Velocity maximum specific substrate

This max rate r is called maximum specific substrate utilization velocity. Substituting it into equation (2.349), we receive... 

This equation is fundamental to all aspects of the kinetics of enzyme action. The Michaelis-Menten constant, KM, is defined as the concentration of the substrate at which a given enzyme yields one-half of its maximum velocity. is the maximum velocity, which is the rate approached at infinitely high substrate concentration. The Michaelis-Menten equation is the rate equation for a one-substrate enzyme-catalyzed reaction. It provides the quantitative calculation of enzyme characteristics and the analysis for a specific substrate under defined conditions of pH and temperature. KM is a direct measure of the strength of the binding between the enzyme and the substrate. For example, chymotrypsin has a Ku value of 108 mM when glycyltyrosinylglycine is used as its substrate, while the Km value is 2.5 mM when N-20 benzoyltyrosineamide is used as a substrate... 

Q = flow through the reactor Xg = influent microbial concentration jx = maximum specific growth rate S = substrate concentration = half-velocity constant kj = endogenous decay coefficient... 

Michaelis kinetics (Michaelis-Menten kinetics) A simple and useful model of the kinetics of enzyme-catalyzed reactions. It assumes the formation of a specific enzyme-substrate complex. Many enzymes obey Michaelis kinetics and a plot of reaction velocity (V) against substrate concentration [S] gives a characteristic curve showing that the rate increases quickly at first and then levels off to a maximum value. When substrate concentration is low, the rate of reaction is almost proportional to substrate concentration. When substrate concentration is high, the rate is at a maximum, V iax) independent of substrate concentration. The Michaelis constant is the concentration of substrate at half the maximum rate and can be determined experimentally by measuring reaction rate at varying substrate concentrations. Different types of inhibition can also be distinguished in this way. Allosteric enzymes do not obey Michaelis kinetics. 

Half-velocity constant—Concentration of the substrate that makes the specific growth rate equal to one-half the maximum growth rate. 

ADH was isolated and partially purified from orange juice vesicles and examined for substrate specificity, maximum relative velocity (Vr) and affinity (1/Km) (12) Ethanol is the preferred saturated alcohol for reduction to the aldehyde based on Vr and 1/Km. Unsaturated alcohols, 2-propenol, 2-butenol and 2-hexenol, had comparable to or higher Vr s and l/Km s than ethanol. ADH had 5- to 30-fold greater affinity for saturated aldehydes than the corresponding saturated alcohols, whereas affinities of the unsaturated alcohols and aldehydes were similar. The apparent equilibrium constants (Kapp = 0.003 for ethanol - acetaldehyde pair) favor alcohol formation in the saturated series. Other aldehydes compete with acetaldehyde for the enzyme but the concentration of acetaldehyde is much higher than other aldehydes in juice vesicles and the 1/Km for acetaldehyde is 10 X higher than for other aldehydes found in the juice vesicles. 

Kinetics of carrier-mediated transport processes is similar to enzyme-substrate reactions and can be described by the Michaelis-Menten equation (Eq. (9.2)), assuming that each transport system has one specific binding site for its substrates. Maximum transport velocity (Vmax) is reached when all binding sites of the respective carrier proteins are occupied by substrate molecules. Substrate turnover can be delineated by the Michaelis constant Km corresponding to the substrate concentration [S], at which half-maximum transport velocity has been reached (Figure 9.5). Km also depends on pH and temperature. In cotransport systems transferring several substrates, the transport protein has a characteristic Km for each molecule transported. 

In contrast to the equilibrium-controlled approach the peptidase-catalyzed kinetically controlled peptide synthesis (for a review see reference1851) needs much less enzyme, the reaction time to reach maximal product yield is significantly shorter, and the product yield depends both on the properties of the enzyme used and the substrate specificity. Kinetic control means that the product appearing with the highest rate and disappearing with the lowest velocity would accumulate. Whereas the equilibrium-controlled approach ends with a true equilibrium, in the kinetic approach the concentration of the product formed goes through a maximum before the slower hydrolysis of the product becomes important. The product will be hydrolyzed if the reaction is not stopped after the acyl donor ester is consumed and true equilibrium is allowed to be reached. 

SCFs [14,18-21]. Figure 4.9-3 shows how kinetic parameters can be obtained from a Lineweaver-Burk plot. The example is from the esterification of ibu-profen with propanol in SCCO2 using Mucor miehei lipase (Scheme 4.9-1) [22]. In this case the Michaelis constant was = 2.8 mmol ester per mole of mixture and the maximum reaction velocity V ax = 360 g ester per kg enzyme per hour. The kinetic parameters are specific to the reaction system, reactor type, enzyme and substrate concentrations as well as to reaction conditions. 

In the numerator ps is the substrate density (kgm ), e is the void fraction within the bed, Xm is the maximum biomass concentration (kg-biomass kg-substrate" ) and Y is the heat yield coefficient (J kg-biomass )- The factor 0.25 Xjh arises from the assumed growth kinetics, for which the maximum heat production rate occurs at 0.5X , with a specific growth rate of O.Sp p, [142]. The denominator describes axial convection and evaporation, which are the major contributors to heat removal. If the air is assumed to remain saturated as it moves up the column, then the evaporation of water to maintain this saturation increases the effective heat capacity of the air from Cpa(J kg" °C" ) by an additional factor of f A, where A is the heat of vaporization of water (J kg ) and f is the slope of a linear approximation to the humidity curve (kg-water kg-air °C ). The bed height is given by H (m), Vz is the superficial velocity of the air, and T,., and Tqut the inlet and outlet air temperatures. 

As a reminder both limiting cases are just assumptions leading to approximations/ ). In the same way that the maximum rate in the zero-order case can never be reached as outlined above, even at very low substrate concentrations the calculated velocity from eqn (4.1) will never exactly match the specificity constant (see also the inset of Figure 4.1) ... 

The nucleoside triphosphate effectors themselves do not participate in the reaction that is, they are unchanged by the reduction reaction, in spite of influences upon it. Their effects on the specificity of the reductase are exerted by both decreasing the values of Michaelis constants for substrates and by increasing maximum velocities in their reduction. 

Studies on the chain length specificity of A9 desaturases from rat liver show that there are two enzymes. One (which is widely distributed in other mammalian tissues) has maximum rates with a 18C substrate. The chain length effectiveness is in the order 18C > 17C > 16C > 15C > 14C. The activity with 19C and 20C fatty acids is low but perceptible. The second enzyme has a maximum velocity at 14C, the order in this case being 14C > 13C > 12C > lie. In all cases the double bond was introduced at carbon atoms 9 and 10 counting from the carboxyl end, so that clearly the initial reaction between substrate and enzyme is at the carboxyl end of the fatty acid chain. 

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