Exploring dissipative sources of non-Markovian biochemical reaction systems

Stochastic Transcription with Alterable Synthesis Rates

“…Transcription kinetics are highly gene-specific [4,21]. To confirm the corresponding regulation mechanisms used by genes during transcription, many experimental techniques [34,35] and theoretical models with multiple stages [36,37] or in non-Markovian biochemical reaction systems [16,38] have been established during the last three decades. Using smFISH, Senecal et al [6] detected up to four active c-Fos transcription sites per cell.…”

Inferring entropy production rate from partially observed Langevin dynamics under coarse-graining

“…where C(t|ijk) denotes the probability density function of the time t the system spends at a CG state j before jumping to another CG state k, given that the previous CG state was i, i.e., for ijk transition. The WTD estimator, EPR WTD , or the ''memory dissipation'', 91 is the additional contribution that only exists for non-Markovian systems in contrast to their memoryless Markovian counterpart. It was shown that a semi-Markov process results in non-exponential waiting time distributions, 103 which is related to memory.…”

“…It was shown that a semi-Markov process results in non-exponential waiting time distributions, 103 which is related to memory. 91 Since there is no net current in the observed variable space, the position of the hair-bundle tip, X 1 , we use the KLD estimator 64 to calculate a lower bound on the total EPR. In order to apply this estimator, which was developed for discrete states, to a continuous variable system, we coarse-grain the observed variable into a few discrete states (a realization of 3 CG states is shown in Fig.…”

“…79,80 They found an estimator given observables characterizing one-step transitions and two successive transitions, whereas in another publication the authors proposed an estimator given the observed waiting time distributions. 80 There are several studies on the effect of coarse-graining (CG) on the EPR estimation [81][82][83][84][85][86][87][88][89][90][91][92][93][94] specifically discussing whether the CG procedure preserves the EPR fluctuations or not. In a recent study, using a Markovian model of a driven molecular motor, Hartich et al compared different coarse-graining schemes, ''milestoning'' and ''lumping'', and found that the ''milestoning'' method can restore Markovian dynamics in the case of timescale separation and preserves local detailed balance.…”

“…There are several studies on the effect of coarse-graining (CG) on the EPR estimation 81–94 specifically discussing whether the CG procedure preserves the EPR fluctuations or not. In a recent study, using a Markovian model of a driven molecular motor, Hartich et al compared different coarse-graining schemes, “milestoning” and “lumping”, and found that the “milestoning” method can restore Markovian dynamics in the case of time-scale separation and preserves local detailed balance.…”