Stochastic self-assembly of incommensurate clusters

We examine the classic problem of homogeneous nucleation and growth by deriving and analyzing a fully discrete stochastic master equation. Upon comparison with results obtained from the corresponding mean-field Becker-D\"{o}ring equations we find striking differences between the two corresponding equilibrium mean cluster concentrations. These discrepancies depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass incommensurability arises, a single remainder particle can "emulsify" or "disperse" the system by significantly broadening the mean cluster size distribution. This finite-sized broadening effect is periodic in the total mass of the system and can arise even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. For such finite ratios we show that homogeneous nucleation in the limit of large, closed systems is not accurately described by classical mean-field mass-action approaches.Comment: 5 pages, 4 figures, 1 tabl

Fluctuations in Polymer Translocation

We investigate a model of chaperone-assisted polymer translocation through a nanopore in a membrane. Translocation is driven by irreversible random sequential absorption of chaperone proteins that bind to the polymer on one side of the membrane. The proteins are larger than the pore and hence the backward motion of the polymer is inhibited. This mechanism rectifies Brownian fluctuations and results in an effective force that drags the polymer in a preferred direction. The translocated polymer undergoes an effective biased random walk and we compute the corresponding diffusion constant. Our methods allow us to determine the large deviation function which, in addition to velocity and diffusion constant, contains the entire statistics of the translocated length.Comment: 20 pages, 6 figure

TCR cross-reactivity and allorecognition: new insights into the immunogenetics of allorecognition

Alloreactive T cells are core mediators of graft rejection and are a potent barrier to transplantation tolerance. It was previously unclear how T cells educated in the recipient thymus could recognize allogeneic HLA molecules. Recently it was shown that both naïve and memory CD4+ and CD8+ T cells are frequently cross-reactive against allogeneic HLA molecules and that this allorecognition exhibits exquisite peptide and HLA specificity and is dependent on both public and private specificities of the T cell receptor. In this review we highlight new insights gained into the immunogenetics of allorecognition, with particular emphasis on how viral infection and vaccination may specifically activate allo-HLA reactive T cells. We also briefly discuss the potential for virus-specific T cell infusions to produce GvHD. The progress made in understanding the molecular basis of allograft rejection will hopefully be translated into improved allograft function and/or survival, and eventually tolerance induction

The McKean-Vlasov Equation in Finite Volume

We study the McKean--Vlasov equation on the finite tori of length scale $L$ in $d$--dimensions. We derive the necessary and sufficient conditions for the existence of a phase transition, which are based on the criteria first uncovered in \cite{GP} and \cite{KM}. Therein and in subsequent works, one finds indications pointing to critical transitions at a particular model dependent value, $\theta^{\sharp}$ of the interaction parameter. We show that the uniform density (which may be interpreted as the liquid phase) is dynamically stable for $\theta < \theta^{\sharp}$ and prove, abstractly, that a {\it critical} transition must occur at $\theta = \theta^{\sharp}$. However for this system we show that under generic conditions -- $L$ large, $d \geq 2$ and isotropic interactions -- the phase transition is in fact discontinuous and occurs at some \theta\t < \theta^{\sharp}. Finally, for H--stable, bounded interactions with discontinuous transitions we show that, with suitable scaling, the \theta\t(L) tend to a definitive non--trivial limit as $L\to\infty$

Collective motion of active Brownian particles in one dimension

We analyze a model of active Brownian particles with non-linear friction and velocity coupling in one spatial dimension. The model exhibits two modes of motion observed in biological swarms: A disordered phase with vanishing mean velocity and an ordered phase with finite mean velocity. Starting from the microscopic Langevin equations, we derive mean-field equations of the collective dynamics. We identify the fixed points of the mean-field equations corresponding to the two modes and analyze their stability with respect to the model parameters. Finally, we compare our analytical findings with numerical simulations of the microscopic model.Comment: submitted to Eur. Phys J. Special Topic

