Transport Michaelis-Menten equation

Table 18.2 lists 30 of the molecules used in this study that are known to be substrates for active transport or active efflux. The mechanistic ACAT model was modified to accommodate saturable uptake and saturable efflux using standard Michaelis-Menten equations. It was assumed that enzymes responsible for active uptake of drug molecules from the lumen and active efflux from the enterocytes to the lumen were homogeneously dispersed within each luminal compartment and each corresponding enterocyte compartment, respectively. Equation (5) is the overall mass balance for drug in the enterocyte compartment lining the intestinal wall. 

The rate equation for a single class of transporters acting on a metabolite is analogous to the Michaelis-Menten equation, except that one must also account for the effects of passive diffusion ... 

Drug metabolism, renal tubular secretion, and biliary secretion are usually mediated by metabolizing enzymes or transporter proteins. These protein systems usually possess good substrate selectivity with finite capacities, which are described by the Michaelis-Menten equation,... 

This section describes the theoretical part of the prediction of drug-drug interaction (Fig. 1). Unlike channels, transporters form intermediate complex with its substrate, and thus, the membrane transport involving transporters is characterized by saturation, reaching the maximum transport velocity by increasing the substrate concentrations. The intrinsic clearance of the membrane transport involving transporters (PSint) follows Michaelis-Menten equation (Eq. 1). 

For a substrate that is transported by a facilitated diffusion mechanism, the kinetics follow a rectangular hyperbola (Fig, 1) and can be fit to the foUovring Michaelis-Menten equation ... 

Kinetics of carrier-mediated transport processes is similar to enzyme-substrate reactions and can be described by the Michaelis-Menten equation (Eq. (9.2)), assuming that each transport system has one specific binding site for its substrates. Maximum transport velocity (Vmax) is reached when all binding sites of the respective carrier proteins are occupied by substrate molecules. Substrate turnover can be delineated by the Michaelis constant Km corresponding to the substrate concentration [S], at which half-maximum transport velocity has been reached (Figure 9.5). Km also depends on pH and temperature. In cotransport systems transferring several substrates, the transport protein has a characteristic Km for each molecule transported. 

Nearly all enzymes follow what is known as Michaelis-Menten kinetics, which was encountered in Section 10.2.2 for carrier-mediated transport processes. The Michaelis-Menten equation for the rate of metabolism f mei) c.an be written as... 

Russell R.W. Drane J.W. (1992). Improved rearrangement of the integrated Michaelis-Menten equation for calculating in vivo kinetics of transport and metabolism. / Dairy Set, 75, 3455-3464. 

The kinetics of glucose transport through the membrane follows the Michaelis-Menten equation ... 

The Michaelis-Menten equation can be rearranged so that a plot 1/Vb versus l/[glucose] produces a straight fine. Rearrange the equation and plot the data in order to determine K[ and for glucose transport across the erythrocyte membrane. 

Both active and passive fluxes across the cellular membranes can occur simultaneously, but these movements depend on concentrations in different ways (Fig. 3-17). For passive diffusion, the unidirectional component 7jn is proportional to c°, as is indicated by Equation 1.8 for neutral solutes [Jj = Pj(cJ — cj)] and by Equation 3.16 for ions. This proportionality strictly applies only over the range of external concentrations for which the permeability coefficient is essentially independent of concentration, and the membrane potential must not change in the case of charged solutes. Nevertheless, ordinary passive influxes do tend to be proportional to the external concentration, whereas an active influx or the special passive influx known as facilitated diffusion—either of which can be described by a Michaelis-Menten type of formalism—shows saturation effects at higher concentrations. Moreover, facilitated diffusion and active transport exhibit selectivity and competition, whereas ordinary diffusion does not (Fig. 3-17). 

Unfortunately, most enzymes do not obey simple Michaelis-Menten kinetics. Substrate and product inhibition, presence of more than one substrate and product, or coupled enzyme reactions in multi-enzyme systems require much more complicated rate equations. Gaseous or solid substrates or enzymes bound in immobilized cells need additional transport barriers to be taken into consideration. Instead of porous spherical particles, other geometries of catalyst particles can be apphed in stirred tanks, plug-flow reactors and others which need some modified treatment of diffusional restrictions and reaction technology. 

After five days, dopamine, L-tryptophan, and l-DOPA passively permeated through the membrane as indicated by fittings with a first-order kinetic process equation. After seven days of co-culture, occludin localizes at EC periphery, dopamine does not cross the barrier to any further extent, while the transfer of L-tryptophan and l-DOPA fits well with a saturable Michaelis-Menten kinetic process, thus indicating the involvement of a specific carrier-mediated transport mechanism. Permeation studies confirmed that culture of ECs in the presence of neurons induces the characteristic permeability limitations of a functional BBB. 

When interfacial electron exchange rate(s) are sufficiently high and the response is free from mass transport hmitations, the catalytic current will be determined by the inherent activity of the enzyme. Variation of current (activity) with potential can be explained by an extension of the Michaelis-Menten description of enzyme kinetics that relates activity to oxidation state through incorporation of the Nemst equation." " The resulting expressions describe the catalytic cycle, and include rates of intramolecular electron exchange, chemical events, substrate binding and product release, together with the reduction potentials of centres in the enzyme, and the influence of... 

Assuming a Michaelis-Menten rate equation, substrate mass transport through region 1 is governed by ... 

Sometimes abnormally high rates of transport of molecules across membranes are associated with other types of behavior, and a special explanation has to be invoked. For example, the rate of permeation of a substance S frequently varies with its concentration according to an equation of the same form as the Michaelis-Menten... 

Cohen and Monod (C2) have summarized experimental evidence which shows indeed that special mechanisms of transport of organic nutrients occur in bacteria. They call such transport systems permeases. This term ending in -use implies that the system involves enzymes—an implication not yet proved by available data. At any rate, it is found that permease systems can lead to transport against an apparent rise in concentration, as well as other effects not possible with Fickian diffusion. Various hypothetical mechanisms for operation of permease systems yield rates of permeation which exhibit the Michaelis-Menten type of dependence on substrate (including water) concentration. Perhaps it is in the occurrence of one of these mechanisms that the rate equation [Eq. (38)] assumed by Monod and almost all subsequent workers finds its justification. [For further information on biological transport, see, e.g., Christensen (Cl).]... 

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