Wigner Surmise For Domain Systems

In random matrix theory, the spacing distribution functions $p^{(n)}(s)$ are well fitted by the Wigner surmise and its generalizations. In this approximation the spacing functions are completely described by the behavior of the exact functions in the limits s->0 and s->infinity. Most non equilibrium systems do not have analytical solutions for the spacing distribution and correlation functions. Because of that, we explore the possibility to use the Wigner surmise approximation in these systems. We found that this approximation provides a first approach to the statistical behavior of complex systems, in particular we use it to find an analytical approximation to the nearest neighbor distribution of the annihilation random walk

Effects of differential mobility on biased diffusion of two species

Using simulations and a simple mean-field theory, we investigate jamming transitions in a two-species lattice gas under non-equilibrium steady-state conditions. The two types of particles diffuse with different mobilities on a square lattice, subject to an excluded volume constraint and biased in opposite directions. Varying filling fraction, differential mobility, and drive, we map out the phase diagram, identifying first order and continuous transitions between a free-flowing disordered and a spatially inhomogeneous jammed phase. Ordered structures are observed to drift, with a characteristic velocity, in the direction of the more mobile species.Comment: 15 pages, 4 figure

Global entrainment of transcriptional systems to periodic inputs

This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems. The basic mathematical results needed from contraction theory are proved in the paper, making it self-contained

Bridging Time Scales in Cellular Decision Making with a Stochastic Bistable Switch

Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.Comment: 14 pages, 4 figure

Trade-offs and Noise Tolerance in Signal Detection by Genetic Circuits

Genetic circuits can implement elaborated tasks of amplitude or frequency signal detection. What type of constraints could circuits experience in the performance of these tasks, and how are they affected by molecular noise? Here, we consider a simple detection process–a signal acting on a two-component module–to analyze these issues. We show that the presence of a feedback interaction in the detection module imposes a trade-off on amplitude and frequency detection, whose intensity depends on feedback strength. A direct interaction between the signal and the output species, in a type of feed-forward loop architecture, greatly modifies these trade-offs. Indeed, we observe that coherent feed-forward loops can act simultaneously as good frequency and amplitude noise-tolerant detectors. Alternatively, incoherent feed-forward loop structures can work as high-pass filters improving high frequency detection, and reaching noise tolerance by means of noise filtering. Analysis of experimental data from several specific coherent and incoherent feed-forward loops shows that these properties can be realized in a natural context. Overall, our results emphasize the limits imposed by circuit structure on its characteristic stimulus response, the functional plasticity of coherent feed-forward loops, and the seemingly paradoxical advantage of improving signal detection with noisy circuit components

Probing Cellular Dynamics with a Chemical Signal Generator

Observations of material and cellular systems in response to time-varying chemical stimuli can aid the analysis of dynamic processes. We describe a microfluidic “chemical signal generator,” a technique to apply continuously varying chemical concentration waveforms to arbitrary locations in a microfluidic channel through feedback control of the interface between parallel laminar (co-flowing) streams. As the flow rates of the streams are adjusted, the channel walls are exposed to a chemical environment that shifts between the individual streams. This approach can be used to probe the dynamic behavior of objects or substances adherent to the interior of the channel. To demonstrate the technique, we exposed live fibroblast cells to ionomycin, a membrane-permeable calcium ionophore, while assaying cytosolic calcium concentration. Through the manipulation of the laminar flow interface, we exposed the cells' endogenous calcium handling machinery to spatially-contained discrete and oscillatory intracellular disturbances, which were observed to elicit a regulatory response. The spatiotemporal precision of the generated signals opens avenues to previously unapproachable areas for potential investigation of cell signaling and material behavior

Automated Ensemble Modeling with modelMaGe: Analyzing Feedback Mechanisms in the Sho1 Branch of the HOG Pathway

