arXiv subjects

Thomas R. Weikl

Publications and source records attributed to Thomas R. Weikl.

At least 37 records · Page 2Linked to original sources

arXiv2009

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.

cond-mat.stat-mech↗

arXiv2009

Adhesion of membranes via receptor-ligand complexes: Domain formation, binding cooperativity, and active processes

Cell membranes interact via anchored receptor and ligand molecules. Central questions on cell adhesion concern the binding affinity of these membrane-anchored molecules, the mechanisms leading to the receptor-ligand domains observed during adhesion, and the role of cytoskeletal and other active processes. In this review, these questions are addressed from a theoretical perspective. We focus on models in which the membranes are described as elastic sheets, and the receptors and ligands as anchored molecules. In these models, the thermal membrane roughness on the nanometer scale leads to a cooperative binding of anchored receptor and ligand molecules, since the receptor-ligand binding smoothens out the membranes and facilitates the formation of additional bonds. Patterns of receptor domains observed in Monte Carlo simulations point towards a joint role of spontaneous and active processes in cell adhesion. The interactions mediated by the receptors and ligand molecules can be characterized by effective membrane adhesion potentials that depend on the concentrations and binding energies of the molecules.

cond-mat.soft↗

arXiv2009

Binding cooperativity of membrane adhesion receptors

The adhesion of cells is mediated by receptors and ligands anchored in apposing membranes. A central question is how to characterize the binding affinity of these membrane-anchored molecules. For soluble molecules, the binding affinity is typically quantified by the binding equilibrium constant K3D in the linear relation [RL] = K3D [R][L] between the volume concentration [RL] of bound complexes and the volume concentrations [R] and [L] of unbound molecules. For membrane-anchored molecules, it is often assumed by analogy that the area concentration of bound complexes [RL] is proportional to the product [R][L] of the area concentrations for the unbound receptor and ligand molecules. We show here (i) that this analogy is only valid for two planar membranes immobilized on rigid surfaces, and (ii) that the thermal roughness of flexible membranes leads to cooperative binding of receptors and ligands. In the case of flexible membranes, the area concentration [RL] of receptor-ligand bonds is proportional to the square of [R][L] for typical lengths and concentrations of receptors and ligands in cell adhesion zones. The cooperative binding helps to understand why different experimental methods for measuring the binding affinity of membrane-anchored molecules have led to values differing by several orders of magnitude.

cond-mat.soft↗

arXiv2009

Transition states in protein folding

The folding dynamics of small single-domain proteins is a current focus of simulations and experiments. Many of these proteins are 'two-state folders', i.e. proteins that fold rather directly from the denatured state to the native state, without populating metastable intermediate states. A central question is how to characterize the instable, partially folded conformations of two-state proteins, in particular the rate-limiting transition-state conformations between the denatured and the native state. These partially folded conformations are short-lived and cannot be observed directly in experiments. However, experimental data from detailed mutational analyses of the folding dynamics provide indirect access to transition states. The interpretation of these data, in particular the reconstruction of transition-state conformations, requires simulation and modeling. The traditional interpretation of the mutational data aims to reconstruct the degree of structure formation of individual residues in the transition state, while a novel interpretation aims at degrees of structure formation of cooperative substructures such as alpha-helices and beta-hairpins. By splitting up mutation-induced free energy changes into secondary and tertiary structural components, the novel interpretation resolves some of the inconsistencies of the traditional interpretation.

q-bio.BM↗

arXiv2008

Effective surface interactions mediated by adhesive particles

In biomimetic and biological systems, interactions between surfaces are often mediated by adhesive molecules, nanoparticles, or colloids dispersed in the surrounding solution. We present here a general, statistical-mechanical model for two surfaces that interact via adhesive particles. The effective, particle-mediated interaction potential of the surfaces is obtained by integrating over the particles' degrees of freedom in the partition function. Interestingly, the effective adhesion energy of the surfaces exhibits a maximum at intermediate particle concentrations, and is considerably smaller both at low and high concentrations. The effective adhesion energy corresponds to a minimum in the interaction potential at surface separations slightly larger than the particle diameter, while a secondary minimum at surface contact reflects depletion interactions. Our results can be generalized to surfaces with specific receptors for solute particles, and have direct implications for the adhesion of biomembranes and for phase transitions in colloidal systems.

cond-mat.soft↗

arXiv2008

Selected-fit versus induced-fit protein binding: Kinetic differences and mutational analysis

The binding of a ligand molecule to a protein is often accompanied by conformational changes of the protein. A central question is whether the ligand induces the conformational change (induced-fit), or rather selects and stabilizes a complementary conformation from a pre-existing equilibrium of ground and excited states of the protein (selected-fit). We consider here the binding kinetics in a simple four-state model of ligand-protein binding. In this model, the protein has two conformations, which can both bind the ligand. The first conformation is the ground state of the protein when the ligand is off, and the second conformation is the ground state when the ligand is bound. The induced-fit mechanism corresponds to ligand binding in the unbound ground state, and the selected-fit mechanism to ligand binding in the excited state. We find a simple, characteristic difference between the on- and off-rates in the two mechanisms if the conformational relaxation into the ground states is fast. In the case of selected-fit binding, the on-rate depends on the conformational equilibrium constant, while the off-rate is independent. In the case of induced-fit binding, in contrast, the off-rate depends on the conformational equilibrium, while the on-rate is independent. Whether a protein binds a ligand via selected-fit or induced-fit thus may be revealed by mutations far from the protein's binding pocket, or other "perturbations" that only affect the conformational equilibrium. In the case of selected-fit, such mutations will only change the on-rate, and in the case of induced-fit, only the off-rate.

