TY - GEN

T1 - The Effect of Stochastic Bursting on Biological Clock Precision

AU - Maclaurin, James

AU - Singh, Abhyudai

N1 - Publisher Copyright:
© 2020 EUCA.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/5

Y1 - 2020/5

N2 - We study stochasticity in gene transcription oscillations. The oscillations in the protein concentration occur due to stochastic bursting of gene transcription being modulated by a delayed negative feedback. The oscillator dynamics is such that the mean dynamics (which the system converges towards in the large size limit) supports an attracting limit cycle. However, since there are only a finite-number of particles in biologically-realistic systems, this results in stochastic effects which perturb the system away from the limit cycle. We define an isochronal phase for the oscillation, and argue that it allows a much more powerful analysis than the Linear Noise Approximation. We demonstrate that the isochronal phase is accurate for very long periods of time: this results from the attracting dynamics of the limit cycle damping down stochasticity from the finite-size effects. Furthermore, because the system stays close to the oscillator for very long periods of time, we can obtain an estimate for the increase in errors over time due to the stochastic nature of the chemical reactions. We investigate numerically how various parametric regimes affect the resulting limit cycle dynamics.

AB - We study stochasticity in gene transcription oscillations. The oscillations in the protein concentration occur due to stochastic bursting of gene transcription being modulated by a delayed negative feedback. The oscillator dynamics is such that the mean dynamics (which the system converges towards in the large size limit) supports an attracting limit cycle. However, since there are only a finite-number of particles in biologically-realistic systems, this results in stochastic effects which perturb the system away from the limit cycle. We define an isochronal phase for the oscillation, and argue that it allows a much more powerful analysis than the Linear Noise Approximation. We demonstrate that the isochronal phase is accurate for very long periods of time: this results from the attracting dynamics of the limit cycle damping down stochasticity from the finite-size effects. Furthermore, because the system stays close to the oscillator for very long periods of time, we can obtain an estimate for the increase in errors over time due to the stochastic nature of the chemical reactions. We investigate numerically how various parametric regimes affect the resulting limit cycle dynamics.

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M3 - Conference contribution

AN - SCOPUS:85090127704

T3 - European Control Conference 2020, ECC 2020

SP - 1135

EP - 1140

BT - European Control Conference 2020, ECC 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 18th European Control Conference, ECC 2020

Y2 - 12 May 2020 through 15 May 2020

ER -