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.Comment: to appear in Journal of Statistical Mechanics: Theory and Experimen

Phase Transitions in Multicomponent String Model

We propose a one-dimensional model of a string decorated with adhesion molecules (stickers) to mimic multicomponent membranes in restricted geometries. The string is bounded by two parallel walls and it interacts with one of them by short range attractive forces while the stickers are attracted by the other wall. The exact solution of the model in the case of infinite wall separation predicts both continuous and discontinuous transitions between phases characterised by low and high concentration of stickers on the string. Our model exhibits also coexistence of these two phases, similarly to models of multicomponent membranes.Comment: letter, 8 pages, 3 figure

Cooperative stabilization of close-contact zones leads to sensitivity and selectivity in T-cell recognition

T cells are sensitive to 1 to 10 foreign-peptide-MHC complexes among a vast majority of self-peptide-MHC complexes, and discriminate selectively between peptide-MHC complexes that differ not much in their binding affinity to T-cell receptors (TCRs). Quantitative models that aim to explain this sensitivity and selectivity largely focus on single TCR/peptide-MHC complexes, but T cell adhesion involves a multitude of different complexes. In this article, we demonstrate in a three-dimensional computational model of T-cell adhesion that the cooperative stabilization of close-contact zones is sensitive to one to three foreign-peptide-MHC complexes and occurs at a rather sharp threshold affinity of these complexes, which implies selectivity. In these close-contact zones with lateral extensions of hundred to several hundred nanometers, few TCR/foreign-peptide-MHC complexes and many TCR/self-peptide-MHC complexes are segregated from LFA-1/ICAM-1 complexes that form at larger membrane separations. Previous high-resolution microscopy experiments indicate that the sensitivity and selectivity in the formation of closed-contact zones reported here are relevant for T-cell recognition, because the stabilization of close-contact zones by foreign, agonist peptide-MHC complexes precedes T-cell signaling and activation in the experiments

Structural variability and concerted motions of the T cell receptor - CD3 complex

We investigate the structural and orientational variability of the membrane-embedded T cell receptor (TCR) - CD3 complex in extensive atomistic molecular dynamics simulations based on the recent cryo-EM structure determined by Dong et al. (2019). We find that the TCR extracellular (EC) domain is highly variable in its orientation by attaining tilt angles relative to the membrane normal that range from 15° to 55°. The tilt angle of the TCR EC domain is both coupled to a rotation of the domain and to characteristic changes throughout the TCR - CD3 complex, in particular in the EC interactions of the C_FG loop of the TCR, as well as in the orientation of transmembrane helices. The concerted motions of the membrane-embedded TCR - CD3 complex revealed in our simulations provide atomistic insights on conformational changes of the complex in response to tilt-inducing forces on antigen-bound TCRs

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.Comment: 23 pages, 6 figure

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.Comment: 6 pages, 5 figures; to appear in Europhys. Let

Natural vibrations of a beam on stochastic two-layered subsoil with significantly different thickness

W artykule analizowano wpływ zmiany modułu Younga warstw podłoża gruntowego na częstości drgań własnych układu belka-dwuwarstwowe podłoże przy założeniu, że pierwsza warstwa podłoża jest znacznie cieńsza i sztywniejsza od drugiej. Taka nietypowa sytuacja stwarza czasem szczególne trudności w geotechnice. Obliczenia przeprowadzono najpierw w ujęciu deterministycznym, a następnie stochastycznym. W analizie stochastycznej założono przestrzenną korelację modułu Younga gruntu po długości każdej z warstw przyjmując dwa stopnie korelacji, korelację pełną lub jej brak. W obliczeniach uwzględniono pełną korelację modułu Younga gruntu pomiędzy warstwami, co wynika z badań, które autorzy zamieścili we wcześniejszej pracy. Do rozwiązania stochastycznego zagadnienia własnego zastosowano metodę Monte Carlo łącznie z metodą elementów skończonych (MES). Prezentowana analiza jest kontynuacją problematyki przedstawionej w poprzednich pracach autorów.In this paper the influence of variability of Young modulus of the subsoil layers on the natural frequency of the beam-two-layered subsoil system was analyzed. Assuming the first layer was thinner and more rigid then the second one (10 and 20 times). The calculations were made by using deterministic and stochastic approach. In the stochastic approach, the spatial correlation of Young modulus of the subsoil along the length of both layers was taken into account. Two cases of the correlation were considered, i.e. without and with full correlation. Regarding the results of the authors’ research which were published in the previous article, in the calculations the full stochastic correlation of Young modulus of subsoil between both layers was taken into account. In order to solve the stochastic eigenvalue problem, Monte Carlo simulation techniques with Finite Element Method (FEM) were used. The present analysis is a continuation research demonstrated in the authors’ previous papers