Interplay of cellular states: Role of delay as control mechanism

Abstract

Delay is everywhere, no matter how small or big it is. Experimental evidences show the existence and importance of time delayed reactions specially in biological systems. The role of delay is found to be multifunctional and is seemed to be system dependent. The analytically solved P (X, t) of gene regulatory process shows universal class of Poisson process at stationary condition. However, time delay creates a possible condition to the system to impart correlation in the stochastic process as sub-Poissonian or noise enhancement process which could be important in regulating and controlling the system. The results of simulation of few biological systems (gene regulation, circadian rhythm, and repressilator) using delay stochastic simulation algorithm show the possibilities of delay induced onset of oscillating states, which could be the active states of the systems, where, the system can establish coherence among the system variables, enhance the signal processing, optimize the system activities, etc. On the other hand, delay can also induce switching off of the oscillating states, which may correspond to inactive state or system failure. Further, delay can also create coherent bistable states of the system variables, at which the system can stay longer to make decisions about the fate of the system. IntroductionComplex dynamical molecular reaction systems are generally inbuilt with delay. In such homogeneously well-mixed molecular reaction system, incorporation of time delay (T ) in some of the reactions allows the probability distribution to be at state (x, t) from an initial state (x i , t − T ) i.e., P (x, t; x i , t − T ) describing the Master equation of the system, to follow non-Markovian process [1]. This time delay plays a vital role in a system to accurately study the dynamical behavior, mechanism to maintain stabilization [2], controlling of signal processing [3] and regulation in the systems [4]. Further, in most biological systems, time delay, which is associated with varied set of reactions having different reaction firing times, can be considered to be an inherent important parameter, and also controls the Master equation describing the dynamics of chemical species. Moreover, time delay, in biological system, is believed to be as a combination of transmission, error detecting, processing and acting times [5]. This biological time delay can be measured experimentally by including maturation and gestation times, voluntary movement reaction times, certain neural reflexes, and the duration to make a protein [6]. There are many biological examples which indicate involvement of delay time. For example, in eukaryotic cells the speed of transcription is approximately twenty nucleotides per second [7], whereas the speed of translation is approximately two codons per second [7]. Human genes are approximately 55,000 nucleotides large [8], and takes 2,750 seconds to transcribe a gene of human [8], however, for translation process, it takes 450 seconds [9]. Other experimental examples show that delay in protein ...

Transient and delay chemical master equations

“…Delayed regulation has been implicated in the p53 (37) and Hes1 systems (38). Delay has been described as a regulatory motif in its own right capable of modulating, suppressing, and buffering noise (39)(40)(41)(42), even beyond Markovian limits (41,42), as well as inducing oscillations (37,(42)(43)(44).…”

Effects of noise and time delay on E2F's expression level in a bistable Rb‐E2F gene’s regulatory network

“…Generally, the role of time delay is rather complex and system dependent. It can induce either on/off switching of oscillation states and create coherent bistability that can aid in the decision‐making of the system [ 61 ]. Since E2F plays a vital role in the cell cycle process, it is essential to know how noise and time delay regulate this gene expression.…”

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