Joseph Higgins

DYNAMICS AND CONTROL IN CELLULAR REACTIONS

Publisher Summary This chapter focuses on dynamics and control in cellular reactions. The equations of motion at the metabolic level are derived from the application of the law of Guildberg and Waage to the various enzymatic interactions. The dynamical equations for some particular level can in practice be determined experimentally without regard to those substructures that are not normally excited. A frequent finding that suggests that certain metabolic intermediates maintain a constant ratio is only indicative of the fact that they are engaged in fast reactions. In regard to the theoretical aspects, further studies are required to integrate the concepts of feedback and control with the energetic and synthesizing reactions of the cell, particularly with respect to the ability of the cell to turn these reactions on and off in accordance with external and internal demands.

Waveform generation by enzymatic oscillators

The control of cell chemistry is being investigated through a multipronged approach combining the techniques of physics, chemistry, and biology with the development of electronic instrumentation and the application of analog and digital computers. An example of such metabolic control phenomena is provided by biological oscillators involving enzymatic reactions. These oscillators, which may exist in nearly every kind of cell and even in several forms in a single cell, reveal basic instabilities in biochemical reactions and metabolic control that may be of significance to health and disease. In addition, the high-frequency oscillations observed in simple enzyme systems may be models for the longer-period rhythms that regulate the activities of nearly all biological systems.

ANALYSIS OF SEQUENTIAL REACTIONS

The determination of reaction mechanisms through kinetic analysis is generally a difficult and tedious problem. Ordinarily a mechanism is postulated, analyzed, and tested against the experimental data. If the data do not fit the mechanism, it is modified and the procedure repeated. The test of the mechanism selected usually involves the evaluation of rate constants or composite constants; however, it is the “constancy” of these constants and not their specific values that verifies the satisfactory character of the mechanism. The labor required for success in this indirect approach is strongly dependent on a judicious choice for the post.ulated mechanism. An attempt has been made to develop a method that can relate the kinetic properties directly to the reaction mechanism. In principle the method involves the study of general types of mechanisms to determine the qualitative and quantitative kinetic properties which can be used as distinguishing features. Particular emphasis is placed on properties sensitive to the stoichiometry without regard to the specific values of the rate constants. Such properties have been established for a large class of sequential reactions by a technique combining computer study with mathematical analysis.’ As the use of the computer has been discussed elsewhere,* results primarily due to its application will only be summarized. However, one particular mathematical technique, baaed on the concept of a “stoichiometric reflection coefficient,” will be discussed in greater detail. This technique provides not only a mathematical approach to the analysis of complex mechanisms, but also an experimental method for the partial determination of the mechanism from studies of the stationary or steadystate characteristics.

The mechanism of catalase action. II. Electric analog computer studies.

Abstract An electric analog computer has been constructed for a study of the kinetics of catalase action. This computer gives results for the formation and disappearance of the catalase-hydrogen peroxide complex that are in good agreement with the experimental data. The computer study verifies an approximate method for the computation of the velocity constant for the combination of hydrogen peroxide and catalase and justifies the simple formula used previously to compute the velocity constant for the reaction of the catalase-hydrogen peroxide complex with donor molecules. Finally, the computer data show that the binding of peroxide to catalase is a practically irreversible reaction.

Simulation and analysis of biochemical systems: I. representation of chemical kinetics

In the study of problems in chemical kinetics in ordinary solution, reactions which may be represented by chemical equations of the form<supscrpt>3</supscrpt> <italic>A</italic> + <italic>B</italic> = <italic>C</italic> + <italic>D</italic> (1) are represented kinetically by the differential equations <italic>d</italic>(<italic>C</italic>)/<italic>dt</italic> = <italic>d</italic>(<italic>D</italic>/<italic>dt</italic> = -<italic>d</italic>(<italic>A</italic>)/<italic>dt</italic> = - <italic>d</italic>(<italic>B</italic>)/<italic>dt</italic> = <italic>k</italic>(<italic>A</italic>)(<italic>B</italic>) (2) where (<italic>A</italic>), (<italic>B</italic>), (<italic>C</italic>), ··· , are the concentrations of <italic>A</italic>, <italic>B</italic>, <italic>C</italic>, ··· , and <italic>k</italic> is the kinetic constant for the reaction (assuming it to be occurring in ordinary solution).

Peroxidase kinetics in coupled oxidation; an experimental and theoretical study.

Abstract The current mechanism for the peroxidase system adequately explains the rather peculiar kinetics of the formation of peroxidase complexes in coupled oxidation reactions. The apparent absence of complex I is caused by its low steady-state concentrations. The concept of a “double” steady state in coupled oxidations is introduced and affords an explanation for the induction period in the formation of complex II. The delayed rise of the concentration of this complex to its maximum value is caused by the exhaustion of endogenous donor in the peroxidase preparation. The stability of “double” steady states in biological systems utilizing coupled oxidations is briefly discussed, and the importance of catalase in such systems is emphasized.

THE CONTROL THEORETIC APPROACH TO THE ANALYSIS OF GLYCOLYTIC OSCILLATORS

Publisher Summary For the glycolytic pathway, based on the in vitro control character of the enzymes, there are a dozen mechanisms, corresponding to distinct control situations, which could account for the oscillatory dynamics. At this stage, the problem is no longer one of providing a basic understanding of biochemical oscillations, but the determination of the details that account for the oscillations in specific circumstances. The analysis and formulation of this aspect is not limited to oscillatory dynamics; the approach is just as applicable to the analysis of any dynamic response and the oscillatory kinetics provides just one example, though it is of particular interest at this time. This chapter presents the studies of the oscillating glycolytic system and discusses its utility as a basis for theoretical deductions, for the formulation of computer models and for the direct analysis of kinetic data for multi-enzyme systems in terms of the underlying properties of the individual reactions

History and Original Thoughts on the Control Theoretic Approach

I have been asked to present some historical background on the early theory of metabolic control; I am pleased to do so. I guess I was asked to do this because to some, at least, I am considered a grandfather of the field. I am not sure how I came to be a grandfather without ever being a father. Yet let that be, for I accept the accolade with sincere appreciation even though I think it partly, if not wholly, apocryphal. But if there are grandfathers, there must also be great-grandfathers and even great-great-grandfathers lurking in the woods. So with no small concern about the validity of such terms, I shall nevertheless address this history in those terms. Hopefully some grandchildren will be reading too. But let me note at the outset that I am not a scientific historian and that I present this history from a rather personal view.