Force Modulating Dynamic Disorder: Physical Theory of Catch-slip bond Transitions in Receptor-Ligand Forced Dissociation Experiments

Recently experiments showed that some adhesive receptor-ligand complexes increase their lifetimes when they are stretched by mechanical force, while the force increase beyond some thresholds their lifetimes decrease. Several specific chemical kinetic models have been developed to explain the intriguing transitions from the "catch-bonds" to the "slip-bonds". In this work we suggest that the counterintuitive forced dissociation of the complexes is a typical rate process with dynamic disorder. An uniform one-dimension force modulating Agmon-Hopfield model is used to quantitatively describe the transitions observed in the single bond P-selctin glycoprotein ligand 1(PSGL-1)$-$P-selectin forced dissociation experiments, which were respectively carried out on the constant force [Marshall, {\it et al.}, (2003) Nature {\bf 423}, 190-193] and the force steady- or jump-ramp [Evans {\it et al.}, (2004) Proc. Natl. Acad. Sci. USA {\bf 98}, 11281-11286] modes. Our calculation shows that the novel catch-slip bond transition arises from a competition of the two components of external applied force along the dissociation reaction coordinate and the complex conformational coordinate: the former accelerates the dissociation by lowering the height of the energy barrier between the bound and free states (slip), while the later stabilizes the complex by dragging the system to the higher barrier height (catch).Comment: 8 pages, 3 figures, submitte

Quenched large deviations for multidimensional random walk in random environment with holding times

We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and the laws of the holding times are randomly distributed over the integer lattice. Our main result is a quenched large deviation principle for the position of the random walk. The rate function is given by the Legendre transform of the so-called Lyapunov exponents for the Laplace transform of the first passage time. By using this representation, we derive some asymptotics of the rate function in some special cases.Comment: This is the corrected version of the paper. 24 page

Effect of Poisson ratio on cellular structure formation

Mechanically active cells in soft media act as force dipoles. The resulting elastic interactions are long-ranged and favor the formation of strings. We show analytically that due to screening, the effective interaction between strings decays exponentially, with a decay length determined only by geometry. Both for disordered and ordered arrangements of cells, we predict novel phase transitions from paraelastic to ferroelastic and anti-ferroelastic phases as a function of Poisson ratio.Comment: 4 pages, Revtex, 4 Postscript figures include

Moderate deviation principle for ergodic Markov chain. Lipschitz summands

For ${1/2}<\alpha<1$, we propose the MDP analysis for family $$S^\alpha_n=\frac{1}{n^\alpha}\sum_{i=1}^nH(X_{i-1}), n\ge 1,$$ where $(X_n)_{n\ge 0}$ be a homogeneous ergodic Markov chain, $X_n\in \mathbb{R}^d$, when the spectrum of operator $P_x$ is continuous. The vector-valued function $H$ is not assumed to be bounded but the Lipschitz continuity of $H$ is required. The main helpful tools in our approach are Poisson's equation and Stochastic Exponential; the first enables to replace the original family by $\frac{1}{n^\alpha}M_n$ with a martingale $M_n$ while the second to avoid the direct Laplace transform analysis

A Two-populations Ising model on diluted Random Graphs

We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the existence of a phase transition at a value of the inter-groups interaction coupling $J_{12}^C$ which depends algebraically on the dilution of the graph and on the relative width of the two populations, as explained by means of scaling arguments. We also measure the critical exponents, which are consistent with those of the Curie-Weiss model, hence suggesting a wide robustness of the universality class.Comment: 11 pages, 4 figure

Discrete-time classical and quantum Markovian evolutions: Maximum entropy problems on path space

The theory of Schroedinger bridges for diffusion processes is extended to classical and quantum discrete-time Markovian evolutions. The solution of the path space maximum entropy problems is obtained from the a priori model in both cases via a suitable multiplicative functional transformation. In the quantum case, nonequilibrium time reversal of quantum channels is discussed and space-time harmonic processes are introduced.Comment: 34 page

Viscous Fingering-like Instability of Cell Fragments

We present a novel flow instability that can arise in thin films of cytoskeletal fluids if the friction with the substrate on which the film lies is sufficiently strong. We consider a two dimensional, membrane-bound fragment containing actin filaments that is perturbed from its initially circular state, where actin polymerizes at the edge and flows radially inward while depolymerizing in the fragment. Performing a linear stability analysis of the initial state due to perturbations of the fragment boundary, we find, in the limit of very large friction, that the perturbed actin velocity and pressure fields obey the very same laws governing the viscous fingering instability of an interface between immiscible fluids in a Hele-Shaw cell. A feature of this instability that is remarkable in the context of cell motility, is that its existence is independent of the strength of the interaction between cytoskeletal filaments and myosin motors, and moreover that it is completely driven by the free energy of actin polymerization at the fragment edge

Dynamical fluctuations for semi-Markov processes

We develop an Onsager-Machlup-type theory for nonequilibrium semi-Markov processes. Our main result is an exact large time asymptotics for the joint probability of the occupation times and the currents in the system, establishing some generic large deviation structures. We discuss in detail how the nonequilibrium driving and the non-exponential waiting time distribution influence the occupation-current statistics. The violation of the Markov condition is reflected in the emergence of a new type of nonlocality in the fluctuations. Explicit solutions are obtained for some examples of driven random walks on the ring.Comment: Minor changes, accepted for publication in Journal of Physics

Random Planar Lattices and Integrated SuperBrownian Excursion

In this paper, a surprising connection is described between a specific brand of random lattices, namely planar quadrangulations, and Aldous' Integrated SuperBrownian Excursion (ISE). As a consequence, the radius r_n of a random quadrangulation with n faces is shown to converge, up to scaling, to the width r=R-L of the support of the one-dimensional ISE. More generally the distribution of distances to a random vertex in a random quadrangulation is described in its scaled limit by the random measure ISE shifted to set the minimum of its support in zero. The first combinatorial ingredient is an encoding of quadrangulations by trees embedded in the positive half-line, reminiscent of Cori and Vauquelin's well labelled trees. The second step relates these trees to embedded (discrete) trees in the sense of Aldous, via the conjugation of tree principle, an analogue for trees of Vervaat's construction of the Brownian excursion from the bridge. From probability theory, we need a new result of independent interest: the weak convergence of the encoding of a random embedded plane tree by two contour walks to the Brownian snake description of ISE. Our results suggest the existence of a Continuum Random Map describing in term of ISE the scaled limit of the dynamical triangulations considered in two-dimensional pure quantum gravity.Comment: 44 pages, 22 figures. Slides and extended abstract version are available at http://www.loria.fr/~schaeffe/Pub/Diameter/ and http://www.iecn.u-nancy.fr/~chassain

The Non--Ergodicity Threshold: Time Scale for Magnetic Reversal

We prove the existence of a non-ergodicity threshold for an anisotropic classical Heisenberg model with all-to-all couplings. Below the threshold, the energy surface is disconnected in two components with positive and negative magnetizations respectively. Above, in a fully chaotic regime, magnetization changes sign in a stochastic way and its behavior can be fully characterized by an average magnetization reversal time. We show that statistical mechanics predicts a phase--transition at an energy higher than the non-ergodicity threshold. We assess the dynamical relevance of the latter for finite systems through numerical simulations and analytical calculations. In particular, the time scale for magnetic reversal diverges as a power law at the ergodicity threshold with a size-dependent exponent, which could be a signature of the phenomenon.Comment: 4 pages 4 figure