particle pairs exceed the thermal energy kT and can lead to particle ordering and aggregation. The interactions strongly decrease with increasing curvature of the membrane shape and are minimal for tubular shapes with membrane curvatures close to the particle curvature.

cond-mat.soft↗

arXiv2024

Non-additivity in many-body interactions between membrane-deforming spheres increases disorder

Membrane-induced interactions have been predicted to be important for the organization of membrane proteins. Measurements of the interactions between two and three membrane deforming objects have revealed their non-additive nature. They are thought to lead to complex many-body effects, however, experimental evidence is lacking to date. We here present an experimental method to measure many-body effects in membrane-mediated interactions using colloidal spheres placed between a deflated giant unilamellar vesicles and a planar substrate. The thus confined colloidal particles cause a large deformation of the membrane while not being physochemically attached to it and interact through it. Two particles are found to attract with a maximum force of 0.2~pN. For three particles, we observe a preference for forming compact equilateral triangles over a linear arrangement. We use numerical energy minimization to establish that the attraction stems from a reduction in the membrane-deformation energy caused by the particles. Confining up to 36 particles, we find a preference for hexagonally close packed clusters. However, with increasing number of particles the order of the confined particles decreases, while at the same time, diffusivity of the particles increases. Our experiments for the first time show that the non-additive nature of membrane-mediated interactions affects the interactions and arrangements and ultimately leads to spherical aggregates with liquid-like order of potential importance for cellular processes.

cond-mat.soft↗

arXiv2020

Weak carbohydrate-carbohydrate interactions in membrane adhesion are fuzzy and generic

Carbohydrates such as the trisaccharide motif LeX are key constituents of cell surfaces. Despite intense research, the interactions between carbohydrates of apposing cells or membranes are not well understood. In this article, we investigate carbohydrate-carbohydrate interactions in membrane adhesion as well as in solution with extensive atomistic molecular dynamics simulations that exceed the simulation times of previous studies by orders of magnitude. For LeX, we obtain association constants of soluble carbohydrates, adhesion energies of lipid-anchored carbohydrates, and maximally sustained forces of carbohydrate complexes in membrane adhesion that are in good agreement with experimental results in the literature. Our simulations thus appear to provide a realistic, detailed picture of LeX-LeX interactions in solution and during membrane adhesion. In this picture, the LeX-LeX interactions are fuzzy, i.e. LeX pairs interact in a large variety of short-lived, bound conformations. For the synthetic tetrasaccharide Lac 2, which is composed of two lactose units, we observe similarly fuzzy interactions and obtain association constants of both soluble and lipid-anchored variants that are comparable to the corresponding association constants of LeX. The fuzzy, weak carbohydrate-carbohydrate interactions quantified in our simulations thus appear to be a generic feature of small, neutral carbohydrates such as LeX and Lac 2.

q-bio.BM↗

arXiv2020

Membrane morphologies induced by mixtures of arc-shaped particles with opposite curvature

Biological membranes are shaped by various proteins that either generate inward or outward membrane curvature. In this article, we investigate the membrane morphologies induced by mixtures of arc-shaped particles with coarse-grained modeling and simulations. The particles bind to the membranes either with their inward, concave side or their outward, convex side and, thus, generate membrane curvature of opposite sign. We find that small fractions of convex-binding particles can stabilize three-way junctions of membrane tubules, as suggested for the protein lunapark in the endoplasmic reticulum of cells. For comparable fractions of concave-binding and convex-binding particles, we observe lines of particles of the same type, and diverse membrane morphologies with grooves and bulges induced by these particle lines. The alignment and segregation of the particles is driven by indirect, membrane-mediated interactions.

q-bio.SC↗

arXiv2019

Binding and segregation of proteins in membrane adhesion: Theory, modelling, and simulations

