Formation of morphogen gradient based on information geometry

Abstract

Morphogen gradient possesses stem cells’ spatial information to control these cells’ differentiation toward distinct directions. In embryos, the formation of this gradient is a dynamic process with time. However, how the information during the process of forming morphogen gradient is measured remains unsolved. Here, according to the theory of information geometry, the information length based on Fisher information is introduced to measure the change in the information from morphogen gradient’s initial state to its steady state. We find that morphogen’s diffusion rate, degradation rate and production rate have important effects on the information length. Specially, morphogen gradation’s degradation rate and diffusion rate have opposite effects on the information length. Our results enrich the current ones about morphogen gradients.