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Stochastic modeling

Claire Guerrier, David Holcman
Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian...
October 18, 2016: Scientific Reports
Edwin D Hawkins, Delfim Duarte, Olufolake Akinduro, Reema A Khorshed, Diana Passaro, Malgorzata Nowicka, Lenny Straszkowski, Mark K Scott, Steve Rothery, Nicola Ruivo, Katie Foster, Michaela Waibel, Ricky W Johnstone, Simon J Harrison, David A Westerman, Hang Quach, John Gribben, Mark D Robinson, Louise E Purton, Dominique Bonnet, Cristina Lo Celso
It is widely accepted that complex interactions between cancer cells and their surrounding microenvironment contribute to disease development, chemo-resistance and disease relapse. In light of this observed interdependency, novel therapeutic interventions that target specific cancer stroma cell lineages and their interactions are being sought. Here we studied a mouse model of human T-cell acute lymphoblastic leukaemia (T-ALL) and used intravital microscopy to monitor the progression of disease within the bone marrow at both the tissue-wide and single-cell level over time, from bone marrow seeding to development/selection of chemo-resistance...
October 17, 2016: Nature
Ornella Affinito, Giovanni Scala, Domenico Palumbo, Ermanno Florio, Antonella Monticelli, Gennaro Miele, Vittorio Enrico Avvedimento, Alessandro Usiello, Lorenzo Chiariotti, Sergio Cocozza
DNA methylation is often analyzed by reporting the average methylation degree of each cytosine. In this study, we used a single molecule methylation analysis in order to look at the methylation conformation of individual molecules. Using D-aspartate oxidase as a model gene, we performed an in-depth methylation analysis through the developmental stages of three different mouse tissues (brain, lung, and gut), where this gene undergoes opposite methylation destiny. This approach allowed us to track both methylation and demethylation processes at high resolution...
October 17, 2016: Epigenetics: Official Journal of the DNA Methylation Society
Sylvain Billiard, Pierre Collet, Régis Ferrière, Sylvie Méléard, Viet Chi Tran
Horizontal transfer (HT) of heritable information or 'traits' (carried by genetic elements, plasmids, endosymbionts, or culture) is widespread among living organisms. Yet current ecological and evolutionary theory addressing HT is scant. We present a modeling framework for the dynamics of two populations that compete for resources and horizontally exchange (transfer) an otherwise vertically inherited trait. Competition infuences individual demographics, thereby affecting population size, which feeds back on the dynamics of transfer...
October 11, 2016: Journal of Theoretical Biology
Alireza Karbalayghareh, Ulisses Braga-Neto, Jianping Hua, Edward R Dougherty
Gene-expression-based phenotype classification is used for disease diagnosis and prognosis relating to treatment strategies. The present paper considers classification based on sequential measurements of multiple genes using gene regulatory network (GRN) modeling. There are two networks, original and mutated, and observations consist of trajectories of network states. The problem is to classify an observation trajectory as coming from either the original or mutated network. GRNs are modeled via probabilistic Boolean networks, which incorporate stochasticity at both the gene and network levels...
October 11, 2016: IEEE/ACM Transactions on Computational Biology and Bioinformatics
Debasish Chaudhuri
Nonequilibrium stochastic dynamics of several active Brownian systems are modeled in terms of nonlinear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for total entropy production in such systems using the Fokker-Planck equation. The result is consistent with the expression for stochastic entropy production in the reservoir that we obtain from probabilities of time-forward and time-reversed trajectories, leading to fluctuation theorems...
September 2016: Physical Review. E
S Murray, M F Lightstone, S Tullis
The target Lagrangian kinematic simulation method was motivated as a stochastic Lagrangian particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target Lagrangian integral timescale. In addition to recovering the expected Lagrangian properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark...
September 2016: Physical Review. E
Jakub Jędrak, Anna Ochab-Marcinek
We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability distribution and the model parameters depend on time in an arbitrary (e.g., oscillatory) manner, and for arbitrary initial conditions. We show that in the case of periodic external activation and constant protein degradation rate, the response of the gene is analogous to the resistor-capacitor low-pass filter, where slow oscillations of the external driving have a greater effect on gene expression than the fast ones...
September 2016: Physical Review. E
Marco A Amaral, Lucas Wardil, Matjaž Perc, Jafferson K L da Silva
In times of plenty expectations rise, just as in times of crisis they fall. This can be mathematically described as a win-stay-lose-shift strategy with dynamic aspiration levels, where individuals aspire to be as wealthy as their average neighbor. Here we investigate this model in the realm of evolutionary social dilemmas on the square lattice and scale-free networks. By using the master equation and Monte Carlo simulations, we find that cooperators coexist with defectors in the whole phase diagram, even at high temptations to defect...
September 2016: Physical Review. E
Yohannes Shiferaw
Spontaneous calcium (Ca) waves in cardiac myocytes are known to underlie a wide range of cardiac arrhythmias. However, it is not understood which physiological parameters determine the onset of waves. In this study, we explore the relationship between Ca signaling between ion channels and the nucleation of Ca waves. In particular, we apply a master equation approach to analyze the stochastic interaction between neighboring clusters of ryanodine receptor (RyR) channels. Using this analysis, we show that signaling between clusters can be described as a barrier hopping process with exponential sensitivity to system parameters...