q-bio.BM↗

arXiv2008

Stable patterns of membrane domains at corrugated substrates

Multi-component membranes such as ternary mixtures of lipids and cholesterol can exhibit coexistence regions between two liquid phases. When such membranes adhere to a corrugated substrate, the phase separation process strongly depends on the interplay between substrate topography, bending rigidities, and line tension of the membrane domains as we show theoretically via energy minimization and Monte Carlo simulations. For sufficiently large bending rigidity contrast between the two membrane phases, the corrugated substrate truncates the phase separation process and leads to a stable pattern of membrane domains. Our theory is consistent with recent experimental observations and provides a possible control mechanism for domain patterns in biological membranes.

cond-mat.soft↗

arXiv2007

Membrane adhesion and domain formation

We review theoretical results for the adhesion-induced phase behavior of biomembranes. The focus is on models in which the membranes are represented as discretized elastic sheets with embedded adhesion molecules. We present several mechanism that lead to the formation of domains during adhesion, and discuss the time-dependent evolution of domain patterns obtained in Monte-Carlo simulations. The simulated pattern dynamics has striking similarities to the pattern evolution observed during T cell adhesion.

cond-mat.soft↗

arXiv2007

Loop-closure principles in protein folding

Simple theoretical concepts and models have been helpful to understand the folding rates and routes of single-domain proteins. As reviewed in this article, a physical principle that appears to underly these models is loop closure.

q-bio.BM↗

arXiv2007

Transition states in protein folding kinetics: Modeling Phi-values of small beta-sheet proteins

Small single-domain proteins often exhibit only a single free-energy barrier, or transition state, between the denatured and the native state. The folding kinetics of these proteins is usually explored via mutational analysis. A central question is which structural information on the transition state can be derived from the mutational data. In this article, we model and structurally interpret mutational Phi-values for two small beta-sheet proteins, the PIN and the FBP WW domain. The native structure of these WW domains comprises two beta-hairpins that form a three-stranded beta-sheet. In our model, we assume that the transition state consists of two conformations in which either one of the hairpins is formed. Such a transition state has been recently observed in Molecular Dynamics folding-unfolding simulations of a small designed three-stranded beta-sheet protein. We obtain good agreement with the experimental data (i) by splitting up the mutation-induced free-energy changes into terms for the two hairpins and for the small hydrophobic core of the proteins, and (ii) by fitting a single parameter, the relative degree to which hairpin 1 and 2 are formed in the transition state. The model helps to understand how mutations affect the folding kinetics of WW domains, and captures also negative Phi-values that have been difficult to interpret.

q-bio.BM↗

arXiv2006

Membrane adhesion via competing receptor/ligand bonds

The adhesion of biological membranes is controlled by various types of receptor and ligand molecules. In this letter, we present a statistical-mechanical model for membranes that interact via receptor/ligand bonds of two different lengths. We show that the equilibrium phase behavior of the membranes is governed by an effective double-well potential. The depths of the two potential wells depend on the concentrations and binding energies of the receptors and ligands. The membranes are unbound for small, and bound for larger potential depths. In the bound state, the length mismatch of the receptor/ligand bonds can lead to lateral phase separation. We derive explicit scaling laws for the critical points of unbinding and phase separation, and determine the prefactors by comparison with Monte Carlo results.

cond-mat.soft↗

arXiv2006

Transition States in Protein Folding Kinetics: The Structural Interpretation of Phi-values

Phi-values are experimental measures of the effects of mutations on the folding kinetics of a protein. A central question is which structural information Phi-values contain about the transition state of folding. Traditionally, a Phi-value is interpreted as the 'nativeness' of a mutated residue in the transition state. However, this interpretation is often problematic because it assumes a linear relation between the nativeness of the residue and its free-energy contribution. We present here a better structural interpretation of Phi-values for mutations within a given helix. Our interpretation is based on a simple physical model that distinguishes between secondary and tertiary free-energy contributions of helical residues. From a linear fit of our model to the experimental data, we obtain two structural parameters: the extent of helix formation in the transition state, and the nativeness of tertiary interactions in the transition state. We apply our model to all proteins with well-characterized helices for which more than 10 Phi-values are available: protein A, CI2, and protein L. The model captures nonclassical Phi-values <0 or >1 in these helices, and explains how different mutations at a given site can lead to different Phi-values.

q-bio.BM↗

arXiv2006

Substructural cooperativity and parallel versus sequential events during protein unfolding

