Selection and control of pathways by using externally adjustable noise on a stochastic cubic autocatalytic chemical system

Abstract

We investigate the effect of noisy feed rates on the behavior of a cubic autocatalytic chemical reaction model. By combining the renormalization group and stoichiometric network analysis, we demonstrate how externally adjustable random perturbations (extrinsic noise) can be used to select reaction pathways and therefore control reaction yields. This method is general and provides the means to explore the impact that changing statistical parameters in a noisy external environment (such as noisy feed rates, fluctuating reaction rates induced by noisy light, etc) has on chemical fluxes and pathways, thus demonstrating how external noise may be used to control, promote, direct and optimize chemical progress through a given reaction pathway. *

Renormalization of stochastic differential equations with multiplicative noise using effective potential methods

“…And this scaling, can be accounted for quantitatively by solutions of the corresponding RG equations (see Refs. [20][21][22][23] for examples of computation of running parameters using perturbative RG techniques). Just as in quantum field theory, our one-loop effective potential for stochastic field theories (27) can be used to identify and then calculate these renormalization group equations and hence, to obtain the scaling in the SDE's parameters.…”

“…Refs. [22]. It involves a certain chemical φ reacting with another chemical U via the autocatalytic reaction 2φ + U → 3φ, and the removal of φ from the continuously stirred tank reactor (this is a variant of the Gray-Scott reaction in which U is considered very abundant and thus having a constant concentration).…”

“…However, applying the same methods developed in Refs. [15,[19][20][21][22] to SDEs subjected to multiplicative noise is untenable, as there is no simple way of truncating the formal solution to the differential equation. To our knowledge, and despite progress in analytical [27][28][29][30][31] and numerical [7,[32][33][34] techniques, the computation of running parameters for stochastic differential equations subject to multiplicative noise is still lacking (a notable exception is Ref.…”

Renormalization of stochastic differential equations with multiplicative noise using effective potential methods

“…In Refs. [15,[19][20][21][22], perturbative renormalization group methods [3,23] are used to compute the running of parameters for additive power-law noise in a simple cubic autocatalytic reaction-diffusion model. In this toy model, the additive noise represents possible fluctuations in the inflow of chemicals into the system and constitutes a possible way for an experimentalist to control the dynamic of the reaction.…”

“…However, applying the same methods developed in Refs. [15,[19][20][21][22] to SDEs subjected to multiplicative noise is untenable, as there is no simple way of truncating the formal solution to the differential equation. To our knowledge and despite progress in analytical [27][28][29][30][31] and numerical [7,[32][33][34] techniques, the computation of running parameters for stochastic differential equations subject to multiplicative noise is still lacking (a notable exception is Ref.…”