Chemical reaction motifs driving non-equilibrium behaviors in phase separating materials

Abstract

The design of chemical reaction networks (CRNs) that couple to systems that phase separate is a promising avenue towards the realization of functional materials capable of displaying controlled non-equilibrium behaviors. However, how a particular CRN would affect the behaviors of a phase separating system is difficult to fully predict theoretically. In this paper, we analyze a mean field theory coupling CRNs to phase separating materials and expound on how the properties of the CRNs affect different classes of non-equilibrium behaviors. We examine the problem of achieving control over the size of phase separated condensates, by first considering tractable problems and illustrating the mathematical conditions leading to small wavelength instability. We then identify CRN motifs that are likely to yield size control by examining randomly generated networks and parameters. By analyzing the probabilities to observe particular states, we define simple design rules of CRNs that lead to desired non-equilibrium behavior. For example, we show that chemical interactions generating negative feedback facilitate size control, and that, similarly, chemical interactions should have effects counteracting those introduced by spatial interactions. We also adapt our mean field approach to the emergence of temporally oscillating patterns. Our results provide guidance toward the design of self-regulating material CRNs provide instructions to manage the formation, dissolution, and organization of compartments.

Robust Microphase Separation Through Chemical Reaction Networks

“…where γ > 0 is a length scale, ∈ R n×n is a matrix of constant attraction/repulsion parameters, and ν is an energy scale. See also [27] and [14], [29] for similar approaches combining the Cahn-Hilliard model for phase separation and chemical dynamics. We infer the corresponding time evolution via "model B" dynamics [18].…”

“…The design space of such a problem is large, in that we have many possible chemical reaction networks (CRNs) that can couple to phase separating systems. To assess the likelihood of MS and identify interesting candidate CRNs for experimental realization, in previous work we computationally explored the parameters and chemical reaction networks that lead to matrices J I (κ) and J R in (3) [27]. The probability that ρ(κ) has three roots was evaluated when generating either random J R matrices or random CRNs [28].…”

“…1: the size of condensates shrinks for small κ, grows for intermediate values of κ, shrinks again for large κ. For known parameters, the condition can be tested by directly computing the eigenvalue curves [27]. Departing from this approach, our analysis aims to develop efficient methods to tackle the case of uncertain CRN parameters: given a range of possible parameter values, by taking advantage of the BDC decomposition of the Jacobian of the chemical reaction dynamics, we check whether the condition can or cannot hold for some parameters in the range, and whether it holds robustly for all parameters in the range.…”