The adhesion of biomembranes is mediated by the binding of membrane-anchored receptor and ligand proteins. The proteins can only bind if the separation between apposing membranes is sufficiently close to the length of the protein complexes, which leads to an interplay between protein binding and membrane shape. In this article, we review current models of biomembrane adhesion and novel insights obtained from the models. Theory and simulations with elastic-membrane and coarse-grained molecular models of biomembrane adhesion indicate that the binding of proteins in membrane adhesion strongly depends on nanoscale shape fluctuations of the apposing membranes, which results in binding cooperativity. A length mismatch between protein complexes leads to repulsive interactions that are caused by membrane bending and act as a driving force for the length-based segregation of proteins during membrane adhesion.

q-bio.SC↗

arXiv2019

Membrane morphologies induced by arc-shaped scaffolds are determined by arc angle and coverage

The intricate shapes of biological membranes such as tubules and membrane stacks are induced by proteins. In this article, we systematically investigate the membrane shapes induced by arc-shaped scaffolds such as proteins and protein complexes with coarse-grained modeling and simulations. We find that arc-shaped scaffolds induce membrane tubules at membrane coverages larger than a threshold of about 40%, irrespective of their arc angle. The membrane morphologies at intermediate coverages below this tubulation threshold, in contrast, strongly depend on the arc angle. Scaffolds with arc angles of about 60 degree akin to N-BAR domains do not change the membrane shape at coverages below the tubulation threshold, while scaffolds with arc angles larger than about 120 degree induce double-membrane stacks at intermediate coverages. The scaffolds stabilize the curved membrane edges that connect the membrane stacks, as suggested for complexes of reticulon proteins. Our results provide general insights on the determinants of membrane shaping by arc-shaped scaffolds.

q-bio.SC↗

arXiv2018

Particle-based membrane model for mesoscopic simulation of cellular dynamics

We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending, and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model, and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis...

physics.bio-ph↗

arXiv2016

How to distinguish conformational selection and induced fit based on chemical relaxation rates

Protein binding often involves conformational changes. Important questions are whether a conformational change occurs prior to a binding event ('conformational selection') or after a binding event ('induced fit'), and how conformational transition rates can be obtained from experiments. In this article, we present general results for the chemical relaxation rates of conformational-selection and induced-fit binding processes that hold for all concentrations of proteins and ligands and, thus, go beyond the standard pseudo-first-order approximation of large ligand concentration. These results allow to distinguish conformational-selection from induced-fit processes - also in cases in which such a distinction is not possible under pseudo-first-order conditions - and to extract conformational transition rates of proteins from chemical relaxation data.

q-bio.BM↗

arXiv2016

Membrane tubulation by elongated and patchy nanoparticles

Advances in nanotechnology lead to an increasing interest in how nanoparticles interact with biomembranes. Nanoparticles are wrapped spontaneously by biomembranes if the adhesive interactions between the particles and membranes compensate for the cost of membrane bending. In the last years, the cooperative wrapping of spherical nanoparticles in membrane tubules has been observed in experiments and simulations. For spherical nanoparticles, the stability of the particle-filled membrane tubules strongly depends on the range of the adhesive particle-membrane interactions. In this article, we show via modeling and energy minimization that elongated and patchy particles are wrapped cooperatively in membrane tubules that are highly stable for all ranges of the particle-membrane interactions, compared to individual wrapping of the particles. The cooperative wrapping of linear chains of elongated or patchy particles in membrane tubules may thus provide an efficient route to induce membrane tubulation, or to store such particles in membranes.

q-bio.SC↗

arXiv2016

Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: insights from computational model systems and theory

The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant K2D and the on- and off-rate constants of anchored receptors and ligands in their 'two-dimensional' (2D) membrane environment strongly depend on the membrane roughness from thermally excited shape fluctuations on nanoscales. Recent theory corroborated by simulations provides a general relation between K2D} and the binding constant K3D of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in three dimensions (3D).

q-bio.BM↗

arXiv2015

Binding constants of membrane-anchored receptors and ligands: a general theory corroborated by Monte Carlo simulations

