Influence of e on the substrate x r profiles

Other processes that lead to nonlinear compartmental models are processes dealing with transport of materials across cell membranes that represent the transfers between compartments. The amounts of various metabolites in the extracellular and intracellular spaces separated by membranes may be sufficiently distinct kinetically to act like compartments. It should be mentioned here that Michaelis-Menten kinetics also apply to the transfer of many solutes across cell membranes. This transfer is called facilitated diffusion or in some cases active transport (cf. Chapter 2). In facilitated diffusion, the substrate combines with a membrane component called a carrier to form a carrier-substrate complex. The carrier-substrate complex undergoes a change in conformation that allows dissociation and release of the unchanged substrate on the opposite side of the membrane. In active transport processes not only is there a carrier to facilitate crossing of the membrane, but the carrier mechanism is somehow coupled to energy dissipation so as to move the transported material up its concentration gradient. 

The branching pattern of the vascular system and the blood flow through it has continued to be of interest to anatomists, physiologists, and theoreticians [4,317,318]. The studies focusing on the geometric properties such as 

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