The Extended Basic System

To develop analytical models that describe the performance of a cyclic enzyme system (herein termed the basic system) and a cyclic enzyme system with an external inhibitor (termed the extended basic system) when operated in different modes as a fed-batch reactor or a continuous reactor. These models enable us to design systems and select operational conditions according to needs. 

The basic system considered in this study relies on well-dehned enzymic reactions and is designed to function as a node or biochemical neuron in biochemical networks. This system involves two enzyme-catalyzed reactions, coupled to one another by the use of a cofactor, the latter being cycled continuously between the two. In addition, the two consumable substrates are fed into the system continuously at predetermined concentrations and rates. Also considered in this work was an extension of the basic system termed the extended basic system. The extended system relies on the same reactions as those in the basic system in addition, an external compound, inhibitory to one of the enzymes, is fed into the system. 

The research was carried out on two main avenues. The first is a theoretical investigation in which analytical models were developed and their characteristics were studied by numerical simulations the second is experimental research in which systems designed and studied in the former part of the program were implemented as biochemical reactors. In the first stage of the research, analytical models were developed for both the basic system and the extended basic system. These models consider that the reactions take place... 

THE EXTENDED BASIC SYSTEM THEORETICAL CONSIDERATIONS AND RESULTS... 

An extension of the basic system considered in this work is termed the extended basic system. This system was also designed to function as an information-processing unit and is characterized in Section 4.4.1. Its chrac-teristics as an informahon-processing unit are described in Section 4.4.2. In Sechon 4.4.3 the analytical model that was written for the extended basic system is presented. Using this model, numerical simulations were carried out and their results are presented in Section 4.4.4. 

The extended basic system shown in Figure 4.71 relies on the same reactions as those utilized in the basic system reactions (1) and (2) of Section 4.1.1. In addition to the processes considered in the basic system, an external inhibitor for enzyme Ei is fed into the system. 

The extended basic system is also designed to function as an informationprocessing unit with the same characteristics as those defined in Section... 

Table 4.11 Input Signal in the Extended Basic System ...

The analytical models developed in this part are based on those written for the basic system and presented in Section 4.1.3. The extended basic system is considered useful for information processing only with continuous operational modes. This is due to the fact that the inhibitor is not consumed in the reactor, and in a fed-batch reactor it accumulates and causes only decay effects. Therefore, the analytical model presented here refers only to a continuous reactor. 

Applying the compartmental analysis approach leads to equations (32) to (37), which hold for both the basic and the extended basic systems. When the latter is considered, the following equation should also be used ... 

Equations (32) to (37) are related to the reaction mechanism considered. For the extended basic system, the inhibition process is taken into account in rate equations ri and r2. The options considered in this study are detailed in the Sections 4.4.3a and b. 

In this section, results of numerical simulations are presented for the case when the extended basic system is operated in a continuous reactor. Here, the inhibitor enters the reactor as a component of the feed stream and affects the enzyme Ei (it is competitive with Si). In Figures 4.72 to 4.77 the effects of the system parameters on the concentration of B in a PFR with an external inhibitor are presented. The sets of the basic values used for the parameters involved are given in Table 4.12, set I. 

Table 4.12 Numerical Values of the Operational Parameters Used in Simulations of the Extended Basic System When Operated as a Packed Bed Reactor...

Figure 4.72 Effect of K on the concentration profile of B in the extended basic system when operated as a PER (n = 5). The values of Ki are indicated above, [Si]o = [S2],o = 46.6 mM, and the values used for all other parameters are given in Table 4.12, set I.

Figure 4.81 Effect of r of an external inhibitor on the concentration profile of B in the extended basic system when operated as a packed bed reactor (n = 3). The external inhibitor concentration varies between 0 and 20 mM. Data for r = 1, 5, and 10 min are taken from Figures 4.78, 4.79, and 4.80, respectively. The size of the bars indicates the values of r.

This new system is an extension of the basic system discussed above. In the extended basic system an external inhibitor is also involved in the processes taking place. This component provides an additional path for control of the enzymic activity. Thus, whereas in the basic system the input signal is composed of concentration profiles of the consumable substrates, here the input signal contains a component that is an effector for one of the enzymes but is not consumed in the reactions. Due to this characteristic, this system is considered useful in terms of information processing only with continuous operational modes. 

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