| The morphogen is a class of signaling molecules with important roles during embryonic development that control the direction of cell differentiation and tissue growth.The morphogen molecules are formed first in local regions of the embryo and then spread to other regions of the embryo by transmission mechanisms such as natural diffusion,transcytosis,super diffusion,etc.,thereby forming a morphogen concentration gradient.The morphogen downstream signaling pathway transmits the concentration information of this gradient,activates different downstream target genes,and finally forms tissue cells with different functions.Therefore,the morphogen gradient contains accurate spatial and temporal information of stem cells,which can accurately control the development of embryos.Therefore,studying the formation of morphogen gradient has important biological significance.In this dissertation,using a combination of mathematical modeling,theoretical analysis,and numerical simulation,based on information geometry theory,information length is introduced to measure the cumulative amount of information change from the initial state of the formability gradient to its steady-state state based on Fisher information.We found that the diffusion rate,degradation rate,and production rate of morphogen have important effects on the information length.In particular,the degradation rate and diffusion rate of morphogen have opposite effects on the information length.The results of this dissertation enrich the current research on morphogen gradient.This paper focuses on the following two aspects of the morphogen gradient:1)Introduce the diffusion and transportation modes of morphogen molecules between cells,and two robust mechanisms of morphogen gradient: transcytosis mechanism and self-enhancing ligand degradation mechanism.2)Based on the discrete-state version of the SDD model,establish a master equation for the diffusion of morphogen and obtain a probabilistic analytical solution for the steady-state gradient of morphogen.Study the effects of morphogen generation rate,diffusion rate,and degradation rate on the morphogen gradient and information length.Study the effects of internalization and externalization on information length based on the model of transcytosis,and study the effect of degradation power n of the self-enhanced degradation model on information length. |
