scholarly journals A Novel Approach for Calculating Exact Forms of mRNA Distribution in Single-Cell Measurements

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Jiaxin Chen ◽  
Feng Jiao
Keyword(s):  
Steady State ◽  
Single Cell ◽  
Gene Activation ◽  
State Model ◽  
Distribution Data ◽  
Mrna Levels ◽  
Novel Approach ◽  
Kinetic Rates ◽  
Three State Model ◽  
Two State Model

Gene transcription is a stochastic process manifested by fluctuations in mRNA copy numbers in individual isogenic cells. Together with mathematical models of stochastic transcription, the massive mRNA distribution data that can be used to quantify fluctuations in mRNA levels can be fitted by Pm(t), which is the probability of producing m mRNA molecules at time t in a single cell. Tremendous efforts have been made to derive analytical forms of Pm(t), which rely on solving infinite arrays of the master equations of models. However, current approaches focus on the steady-state (t→∞) or require several parameters to be zero or infinity. Here, we present an approach for calculating Pm(t) with time, where all parameters are positive and finite. Our approach was successfully implemented for the classical two-state model and the widely used three-state model and may be further developed for different models with constant kinetic rates of transcription. Furthermore, the direct computations of Pm(t) for the two-state model and three-state model showed that the different regulations of gene activation can generate discriminated dynamical bimodal features of mRNA distribution under the same kinetic rates and similar steady-state mRNA distribution.

Worklife and Unemployment: A New Consideration

2021 ◽  
Author(s):  
David I. Rosenbaum ◽  
Kalana Jayanetti
Keyword(s):  
Initial Data ◽  
State Model ◽  
Inactive State ◽  
Three State Model ◽  
Good Proxy ◽  
Two State Model

Abstract Do traditional two-state worklife estimates need adjustment for unemployment? To answer, an augmented three-state model classifies individuals as either 1) employed; 2) unemployed; or 3) inactive but not marginally attached. Periods of unemployment may reduce worklives; however, removal of those marginally attached or discouraged from the inactive state raises worklives. The three-state model results are compared to worklife estimates from the same initial data using the traditional two-state model. Results show that in many cases, the two-state model results are a good proxy for the three-state results that control for unemployment.

scholarly journals SIMULATIONS OF FINANCIAL MARKETS IN A POTTS-LIKE MODEL

2005 ◽  
Vol 16 (08) ◽  
pp. 1311-1317 ◽  
Author(s):  
TETSUYA TAKAISHI
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Potts Model ◽  
State Model ◽  
Exponential Distributions ◽  
Stylized Facts ◽  
Time Correlations ◽  
Long Time ◽  
Three State Model ◽  
Two State Model

A three-state model based on the Potts model is proposed to simulate financial markets. The three states are assigned to "buy", "sell" and "inactive" states. The model shows the main stylized facts observed in the financial market: fat-tailed distributions of returns and long time correlations in the absolute returns. At low inactivity rate, the model effectively reduces to the two-state model of Bornholdt and shows similar results to the Bornholdt model. As the inactivity increases, we observe the exponential distributions of returns.

Three timescales in prism adaptation

2015 ◽  
Vol 113 (1) ◽  
pp. 328-338 ◽  
Author(s):  
Masato Inoue ◽  
Motoaki Uchimura ◽  
Ayaka Karibe ◽  
Jacinta O'Shea ◽  
Yves Rossetti ◽  
...  
Keyword(s):  
Visual Feedback ◽  
Learning System ◽  
Prism Adaptation ◽  
State Model ◽  
Prism Exposure ◽  
The Difference ◽  
Three State Model ◽  
Two State Model ◽  
Adaptation Task ◽  
Plos Biol

It has been proposed that motor adaptation depends on at least two learning systems, one that learns fast but with poor retention and another that learns slowly but with better retention (Smith MA, Ghazizadeh A, Shadmehr R. PLoS Biol 4: e179, 2006). This two-state model has been shown to account for a range of behavior in the force field adaptation task. In the present study, we examined whether such a two-state model could also account for behavior arising from adaptation to a prismatic displacement of the visual field. We first confirmed that an “adaptation rebound,” a critical prediction of the two-state model, occurred when visual feedback was deprived after an adaptation-extinction episode. We then examined the speed of decay of the prism aftereffect (without any visual feedback) after repetitions of 30, 150, and 500 trials of prism exposure. The speed of decay decreased with the number of exposure trials, a phenomenon that was best explained by assuming an “ultraslow” system, in addition to the fast and slow systems. Finally, we compared retention of aftereffects 24 h after 150 or 500 trials of exposure: retention was significantly greater after 500 than 150 trials. This difference in retention could not be explained by the two-state model but was well explained by the three-state model as arising from the difference in the amount of adaptation of the “ultraslow process.” These results suggest that there are not only fast and slow systems but also an ultraslow learning system in prism adaptation that is activated by prolonged prism exposure of 150–500 trials.

