Biochemical neuron

Subsequently, Okamoto and associates [84-86] investigated the connection of several cyclic enzyme systems in order to construct a network. In their models the cyclic enzyme system represents a biochemical neuron that participates in a biochemical neural network. These models are detailed in Table 1.2. Theoretical models of such networks were also proposed by Hjelmfelt and co-workers [109-111,116], and these are also presented in Table 1.2. 

The biochemical neuron has another role as a transducer of external analog signals to impulse signals, where the external signals are received at the receptive field and transduced to impulse signals by cutting off at a certain threshold value. 

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 results obtained from the experimental studies confirm that the information-processing functions predicted by the pertinent analytical models can be achieved experimentally. Moreover, these results support the view that artificial biochemical neurons can be implemented in practice for informationprocessing purposes. Furthermore, because of the very high dependence of the system function on the internal parameters and the relations between them, the analytical models developed are essential tools for the engineering design of such systems as well as for determination of the operational parameters required for these systems to perform the information-processing function desired. 

In principle, there are two main possibilities for connecting biochemical neurons ... 

Chemical species that parhcipate in one biochemical neuron can play the role of effector for another biochemical neuron. 

Chemical species emerging as products from one neuron may be fed as substrates to a subsequent biochemical neuron. 

Network A is designed to funchon as an information processor when each basic system can be seen as a node or a biochemical neuron in the network. In this network, cofactors A and B are shared by all the biochemical neurons of the network. Therefore, these biochemical neurons are fully connected to one another, and the information flows back and forth from each neuron to all others. 

The results presented in Figure 4.43 were obtained with the same feed stream composition as for Figure 4.42, but for different values of Vm,i- Thus, the maximum reachon rates of the first biochemical neuron were increased from 0.4 mM/min to 0.7 mM/min, and the maximum reaction rates of the second biochemical neuron were reduced from 0.4 mM/min to 0.1 mM/min. It can be seen that the output signals obtained here are different from those... 

As mentioned above, simulations were also carried out with higher values of n. However, the signals obtained in these simulations did not differ from those obtained with n = 2. Therefore, for the network system considered here, there is no advantage in employing more than two biochemical neurons in the network. 

Representative results obtained from the numerical simulations performed for network B are presented helow. The results collected in Figures 4.45 to 4.49 were obtained for a network composed of six biochemical neurons. The feedforward type of network has a particular characteristic. Thus, for neuron i in a network composed of neurons (when output signals of neuron i (i.e., P2i-i, P2i, A , and B ), as well as A and B , are independent of n. Moreover, for such a network, the only outputs that depend on n are P2 -i and P2 . Thus, the only effect of adding neurons to the network is to increase the number of output signals available. 

In this network, the information proceeds from one biochemical neuron to a subsequent one and also in the opposite direchon, and this is due to cofactors A and B, which are common to all the biochenaical neurons in the network. Thus, this network is fully connected rather than being of the feedforward type exemplified by network B. 

The results presented in Figure 4.53 were obtained with six biochemical neurons in the network. In this case the types of signal obtained are very similar to those in Figure 4.52. A repetitive signal with a time period of 5 min (that means division by 2) is obtained for Pe. The concentration prohle of P4 is a repetitive signal with a period of 10 min that can be subdivided into two different signal types, each of which is characterized with a time period of 5 min. Therefore, with respect to these prohles, division by 2 is performed by this network as well. 

A series of networks were considered in this study. In all cases the networks were built of a number of basic systems (biochemical neurons), and communication between the individual neurons was achieved by chemical species passing from one neuron to another, where they participate in processes taking place therein. This type of communication is operative in natural neuronic systems, where information from one neuron to the other is passed as neurotransmitter molecules crossing the synapses connecting the participating neurons. 

The networks considered in this study are of three main types (identified as A, B, and C), differing from one another by the mode of connection between the participating biochemical neurons (see Table 5.1). For each network considered, an analytical model was written describing the performance of the network in kinetic terms. As the first stage in this program, analytical models were developed for the case when the reactions of the biochemical networks take place in fed-batch reactors. It is envisaged that these models will be extended to packed bed reactors in the future. 

The biochemical network is built of a number of processing elements (i.e., the biochemical neurons). These are the enzymic basic systems. The term elementary is not an absolute one. However, the processing based on a few enzymic reactions is less complex than the processing of electrical signals as achieved by natural nerve cells. 

The enzymic basic systems can be highly interconnected, due to chemical components that participate in processes that take place in more than one biochemical neuron. 

In the biochemical network each biochemical neuron works only with the substrates required for the specific reactions involved and is not affected by the reactions that take place in other neurons, unless they share a particular component. 

Now we can look at the biochemical networks developed in this work and compare them to the recurrent networks discussed above. Network A (Section 4.2.1) and Network C (Section 4.2.3) are fully connected to one another, and the information flows back and forth from each neuron to all the others. This situation is very much hke the one described for recurrent neural networks, and in these cases, memory, which is a necessary to demonstrate computational power, is clearly incorporated in the networks. Network B (Section 4.2.2) is a feedforward network and thus appears to have no memory in this form. However, when we examine the processes taking place in the biochemical neuron more carefully, we can see that the enzymic reactions take into account the concentration of the relevant substrates present in the system. These substrates can be fed as inputs at any time t. However, part of them also remained from the reactions that took place at time t — and thus the enzymic system in every form is influenced by the processes that took place at early stages. Hence, memory is always incorporated. 

The activation function of the biochemical neuron is defined by the reaction mechanism and the pertinent rate equations. This function is actually a set of differential equations derived from mass balances for the components taking part in the enzymic reactions in each biochemical neuron (see Section 4.1.3). 

The recurrent network models assume that the structure of the network, as well as the values of the weights, do not change in time. Moreover, only the activation values (i.e., the output of each processor that is used in the next iteration) changes in time. In the biochemical network one cannot separate outputs and weights. The outputs of one biochemical neurons are time dependent and enter the following biochemical neurons as they are. However, the coefficients involved in these biochemical processes are the kinetic constants that appear in the rate equations, and these constants are real numbers. The inputs considered in biochemical networks are continuous analog numbers that change over time. The inputs to the recurrent neural networks are sets of binary numbers. 

Enzyme-based biochemical neurons can be built, analyzed, and operated using some of the basic principles of neural networks. 

M. Okamoto, Y. Maki, T. Sekiguchi, and S. Yoshida, Self-organization in a biochemical-neuron network, Physica D Nonlinear Phenomena, 84, 194-203 (1995). 

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