Compartment phenomenological

Represent the underlying mechanistic model with the desired physiological structure through a set of phenomenological compartments with their... 

The phase-type distribution has an interpretation in terms of the compartmental model. Indeed, if the phenomenological compartment in the model, which is associated with a nonexponential retention-time distribution, is considered as consisting of a number of pseudocompartments (phases) with movement... 

Figure 9.6 Pseudocompartment configurations generating Erlang (A), generalized Erlang (B), and phase-type (C) distributions for retention times in phenomenological compartments. Retention times are distributed according to A Exp(Ai) and Ai Exp(A2).

The third configuration (C) is unusual because the phenomenological compartment output takes place from the second pseudocompartment and the output of the last pseudocompartment is fed back to the second pseudocompartment. The transfer-intensity matrix is... 

Express the retention-time distribution for each phenomenological compartment by using phase-type distributions. However, the phase-type distributions for these sites are determined empirically. There is no assurance of finding the best phase-type distribution. This step leads to the expanded model involving pseudocompartments generating the desired phase-type distribution. 

Simulate the kinetic behavior by combining the P (t) probability functions for the pseudocompartments to obtain the state probabilities P ( ) of a particle belonging to the phenomenological compartments at time t. That is defined by means of appropriate matrices Bi and E 2 with indicator variables, i.e., 0 s or l s ... 

The elements of Bi indicate the origin of particles in the pseudocompartment structure and establish the correspondence between the numbering of the original compartments and the sequence of the pseudocompartments. The elements of B2 indicate the summing of pseudocompartments to yield the phenomenological compartment. 

Vs are the partial molar volumes of water and salt, respectively. t// is the electric potential and I the electric current. Here, Jv,and Js represent the virtual flows. Experimentally, Jv is determined by measuring the change in volume of one or both compartments at opposite surfaces of the membranes. Equation (10.84) yields a set of three-flow linear phenomenological equations of conductance type... 

Actually, the compartments R and S in Fig. 6.8.1 may be uniform in their properties so that the changes in P and occur essentially only across the membrane M. In this case and VP may be replaced by the discontinuities A and Ap across the membrane, the constant thickness of the membrane having been absorbed into the phenomenological coefficients. 

According to the scheme of the compartments in the liquid membrane system in Figure 13.5b, all local diffusion fluxes of M species from ktok+1 compartment can be defined by a phenomenological Equation 13.41 corresponding with the first Pick s law for diffusion ... 

Curran pursued the problem of uphill water transport with the proposal of an intraepithelial series membrane system [30], Depicted in Fig. 5, the essentials of this scheme are three compartments separated by two membranes. The thin membrane between compartments A and B is assumed to be such that salt concentration differences between the compartments are manifest as substantial osmotic forces across the membrane. Across the thick membrane between compartments B and C, salt concentration differences result in negligible osmotic forces. In terms of the phenomenological parameters, the reflection coefficient of the thin membrane is close to one, that of the thick membrane close to zero. For this system, direct salt input into the middle compartment, B, would generate strong osmotic forces favoring flow of water from A to B but not from C to B. Any resulting rise in hydrostatic pressure within the middle compartment would produce volume flow... 

The quantitative predictions of the middle compartment model may be appreciated from the analysis of a compartment model of the lateral intercellular space. The purpose of this analysis is to display the behavior of the composite system in terms of the component membrane parameters. Conversely, the phenomenological observations of coupled water transport impose certain restrictions on models of the lateral intercellular space. With this analysis one may also see how these restrictions translate into parameter selection. 

In these hypothetical systems, there is a ground state and two excited states A and A These are considered phenomenologically as separate entities or compartments without any spectroscopic identities as singlets or triplets. Each entity has its time-dependent population density or concentration, which is denoted by square brackets in (1). The system is supposed to be closed, i.e.. 

Phenomenologically speaking, these molecular level events are reminiscent of those that occur during biotic protein synthesis. Within biotic cells, the objective is to provide a micron-sized compartment (reactor) for the synthesis and amplification of a requisite population of structural and functional proteins — the building blocks of life. These steps involve the dynamic transfer of information through space within the cell by specific carrier molecules (i.e., RNA, etc.). This journey begins with a supramolecular transfer of information in the nucleus (core) and terminates with... 

The cell is represented by a single compartment of finite volume II in contact across a living membrane with an external medium I of fixed composition and pH and of unlimited dimension. The whole layer which lies between the vacuole of an aquatic plant cell and the aqueous solution in which it lives (Figure 1). is treated globally as a single transversally homogeneous membrane. In principle it is assumed that an increased sophistication of the model, e.g., distinction between tonoplast and plasmalemma membranes, sets of ionic conductance of separate specific channels should not affect the overall validity of the phenomenological relations. Thus, the results are also valid for the plasmalemma alone. 

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