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

Language dysfunction in schizophrenia: Assessing neural tracking to characterize the underlying disorder(s)?

Deficits in language production and comprehension are characteristic of schizophrenia. To date, it remains unclear whether these deficits arise from dysfunctional linguistic knowledge, or dysfunctional predictions derived from the linguistic context. Alternatively, the deficits could be a result of dysfunctional neural tracking of auditory information resulting in decreased auditory information fidelity and even distorted information. Here, we discuss possible ways for clinical neuroscientists to employ neural tracking methodology to independently characterize deficiencies on the auditory–sensory and abstract linguistic levels. This might lead to a mechanistic understanding of the deficits underlying language related disorder(s) in schizophrenia. We propose to combine naturalistic stimulation, measures of speech–brain synchronization, and computational modeling of abstract linguistic knowledge and predictions. These independent but likely interacting assessments may be exploited for an objective and differential diagnosis of schizophrenia, as well as a better understanding of the disorder on the functional level—illustrating the potential of neural tracking methodology as translational tool in a range of psychotic populations

Distribution of dwell times of a ribosome: effects of infidelity, kinetic proofreading and ribosome crowding

Ribosome is a molecular machine that polymerizes a protein where the sequence of the amino acid residues, the monomers of the protein, is dictated by the sequence of codons (triplets of nucleotides) on a messenger RNA (mRNA) that serves as the template. The ribosome is a molecular motor that utilizes the template mRNA strand also as the track. Thus, in each step the ribosome moves forward by one codon and, simultaneously, elongates the protein by one amino acid. We present a theoretical model that captures most of the main steps in the mechano-chemical cycle of a ribosome. The stochastic movement of the ribosome consists of an alternating sequence of pause and translocation; the sum of the durations of a pause and the following translocation is the time of dwell of the ribosome at the corresponding codon. We derive the analytical expression for the distribution of the dwell times of a ribosome in our model. Whereever experimental data are available, our theoretical predictions are consistent with those results. We suggest appropriate experiments to test the new predictions of our model, particularly, the effects of the quality control mechanism of the ribosome and that of their crowding on the mRNA track.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Physical Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at DOI:10.1088/1478-3975/8/2/02600

Competition for finite resources

The resources in a cell are finite, which implies that the various components of the cell must compete for resources. One such resource is the ribosomes used during translation to create proteins. Motivated by this example, we explore this competition by connecting two totally asymmetric simple exclusion processes (TASEPs) to a finite pool of particles. Expanding on our previous work, we focus on the effects on the density and current of having different entry and exit rates.Comment: 15 pages, 9 figures, v2: minor revisions, v3: additional reference & minor correction

Common NOD2/CARD15 variants are not associated with susceptibility or the clinicopathologic characteristics of sporadic colorectal cancer in Hungarian patients

BACKGROUND: Epidemiological observations suggest that cancer arises from chronically inflamed tissues. Inflammatory bowel disease (IBD) is a typical example as patients with longstanding IBD are at an increased risk for developing colorectal cancer (CRC) and mutations of the NOD2/CARD15 gene increase the risk for Crohn's disease (CD). Recently, NOD2/CARD15 has been associated with a risk for CRC in some studies, which stemmed from ethnically diverse populations. Our aim was to identify common NOD2/CARD15 mutations in Hungarian patients with sporadic CRC. METHODS: A total of 194 sporadic CRC patients (m/f: 108/86, age at diagnosis of CRC: 63.2 ± 9.1 years old) and 200 healthy subjects were included. DNA was screened for SNP8, SNP12 and SNP13 NOD2/CARD15 mutations by denaturing-HPLC and confirmed by direct sequencing. RESULTS: NOD2/CARD15 mutations were found in 28 patients (14.4%) and in 23 controls (11.5%, p = NS). Allele frequencies for SNP8/R702W (1.8% vs. 1.5%) SNP12/G908R (1.8% vs. 1.8%) and SNP13/3020insC (3.6% vs. 2.5%) were also not statistically different between patients and controls. The clinicopathologic characteristics of CRC patients with or without NOD2/CARD15 mutations were not significantly different. CONCLUSION: Our results suggest that common NOD2/CARD15 mutations alone do not contribute to CRC risk in the Hungarian population

Multivariate moment closure techniques for stochastic kinetic models.

