Stochastic modeling of biochemical systems with multistep reactions using state-dependent time delay

Wu, Qian; Tian, Tianhai

doi:10.1038/srep31909

Cited by 5 publications

(1 citation statement)

References 57 publications

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“…In the context of plants and crops, Hartmann and Schreiber analyzed sucrose degradation using various formalisms, including stochastic Petri net (SPN) simulations in potato (Solanum tuberosum) [136]. Wu and Tian developed a stochastic multistep modeling framework to improve the accuracy of delayed reactions [137], and applied their method to the aliphatic glucosinolate biosynthesis pathway. One notable phenomenon in plants is the circadian clock, which has been studied in detail in the bread mold Neurospora crassa [138,139].…”

Section: Other Approaches: Stochastic Spatial and Multi-scale Modelsmentioning

confidence: 99%

Improving Bioenergy Crops through Dynamic Metabolic Modeling

Faraji

Voit

2017

Processes

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Enormous advances in genetics and metabolic engineering have made it possible, in principle, to create new plants and crops with improved yield through targeted molecular alterations. However, while the potential is beyond doubt, the actual implementation of envisioned new strains is often difficult, due to the diverse and complex nature of plants. Indeed, the intrinsic complexity of plants makes intuitive predictions difficult and often unreliable. The hope for overcoming this challenge is that methods of data mining and computational systems biology may become powerful enough that they could serve as beneficial tools for guiding future experimentation. In the first part of this article, we review the complexities of plants, as well as some of the mathematical and computational methods that have been used in the recent past to deepen our understanding of crops and their potential yield improvements. In the second part, we present a specific case study that indicates how robust models may be employed for crop improvements. This case study focuses on the biosynthesis of lignin in switchgrass (Panicum virgatum). Switchgrass is considered one of the most promising candidates for the second generation of bioenergy production, which does not use edible plant parts. Lignin is important in this context, because it impedes the use of cellulose in such inedible plant materials. The dynamic model offers a platform for investigating the pathway behavior in transgenic lines. In particular, it allows predictions of lignin content and composition in numerous genetic perturbation scenarios.

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Section: Other Approaches: Stochastic Spatial and Multi-scale Modelsmentioning

confidence: 99%

Improving Bioenergy Crops through Dynamic Metabolic Modeling

Faraji

Voit

2017

Processes

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Analytical refractory period distribution for a class of time-variant biochemical systems with second-order reactions

Rao,

Lin,

Song

2023

The Journal of Chemical Physics

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Refractory period (RP), the waiting time between signals, can induce complex signaling dynamics, such as acceleration, adaptation, and oscillation, within many cellular biochemical networks. However, its underlying molecular mechanisms are still unclear. Rigorously estimating the RP distribution may be essential to identify its causal regulatory mechanisms. Traditional methods of estimating the RP distribution depend on solving the underlying Chemical Master Equations (CMEs), the dominant modeling formalism of biochemical systems. However, exact solutions of the CME are only known for simple reaction systems with zero- and first-order reactions or specific systems with second-order reactions. General solutions still need to be derived for systems with bimolecular reactions. It is even more challenging if large state-space and nonconstant reaction rates are involved. Here, we developed a direct method to gain the analytical RP distribution for a class of second-order reaction systems with nonconstant reaction rates and large state space. Instead of using the CME, we used an equivalent path-wise representation, which is the solution to a transformed martingale problem of the CME. This allowed us to bypass solving a CME. We then applied the method to derive the analytical RP distribution of a real complex biochemical network with second-order reactions, the Drosophila phototransduction cascade. Our approach provides an alternative to the CMEs in deriving the analytical RP distributions of a class of second-order reaction systems. Since the bimolecular reactions are common in biological systems, our approach could enhance understanding real-world biochemical processes.

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The impact of time delays on mutant fixation in pairwise social dilemma games

Mohamadichamgavi,

Broom

2024

Proc. R. Soc. A.

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Evolutionary game theory examines how strategies spread and persist in populations through reproduction and imitation based on their fitness. Traditionally, models assume instantaneous dynamics where fitness depends on the current population state. However, some real-world processes unfold over time, with outcomes emerging from history. This motivates incorporating time delays into evolutionary game models, where fitness relies on the past. We study the impact of time delays on mutant fixation in a Moran Birth–death process with two strategies in a well-mixed population. At each time step of the process, an individual reproduces proportionally to fitness coming from the past. We model this as an absorbing Markov chain, allowing computational calculation of the fixation probability and time. We focus on three important games: the Stag-Hunt, Snowdrift and Prisoner’s Dilemma. We will show time delays reduce the fixation probability in the Stag-Hunt and the Prisoner’s Dilemma but increase it in the Snowdrift. For the Stag-Hunt and the Prisoner’s Dilemma, time delays lengthen the fixation time until a critical point, then reduce it. The Snowdrift exhibits the opposite trend.

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Stochastic modeling of biochemical systems with multistep reactions using state-dependent time delay

Cited by 5 publications

References 57 publications

Improving Bioenergy Crops through Dynamic Metabolic Modeling

Improving Bioenergy Crops through Dynamic Metabolic Modeling

Analytical refractory period distribution for a class of time-variant biochemical systems with second-order reactions

The impact of time delays on mutant fixation in pairwise social dilemma games

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