Transport processes, compartmentalized

For biochemical reactions, the stoichiometric coefficients are usually integer and correspond to the (relative) molecularities in which the reactants enter the reaction. Note that for transport processes, and unless metabolites are measured in absolute quantities, the stoichiometric coefficient also reflect differences in compartmental volumes. 

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. 

During the light period, when COi is being fixed in the chloroplasts by the RPP pathway, it is likely that the mechanisms discussed above for C3 photosynthesis are also functional in CAM plants [19]. Additional control mechanisms are expected to provide for the efficient functioning of the diurnal cycle of CO2 fixation. The functioning of CAM cannot, however, be interpreted solely in terms of enzymolo-gy, but rather will involve cellular compartmentation of enzymes and metabolites together with intracellular transport processes [17]. 

A step-by-step simulation of the system can be carried out by numerical calculations when the initial values of capacitances and the values of parameters (constants) are assigned. The calculations have been performed using the model from Table 13.1 after assuming n = A. This value is sufficient [86] to achieve reliable simulation data of typical liquid transport processes under study. However, it should be noted that the increase in the number of layers, i.e., increasing in n will always result in more precise calculations and predictions comparable to those achieved by analytic calculation methods. The n-value equal to 4 should be treated as the lowest limit required for obtaining quantitative data sufficient for the interpretation of the separation effects. The problem of proper compartmentalization can be especially significant when reactions locally attain quasi-equUibrium conditions. 

The overall physical state and function of a liquid can be understood by examining transport processes in it. Microemulsions are compartmentalized liquids transport in them can help to reveal their internal consistency, interparticle interaction, overall particle geometry and stability, etc. In line with the scope of this review, concise descriptions and discussions of investigations related to (1) self-... 

CoMPARTMENTAL BoX MODELS AdVECTIVE PlUS DIFFUSIVE Transport Processes... 

Figure 13.3. Model of Stella and Himmelstein, adapted from reference [5] (Section 13.3.1). The drug-carrier conjugate (DC) is administered at a rate i c(DC) into the central compartment of DC, which is characterized by a volume of distribution Fc(DC). DC is transported with an inter-compartmental clearance CLcr(DC) to and from the response (target) compartment with volume Fr(DC), and is eliminated from the central compartment with a clearance CZ.c(DC). The active drug (D) is released from DC in the central and response compartments via saturable processes obeying Michaelis-Menten kinetics defined by Fmax and Km values. D is distributed over the volumes Fc(D) and Fr(D) of the central and response compartment, respectively. D is transported with an inter-compartmental clearance CLcr(D) between the central compartment and response compartment, and is eliminated from the central compartment with a clearance CLc(D).

The discussion above provides a brief qualitative introduction to the transport and fate of chemicals in the environment. The goal of most fate chemists and engineers is to translate this qualitative picture into a conceptual model and ultimately into a quantitative description that can be used to predict or reconstruct the fate of a chemical in the environment (Figure 27.1). This quantitative description usually takes the form of a mass balance model. The idea is to compartmentalize the environment into defined units (control volumes) and to write a mathematical expression for the mass balance within the compartment. As with pharmacokinetic models, transfer between compartments can be included as the complexity of the model increases. There is a great deal of subjectivity to assembling a mass balance model. However, each decision to include or exclude a process or compartment is based on one or more assumptions—most of which can be tested at some level. Over time the applicability of various assumptions for particular chemicals and environmental conditions become known and model standardization becomes possible. 

Fig. 10.8. Simple biogeochemical model for metal mineral transformations in the mycorhizosphere (the roles of the plant and other microorganisms contributing to the overall process are not shown). (1) Proton-promoted (proton pump, cation-anion antiport, organic anion efflux, dissociation of organic acids) and ligand-promoted (e.g. organic adds) dissolution of metal minerals. (2) Release of anionic (e.g. phosphate) nutrients and metal cations. (3) Nutrient uptake. (4) Intra- and extracellular sequestration of toxic metals biosorption, transport, compartmentation, predpitation etc. (5) Immobilization of metals as oxalates. (6) Binding of soluble metal species to soil constituents, e.g. clay minerals, metal oxides, humic substances.

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