Substrate transport effectiveness factor

Substrate transport through the film may be formally assimilated to membrane diffusion with a diffusion coefficient defined as12 Ds = Dch( 1 — 9)/pjort. In this equation, the effect of film structure on the transport process in taken into account in two ways. The factor 1—0 stands for the fact that in a plane parallel to the electrode surface and to the coating-solution interface, a fraction 9 of the surface area in made unavailable for linear diffusion (diffusion coefficient Dcj,) by the presence of the film. The tortuosity factor,, defined as the ratio between the average length of the channel and the film thickness, accounts for the fact that the substrate... 

In the case of gel entrapped biocatalysts, or where the biocatalyst has been immobilised in the pores of the carrier, then the reaction is unlikely to occur solely at the surface. Similarly, the consumption of substrate by a microbial film or floe would be expected to occur at some depth into the microbial mass. The situation is more complex than in the case of surface immobilisation since, in this case, transport and reaction occur in parallel. By analogy with the case of heterogeneous catalysis, which is discussed in Chapter 3, the flux of substrate is related to the rate of reaction by the use of an effectiveness factor rj. The rate of reaction is itself expressed in terms of the surface substrate concentration which in many instances will be very close to the bulk substrate concentration. In general, the flux of substrate will be given by ... 

The molecular weight differences between lignin and its model compounds also complicate the use of model compound kinetics in a predictive simulation. The mobility of a high-molecular weight polymer would be much less than that of smaller model substrates (14). As for catalyst decay, a simple model was used to probe transport issues. For a first order, irreversible reaction in an isothermal, spherical catalyst pellet with equimolar counterdiffusion, the catalyst effectiveness factor and Thiele modulus provide the relevant information as... 

The mathematical model for substrate transport with reaction can be used to devise a general approach to predict reaction rates in catalyst particles. The observed rate is defined in terms of the intrinsic rate and an effectiveness factor... 

The constancy of the effective diffusion coefficient In the substrate transport with reaction model. Equation 26 versus Equation 27, depends on two factors. First, if the volume fraction of polymer is not constant with time, radial position in the gel, or extent of reaction, then D is influenced by the relation given in Equation 40. Dooley ct al. (11) present an example of this in their study. Second, if the substrate s diffusion coefficient in the solvent alone is dependent on substrate concentration at the range of concentrations in the reaction system, then D is Influenced similarly according to Equation 39. The assumption of a constant diffusion coefficient in the substrate transport with reaction model must always be justified. 

Electrode response Substrate addition Concept of effectivity factors Transport limitation Transport enhancement... 

Figure 4.32. Plots of effectiveness factor of reaction f/r,ext versus modulus in case of external transport limitation as a function of substrate concentration s/Xg. The rate-determining steps (rds) are indicated with their range of validity by dotted lines, together with the limiting first-order effectiveness factor at low s values. (From Horvath and Engasser, 1974.)...

It is useful to calculate the effectiveness factor q that is a measure of the correct use of the biocatalyst. Effectiveness factor represents the ratio between the actual kinetic rate, when transport resistance actually occurs, and the kinetic rate that would have been observed if all the substrate were exposed to the enzyme, without any transport resistance (Aris, 1965 Bailey and OUis, 1986 Perry and Geen, 1997 Satterfield and Sherwood, 1963). It is estimated as ... 

When the substrate is first transported in a boundary layer surrounding the particle, before diffusing within the catalyst support where reaction occurs, external resistance needs to be considered (Calabro et al, 2008 Truskey et al., 2004). An example is the case of a packed bed bioreactor, where fluid-dynamics play a significant role in the optimization of system performances. In such a case the kinetic contribution has to be expressed in terms of overall effectiveness factor ri y. To estimate it, the mass balance. Equation [1.29], has to be solved by imposing the continuity of mass flux at the wall. For a flat-sheet support it corresponds to ... 

However, the presented effects of a proton gradient on the selectivity of the substrate transported by the phosphate translocator can not fully explain the observed DHAP/PGA gradients between illumination and darkness as measured in spinach leaves (Heldt et al. these proceedings) or isolated chloroplasts (Heldt et al. 1978) One additional factor might be the increasing stromal Mg concentration in the light, which results in an inhibition of 3-PGA transport and a stimulation of Pi and DHAP transport (Fliigge, unpubl. results). 

However, in subsequent studies [23-25,88-90] it was demonstrated that in reality the particle deposition is not a purely geometric effect, and the maximum surface coverage depends on several parameters, such as transport of particles to the surface, external forces, particle-surface and particle-particle interactions such as repulsive electrostatic forces [25], polydispersity of the particles [89], and ionic strength of the colloidal solution [23,88,90]. Using different kinds of particles and substrates, values of the maximum surface coverage varied by as much as a factor of 10 between the different studies. 

Another limitation is that there is no quantitative relationship between active drug transport in the cell culture models and in vivo e.g. [92, 93]. The reason may be that the expression level of the transporter in Caco-2 cells is not comparable to that in vivo or that there is a difference in effective surface area (see Section 4.3.2.2 below). One solution to this problem is to determine the apparent transport constants, Km and Vmax, for each transporter and subsequently, to determine a scaling factor. However, this is not readily done. In addition these studies are further complicated by the lack of specific substrates. For example, there are almost no specific substrates for the drug efflux transporters [18]. Therefore, other epithelial... 

Yet another way to alter the effective activity of an enzyme is to change the accessibility of its substrate. The hexokinase of muscle cannot act on glucose until the sugar enters the myocyte from the blood, and the rate at which it enters depends on the activity of glucose transporters in the plasma membrane. Within cells, membrane-bounded compartments segregate certain enzymes and enzyme systems, and the transport of substrate into these compartments may be the limiting factor in enzyme action. 

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