Chaperone-assisted translocation of a polymer through a nanopore

Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy $\epsilon$ between the chaperone and the chain and the chaperone concentration $N_c$ can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation probability is observed for weak binding. For a fixed chaperone concentration, the histogram of translocation time $\tau$ has a transition from long-tailed distribution to Gaussian distribution with increasing $\epsilon$. $\tau$ rapidly decreases and then almost saturates with increasing binding energy for short chain, however, it has a minimum for longer chains at lower chaperone concentration. We also show that $\tau$ has a minimum as a function of the chaperone concentration. For different $\epsilon$, a nonuniversal dependence of $\tau$ on the chain length $N$ is also observed. These results can be interpreted by characteristic entropic effects for flexible polymers induced by either crowding effect from high chaperone concentration or the intersegmental binding for the high binding energy.Comment: 10 pages, to appear in J. Am. Chem. So

Abacavir-Reactive memory T Cells are present in drug naïve individuals

Background Fifty-five percent of individuals with HLA-B*57:01 exposed to the antiretroviral drug abacavir develop a hypersensitivity reaction (HSR) that has been attributed to naïve T-cell responses to neo-antigen generated by the drug. Immunologically confirmed abacavir HSR can manifest clinically in less than 48 hours following first exposure suggesting that, at least in some cases, abacavir HSR is due to re-stimulation of a pre-existing memory T-cell population rather than priming of a high frequency naïve T-cell population. Methods To determine whether a pre-existing abacavir reactive memory T-cell population contributes to early abacavir HSR symptoms, we studied the abacavir specific naïve or memory T-cell response using HLA-B*57:01 positive HSR patients or healthy controls using ELISpot assay, intra-cellular cytokine staining and tetramer labelling. Results Abacavir reactive CD8+ T-cell responses were detected in vitro in one hundred percent of abacavir unexposed HLA-B*57:01 positive healthy donors. Abacavir-specific CD8+ T cells from such donors can be expanded from sorted memory, and sorted naïve, CD8+ T cells without need for autologous CD4+ T cells. Conclusions We propose that these pre-existing abacavir-reactive memory CD8+ T-cell responses must have been primed by earlier exposure to another foreign antigen and that these T cells cross-react with an abacavir-HLA-B*57:01-endogenous peptide ligand complex, in keeping with the model of heterologous immunity proposed in transplant rejection

Uncertainty quantification for kinetic models in socio-economic and life sciences

Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronization phenomena in biological systems and lane formation in pedestrian traffic. The construction of kinetic models describing the above processes, however, has to face the difficulty of the lack of fundamental principles since physical forces are replaced by empirical social forces. These empirical forces are typically constructed with the aim to reproduce qualitatively the observed system behaviors, like the emergence of social structures, and are at best known in terms of statistical information of the modeling parameters. For this reason the presence of random inputs characterizing the parameters uncertainty should be considered as an essential feature in the modeling process. In this survey we introduce several examples of such kinetic models, that are mathematically described by nonlinear Vlasov and Fokker--Planck equations, and present different numerical approaches for uncertainty quantification which preserve the main features of the kinetic solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic Equations

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Continuum modeling of the equilibrium and stability of animal flocks

Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where the density goes continuously to zero at a well-defined flock edge, and we discuss conditions on the model that allow for such solutions. We also demonstrate conditions under which, as the flock size increases, the interior density in our equilibria tends to an approximately uniform value. Motivated by observations of starling flocks that are relatively thin in a direction transverse to the direction of flight, we investigate the stability of infinite, planar-sheet flock equilibria. We find that long- wavelength perturbations along the sheet are unstable for the class of models that we investigate. This has the conjectured consequence that sheet-like flocks of arbitrarily large transverse extent relative to their thickness do not occur. However, we also show that our model admits approximately sheet-like, 'pancake-shaped', three-dimensional ellipsoidal equilibria with definite aspect ratios (transverse length- scale to flock thickness) determined by anisotropic perceptual/response characteristics of the flocking individuals, and we argue that these pancake-like equilibria are stable to the previously mentioned sheet instability.Comment: 37 pages, 8 figure