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The fundamental biological processes of development of tissues and organs inmulticellular organisms is governed by various signaling molecules, which arecalled morphogens. It is known that spatial and temporal variations inconcentration profiles of signaling molecules, which are frequently referred asmorphogen gradients, lead to cell differentiation via activating specific genesin a concentration-dependent manner. It is widely accepted that theestablishment of the morphogen gradients involves multiple biochemicalreactions and diffusion processes. One of the critical elements in theformation of morphogen gradients is a degradation of signaling molecules. Wedevelop a new theoretical approach that provides a comprehensive description ofthe degradation mechanisms. It is based on the idea that the degradation worksas an effective potential that drives the signaling molecules away from thesource region. Utilizing the method of first-passage processes, the dynamics ofthe formation of morphogen gradients for various degradation mechanisms isexplicitly evaluated. It is found that the linear degradation leads to adynamic behavior specified by times to form the morphogen gradients that dependlinearly on the distance from the source. This is because the effectivepotential due to degradation is quite strong. At the same time, the nonlineardegradation mechanisms yield a quadratic scaling in the morphogen gradientsformation times since the effective potentials are much weaker.Physical-chemical explanations of these phenomena are presented.

Theoretical analysis of degradation mechanisms in the formation of morphogen gradients