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs

Exclusion process for particles of arbitrary extension: Hydrodynamic limit and algebraic properties

The behaviour of extended particles with exclusion interaction on a one-dimensional lattice is investigated. The basic model is called $\ell$-ASEP as a generalization of the asymmetric exclusion process (ASEP) to particles of arbitrary length $\ell$. Stationary and dynamical properties of the $\ell$-ASEP with periodic boundary conditions are derived in the hydrodynamic limit from microscopic properties of the underlying stochastic many-body system. In particular, the hydrodynamic equation for the local density evolution and the time-dependent diffusion constant of a tracer particle are calculated. As a fundamental algebraic property of the symmetric exclusion process (SEP) the SU(2)-symmetry is generalized to the case of extended particles

Understanding the edge effect in TASEP with mean-field theoretic approaches

We study a totally asymmetric simple exclusion process (TASEP) with one defect site, hopping rate $q<1$, near the system boundary. Regarding our system as a pair of uniform TASEP's coupled through the defect, we study various methods to match a \emph{finite} TASEP and an \emph{infinite} one across a common boundary. Several approximation schemes are investigated. Utilizing the finite segment mean-field (FSMF) method, we set up a framework for computing the steady state current $J$ as a function of the entry rate $$ and $q$. For the case where the defect is located at the entry site, we obtain an analytical expression for $J(\alpha, q)$ which is in good agreement with Monte Carlo simulation results. When the defect is located deeper in the bulk, we refined the scheme of MacDonald, et.al. [Biopolymers, \textbf{6}, 1 (1968)] and find reasonably good fits to the density profiles before the defect site. We discuss the strengths and limitations of each method, as well as possible avenues for further studies.Comment: 16 pages, 4 figure

Cracking the code of oscillatory activity

Neural oscillations are ubiquitous measurements of cognitive processes and dynamic routing and gating of information. The fundamental and so far unresolved problem for neuroscience remains to understand how oscillatory activity in the brain codes information for human cognition. In a biologically relevant cognitive task, we instructed six human observers to categorize facial expressions of emotion while we measured the observers' EEG. We combined state-of-the-art stimulus control with statistical information theory analysis to quantify how the three parameters of oscillations (i.e., power, phase, and frequency) code the visual information relevant for behavior in a cognitive task. We make three points: First, we demonstrate that phase codes considerably more information (2.4 times) relating to the cognitive task than power. Second, we show that the conjunction of power and phase coding reflects detailed visual features relevant for behavioral response-that is, features of facial expressions predicted by behavior. Third, we demonstrate, in analogy to communication technology, that oscillatory frequencies in the brain multiplex the coding of visual features, increasing coding capacity. Together, our findings about the fundamental coding properties of neural oscillations will redirect the research agenda in neuroscience by establishing the differential role of frequency, phase, and amplitude in coding behaviorally relevant information in the brai

Development of a novel 3D culture system for screening features of a complex implantable device for CNS repair

Tubular scaffolds which incorporate a variety of micro- and nanotopographies have a wide application potential in tissue engineering especially for the repair of spinal cord injury (SCI). We aim to produce metabolically active differentiated tissues within such tubes, as it is crucially important to evaluate the biological performance of the three-dimensional (3D) scaffold and optimize the bioprocesses for tissue culture. Because of the complex 3D configuration and the presence of various topographies, it is rarely possible to observe and analyze cells within such scaffolds in situ. Thus, we aim to develop scaled down mini-chambers as simplified in vitro simulation systems, to bridge the gap between two-dimensional (2D) cell cultures on structured substrates and three-dimensional (3D) tissue culture. The mini-chambers were manipulated to systematically simulate and evaluate the influences of gravity, topography, fluid flow, and scaffold dimension on three exemplary cell models that play a role in CNS repair (i.e., cortical astrocytes, fibroblasts, and myelinating cultures) within a tubular scaffold created by rolling up a microstructured membrane. Since we use CNS myelinating cultures, we can confirm that the scaffold does not affect neural cell differentiation. It was found that heterogeneous cell distribution within the tubular constructs was caused by a combination of gravity, fluid flow, topography, and scaffold configuration, while cell survival was influenced by scaffold length, porosity, and thickness. This research demonstrates that the mini-chambers represent a viable, novel, scale down approach for the evaluation of complex 3D scaffolds as well as providing a microbioprocessing strategy for tissue engineering and the potential repair of SCI