Kinetics of biochemical reactions

Brezonik, P. L. (1994). Kinetics of biochemical reactions and microbial processes in natural waters. In Chemical Kinetics and Process Dynamics in Aquatic Systems. Lewis Publishers, Boca Raton, FL, pp. 419-552. 

In the design and operation of various bioreactors, a practical knowledge of physical transfer processes - that is, mass and heat transfer, as described in the relevant previous chapters - are often also required in addition to knowledge of the kinetics of biochemical reactions and of cell kinetics. Some basic concepts on the effects of diffusion inside the particles of catalysts, or of immobilized enzymes or cells, is provided in the following section. 

A note on mechanism and memory in the kinetics of biochemical reactions. Math. BioscL 3,421-429 (1968). 

B20. Bodansky, 0., The use of different measures of reaction velocity in the study of the kinetics of biochemical reactions. J. Biol. Chem. 120, 555-574 (1937). 

The usefulness of undercooled water as a reaction medium has also been demonstrated in biochemical studies. Thus, the kinetics of biochemical reaction sequences can be sufficiently slowed down to become time resolved at subzero temperatures in the unfrozen state. Even more importantly, complex reaction pathways (mechanisms) are unaffected by undercooling, whereas the use of conventional cryoprotectants (glycerol, ethane diol, dimethylsulfoxide, etc.) alters the pathways, although not necessarily the nature of the end products. Finally, single cells or even cell clusters can be stored and kept intact for considerable periods in undercooled aqueous media. 

A classic paper in the evolution of knowledge of the kinetics of biochemical reactions is that of J. Monod [Ann. Rev. Microbiol., 3,371(1942)]. His paper indicates that the kinetics of the growth of E. coli are of the form... 

The rate of reactions in terms of the amount of converted reactant per volume of reactor and time may vary over several orders of magnitude. The kinetics of biochemical reactions are often slow, and take place on a time scale of hours and days, whereas chemical reactions proceed at rates that are orders of magnitude higher. 

Genetic circuits must integrate specific components or network motifs that make them robust to fluctuations in the kinetics of biochemical reactions. Gene expression tends to be noisy because of the stochastic nature of the constituent biochemical reactions (Elowitz et al., 2002 McAdams and Arkin, 1997). In addition, fluctuations in environmental conditions, such as temperature and nutrient levels, affect cellular metabolism and consequently the operation of genetic circuits. Circuits that achieve reproducible, reliable behavior must do so despite components whose behavior fluctuates considerably. Mitigating the effects of gene expression noise will probably require a solution that incorporates positive and negative feedback loops. 

Biochemical pathways consist of networks of individual reactions that have many feedback mechanisms. This makes their study and the elucidation of kinetics of individual reaction steps and their regulation so difficult. Nevertheless, important inroads have already been achieved. Much of this has been done by studying the metabolism of microorganisms in fermentation reactors. 

This chapter solely reviews tlie kinetics of enzyme reactions, modeling, and simulation of biochemical reactions and scale-up of bioreactors. More comprehensive treatments of biochemical reactions, modeling, and simulation are provided by Bailey and Ollis [2], Bungay [3], Sinclair and Kristiansen [4], Volesky and Votruba [5], and Ingham et al. [6]. 

This chapter discusses the kinetics, modeling and simulation of biochemical reactions, types and scale-up of bioreactors. The chapter provides definitions and summary of biological characteristics. 

Each of the processes shown in Figure 2.8 can be described by a Michaelis-Menten type of biochemical reaction, a standard generalized mathematical equation describing the interaction of a substrate with an enzyme. Michaelis and Men ten realized in 1913 that the kinetics of enzyme reactions differed from the kinetics of conventional... 

Gorin, G., Martin, P.A., and Doughty, G. (1966) Kinetics of the reaction of N-ethylmaleimide with cysteine and some congeners. Arch. Biochem. Biophys. 115, 593. 

The subject of biochemical reactions is very broad, covering both cellular and enzymatic processes. While there are some similarities between enzyme kinetics and the kinetics of cell growth, cell-growth kinetics tend to be much more complex, and are subject to regulation by a wide variety of external agents. The enzymatic production of a species via enzymes in cells is inherently a complex, coupled process, affected by the activity of the enzyme, the quantity of the enzyme, and the quantity and viability of the available cells. In this chapter, we focus solely on the kinetics of enzyme reactions, without considering the source of the enzyme or other cellular processes. For our purpose, we consider the enzyme to be readily available in a relatively pure form, off the shelf, as many enzymes are. 