According to the 'old view', proteins fold along well-defined sequential pathways, whereas the 'new view' sees protein folding as a highly parallel stochastic process on funnel-shaped energy landscapes. We have analyzed parallel and sequential processes on a large number of Molecular Dynamics unfolding trajectories of the protein CI2 at high temperatures. Using rigorous statistical measures, we quantify the degree of sequentiality on two structural levels. The unfolding process is highly parallel on the microstructural level of individual contacts. On a coarser, macrostructural level of contact clusters, characteristic parallel and sequential events emerge. These characteristic events can be understood from loop-closure dependencies between the contact clusters. A correlation analysis of the unfolding times of the contacts reveals a high degree of substructural cooperativity within the contact clusters.

q-bio.BM↗

arXiv2006

A simple measure of native-state topology and chain connectivity predicts the folding rates of two-state proteins with and without crosslinks

The folding rates of two-state proteins have been found to correlate with simple measures of native-state topology. The most prominent among these measures is the relative contact order (CO), which is the average CO or 'localness' of all contacts in the native protein structure, divided by the chain length. Here, we test whether such measures can be generalized to capture the effect of chain crosslinks on the folding rate. Crosslinks change the chain connectivity and therefore also the localness of some of the the native contacts. These changes in localness can be taken into account by the graph-theoretical concept of effective contact order (ECO). The relative ECO, however, the natural extension of the relative CO for proteins with crosslinks, overestimates the changes in the folding rates caused by crosslinks. We suggest here a novel measure of native-state topology, the relative logCO, and its natural extension, the relative logECO. The relative logCO is the average value for the logarithm of the CO of all contacts, divided by the logarithm of the chain length. The relative log(E)CO reproduces the folding rates of a set of 26 two-state proteins without crosslinks with essentially the same high correlation coefficient as the relative CO. In addition, it also captures the folding rates of 8 two-state proteins with crosslinks.

q-bio.BM↗

arXiv2005

Adhesion of membranes via actively switched receptors

We consider a theoretical model for membranes with adhesive receptors, or stickers, that are actively switched between two conformational states. In their 'on'-state, the stickers bind to ligands in an apposing membrane, whereas they do not interact with the ligands in their 'off'-state. We show that the adhesiveness of the membranes depends sensitively on the rates of the conformational switching process. This dependence is reflected in a resonance at intermediate switching rates, which can lead to large membrane separations and unbinding. Our results may provide insights into novel mechanisms for the controlled adhesion of biological or biomimetic membranes.

cond-mat.soft↗

arXiv2005

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.

q-bio.BM↗

arXiv2005

Loop-closure events during protein folding: Rationalizing the shape of Phi-value distributions

In the past years, the folding kinetics of many small single-domain proteins has been characterized by mutational Phi-value analysis. In this article, a simple, essentially parameter-free model is introduced which derives folding routes from native structures by minimizing the entropic loop-closure cost during folding. The model predicts characteristic folding sequences of structural elements such as helices and beta-strand pairings. Based on few simple rules, the kinetic impact of these structural elements is estimated from the routes and compared to average experimental Phi-values for the helices and strands of 15 small, well-characterized proteins. The comparison leads on average to a correlation coefficient of 0.62 for all proteins with polarized Phi-value distributions, and 0.74 if distributions with negative average Phi-values are excluded. The diffuse Phi-value distributions of the remaining proteins are reproduced correctly. The model shows that Phi-value distributions, averaged over secondary structural elements, can often be traced back to entropic loop-closure events, but also indicates energetic preferences in the case of a few proteins governed by parallel folding processes.

q-bio.BM↗

arXiv2004

Mechanisms of pattern formation during T cell adhesion

T cells form intriguing patterns during adhesion to antigen-presenting cells. The patterns at the cell-cell contact zone are composed of two types of domains, which either contain short TCR/MHCp receptor-ligand complexes or the longer LFA-1/ICAM-1 complexes. The final pattern consists of a central TCR/MHCp domain surrounded by a ring-shaped LFA-1/ICAM-1 domain, while the characteristic pattern formed at intermediate times is inverted with TCR/MHCp complexes at the periphery of the contact zone and LFA-1/ICAM-1 complexes in the center. In this article, we present a statistical-mechanical model of cell adhesion and propose a novel mechanism for the T cell pattern formation. Our mechanism for the formation of the intermediate inverted pattern is based (i) on the initial nucleation of numerous TCR/MHCp microdomains, and (ii) on the diffusion of free receptors and ligands into the contact zone. Due to this inward diffusion, TCR/MHCp microdomains at the rim of the contact zone grow faster and form an intermediate peripheral ring for sufficiently large TCR/MHCp concentrations. In agreement with experiments, we find that the formation of the final pattern with a central TCR/MHCp domain requires active cytoskeletal transport processes. Without active transport, the intermediate inverted pattern seems to be metastable in our model, which might explain patterns observed during natural killer (NK) cell adhesion. At smaller TCR/MHCp complex concentrations, we observe a different regime of pattern formation with intermediate multifocal TCR/MHCp patterns which resemble experimental patterns found during thymozyte adhesion.

q-bio.SC↗