Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response

We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization of a Brownian dynamics for which the model reaction kinetics takes on the form of a stochastic differential equation. After eliminating a fast kinetics, the model can be rephrased into a form of a one-dimensional overdamped Langevin equation. We discuss physical aspects of environmental noises acting in such a reduced system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena can be observed together.Comment: 18 pages, 11 figures, published in Physical Review E 74, 041904 (2006

Mean first-passage times of non-Markovian random walkers in confinement

The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the efficiency of processes as varied as diffusion-limited reactions, target search processes or spreading of diseases. Most methods to determine the FPT properties in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects can not be neglected. Examples of non Markovian dynamics include single-file diffusion in narrow channels or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics \cite{turiv2013effect}, dense soft colloids or viscoelastic solution. Here, we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean FPT of a Gaussian non-Markovian random walker to a target point. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the trajectory of the random walker in the future of the first-passage event, which are shown to govern the FPT kinetics.This analysis is applicable to a broad range of stochastic processes, possibly correlated at long-times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes including the emblematic case of the Fractional Brownian Motion in one or higher dimensions. These results show, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.Comment: Submitted version. Supplementary Information can be found on the Nature website : http://www.nature.com/nature/journal/v534/n7607/full/nature18272.htm

Modelling radiation-induced cell cycle delays

Ionizing radiation is known to delay the cell cycle progression. In particular after particle exposure significant delays have been observed and it has been shown that the extent of delay affects the expression of damage such as chromosome aberrations. Thus, to predict how cells respond to ionizing radiation and to derive reliable estimates of radiation risks, information about radiation-induced cell cycle perturbations is required. In the present study we describe and apply a method for retrieval of information about the time-course of all cell cycle phases from experimental data on the mitotic index only. We study the progression of mammalian cells through the cell cycle after exposure. The analysis reveals a prolonged block of damaged cells in the G2 phase. Furthermore, by performing an error analysis on simulated data valuable information for the design of experimental studies has been obtained. The analysis showed that the number of cells analyzed in an experimental sample should be at least 100 to obtain a relative error less than 20%.Comment: 19 pages, 11 figures, accepted for publication in Radiation and Environmental Biophysic

Linear mapping approximation of gene regulatory networks with stochastic dynamics

The intractability of most stochastic models of gene regulatory networks (GRNs) limits their utility. Here, the authors present a linear-mapping approximation mapping models onto simpler ones, giving approximate but accurate analytic or semi- analytic solutions for a wide range of model GRNs

Speed, Sensitivity, and Bistability in Auto-activating Signaling Circuits

Cells employ a myriad of signaling circuits to detect environmental signals and drive specific gene expression responses. A common motif in these circuits is inducible auto-activation: a transcription factor that activates its own transcription upon activation by a ligand or by post-transcriptional modification. Examples range from the two-component signaling systems in bacteria and plants to the genetic circuits of animal viruses such as HIV. We here present a theoretical study of such circuits, based on analytical calculations, numerical computations, and simulation. Our results reveal several surprising characteristics. They show that auto-activation can drastically enhance the sensitivity of the circuit's response to input signals: even without molecular cooperativity, an ultra-sensitive threshold response can be obtained. However, the increased sensitivity comes at a cost: auto-activation tends to severely slow down the speed of induction, a stochastic effect that was strongly underestimated by earlier deterministic models. This slow-induction effect again requires no molecular cooperativity and is intimately related to the bimodality recently observed in non-cooperative auto-activation circuits. These phenomena pose strong constraints on the use of auto-activation in signaling networks. To achieve both a high sensitivity and a rapid induction, an inducible auto-activation circuit is predicted to acquire low cooperativity and low fold-induction. Examples from Escherichia coli's two-component signaling systems support these predictions

Identification of novel targets for breast cancer by exploring gene switches on a genome scale

<p>Abstract</p> <p>Background</p> <p>An important feature that emerges from analyzing gene regulatory networks is the "switch-like behavior" or "bistability", a dynamic feature of a particular gene to preferentially toggle between two steady-states. The state of gene switches plays pivotal roles in cell fate decision, but identifying switches has been difficult. Therefore a challenge confronting the field is to be able to systematically identify gene switches.</p> <p>Results</p> <p>We propose a top-down mining approach to exploring gene switches on a genome-scale level. Theoretical analysis, proof-of-concept examples, and experimental studies demonstrate the ability of our mining approach to identify bistable genes by sampling across a variety of different conditions. Applying the approach to human breast cancer data identified genes that show bimodality within the cancer samples, such as estrogen receptor (ER) and ERBB2, as well as genes that show bimodality between cancer and non-cancer samples, where tumor-associated calcium signal transducer 2 (TACSTD2) is uncovered. We further suggest a likely transcription factor that regulates TACSTD2.</p> <p>Conclusions</p> <p>Our mining approach demonstrates that one can capitalize on genome-wide expression profiling to capture dynamic properties of a complex network. To the best of our knowledge, this is the first attempt in applying mining approaches to explore gene switches on a genome-scale, and the identification of TACSTD2 demonstrates that single cell-level bistability can be predicted from microarray data. Experimental confirmation of the computational results suggest TACSTD2 could be a potential biomarker and attractive candidate for drug therapy against both ER+ and ER- subtypes of breast cancer, including the triple negative subtype.</p

Time-course of aberrations and their distribution: impact of LET and track structure

The biological response to high linear energy transfer (LET) radiation differs considerably from that to low LET radiation and this has been attributed to differences in the spatial energy deposition of both radiation qualities. In the case of X-rays the energy is deposited uniformly within the cell nucleus and produces damages in a purely stochastic manner. In contrast, for particles the energy is deposited inhomogeneously along the ion trajectory and the local dose decays with the square radial distance from the center of the track. This nonuniformity affects the yield and the distribution of aberrations among cells. Moreover, after high LET exposure a relationship between the aberration yield and cell cycle delay was observed. In this study, we present a detailed analysis of the distribution of aberrations in human lymphocytes reaching mitosis at early and later times after low and high LET exposure. Aberration data were fit to stochastic distributions demonstrating that the delay is related to the number of particle traversals per cell nucleus. To further elucidate this relationship, we introduce a Monte Carlo phenomenological model which incorporates the number of particle hits per nucleus. This value was derived by fitting theoretical distributions to the experimental data. Additionally, the probability that a cell traversed by a particle reaches mitosis at a given time was calculated. The analysis of biological data and numerical simulations clearly show the impact of the track structure on the formation of chromosome aberrations and their distribution among cells