scholarly journals Analysis of stochastic timing of intracellular events with gene switching

2019 ◽  
Author(s):  
Khem Raj Ghusinga ◽  
Abhyudai Singh
Keyword(s):  
First Passage Time ◽  
Regulatory Protein ◽  
Gene Activation ◽  
Threshold Level ◽  
Passage Time ◽  
First Passage ◽  
Cellular Processes ◽  
Event Timing ◽  
Activation Rates ◽  
Gene Switching

AbstractAn important step in execution of several cellular processes is accumulation of a regulatory protein up to a specific threshold level. Since production of a protein is inherently stochastic, the time at which its level crosses a threshold exhibits cell-to-cell variation. A problem of interest is to characterize how the statistics of event timing is affected by various steps of protein expression. Our previous work studied this problem by considering a gene expression model where gene was always active. Here we extend our analysis to a scenario where gene stochastically switches between active and inactive states. We formulate event timing as the first-passage time for a protein’s level to cross a threshold and investigate how the rates of gene activation/inactivation affect the distribution and moments of the first-passage time. Our results show that both the time-scale of gene switching with respect to the protein degradation rate as well as the ratio of the gene inactivation to gene activation rates are important parameters in shaping the event-timing distribution.

scholarly journals First-passage time approach to controlling noise in the timing of intracellular events

2017 ◽  
Vol 114 (4) ◽  
pp. 693-698 ◽  
Author(s):  
Khem Raj Ghusinga ◽  
John J. Dennehy ◽  
Abhyudai Singh
Keyword(s):  
Fundamental Problem ◽  
First Passage Time ◽  
Feedback Regulation ◽  
Passage Time ◽  
Feedback Mechanism ◽  
Critical Threshold ◽  
First Passage ◽  
Event Timing ◽  
Cellular Environment ◽  
Time Problem

In the noisy cellular environment, gene products are subject to inherent random fluctuations in copy numbers over time. How cells ensure precision in the timing of key intracellular events despite such stochasticity is an intriguing fundamental problem. We formulate event timing as a first-passage time problem, where an event is triggered when the level of a protein crosses a critical threshold for the first time. Analytical calculations are performed for the first-passage time distribution in stochastic models of gene expression. Derivation of these formulas motivates an interesting question: Is there an optimal feedback strategy to regulate the synthesis of a protein to ensure that an event will occur at a precise time, while minimizing deviations or noise about the mean? Counterintuitively, results show that for a stable long-lived protein, the optimal strategy is to express the protein at a constant rate without any feedback regulation, and any form of feedback (positive, negative, or any combination of them) will always amplify noise in event timing. In contrast, a positive feedback mechanism provides the highest precision in timing for an unstable protein. These theoretical results explain recent experimental observations of single-cell lysis times in bacteriophage λ. Here, lysis of an infected bacterial cell is orchestrated by the expression and accumulation of a stable λ protein up to a threshold, and precision in timing is achieved via feedforward rather than feedback control. Our results have broad implications for diverse cellular processes that rely on precise temporal triggering of events.

scholarly journals Controlling Noise in the Timing of Intracellular Events: A First-Passage Time Approach

2016 ◽  
Author(s):  
Khem Raj Ghusinga ◽  
John J. Dennehy ◽  
Abhyudai Singh
Keyword(s):  
Fundamental Problem ◽  
First Passage Time ◽  
Feedback Regulation ◽  
Passage Time ◽  
Feedback Mechanism ◽  
Critical Threshold ◽  
First Passage ◽  
Event Timing ◽  
Cellular Environment ◽  
Time Problem

AbstractIn the noisy cellular environment, gene products are subject to inherent random fluctuations in copy numbers over time. How cells ensure precision in the timing of key intracellular events, in spite of such stochasticity is an intriguing fundamental problem. We formulate event timing as a first-passage time problem, where an event is triggered when the level of a protein crosses a critical threshold for the first time. Novel analytical calculations are preformed for the first-passage time distribution in stochastic models of gene expression, including models with feedback regulation. Derivation of these formulas motivates an interesting question: is there an optimal feedback strategy to regulate the synthesis of a protein to ensure that an event will occur at a precise time, while minimizing deviations or noise about the mean. Counter-intuitively, results show that for a stable long-lived protein, the optimal strategy is to express the protein at a constant rate without any feedback regulation, and any form of feedback (positive, negative or any combination of them) will always amplify noise in event timing. In contrast, a positive feedback mechanism provides the highest precision in timing for an unstable protein. These theoretical results explain recent experimental observations of single-cell lysis times in bacteriophage λ. Here, lysis of an infected bacterial cell is orchestrated by the expression and accumulation of a stable λ protein up to a threshold, and precision in timing is achieved via feedforward, rather than feedback control. Our results have broad implications for diverse cellular processes that rely on precise temporal triggering of events.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap

Spectral Theory for Skip-Free Markov Chains

1989 ◽  
Vol 3 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Joseph Abate ◽  
Ward Whitt
Keyword(s):  
Markov Chains ◽  
Spectral Theory ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage Times ◽  
Simple Relationship ◽  
First Passage ◽  
Birth And Death Processes ◽  
The Laplace Transform ◽  
Passage Times

The distribution of upward first passage times in skip-free Markov chains can be expressed solely in terms of the eigenvalues in the spectral representation, without performing a separate calculation to determine the eigenvectors. We provide insight into this result and skip-free Markov chains more generally by showing that part of the spectral theory developed for birth-and-death processes extends to skip-free chains. We show that the eigenvalues and eigenvectors of skip-free chains can be characterized in terms of recursively defined polynomials. Moreover, the Laplace transform of the upward first passage time from 0 to n is the reciprocal of the nth polynomial. This simple relationship holds because the Laplace transforms of the first passage times satisfy the same recursion as the polynomials except for a normalization.

Sign in / Sign up

Export Citation Format

Share Document