Fluctuation theorem for stochastic dynamics

The fluctuation theorem of Gallavotti and Cohen holds for finite systems undergoing Langevin dynamics. In such a context all non-trivial ergodic theory issues are by-passed, and the theorem takes a particularly simple form. As a particular case, we obtain a nonlinear fluctuation-dissipation theorem valid for equilibrium systems perturbed by arbitrarily strong fields.Comment: 15 pages, a section rewritte

One-particle and few-particle billiards

We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and against each other. In the one-particle case, we investigate the formation and destruction of resonance islands in (generalized) mushroom billiards, which are a recently discovered class of Hamiltonian systems with mixed regular-chaotic dynamics. In the few-particle case, we compare the dynamics in container geometries whose counterpart one-particle billiards are integrable, chaotic, and mixed. One of our findings is that two-, three-, and four-particle billiards confined to containers with integrable one-particle counterparts inherit some integrals of motion and exhibit a regular partition of phase space into ergodic components of positive measure. Therefore, the shape of a container matters not only for noninteracting particles but also for interacting particles

Evolution of collision numbers for a chaotic gas dynamics

We put forward a conjecture of recurrence for a gas of hard spheres that collide elastically in a finite volume. The dynamics consists of a sequence of instantaneous binary collisions. We study how the numbers of collisions of different pairs of particles grow as functions of time. We observe that these numbers can be represented as a time-integral of a function on the phase space. Assuming the results of the ergodic theory apply, we describe the evolution of the numbers by an effective Langevin dynamics. We use the facts that hold for these dynamics with probability one, in order to establish properties of a single trajectory of the system. We find that for any triplet of particles there will be an infinite sequence of moments of time, when the numbers of collisions of all three different pairs of the triplet will be equal. Moreover, any value of difference of collision numbers of pairs in the triplet will repeat indefinitely. On the other hand, for larger number of pairs there is but a finite number of repetitions. Thus the ergodic theory produces a limitation on the dynamics.Comment: 4 pages, published versio

Motion of a random walker in a quenched power law correlated velocity field

We study the motion of a random walker in one longitudinal and d transverse dimensions with a quenched power law correlated velocity field in the longitudinal x-direction. The model is a modification of the Matheron-de Marsily (MdM) model, with long-range velocity correlation. For a velocity correlation function, dependent on transverse co-ordinates y as 1/(a+|{y_1 - y_2}|)^alpha, we analytically calculate the two-time correlation function of the x-coordinate. We find that the motion of the x-coordinate is a fractional Brownian motion (fBm), with a Hurst exponent H = max [1/2, (1- alpha/4), (1-d/4)]. From this and known properties of fBM, we calculate the disorder averaged persistence probability of x(t) up to time t. We also find the lines in the parameter space of d and alpha along which there is marginal behaviour. We present results of simulations which support our analytical calculation.Comment: 8 pages, 4 figures. To appear in Physical Review

A Cell Cycle-Regulated \u3cem\u3eToxoplasma\u3c/em\u3e Deubiquitinase, TgOTUD3A, Targets Polyubiquitins with Specific Lysine Linkages

The contribution of ubiquitin-mediated mechanisms in the regulation of the Toxoplasma gondii cell cycle has remained largely unexplored. Here, we describe the functional characterization of a T. gondii deubiquitinase (TGGT1_258780) of the ovarian-tumor domain-containing (OTU) family, which, based on its structural homology to the human OTUD3 clade, has been designated TgOTUD3A. The TgOTUD3A protein is expressed in a cell cycle-dependent manner mimicking its mRNA expression, indicating that it is regulated primarily at the transcriptional level. TgOTUD3A, which was found in the cytoplasm at low levels in G1 parasites, increased in abundance with the progression of the cell cycle and exhibited partial localization to the developing daughter scaffolds during cytokinesis. Recombinant TgOTUD3A but not a catalytic-site mutant TgOTUD3A (C229A) exhibited activity against poly- but not monoubiquitinated targets. This activity was selective for polyubiquitin chains with preference for specific lysine linkages (K48 \u3e K11 \u3e K63). All three of these polyubiquitin linkage modifications were found to be present in Toxoplasma, where they exhibited differential levels and localization patterns in a cell cycle-dependent manner. TgOTUD3A removed ubiquitin from the K48- but not the K63-linked ubiquitinated T. gondii proteins independently of the modified target protein, thereby exhibiting the characteristics of an exodeubiquitinase. In addition to cell cycle association, the demonstration of multiple ubiquitin linkages together with the selective deubiquitinase activity of TgOTUD3A reveals an unappreciated level of complexity in the T. gondii “ubiquitin code.

