Studying genetic regulatory networks at the molecular level: Delayed reaction stochastic models

Tuning cell differentiation patterns and single cell dynamics by regulating proteins’ functionalities in a toggle switch

“…Gene expression is modeled by two multi-delayed reactions, one for transcription (reaction 1) and one for translation (reaction 2), to account for the time duration of the multiple steps involved in these processes [8,31,44,52]. P ro i is the promoter of gene i, RNAp is an RNA polymerase, Rib is a ribosome, R i is the ribosome binding site of the transcribed RNA, P i is a translated premature protein, P f,i is a functional protein and D f,i is a functional protein dimer.…”

“…Since the average rate of transcriptional elongation in E. coli is ∼ 50 nt/s, τ 2 is, on average, 90 s (τ 2 = τ 1 + 2500/50), given 2500 nt is the gene length [51]. Note that the delay associated with the time needed to form the ribosome binding site R i is also τ 1 (and not τ 2 as for a complete RNA molecule), since the time to form R i is almost identical to the promoter clearance time given that we model gene expression in prokaryotes, where translation is initiated when the ribosome binding site is formed [44,52]. In translation, the time needed for R i clearance, τ 3 , is set to 2 s [13].…”

“…Each 'cell' is initialized without proteins or RNAs, one promoter of each gene, 40 RNA polymerases [38], and 100 ribosomes [52]. The basic transcription rate is set to k t = 0.01 causing the expected time for an RNAp to bind to the promoter to be 1 kt×RN Ap = 2.5 [23].…”

“…For example, the time needed to form the promoter complex [31] affects the toggling frequency of genetic toggle switches (TS) [42]. The delayed Stochastic Simulation Algorithm (delayed SSA) [45] (a modified version of the original SSA [16]), able to match gene expression at the single RNA and protein level [52,51], allows modeling multiple time delayed reactions [44], and thus is used here to simulate the dynamics of the GRN of each cell.…”

Roman Roads: The Hierarchical Endosymbiosis of Cognitive Modules

“…Here we become enmeshed in a highly recursive phenomenological stochastic differential equations, but at a deeper level than the stochastic reaction model of Zhu et al (2007), and in a dynamic rather than static manner: the objects of this dynamical system are equivalence classes of information sources and their crosstalk, rather than simple final states of a chemical system.…”