Juraj Szavits-Nossan

Inherent Variability in the Kinetics of Autocatalytic Protein Self-Assembly

In small volumes, the kinetics of filamentous protein self-assembly is expected to show significant variability, arising from intrinsic molecular noise. This is not accounted for in existing deterministic models. We introduce a simple stochastic model including nucleation and autocatalytic growth via elongation and fragmentation, which allows us to predict the effects of molecular noise on the kinetics of autocatalytic self-assembly. We derive an analytic expression for the lag-time distribution, which agrees well with experimental results for the fibrillation of bovine insulin. Our expression decomposes the lag-time variability into contributions from primary nucleation and autocatalytic growth and reveals how each of these scales with the key kinetic parameters. Our analysis shows that significant lag-time variability can arise from both primary nucleation and from autocatalytic growth and should provide a way to extract mechanistic information on early-stage aggregation from small-volume experiments.

Constraint-driven condensation in large fluctuations of linear statistics.

Condensation is the phenomenon whereby one of a sum of random variables contributes a finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical systems such as coalescence in granular media, jamming in traffic, and gelation in networks. We show here that the same condensation scenario, which normally happens only if the underlying probability distribution has tails heavier than exponential, can occur for light-tailed distributions in the presence of additional constraints. We demonstrate this phenomenon on the sample variance, whose probability distribution conditioned on the particular value of the sample mean undergoes a phase transition. The transition is manifested by a change in behavior of the large deviation rate function.

Scaling properties of the asymmetric exclusion process with long-range hopping.

The exclusion process in which particles may jump any distance l > or = 1 with the probability that decays as l;{-(1+sigma)} is studied from the coarse-grained equation for density profile in the limit when the lattice spacing goes to zero. For 1<sigma<2 , the usual diffusion term of this equation is replaced by the fractional one, which affects dynamical-scaling properties of the late-time approach to the stationary state. When applied to an open system with totally asymmetric hopping, this approach gives two results: First, it accounts for the sigma -dependent exponent that characterizes the algebraic decay of a density profile in the maximum-current phase for 1<sigma<2 , and second, it shows that in this region of sigma the exponent is of the mean-field type.

Totally asymmetric exclusion process with long-range hopping.

Generalization of the one-dimensional totally asymmetric exclusion process (TASEP) with open boundary conditions in which particles are allowed to jump l sites ahead with the probability pl approximately 1l/sigma+1 is studied by Monte Carlo simulations and the domain-wall approach. For sigma>1 the standard TASEP phase diagram is recovered, but the density profiles display additional features when 1<sigma<2. At the first-order transition line, the domain wall is localized and phase separation is observed. In the maximum-current phase the profile has an algebraic decay with a sigma -dependent exponent. Within the sigma<or=1 regime, where the transitions are found to be absent, analytical results in the continuum mean-field approximation are derived in the limit sigma=-1.

Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges

We study stochastic processes in which the trajectories are constrained so that the process realises a large deviation of the unconstrained process. In particular we consider stochastic bridges and the question of inequivalence of path ensembles between the microcanonical ensemble, in which the end points of the trajectory are constrained, and the canonical or s ensemble in which a bias or tilt is introduced into the process. We show how ensemble inequivalence can be manifested by the phenomenon of temporal condensation in which the large deviation is realised in a vanishing fraction of the duration (for long durations). For diffusion processes we find that condensation happens whenever the process is subject to a confining potential, such as for the Ornstein–Uhlenbeck process, but not in the borderline case of dry friction in which there is partial ensemble equivalence. We also discuss continuous-space, discrete-time random walks for which in the case of a heavy tailed step-size distribution it is known that the large deviation may be achieved in a single step of the walk. Finally we consider possible effects of several constraints on the process and in particular give an alternative explanation of the interaction-driven condensation in terms of constrained Brownian excursions.

Condensation transition in joint large deviations of linear statistics

Real space condensation is known to occur in stochastic models of mass transport in the regime in which the globally conserved mass density is greater than a critical value. It has been shown within models with factorised stationary states that the condensation can be understood in terms of sums of independent and identically distributed random variables: these exhibit condensation when they are conditioned to a large deviation of their sum. It is well understood that the condensation, whereby one of the random variables contributes a finite fraction to the sum, occurs only if the underlying probability distribution (modulo exponential) is heavy-tailed, i.e. decaying slower than exponential. Here we study a similar phenomenon in which condensation is exhibited for non-heavy-tailed distributions, provided random variables are additionally conditioned on a large deviation of certain linear statistics. We provide a detailed theoretical analysis explaining the phenomenon, which is supported by Monte Carlo simulations (for the case where the additional constraint is the sample variance) and demonstrated in several physical systems. Our results suggest that the condensation is a generic phenomenon that pertains to both typical and rare events.

A Kinetic Study of Ovalbumin Fibril Formation: The Importance of Fragmentation and End-Joining

The ability to control the morphologies of biomolecular aggregates is a central objective in the study of self-assembly processes. The development of predictive models offers the surest route for gaining such control. Under the right conditions, proteins will self-assemble into fibers that may rearrange themselves even further to form diverse structures, including the formation of closed loops. In this study, chicken egg white ovalbumin is used as a model for the study of fibril loops. By monitoring the kinetics of self-assembly, we demonstrate that loop formation is a consequence of end-to-end association between protein fibrils. A model of fibril formation kinetics, including end-joining, is developed and solved, showing that end-joining has a distinct effect on the growth of fibrillar mass density (which can be measured experimentally), establishing a link between self-assembly kinetics and the underlying growth mechanism. These results will enable experimentalists to infer fibrillar morphologies from an appropriate analysis of self-assembly kinetic data.

Conditioned random walks and interaction-driven condensation

We consider a discrete-time continuous-space random walk under the constraints that the number of returns to the origin (local time) and the total area under the walk are fixed. We first compute the joint probability of an excursion having area

Disordered exclusion process revisited: some exact results in the low-current regime

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Absence of phase coexistence in disordered exclusion processes with bypassing

and returning to the origin for the first time after time