The Role of Source Delocalization in the Development of Morphogen   Gradients
  Successful biological development via spatial regulation of cell differentiation relies on action of multiple signaling molecules that are known as morphogens. It is now well established that signaling molecules create non-uniform concentration profiles, morphogen gradients, that activate different genes, leading to patterning in the developing embryos. The current view of the formation of morphogen gradients is that it is a result of complex reaction-diffusion processes that include the strongly localized production, diffusion and uniform degradation of signaling molecules. However, multiple experimental studies also suggest that the production of morphogen in many cases is delocalized. We develop a theoretical method that allows us to investigate the role of the delocalization in the formation of morphogen gradients. The approach is based on discrete-state stochastic models that can be solved exactly for arbitrary production lengths and production rates of morphogen molecules. Our analysis shows that the delocalization might have a strong effect on mechanisms of the morphogen gradient formation. The physical origin of this effect is discussed. 
Hamid Teimouri and Anatoly B. Kolomeisky
physics.bio-ph