Hybrid stochastic simplifications for multiscale gene networks

BMC Systems Biology

Table 1 Practical criteria to be satisfied by various reactions.

Reaction set	Approximation	Condition
	hybrid all	<<N and V_i>> (τ)^-1
	hybrid with switching	<<N, V_i>> τ^-1
	hybrid with breaking	~ N
	hybrid with breaking as singular limit	V_i= (ϵ τ)^-1 >> τ^-1
	hybrid with breaking as singular limit	V_i>> (ϵ τ)^-1
cycling reactions	averaged hybrid	k_lim>> (τ_C)^-1
branching reactions	averaged hybrid	k <<k_j, j cycling

See text for definitions of various reaction sets. τ_C, N are typical timescale and number of molecules of the continuous components, respectively. τ = min(τ_C, τ_D), where τ_Dis the mean time between two successive jumps of the discrete components. V_iare the average numbers of reactions per unit time (intensities of jump Markov processes), k are first order kinetic constants and γ_iare the stoichiometric vectors.

ISSN: 1752-0509