Adhesion processes of biological membranes that enclose cells and cellular organelles are essential for immune responses, tissue formation, and signaling. These processes depend sensitively on the binding constant K2D of the membrane-anchored receptor and ligand proteins that mediate adhesion, which is difficult to measure in the 'two-dimensional' (2D) membrane environment of the proteins. An important problem therefore is to relate K2D} to the binding constant K3D} of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in three dimensions (3D). In this article, we present a general theory for the binding constants K2D and K3D of rather stiff proteins whose main degrees of freedom are translation and rotation, along membranes and around anchor points 'in 2D', or unconstrained 'in 3D'. The theory generalizes previous results by describing how K2D depends both on the average separation and thermal nanoscale roughness of the apposing membranes, and on the length and anchoring flexibility of the receptors and ligands. Our theoretical results for the ratio K2D/K3D of the binding constants agree with detailed results from Monte Carlo simulations without any data fitting, which indicates that the theory captures the essential features of the 'dimensionality reduction' due to membrane anchoring. In our Monte Carlo simulations, we consider a novel coarse-grained model of biomembrane adhesion in which the membranes are represented as discretized elastic surfaces, and the receptors and ligands as anchored molecules that diffuse continuously along the membranes and rotate at their anchor points.

q-bio.BM↗

arXiv2015

Binding kinetics of membrane-anchored receptors and ligands: molecular dynamics simulations and theory

The adhesion of biological membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. Central questions are how the binding kinetics of these proteins is affected by the membranes and by the membrane anchoring of the proteins. In this article, we (i) present detailed data for the binding of membrane-anchored proteins from coarse-grained molecular dynamics simulations, and (ii) provide a theory that describes how the binding kinetics depends on the average separation and thermal roughness of the adhering membranes, and on the anchoring, lengths, and length variations of the proteins. An important element of our theory is the tilt of bound receptor-ligand complexes and transition-state complexes relative to the membrane normals. This tilt results from an interplay of the anchoring energy and rotational entropy of the complexes and facilitates the formation of receptor-ligand bonds at membrane separations smaller than the preferred separation for binding. In our simulations, we have considered both lipid-anchored and transmembrane receptor and ligand proteins. We find that the binding equilibrium constant and binding on-rate constant of lipid-anchored proteins are considerably smaller than the binding constant and on-rate constant of rigid transmembrane proteins with identical binding domains.

q-bio.BM↗

arXiv2015

The role of membrane curvature for the wrapping of nanoparticles

Cellular internalization of nanoparticles requires the full wrapping of the nanoparticles by the cell membrane. This wrapping process can occur spontaneously if the adhesive interactions between the nanoparticles and the membranes are sufficiently strong to compensate for the cost of membrane bending. In this article, we show that the membrane curvature prior to wrapping plays a key role for the wrapping process, besides the size and shape of the nanoparticles that have been investigated in recent years. For membrane segments that initially bulge away from nanoparticles by having a mean curvature of the same sign as the mean curvature of the particle surface, we find strongly stable partially wrapped states that can prevent full wrapping. For membrane segments that initially bulge towards the nanoparticles, in contrast, partially wrapped states can constitute a significant energetic barrier for the wrapping process.

q-bio.SC↗

arXiv2014

Conformational selection in protein binding and function

Protein binding and function often involves conformational changes. Advanced NMR experiments indicate that these conformational changes can occur in the absence of ligand molecules (or with bound ligands), and that the ligands may 'select' protein conformations for binding (or unbinding). In this review, we argue that this conformational selection requires transition times for ligand binding and unbinding that are small compared to the dwell times of proteins in different conformations, which is plausible for small ligand molecules. Such a separation of timescales leads to a decoupling and temporal ordering of binding/unbinding events and conformational changes. We propose that conformational-selection and induced-change processes (such as induced fit) are two sides of the same coin, because the temporal ordering is reversed in binding and unbinding direction. Conformational-selection processes can be characterized by a conformational excitation that occurs prior to a binding or unbinding event, while induced-change processes exhibit a characteristic conformational relaxation that occurs after a binding or unbinding event. We discuss how the ordering of events can be determined from relaxation rates and effective on- and off-rates determined in mixing experiments, and from the conformational exchange rates measured in advanced NMR or single-molecule FRET experiments. For larger ligand molecules such as peptides, conformational changes and binding events can be intricately coupled and exhibit aspects of conformational-selection and induced-change processes in both binding and unbinding direction.