September 2016: Physical Review. E
Tayeb Jamali, G R Jafari, S Vasheghani Farahani
The aim of this study is to extend the scope and applicability of the level-crossing method to discrete-time stochastic processes and generalize it to enable us to study multiple discrete-time stochastic processes. In previous versions of the level-crossing method, problems with it correspond to the fact that this method had been developed for analyzing a continuous-time process or at most a multiple continuous-time process in an individual manner. However, since all empirical processes are discrete in time, the already-established level-crossing method may not prove adequate for studying empirical processes...
September 2016: Physical Review. E
Jingchen Feng, Stuart A Sevier, Bin Huang, Dongya Jia, Herbert Levine
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated with a delayed process but instead use an estimated average delay time. In an effort to examine the validity of this approach, we study systems with significant delays by explicitly incorporating intermediate steps. We show that such explicit models often yield significantly different equilibrium distributions and transition times as compared to DDEs with deterministic delay values...
September 2016: Physical Review. E
Gianbiagio Curato, Fabrizio Lillo
We use the linear threshold model to study the diffusion of information on a network generated by the stochastic block model. We focus our analysis on a two-community structure where the initial set of informed nodes lies only in one of the two communities and we look for optimal network structures, i.e., those maximizing the asymptotic extent of the diffusion. We find that, constraining the mean degree and the fraction of initially informed nodes, the optimal structure can be assortative (modular), core-periphery, or even disassortative...
September 2016: Physical Review. E
Kang Hao Cheong, Zong Xuan Tan, Neng-Gang Xie, Michael C Jones
Organisms with environmental sensors that guide survival are considered more likely to be favored by natural selection if they possess more accurate sensors. In this paper, we develop a theoretical model which shows that under certain conditions of environmental stochasticity, selection actually favors sensors of lower accuracy. An analogy between this counter-intuitive phenomenon and the well-known Parrondo's paradox is suggested.
October 14, 2016: Scientific Reports
Jana L Gevertz
The tumor-associated microvasculature is one of the key elements of the microenvironment that helps shape, and is shaped by, tumor progression. Given the important role of the vasculature in tumor progression, and the fact that tumor and normal vasculature are physiologically and molecularly distinct, much effort has gone into the development of vascular-targeting drugs that in theory should target tumors without significant risk to normal tissue. In this chapter, a multiscale hybrid mathematical model of tumor-vascular interactions is presented to provide a theoretical basis for assessing tumor response to vascular-targeting drugs...
2016: Advances in Experimental Medicine and Biology
Christian M Parobek, Frederick I Archer, Michelle E DePrenger-Levin, Sean M Hoban, Libby Liggins, Allan E Strand
Simulations are a key tool in molecular ecology for inference and forecasting, as well as for evaluating new methods. Due to growing computational power and a diversity of software with different capabilities, simulations are becoming increasingly powerful and useful. However, the widespread use of simulations by geneticists and ecologists is hindered by difficulties in understanding these softwares' complex capabilities, composing code and input files, a daunting bioinformatics barrier, and a steep conceptual learning curve...
October 13, 2016: Molecular Ecology Resources
Michael Eid, Christian Geiser, Tobias Koch, Moritz Heene
G-factor models such as the bifactor model and the hierarchical G-factor model are increasingly applied in psychology. Many applications of these models have produced anomalous and unexpected results that are often not in line with the theoretical assumptions on which these applications are based. Examples of such anomalous results are vanishing specific factors and irregular loading patterns. In this article, the authors show that from the perspective of stochastic measurement theory anomalous results have to be expected when G-factor models are applied to a single-level (rather than a 2-level) sampling process...
August 15, 2016: Psychological Methods
Meike J Wittmann, Hanna Stuis, Dirk Metzler
1.It is now widely accepted that genetic processes such as inbreeding depression and loss of genetic variation can increase the extinction risk of small populations. However, it is generally unclear whether extinction risk from genetic causes gradually increases with decreasing population size or whether there is a sharp transition around a specific threshold population size. In the ecological literature, such threshold phenomena are called "strong Allee effects" and they can arise for example from mate limitation in small populations...
October 12, 2016: Journal of Animal Ecology
Vera Schützhold, Jens Hahn, Katja Tummler, Edda Klipp
Lipid metabolism is essential for all major cell functions and has recently gained increasing attention in research and health studies. However, mathematical modeling by means of classical approaches such as stoichiometric networks and ordinary differential equation systems has not yet provided satisfactory insights, due to the complexity of lipid metabolism characterized by many different species with only slight differences and by promiscuous multifunctional enzymes. Here, we present an object-oriented stochastic model approach as a way to cope with the complex lipid metabolic network...
2016: Frontiers in Molecular Biosciences
Mustapha Bouhrara, Richard G Spencer
A number of central nervous system (CNS) diseases exhibit changes in myelin content and magnetic resonance longitudinal, T1, and transverse, T2, relaxation times, which therefore represent important biomarkers of CNS pathology. Among the methods applied for measurement of myelin water fraction (MWF) and relaxation times, the multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) approach is of particular interest. mcDESPOT permits whole brain mapping of multicomponent T1 and T2, with data acquisition accomplished within a clinically realistic acquisition time...
October 8, 2016: NeuroImage
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