Compartmental dynamic systems

An overview of the compartment properties of reverse micelles is illustrated in Figure 9.16, which also gives some of the relevant references. As already mentioned, reverse micelles are dynamic systems that rapidly exchange compartmentalized materials. There is however one limit to this when the enclosed solutes are macromolecules. Thus, if two different populations of reverse micelles are mixed, one, say, with enzymes and the other with nucleic acids, the two macromolecules are not going to interact with each other. 

The techniques described in this section are useful for studying chemical dynamics in the neighborhood of critical points. The remainder of this paper is devoted to the analysis of the global dynamics of nonlinear kinetic equations. In Section 2 a topological theorem is given, which can be used to place restrictions on the entire set of critical points of a chemical network. In Section 3 it is shown that many chemical networks can be classified on the basis of flows between volumes in concentration space. In Section 4, a number of techniques for establishing limit cycle oscillations in three and more dimensions are described. The topological methods are applied to analysis of compartmental chemical systems in Section 5. The results are discussed in Section 6. In the Appendix the principal mathematical results that have been used in the text are summarized. 

Acid hydrolase activity is poised for optimal activity and control by the nature of the enzyme microenvironment within the lysosome-vacuolar apparatus. A significant feature of this control has already been discussed in Section VI A.l. It was demonstrated that an interposed membrane precluded normal access of substrate to active site. In this section we will consider those factors which allow for optimal hydrolase activity within the compartmentalized vacuolar system. It must be realized that the lysosome-vacuolar system is maintained in a dynamic state and that trans-membrane diffusion of intermediates and metabolites may be oc-... 

Almost aU the biological models are nonhnear dynamic systems, including for example saturation or threshold processes. In particular, nonlinear compartmental models. Equation 9.5, are frequently found in biomedical applications. For such models the entries of K are functions of q, most commonly fcy is a function of only few components of q, often q, or qj. Examples of fcy function of q,- or qj are the Hill and... 

The first two sections of Chapter 5 give a practical introduction to dynamic models and their numerical solution. In addition to some classical methods, an efficient procedure is presented for solving systems of stiff differential equations frequently encountered in chemistry and biology. Sensitivity analysis of dynamic models and their reduction based on quasy-steady-state approximation are discussed. The second central problem of this chapter is estimating parameters in ordinary differential equations. An efficient short-cut method designed specifically for PC s is presented and applied to parameter estimation, numerical deconvolution and input determination. Application examples concern enzyme kinetics and pharmacokinetic compartmental modelling. 

Mathematics is now called upon to describe the compartmental configurations and then to simulate their dynamic behavior. To build up mathematical equations expressing compartmental systems, one has to express the mass balance equations for each compartment i ... 

In order to understand these complex metabolic interactions more fully and to maximize the information obtained in these studies, we developed a detailed kinetic model of zinc metabolism(, ). Modeling of the kinetic data obtained from measurements of biological tracers by compartmental analysis allows derivation of information related not only to the transient dynamic patterns of tracer movements through the system, but also information about the steady state patterns of native zinc. This approach provides data for absorption, absorption rates, transfer rates between compartments, zinc masses in the total body and individual compartments and minimum daily requirements. Data may be collected without disrupting the normal living patterns of the subjects and the difficulties and inconveniences of metabolic wards can be avoided. 

The Systems Biology of dynamic intracellular structures and compartmentation has an exciting and bright future. We can only hope that this chapter can help start the new activities. 

Most importantly, reaction rates in nanofluidic systems can be controlled both by shape and volume changes. The important interplay between chemical reactions and geometry has been conceptualized within a theoretical framework for ultra-small volumes and tested on a number of experimental systems, opening pathways to more complex, dynamically compartmentalized ultra-small volume reactors, or artificial model cells, that offer more detailed understanding of cellular kinetics and biophysical phenomena, such as macromolecular crowding. 

Recently, the author advocated the application of the systems approach in the analysis and synthesis of a biotechnological process ( 1). The hierarchy of a biological system involves structural, functional, descriptive, control and dynamic organization. Structural and functional hierarchies of a biotechnological process are depicted in Tables I and II. In Table II a compartmental level is omitted. This is possible as long as the translocation of substances between organelles and cytoplasm is not important. The scheme of functions should be understood in both directions,... 

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