Compartmental modeling membrane transport

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 mechanism of the competitive pertraction system (CPS) is presented schematically in Fig. 5.4 together with the compartmental model necessary for constructing the reaction-diffusion network. The simple flat-layered bulk liquid membrane of the thickness En and interface area S separates the two reservoirs (f, feed and s, stripping) containing transported divalent cations A2+ and B2+ (most frequently Zn2+ and Cu2+ or Ca2+ and Mg2+) and/or antiported univalent cations H+. At any time of pertraction t, their concentrations are [A]f, [B]f, and [H]f and [A]s, [Bj, and [H]s, for the feed and stripping solution, respectively. The hydrophobic liquid membrane contains a carrier of total concentration [C]. Its main property is the ability to react reversibly with cations at respective reaction zone and to diffuse throughout the liquid membrane phase. 

Compartments. Transitions also include transport of molecules between cell compartments. The set of transitions that a state can be involved in is strictly related to its compartment accordingly, a change in the compartment means a change in the state s information context. The state s compartment is a part of the ontology. As the compartments and their vicinity are cell-type dependent, compartmental structure can be modeled as part of the ontology. Cell membranes create an additional complexity because not only can a molecule be located completely inside the membrane, but it may also communicate with both sides of the membrane as part of the events involved in adjacent compartments. So membranes are considered as separate compartments in the ontology. 

---