Tuning the diffusion constant to optimize the readout of positional information of spatial concentration patterns

Positional information encoded in spatial concentration patterns is crucial for the development of multicellular organisms. However, it is still unclear how such information is affected by the physically dissipative diffusion process. Here we study one-dimensional patterning systems with analytical derivation and numerical simulations. We find that the diffusion constant of the patterning molecules exhibits a nonmonotonic effect on the readout of the positional information from the concentration patterns. Specifically, there exists an optimal diffusion constant that maximizes the positional information. Moreover, we find that the energy dissipation due to the physical diffusion imposes a fundamental upper limit on the positional information.