Biochemical networks, under mass-action kinetics, containing reactions with three or more reactants (called high-molecular reactions) are investigated. An algorithm for stochastically approximating the high-molecular reactions with a set of bi-molecular ones, involving at most two reactants, is presented. Properties of the algorithm and convergence are established by applying singular perturbation theory on the underlying chemical master equation . The algorithm is applied to a variety of examples from both systems and synthetic biology, demonstrating that biochemically plausible bi-molecular reaction networksmay display a variety of noise-induced phenomena, and may be designed in a systematic manner .
Biochemical reactions involving three or more reactants , called higher-molecular reactions, play an important role in theoretical systems and synthetic biology. In particular, such reactions underpin a variety of important bio-dynamical phenomena, such as multi-stability/multi-modality, oscillations, bifurcations, and noise-induced effects. However, only reactions with at most two reactants, called bi-molecular reactions, are experimentally feasible. To bridge the gap, in this paper we put forward an algorithm for systematically approximating arbitrary higher-molecular reactions with bi-molecular ones, while preserving the underlying stochastic dynamics. Properties of the algorithm and convergence are established via singular perturbation theory . The algorithm is applied to a variety of higher-molecular biochemical networks, and is shown to play an important role in nucleic-acid-based synthetic biology .
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networks, under mass-action kinetics, containing reactions with
reactions involving
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(called high-molecular reactions) are investigated. An algorithm for stochastically approximating the high-molecular reactions with a set of bi-molecular ones, involving
, called higher-molecular reactions, play an important role in theoretical systems and synthetic biology. In particular, such reactions underpin a variety of important bio-dynamical phenomena, such as multi-stability/multi-modality, oscillations, bifurcations, and noise-induced effects. However, only reactions with
R
is presented.
called bi-molecular reactions, are experimentally feasible. To bridge the gap, in this paper we put forward an algorithm for systematically approximating arbitrary higher-molecular reactions with bi-molecular ones, while preserving the underlying stochastic dynamics.
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by applying
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on the underlying chemical master equation
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examples from both systems and synthetic biology, demonstrating that biochemically plausible bi-molecular reaction networksmay display a variety of noise-induced phenomena, and may be designed in a systematic manner
higher-molecular biochemical networks, and is shown to play an important role in nucleic-acid-based synthetic biology