q-bio.BM↗

arXiv2014

Cooperative wrapping of nanoparticles by membrane tubes

The bioactivity of nanoparticles crucially depends on their ability to cross biomembranes. Recent simulations indicate the cooperative wrapping and internalization of spherical nanoparticles in tubular membrane structures. In this article, we systematically investigate the energy gain of this cooperative wrapping by minimizing the energies of the rotationally symmetric shapes of the membrane tubes and of membrane segments wrapping single particles. We find that the energy gain for the cooperative wrapping of nanoparticles in membrane tubes relative to their individual wrapping as single particles strongly depends on the ratio of the particle radius and the range of the particle-membrane adhesion potential. For a potential range of the order of one nanometer, the cooperative wrapping in tubes is highly favorable for particles with a radius of tens of nanometers and intermediate adhesion energies, but not for particles that are significantly larger.

cond-mat.soft↗

arXiv2013

How conformational changes can affect catalysis, inhibition and drug resistance of enzymes with induced-fit binding mechanism such as the HIV-1 protease

A central question is how the conformational changes of proteins affect their function and the inhibition of this function by drug molecules. Many enzymes change from an open to a closed conformation upon binding of substrate or inhibitor molecules. These conformational changes have been suggested to follow an induced-fit mechanism in which the molecules first bind in the open conformation in those cases where binding in the closed conformation appears to be sterically obstructed such as for the HIV-1 protease. In this article, we present a general model for the catalysis and inhibition of enzymes with induced-fit binding mechanism. We derive general expressions that specify how the overall catalytic rate of the enzymes depends on the rates for binding, for the conformational changes, and for the chemical reaction. Based on these expressions, we analyze the effect of mutations that mainly shift the conformational equilibrium on catalysis and inhibition. If the overall catalytic rate is limited by product unbinding, we find that mutations that destabilize the closed conformation relative to the open conformation increase the catalytic rate in the presence of inhibitors by a factor exp(ddG/RT) where ddG is the mutation-induced shift of the free-energy difference between the conformations. This increase in the catalytic rate due to changes in the conformational equilibrium is independent of the inhibitor molecule and, thus, may help to understand how non-active-site mutations can contribute to the multi-drug-resistance that has been observed for the HIV-1 protease. A comparison to experimental data for the non-active-site mutation L90M of the HIV-1 protease indicates that the mutation slightly destabilizes the closed conformation of the enzyme.

q-bio.BM↗

arXiv2012

Conformational selection and induced changes along the catalytic cycle of E. coli DHFR

Protein function often involves changes between different conformations. Central questions are how these conformational changes are coupled to the binding or catalytic processes during which they occur, and how they affect the catalytic rates of enzymes. An important model system is the enzyme dihydrofolate reductase (DHFR) from E. coli, which exhibits characteristic conformational changes of the active-site loop during the catalytic step and during unbinding of the product. In this article, we present a general kinetic framework that can be used (1) to identify the ordering of events in the coupling of conformational changes, binding and catalysis and (2) to determine the rates of the substeps of coupled processes from a combined analysis of NMR R2 relaxation dispersion experiments and traditional enzyme kinetics measurements. We apply this framework to E. coli DHFR and find that the conformational change during product unbinding follows a conformational-selection mechanism, i.e. the conformational change occurs predominantly prior to unbinding. The conformational change during the catalytic step, in contrast, is an induced change, i.e. the change occurs after the chemical reaction. We propose that the reason for these conformational changes, which are absent in human and other vertebrate DHFRs, is robustness of the catalytic rate against large pH variations and changes to substrate/product concentrations in E. coli.

q-bio.BM↗

arXiv2010

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.

cond-mat.soft↗