Noise in gene expression can be substantively affected by the presence of production delay. Here we consider a mathematical model with bursty production of protein, a one-step production delay (the passage of which activates the protein), and feedback in the frequency of bursts. We specifically focus on examining the steady-state behaviour of the model in the slow-activation (i.e. large-delay) regime. Using a formal asymptotic approach, we derive an autonomous ordinary differential equation for the inactive protein that applies in the slow-activation regime. If the differential equation is monostable, the steady-state distribution of the inactive (active) protein is approximated by a single Gaussian (Poisson) mode located at the globally stable fixed point of the differential equation. If the differential equation is bistable (due to cooperative positive feedback), the steady-state distribution of the inactive (active) protein is approximated by a mixture of Gaussian (Poisson) modes located at the stable fixed points; the weights of the modes are determined from a WKB approximation to the stationary distribution. The asymptotic results are compared to numerical solutions of the chemical master equation.

Bokes, P., Borri, A., Palumbo, P., Singh, A. (2020). Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach. JOURNAL OF MATHEMATICAL BIOLOGY, 81(1), 343-367 [10.1007/s00285-020-01512-y].

Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach

Palumbo P.
Co-primo
;
2020

Abstract

Noise in gene expression can be substantively affected by the presence of production delay. Here we consider a mathematical model with bursty production of protein, a one-step production delay (the passage of which activates the protein), and feedback in the frequency of bursts. We specifically focus on examining the steady-state behaviour of the model in the slow-activation (i.e. large-delay) regime. Using a formal asymptotic approach, we derive an autonomous ordinary differential equation for the inactive protein that applies in the slow-activation regime. If the differential equation is monostable, the steady-state distribution of the inactive (active) protein is approximated by a single Gaussian (Poisson) mode located at the globally stable fixed point of the differential equation. If the differential equation is bistable (due to cooperative positive feedback), the steady-state distribution of the inactive (active) protein is approximated by a mixture of Gaussian (Poisson) modes located at the stable fixed points; the weights of the modes are determined from a WKB approximation to the stationary distribution. The asymptotic results are compared to numerical solutions of the chemical master equation.
Articolo in rivista - Articolo scientifico
Bursting; Exponential asymptotics; Large deviations; Production delay; Stochastic gene expression; WKB approximation;
English
24-giu-2020
2020
81
1
343
367
open
Bokes, P., Borri, A., Palumbo, P., Singh, A. (2020). Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach. JOURNAL OF MATHEMATICAL BIOLOGY, 81(1), 343-367 [10.1007/s00285-020-01512-y].
File in questo prodotto:
File Dimensione Formato  
biorchiv_855783.pdf

accesso aperto

Descrizione: Preprint
Tipologia di allegato: Submitted Version (Pre-print)
Dimensione 649.91 kB
Formato Adobe PDF
649.91 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/284055
Citazioni
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 6
Social impact