Kinetics biochemical reaction

We can view an enzyme as a biological catalyst, and as such it leads to kinetic rate expressions that are of similar form to those derived in heterogeneous reaction 

The reaction rate for the formation of product (rP) can then be derived from certain assumptions to take the following form that represents observed experimental 

Here k is the rate constant for the irreversible reaction, Ceo is the total enzyme concentration, Cs is the substrate concentration, and is the Michaelis-Menton constant. Both k and KM may be functions of pH, temperature, and other properties of the fermentation medium. From this kinetic expression, we see that at high substrate concentrations the rate of product formation is independent of Cs and is approximately equal to kCm-This is due to the presence of a limited amount of enzyme, which is required for the reaction to proceed, and adding more substrate under these conditions will not cause the reaction rate to increase further. At low substrate concentrations, the rate of product formation becomes first-order with respect to Cs- Under these conditions the substrate concentration becomes the determinant for product formation, and increasing Cs produces a proportional increase in rate. The rate is also proportional to the total enzyme concentration under all conditions of substrate concentration. 

Fermentations may be aerobic when the cells must be in the presence of an O2 environment or anaerobic when they cannot. Water is the standard fermentation medium and is also one of the products, as is carbon dioxide, which is removed from the liquid and leaves in a vapor product stream since it may have a negative effect on the cells. Other nutrients or media (sources of nitrogen, phosphorus, minerals, vitamins, etc.) typically must be supplied to keep the organisms happy and healthy. 

Since many biochemical reactions and their stoichiometry are not well understood, we often find a more empirical approach to the quantitative assessment of the kinetics. Mass concentration units (e.g., g/L) are often used along with yield coefficients to calculate the distribution of products formed and the amount of substrate consumed. In the absence of any inhibition effects and in the presence of an infinite supply of substrate, the rate of cell growth rx is autocatalytic, that is, it depends only on the concentration of cells (Cx), and the more cells we have, the higher the growth rate. The cell biomass is typically represented by X  

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All enzymatic reactions are initiated by formation of a binary encounter complex between the enzyme and its substrate molecule (or one of its substrate molecules in the case of multiple substrate reactions see Section 2.6 below). Formation of this encounter complex is almost always driven by noncovalent interactions between the enzyme active site and the substrate. Hence the reaction represents a reversible equilibrium that can be described by a pseudo-first-order association rate constant (kon) and a first-order dissociation rate constant (kM) (see Appendix 1 for a refresher on biochemical reaction kinetics) ... 

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. 

Simulation of biochemical reaction kinetics in microfluidic systems, in Ehrfeld, W. (Ed.), Microreaction Technology 3rd International Conference on Microreaction Technology, Proc. of IMRET 3, Springer-Verlag, Berlin, 2000, 441 450. 

Part II of this book represents the bulk of the material on the analysis and modeling of biochemical systems. Concepts covered include biochemical reaction kinetics and kinetics of enzyme-mediated reactions simulation and analysis of biochemical systems including non-equilibrium open systems, metabolic networks, and phosphorylation cascades transport processes including membrane transport and electrophysiological systems. Part III covers the specialized topics of spatially distributed transport modeling and blood-tissue solute exchange, constraint-based analysis of large-scale biochemical networks, protein-protein interactions, and stochastic systems. 

Wu B. Integration of mixing, heat transfer, and biochemical reaction kinetics in anaerobic methane fermentation. Biotechnol Bioeng 2012 109(11) 2864-74. 

Divinylbenzene copolymers with styrene are produced extensively as supports for the active sites of ion-exchange resins and in biochemical synthesis. About 1—10 wt % divinylbenzene is used, depending on the required rigidity of the cross-linked gel, and the polymerization is carried out as a suspension of the monomer-phase droplets in water, usually as a batch process. Several studies have been reported on the reaction kinetics (200,201). 

Except as an index of respiration, carbon dioxide is seldom considered in fermentations but plays important roles. Its participation in carbonate equilibria affects pH removal of carbon dioxide by photosynthesis can force the pH above 10 in dense, well-illuminated algal cultures. Several biochemical reactions involve carbon dioxide, so their kinetics and equilibrium concentrations are dependent on gas concentrations, and metabolic rates of associated reactions may also change. Attempts to increase oxygen transfer rates by elevating pressure to get more driving force sometimes encounter poor process performance that might oe attributed to excessive dissolved carbon dioxide. 

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... 

In studies of reactions in nanomaterials, biochemical reactions within the cell, and other systems with small length scales, it is necessary to deal with reactive dynamics on a mesoscale level that incorporates the effects of molecular fluctuations. In such systems mean field kinetic approaches may lose their validity. In this section we show how hybrid MPC-MD schemes can be generalized to treat chemical reactions. 

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). 

Chapter 10 Biochemical Reactions Enzyme Kinetics SOLUTION... 

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