A boundary integral formalism for stochastic ray tracing in billiards

Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain

The \u3cem\u3eToxoplasma gondii\u3c/em\u3e Protein ROP2 Mediates Host Organelle Association with the Parasitophorous Vacuole Membrane

Toxoplasma gondii replicates within a specialized vacuole surrounded by the parasitophorous vacuole membrane (PVM). The PVM forms intimate interactions with host mitochondria and endoplasmic reticulum (ER) in a process termed PVM–organelle association. In this study we identify a likely mediator of this process, the parasite protein ROP2. ROP2, which is localized to the PVM, is secreted from anterior organelles termed rhoptries during parasite invasion into host cells. The NH2-terminal domain of ROP2 (ROP2hc) within the PVM is exposed to the host cell cytosol, and has characteristics of a mitochondrial targeting signal. In in vitro assays, ROP2hc is partially translocated into the mitochondrial outer membrane and behaves like an integral membrane protein. Although ROP2hc does not translocate across the ER membrane, it does exhibit carbonate-resistant binding to this organelle. In vivo, ROP2hc expressed as a soluble fragment in the cytosol of uninfected cells associates with both mitochondria and ER. The 30–amino acid (aa) NH2-terminal sequence of ROP2hc, when fused to green fluorescent protein (GFP), is sufficient for mitochondrial targeting. Deletion of the 30-aa NH2-terminal signal from ROP2hc results in robust localization of the truncated protein to the ER. These results demonstrate a new mechanism for tight association of different membrane-bound organelles within the cell cytoplasm

The Toxoplasma gondii protein ROP2 mediates host organelle association with the parasitophorous vacuole membrane

Toxoplasma gondii replicates within a specialized vacuole surrounded by the parasitophorous vacuole membrane (PVM). The PVM forms intimate interactions with host mitochondria and endoplasmic reticulum (ER) in a process termed PVM–organelle association. In this study we identify a likely mediator of this process, the parasite protein ROP2. ROP2, which is localized to the PVM, is secreted from anterior organelles termed rhoptries during parasite invasion into host cells. The NH2-terminal domain of ROP2 (ROP2hc) within the PVM is exposed to the host cell cytosol, and has characteristics of a mitochondrial targeting signal. In in vitro assays, ROP2hc is partially translocated into the mitochondrial outer membrane and behaves like an integral membrane protein. Although ROP2hc does not translocate across the ER membrane, it does exhibit carbonate-resistant binding to this organelle. In vivo, ROP2hc expressed as a soluble fragment in the cytosol of uninfected cells associates with both mitochondria and ER. The 30–amino acid (aa) NH2-terminal sequence of ROP2hc, when fused to green fluorescent protein (GFP), is sufficient for mitochondrial targeting. Deletion of the 30-aa NH2-terminal signal from ROP2hc results in robust localization of the truncated protein to the ER. These results demonstrate a new mechanism for tight association of different membrane-bound organelles within the cell cytoplasm

Thermodynamic formalism for field driven Lorentz gases

We analytically determine the dynamical properties of two dimensional field driven Lorentz gases within the thermodynamic formalism. For dilute gases subjected to an iso-kinetic thermostat, we calculate the topological pressure as a function of a temperature-like parameter \ba up to second order in the strength of the applied field. The Kolmogorov-Sinai entropy and the topological entropy can be extracted from a dynamical entropy defined as a Legendre transform of the topological pressure. Our calculations of the Kolmogorov-Sinai entropy exactly agree with previous calculations based on a Lorentz-Boltzmann equation approach. We give analytic results for the topological entropy and calculate the dimension spectrum from the dynamical entropy function.Comment: 9 pages, 5 figure