A stochastic model of cellular senescence. II. Concordance with experimental data

1982 ◽  
Vol 96 (3) ◽  
pp. 443-460 ◽  
Author(s):  
Richard B. Jones ◽  
James R. Smith
Keyword(s):  
Experimental Data ◽  
Stochastic Model ◽  
Cellular Senescence

Stochastic model of nonideal mixer. Boundary conditions in batch system

1984 ◽  
Vol 49 (2) ◽  
pp. 490-505
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Jiří Vlček
Keyword(s):  
Experimental Data ◽  
Stochastic Model ◽  
Boundary Conditions ◽  
Closed System ◽  
Batch System ◽  
Ideal Mixer

The earlier proposed general approach for description of the non-ideal mixer is coupled with corresponding boundary conditions for the closed system. Some simplifications in this procedure result in relations which are in agreement with experimental data.

scholarly journals Statistics of nascent and mature RNA fluctuations in a stochastic model of transcriptional initiation, elongation, pausing, and termination

2020 ◽  
Author(s):  
Tatiana Filatova ◽  
Nikola Popovic ◽  
Ramon Grima
Keyword(s):  
Experimental Data ◽  
Fluorescence Microscopy ◽  
Stochastic Model ◽  
Explicit Dependence ◽  
Transcriptional Initiation ◽  
Estimate Parameter ◽  
Mean And Variance ◽  
The Mean ◽  
Nascent Rna ◽  
Parameter Values

AbstractRecent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. By computational binning of the gene into smaller segments, we derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations in each of these segments, as well as for the total nascent RNA on a gene. We also derive exact expressions for the first two moments of mature RNA fluctuations, and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

scholarly journals Bursting on a two state stochastic model for gene transcription in Drosophila embryos

2017 ◽  
Author(s):  
Romain Yvinec ◽  
Luiz Guilherme S. da Silva ◽  
Guilherme N. Prata ◽  
John Reinitz ◽  
Alexandre Ferreira Ramos
Keyword(s):  
Experimental Data ◽  
Stochastic Model ◽  
Gene Transcription ◽  
Fruit Fly ◽  
Synthesis Rate ◽  
Recent Experimental Data ◽  
Gillespie Algorithm ◽  
Noisy Environment ◽  
Intrinsic Stochasticity

AbstractRecent experimental data on the transcription dynamics of eve gene stripe two formation of Drosophila melanogaster embryos occurs in bursts of multiple sizes and durations. That has motivated the proposition of a transcription model having multiple ON states for the promoter of the eve gene each of them characterized by different synthesis rate. To understand the role of multiple ON states on gene transcription we approach the exact solutions for a two state stochastic model for gene transcription in D. melanogaster embryos and derive its bursting limit. Simulations based on the Gillespie algorithm at the bursting limit show the occurrence of bursts of multiple sizes and durations. Based on our theoretical approach, we interpret the aforementioned experimental data as a demonstration of the intrinsic stochasticity of the transcriptional processes in fruit fly embryos. Then, we conceive the experimental arrangement to determine when gene transcription has multiple ON promoter state in a noisy environment.

Statistics of Pit Initiation: Analysis of Current Transients During Passive Film Breakdown

1986 ◽  
Vol 84 ◽  
Author(s):  
Ugo Bertocci ◽  
S. Leigh ◽  
A. C. Van Orden ◽  
G. Yang
Keyword(s):  
Experimental Data ◽  
Statistical Analysis ◽  
Stochastic Model ◽  
Incubation Period ◽  
Passive Film ◽  
Computer Simulations ◽  
Stochastic Models ◽  
Current Fluctuations ◽  
Pit Initiation ◽  
Current Transients

AbstractDuring the incubation period preceding pitting, current fluctuations indicate the beginning of the breakdown of the passive film. The charac- teristics of these current transients are being examined as a possible way to predict pitting. Stochastic models applied to the breakdown process have been proposed, and in order to test how well they account for the experi- mental results, various forms of processing of the current vs. time records are necessary. This paper describes the experimental data-taking methods, the processing routines so far developed for the statistical analysis of the data, and compares the experimental results with computer simulations based on a stochastic model.

A stochastic model for cellular senescence. Part I. Theoretical considerations

1980 ◽  
Vol 86 (3) ◽  
pp. 581-592 ◽  
Author(s):  
Richard B. Jones ◽  
Charles K. Lumpkin ◽  
James R. Smith
Keyword(s):  
Stochastic Model ◽  
Cellular Senescence ◽  
Theoretical Considerations

Stochastic model for supersymmetric particle branching process

2017 ◽  
Vol 32 (03) ◽  
pp. 1750020 ◽  
Author(s):  
Yuanyuan Zhang ◽  
Aik Hui Chan ◽  
Choo Hiap Oh
Keyword(s):  
Experimental Data ◽  
Stochastic Model ◽  
Poisson Process ◽  
Branching Process ◽  
Collision Energy ◽  
Supersymmetric Particle ◽  
Birth Process ◽  
Two Phase ◽  
Branching Model ◽  
Multiplicity Distributions

We develop a stochastic branching model to describe the jet evolution of supersymmetric (SUSY) particles. This model is a modified two-phase branching process, or more precisely, a two-phase simple birth process plus Poisson process. Both pure SUSY partons initiated jets and SUSY plus ordinary partons initiated jets scenarios are considered. The stochastic branching equations are established and the Multiplicity Distributions (MDs) are derived for these two scenarios. We also fit the distribution of the general case (SUSY plus ordinary partons initiated jets) with experimental data. The fitting shows the SUSY particles have not participated in branching at current collision energy yet.

scholarly journals A STOCHASTIC MODEL FOR GERMINATION

2020 ◽  
Vol 27 (2) ◽  
pp. 375-385
Author(s):  
JOSÉ VILLA-MORALES
Keyword(s):  
Experimental Data ◽  
Markov Chain ◽  
Stochastic Model ◽  
Continuous Time ◽  
Continuous Time Markov Chain ◽  
Germination Time ◽  
Germination Process ◽  
Proposed Model

Assuming that the germination process of a seed passes through several stages (or states), including a state of non-germination, we model this phenomenon by means of a continuous-time Markov chain. The distribution of the germination time and the average of the first germination is obtained. In particular, when the duration of the process at each stage is on average the same we see that the proposed model adjusts rather well some experimental data.

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