In systems biology uncertainty about biological processes translates into alternative mathematical model candidates. Here, the goal is to generate, fit and discriminate several candidate models that represent different hypotheses for feedback mechanisms responsible for downregulating the response of the Sho1 branch of the yeast high osmolarity glycerol (HOG) signaling pathway after initial stimulation. Implementing and testing these candidate models by hand is a tedious and error-prone task. Therefore, we automatically generated a set of candidate models of the Sho1 branch with the tool modelMaGe. These candidate models are automatically documented, can readily be simulated and fitted automatically to data. A ranking of the models with respect to parsimonious data representation is provided, enabling discrimination between candidate models and the biological hypotheses underlying them. We conclude that a previously published model fitted spurious effects in the data. Moreover, the discrimination analysis suggests that the reported data does not support the conclusion that a desensitization mechanism leads to the rapid attenuation of Hog1 signaling in the Sho1 branch of the HOG pathway. The data rather supports a model where an integrator feedback shuts down the pathway. This conclusion is also supported by dedicated experiments that can exclusively be predicted by those models including an integrator feedback

Phenotypic Signatures Arising from Unbalanced Bacterial Growth

Fluctuations in the growth rate of a bacterial culture during unbalanced growth are generally considered undesirable in quantitative studies of bacterial physiology. Under well-controlled experimental conditions, however, these fluctuations are not random but instead reflect the interplay between intra-cellular networks underlying bacterial growth and the growth environment. Therefore, these fluctuations could be considered quantitative phenotypes of the bacteria under a specific growth condition. Here, we present a method to identify “phenotypic signatures” by time-frequency analysis of unbalanced growth curves measured with high temporal resolution. The signatures are then applied to differentiate amongst different bacterial strains or the same strain under different growth conditions, and to identify the essential architecture of the gene network underlying the observed growth dynamics. Our method has implications for both basic understanding of bacterial physiology and for the classification of bacterial strains

Simple molecular networks that respond optimally to time-periodic stimulation

<p>Abstract</p> <p>Background</p> <p>Bacteria or cells receive many signals from their environment and from other organisms. In order to process this large amount of information, Systems Biology shows that a central role is played by regulatory networks composed of genes and proteins. The objective of this paper is to present and to discuss simple regulatory network motifs having the property to maximize their responses under time-periodic stimulations. In elucidating the mechanisms underlying these responses through simple networks the goal is to pinpoint general principles which optimize the oscillatory responses of molecular networks.</p> <p>Results</p> <p>We took a look at basic network motifs studied in the literature such as the Incoherent Feedforward Loop (IFFL) or the interlerlocked negative feedback loop. The former is also generalized to a diamond pattern, with network components being either purely genetic or combining genetic and signaling pathways. Using standard mathematics and numerical simulations, we explain the types of responses exhibited by the IFFL with respect to a train of periodic pulses. We show that this system has a non-vanishing response only if the inter-pulse interval is above a threshold. A slight generalisation of the IFFL (the diamond) is shown to work as an ideal pass-band filter. We next show a mechanism by which average of oscillatory response can be maximized by bursting temporal patterns. Finally we study the interlerlocked negative feedback loop, i.e. a 2-gene motif forming a loop where the nodes respectively activate and repress each other, and show situations where this system possesses a resonance under periodic stimulation.</p> <p>Conclusion</p> <p>We present several simple motif designs of molecular networks producing optimal output in response to periodic stimulations of the system. The identified mechanisms are simple and based on known network motifs in the literature, so that that they could be embodied in existing organisms, or easily implementable by means of synthetic biology. Moreover we show that these designs can be studied in different contexts of molecular biology, as for example in genetic networks or in signaling pathways.</p

Stochastic Modeling for the Expression of a Gene Regulated by Competing Transcription Factors

It is widely accepted that gene expression regulation is a stochastic event. The common approach for its computer simulation requires detailed information on the interactions of individual molecules, which is often not available for the analyses of biological experiments. As an alternative approach, we employed a more intuitive model to simulate the experimental result, the Markov-chain model, in which a gene is regulated by activators and repressors, which bind the same site in a mutually exclusive manner. Our stochastic simulation in the presence of both activators and repressors predicted a Hill-coefficient of the dose-response curve closer to the experimentally observed value than the calculated value based on the simple additive effects of activators alone and repressors alone. The simulation also reproduced the heterogeneity of gene expression levels among individual cells observed by Fluorescence Activated Cell Sorting analysis. Therefore, our approach may help to apply stochastic simulations to broader experimental data