Pareto-optimal information trade-offs in boundary-driven reaction-diffusion systems

Abstract

Individual components such as cells, particles, or agents within a larger system often require detailed understanding of their relative position to act accordingly, enabling the system as a whole to function in an organized and efficient manner. Through the concept of positional information, such components are able to specify their position in order to, e.g., create robust spatial patterns or coordinate specific functionality. Such complex behavior generally occurs far from thermodynamic equilibrium and hence requires the dissipation of free energy to sustain it. We show that in boundary-driven simple exclusion systems with position-dependent Langmuir kinetics, non-trivial Pareto-optimal trade-offs exist between the positional information, entropy production rate and global reaction current. Phase transitions in the optimal protocols that tune the densities of the system boundaries emerge as a result, showing that for some Langmuir distributions distinct protocols are able to exchange global optimality similar to phase coexistence in liquid-gas phase transitions, and that increasing the positional information can lead to diminishing returns when considering increased dissipation.