scholarly journals Correlated Gene Modules Uncovered by Single-Cell Transcriptomics with High Detectability and Accuracy

2020 ◽  
Author(s):  
Alec R. Chapman ◽  
David F. Lee ◽  
Wenting Cai ◽  
Wenping Ma ◽  
Xiang Li ◽  
...  
Keyword(s):  
Steady State ◽  
Single Cell ◽  
Protein Interactions ◽  
Cancer Cell Line ◽  
Cell Types ◽  
Mrna Levels ◽  
Functional Understanding ◽  
Gene Modules ◽  
Cell Transcriptome ◽  
Different Cell Types

AbstractSingle cell transcriptome sequencing has become extremely useful for cell typing. However, such differential expression data has shed little light on regulatory relationships among genes. Here, by examining pairwise correlations between mRNA levels of any two genes under steady-state conditions, we uncovered correlated gene modules (CGMs), clusters of intercorrelated genes that carry out certain biological functions together. We report a novel single-cell RNA-seq method called MALBAC-DT with higher detectability and accuracy, allowing determination of the covariance matrix of the expressed mRNAs for a homogenous cell population. We observed a prevalence of positive correlations between pairs of genes, with higher correlations corresponding to higher likelihoods of protein-protein interactions. Some CGMs, such as the p53 module in a cancer cell line, are cell type specific, while others, such as the protein synthesis CGM, are shared by different cell types. CGMs distinguished direct targets of p53 and exposed different modes of regulation of these genes in different cell types. Our covariance analyses of steady-state fluctuations provides a powerful way to advance our functional understanding of gene-to-gene interactions.

scholarly journals The mechanism of thin filament regulation: Models in conflict?

2019 ◽  
Vol 151 (11) ◽  
pp. 1265-1271 ◽  
Author(s):  
Michael A. Geeves ◽  
Sherwin S. Lehrer ◽  
William Lehman
Keyword(s):  
Rate Constant ◽  
Binding Sites ◽  
Thin Filament ◽  
State Model ◽  
Muscle Contractility ◽  
Thin Filaments ◽  
Thin Filament Regulation ◽  
Three State Model ◽  
State Models ◽  
Two State Model

In a recent JGP article, Heeley et al. (2019. J. Gen. Physiol. https://doi.org/10.1085/jgp.201812198) reopened the debate about two- versus three-state models of thin filament regulation. The authors review their work, which measures the rate constant of Pi release from myosin.ADP.Pi activated by actin or thin filaments under a variety of conditions. They conclude that their data can be described by a two-state model and raise doubts about the generally accepted three-state model as originally formulated by McKillop and Geeves (1993. Biophys. J. https://doi.org/10.1016/S0006-3495(93)81110-X). However, in the following article, we follow Plato’s dictum that “twice and thrice over, as they say, good it is to repeat and review what is good.” We have therefore reviewed the evidence for the three- and two-state models and present our view that the evidence is overwhelmingly in favor of three structural states of the thin filament, which regulate access of myosin to its binding sites on actin and, hence, muscle contractility.

scholarly journals Analytical expressions and physical principles for single-cell mRNA distributions of the lac operon of Escherichia coli

2019 ◽  
Author(s):  
Krishna Choudhary ◽  
Atul Narang
Keyword(s):  
Perturbation Theory ◽  
Steady State ◽  
Bound States ◽  
Detailed Balance ◽  
Regulatory Elements ◽  
Dna Looping ◽  
State Model ◽  
Lac Operon ◽  
Two State Model ◽  
Analytical Expressions

ABSTRACTMechanistic models of stochastic gene expression are of considerable interest, but their complexity often precludes tractable analytical expressions for mRNA and protein distributions. The lac operon of E. coli is a model system with regulatory elements such as multiple operators and DNA looping that are shared by many operons. Although this system is complex, intuition suggests that fast DNA looping may simplify it by causing the repressor-bound states of the operon to equilibrate rapidly, thus ensuring that the subsequent dynamics are governed by slow transitions between the repressor-free and the equilibrated repressor-bound states. Here, we show that this intuition is correct by applying singular perturbation theory to a mechanistic model of lac transcription with the scaled time constant of DNA looping as the perturbation parameter. We find that at steady state, the repressor-bound states satisfy detailed balance and are dominated by the looped states; moreover, the interaction between the repressor-free and the equilibrated repressor-bound states is described by an extension of the Peccoud-Ycart two-state model in which both (repressor-free and repressor-bound) states support transcription. The solution of this extended two-state model reveals that the steady state mRNA distribution is a mixture of the Poisson and negative hypergeometric distributions which reflects mRNAs obtained by transcription from the repressor-bound and repressor-free states, respectively. Finally, we show that the physics revealed by perturbation theory makes it easy to derive the extended two-state model equations for complex regulatory architectures.

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