A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

Background Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. Results In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. Conclusions We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

Detailed balance, local detailed balance, and global potential for stochastic chemical reaction networks

Detailed balance of a chemical reaction network can be defined in several different ways. Here we investigate the relationship among four types of detailed balance conditions: deterministic, stochastic, local, and zero-order local detailed balance. We show that the four types of detailed balance are equivalent when different reactions lead to different species changes and are not equivalent when some different reactions lead to the same species change. Under the condition of local detailed balance, we further show that the system has a global potential defined over the whole space, which plays a central role in the large deviation theory and the Freidlin–Wentzell-type metastability theory of chemical reaction networks. Finally, we provide a new sufficient condition for stochastic detailed balance, which is applied to construct a class of high-dimensional chemical reaction networks that both satisfies stochastic detailed balance and displays multistability.

Autonomous DNA nanostructures instructed by hierarchically concatenated chemical reaction networks

Concatenation and communication between chemically distinct chemical reaction networks (CRNs) is an essential principle in biology for controlling dynamics of hierarchical structures. Here, to provide a model system for such biological systems, we demonstrate autonomous lifecycles of DNA nanotubes (DNTs) by two concatenated CRNs using different thermodynamic principles: (1) ATP-powered ligation/restriction of DNA components and (2) input strand-mediated DNA strand displacement (DSD) using energy gains provided in DNA toeholds. This allows to achieve hierarchical non-equilibrium systems by concurrent ATP-powered ligation-induced DSD for activating DNT self-assembly and restriction-induced backward DSD reactions for triggering DNT degradation. We introduce indirect and direct activation of DNT self-assemblies, and orthogonal molecular recognition allows ATP-fueled self-sorting of transient multicomponent DNTs. Coupling ATP dissipation to DNA nanostructures via programmable DSD is a generic concept which should be widely applicable to organize other DNA nanostructures, and enable the design of automatons and life-like systems of higher structural complexity.