Theoretical analysis of degradation mechanisms in the formation of morphogen gradients

TL;DR

This paper presents a new theoretical framework to analyze how different degradation mechanisms influence the formation of morphogen gradients, revealing linear and quadratic scaling behaviors in gradient formation times.

Contribution

It introduces a comprehensive theoretical approach based on first-passage processes to describe degradation effects as effective potentials in morphogen gradient formation.

Findings

Linear degradation causes gradient formation times to scale linearly with distance.

Nonlinear degradation results in quadratic scaling of formation times.

Effective potentials vary significantly between degradation types, affecting dynamics.

Abstract

The fundamental biological processes of development of tissues and organs in multicellular organisms is governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in concentration profiles of signaling molecules, which are frequently referred as morphogen gradients, lead to cell differentiation via activating specific genes in a concentration-dependent manner. It is widely accepted that the establishment of the morphogen gradients involves multiple biochemical reactions and diffusion processes. One of the critical elements in the formation of morphogen gradients is a degradation of signaling molecules. We develop a new theoretical approach that provides a comprehensive description of the degradation mechanisms. It is based on the idea that the degradation works as an effective potential that drives the signaling molecules away from the source region. Utilizing the method of first-passage processes, the dynamics of the formation of morphogen gradients for various degradation mechanisms is explicitly evaluated. It is found that the linear degradation leads to a dynamic behavior specified by times to form the morphogen gradients that depend linearly on the distance from the source. This is because the effective potential due to degradation is quite strong. At the same time, the nonlinear degradation mechanisms yield a quadratic scaling in the morphogen gradients formation times since the effective potentials are much weaker. Physical-chemical explanations of these phenomena are presented.