Kinetics and Regulation

Homogeneous versus Heterogeneous Populations of Cross-bridges 

Huxley s model (1957) for muscle contraction states that the mechanical and enzymatic characteristics can be described by the overall apparent attachment and detachment rates of the cross-bridge. Contraction was described as a transition between free and attached states (Huxley, 1957). This simple yet elegant two-state model produces several specific predictions about the relationships between force production, ATPase rates, and shortening as a function of these two rate constants. Although this model is somewhat oversimplified given the actual number of biochemical states, and several of its assumptions may not strictly hold in 

it implies that the cross-bridge theoretically can be regulated in two basic ways by regulating attachment (or perhaps more appropriately the transition to a force-producing state) and by regulating detachment. 

It is not easy to explain how shortening velocity may be averaged by mixing molecular motors with different speeds within a contractile unit. It may be hypothesized that the slower cross-bridges act as an internal load on the faster cross-bridges (Aksoy et al., 1983). However, there is energetic evidence against such an internal load in SM (Butler et al., 1986). Data from an in vitro motility assay, on the other hand, indi- 

The detachment rates of two cycles that occur in a SM must differ to obtain variable cross-bridge cycling rates, that is, k4 and ky of Fig. 2B are unequal. Both 

---

Ugarova N.N., Luciferase of Luciola mingrelica fireflies. Kinetics and regulation mechanism, J. Biolumin. Chemilumin. 1989 4 406-418. 

Klingauf J, Kavalali ET, Tsien RW (1998) Kinetics and regulation of fast endocytosis at hippocampal synapses. Nature 394 581-5... 

GLUT isoforms play a specific role in glucose metabolism determined by their pattern of tissue expression, substrate specificity, transport kinetics and regulated expression in different physiological conditions. 

M. D. Wolfe, D. J. Altier, A. Stubna, C. V. Popescu, E. Miinck, J. D. Lipscomb, Benzoate 1, 2-dioxygenase from Pseudomonas putida Single turnover kinetics and regulation of a two-component Rieske dioxygenase. Biochemistry 41 (2002) 9611. 

Goldfein, M. D., Kozhevnikov, N. V., and Trubnikov, A. V. Kinetics and regulation mechanism of polymer formation processes. Saratov, Saratov Univ. Press, p. 178 (1989). 

Linz, M., Zeng, A.P., Wagner, R, and Deckwer, W.D. (1997) Stoichiometry, kinetics, and regulation of glucose and amino acid metabolism of a recombinant BHK cell line in batch and continuous cultures. Biotechnol. Progr, 13 (4), 453-463. 

Hundreds of metabohc reac tions take place simultaneously in cells. There are branched and parallel pathways, and a single biochemical may participate in sever distinct reactions. Through mass action, concentration changes caused by one reac tion may effect the kinetics and equilibrium concentrations of another. In order to prevent accumulation of too much of a biochemical, the product or an intermediate in the pathway may slow the production of an enzyme or may inhibit the ac tivation of enzymes regulating the pathway. This is termed feedback control and is shown in Fig. 24-1. More complicated examples are known where two biochemicals ac t in concert to inhibit an enzyme. As accumulation of excessive amounts of a certain biochemical may be the key to economic success, creating mutant cultures with defective metabolic controls has great value to the produc tion of a given produc t. 

RA Siegel. pH sensitive gels—Swelling equilibria, kinetics and applications for drug delivery. In J Kost, ed. Pulsed and Self-Regulated Drug Delivery. Boca Raton, FL CRC Press, 1990, pp 129-157. 

Siegel, R. A., pH-Sensitive Gels Swelling Equilibria, Kinetics, and Applications for Drug Delivery, in Pulsed and Self-Regulated Drug Delivery (J. Kost Ed.), pp. 129-155. CRC Press, Boca Raton (1990). 

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. 

Metal ions play an important role as catalysts in many autoxidation reactions and have been considered instrumental in regulating natural as well as industrial processes. In these reactive systems, in particular when the reactions occur under environmental or in vivo biochemical conditions, the metal ions are involved in complicated interactions with the substrate(s) and dioxygen, and the properties of the actual matrix as well as the transport processes also have a pronounced impact on the overall reactions. In most cases, handling and analyzing such a complexity is beyond the capacity of currently available experimental, computational and theoretical methods, and researchers in this field are obliged to use simplified sub-systems to mimic the complex phenomena. When the simplified conditions are properly chosen, these studies provide surprisingly accurate predictions for the real systems. In this paper we review the results obtained in kinetic and mechanistic studies on the model systems, but we do not discuss their broad biological or environmental implications. 

---