Reactions with soluble enzymes are generally conducted in batch reactors (Chapter 12) to avoid loss of the catalyst (enzyme), which is usually expensive. If steps are taken to prevent the loss of enzyme, or facilitate its reuse (by entrapment or immobilization onto a support), flow reactors may be used (e.g., CSTR, Chapter 14). More comprehensive treatments of biochemical reactions, from the point of view of both kinetics and reactors, may be found in books by Bailey and Ollis (1986) and by Atkinson and Mavituna (1983). 

As outlined in the previous section, there is a hierarchy of possible representations of metabolism and no unique definition what constitutes a true model of metabolism exists. Nonetheless, mathematical modeling of metabolism is usually closely associated with changes in compound concentrations that are described in terms of rates of biochemical reactions. In this section, we outline the nomenclature and the essential steps in constructing explicit kinetic models of metabolic networks. 

The approximate kinetic formats discussed above face inherent difficulties to account for fundamental physicochemical properties of biochemical reactions, such as the Haldane relation discussed in Section III.C.4 a major drawback when aiming to formulate thermodynamically consistent models. 

Kinetic parameters Vmax and Km give information about the relative speed of biochemical reactions and the ease of interaction between the enzyme and its substrate respectively. Inhibitors may increase Km or decrease Vmax and metabolic control often relies on these effects. 

Happe, R. P., Roseboom, W. and Albracht, S. P. (1999) Pre-steady-state kinetics of the reactions of [NiFe]-hydrogenase from Chromatium vinosum with H2 and CO. Eur. J. Biochem., 259, 602-8. 

Those experimentalists who use spectrophotometry or spectrofluorimetry to measure rates of biochemical reactions should always be mindful that bubble clearance frequently displays first-order kinetics. This applies to bubbles adhering to the inside wall of the cuvette as well as bubbles released from solution itself. The presence of bubbles within a cuvette may introduce artifactual kinetic behavior resulting (a) from refractive index differences between the gas trapped in the bubbles and that of the test solution, and (b) from the high reflectance of the air/water interface surrounding some bubbles. 

Because cryosolvents must be used in studies of biochemical reactions in water, it is important to recall that the dielectric constant of a solution increases with decreasing temperature. Fink and Geeves describe the following steps (1) preliminary tests to identify possible cryosolvent(s) (2) determination of the effect of cosolvent on the catalytic properties (3) determination of the effect of cosolvent on the structural properties (4) determination of the effect of subzero temperature on the catalytic properties (5) determination of the effect of subzero temperature on the structural properties (6) detection of intermediates by initiating catalytic reaction at subzero temperature (7) kinetic, thermodynamic, and spectral characterization of detected intermediates (8) correlation of low-temperature findings with those under normal conditions and (9) structural studies on trapped intermediates. 

The field of theoretical molecular sciences ranges from fundamental physical questions relevant to the molecular concept, through the statics and dynamics of isolated molecules, aggregates and materials, molecular properties and interactions, and the role of molecules in the biological sciences. Therefore, it involves the physical basis for geometric and electronic structure, states of aggregation, physical and chemical transformations, thermodynamic and kinetic properties, as well as unusual properties such as extreme flexibility or strong relativistic or quantum-field effects, extreme conditions such as intense radiation fields or interaction with the continuum, and the specificity of biochemical reactions. 

One of the most important problems that has been actively studied during the past few years is the hydration of biological molecules, especially carbohydrates, and the effect of hydration on the conformation of the solute molecule, as well as the effect of the latter on the water structure. Different theoretical and experimental methods have been utilized, and the discrepancies between the results, expressed as numbers of hydration, are considerable. In addition, the water molecule is a reactant in a number of biochemical reactions. The kinetics of these reactions is influenced both by the conformation of the carbohydrate and the structure of the water. These questions will be discussed, with particular reference to the contribution of the vibrational, spectroscopic information to an understanding of such complex mechanisms. 

Enzymatic ester hydrolysis is a common and widespread biochemical reaction. Since simple procedures are available to follow the kinetics of hydrolytic reactions, great efforts have been made during the last years to explain this form of catalysis in chemical terms, i.e., in analogy to known non-enzymatic reactions, and to define the components of the active sites. The ultimate aim of this research is the synthesis of an artificial enzyme with the same substrate specificity and comparable speeds of reaction as the natural catalyst. 

J. Przekwas, A. Przekwas, Simulation of Biochemical Reaction Kinetics in Microfluidic Systems, IMRET3 Proceedings of the Third International Conference on Microreaction Technology, Springer, Berlin Heidelberg, New York, 2000, p. 441-450. 

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