45 research outputs found
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
Line Tension and Stability of Domains in Cell-Adhesion Zones Mediated by Long and Short Receptor-Ligand Complexes
Submicron scale domains of membrane-anchored receptors play an important role in cell signaling. Central questions concern the stability of these microdomains, and the mechanisms leading to the domain formation. In immune-cell adhesion zones, microdomains of short receptor-ligand complexes form next to domains of significantly longer receptor-ligand complexes. The length mismatch between the receptor-ligand complexes leads to membrane deformations and has been suggested as a possible cause of the domain formation. The domain formation is a nucleation and growth process that depends on the line tension and free energy of the domains. Using a combination of analytical calculations and Monte Carlo simulations, we derive here general expressions for the line tension between domains of long and short receptor-ligand complexes and for the adhesion free energy of the domains. We argue that the length mismatch of receptor-ligand complexes alone is sufficient to drive the domain formation, and obtain submicron-scale minimum sizes for stable domains that are consistent with the domain sizes observed during immune-cell adhesion
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.Comment: to appear in Physical Review Letter
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.Comment: Review article, 13 pages, 9 figures, to appear in Soft Matte
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.Comment: 9 pages, 4 figures; to appear in Soft Matte
Drgania własne belki na stochastycznym dwuwarstwowym podłożu o znacznie różniących się grubościach
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.
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
Membrane-Mediated Cooperative Interactions of CD47 and SIRP<i>α</i>
The specific binding of the ubiquitous ‘marker of self’ protein CD47 to the SIRPα protein anchored in the macrophage plasma membrane results in the inhibition of the engulfment of ‘self’ cells by macrophages and thus constitutes a key checkpoint of our innate immune system. Consequently, the CD47–SIRPα protein complex has been recognized as a potential therapeutic target in cancer and inflammation. Here, we introduce a lattice-based mesoscale model for the biomimetic system studied recently in fluorescence microscopy experiments where GFP-tagged CD47 proteins on giant plasma membrane vesicles bind to SIRPα proteins immobilized on a surface. Computer simulations of the lattice-based mesoscale model allow us to study the biomimetic system on multiple length scales, ranging from single nanometers to several micrometers and simultaneously keep track of single CD47–SIRPα binding and unbinding events. Our simulations not only reproduce data from the fluorescence microscopy experiments but also are consistent with results of several other experiments, which validates our numerical approach. In addition, our simulations yield quantitative predictions on the magnitude and range of effective, membrane-mediated attraction between CD47–SIRPα complexes. Such detailed information on CD47–SIRPα interactions cannot be obtained currently from experiments alone. Our simulation results thus extend the present understanding of cooperative effects in CD47–SIRPα interactions and may have an influence on the advancement of new cancer treatments