On kinetic behavior at high enzyme concentrations

Abstract

The data of Richardson and Ayers (1959) for glass beads and air and Heertjes and McKibbins (1956) for silica gel and air were compared with calculated heat transfer coefficients for the total surface area. A value of = 0.38 was used as a typical void fraction for a fixed bed. Figure 1 shows this comparison with reasonable agreement between calculated and experimental coefficients. N OT A T I ON C, = specific heat D = diffusivity D, D, = particle diameter d = particle cluster diameter g h, h, h,, k = mass transfer coefficient NR, = Deue/u, Reynolds number N s , = Schmidt number u, us = superficial velocity Greek Letters a! = equivalent diameter of channel = acceleration due to gravity = channel heat transfer coefficient = heat transfer coefficient based on total particle = particle cluster coefficient based on channel area surface = actual velocity in packing channels = thermal diffusivity of fluid f = overall bed void fraction = void fraction of bed for particle clusters =ratio of average channelling length to particle €0 .f p = fluid viscosity p = fluid density ps = solids density $ cp = particle shape factor diameter U = kinematic viscosity of fluid = dimensionless temperature or concentration Currently there are considerable interest and activities in potential applications of enzymes in various forms as industrial catalysts, some of which involve a large concentration of enzymes. For details one may refer to the review paper by Carbonell and Kostin (1972). For enzyme kinetics at high enzyme concentrations Carbonell and Kostin also refer to the work of Cha (1970), who compared what he called the true rate equation with a number of approximate rate equations which includes among others the Michaelis-Menten equation.The purpose of this note is twofold: (1) to show that the rate equation which was developed by Reiner (1969) and subsequently used by Cha (1970) as the true rate is based on a misconception and is entirely equivalent to the Michaelis-Menten equation in the form of present day use (or more correctly Briggs-Haldane) and hence the comparisons made by Cha (1970) are incorrect, and ( 2 ) to bring attention to the fact that when the total enzyme concentration is high relative to the initial substrate concentration the pseudo-steady state (PSS) assumption which leads to the Michaelis-Menten (or Eriggs-Haldane) equation may not hold, and therefore a valid comparison would be with the true rate which must be computed without the PSS assumption. This comparison is made using the data reported in the literature on the hydrolysis of acetyl-L-phenyl-alanine ethyl ether by chymotrypsin AlChE Journal (Vol. 19, No. 3 ) (Gutfreund and Hammond, 1959) at various concentration ratios of enzyme to the initial substrate. I t is very important to fully realize the limitations imposed by the PSS assumption as currently there are being developed many potential applications involving use of concentrated enzymes. RATE EQUATIONSsubstrate-one enzyme reaction in a batch reactor,The reaction under consideration is the simplest...

Applicability of the pseudo-steady state assumption to the irreversible Michaelis-Menten reaction.

“…To makethis conclusion more certain, further calculations were carried out for reactions with the kinetic constants listed in Table 1. The values of the kinetic constants of series 10 are almost the same as those used by Lim,5) and the values for the other series were modified from them. They are all also almost the same as those used by Sakamoto.…”

A Century of Enzyme Kinetics: Reliability of the K M and v max Estimates

“…Lim (1973) showed that expression (11) is not the substrate mass 178 S. Schnell and P. K. Maini balance, it is only a definition for the sum of C and S. The correct conservation law is…”

“…Therefore, the general rate equation is equivalent to the MM equation. In addition, Lim (1973) analyzed the discrepancies between the numerical solution for [S] and the sQSSA solution. The agreement between the sQSSA solution and the numerical solution is quite good when ½E 0 0:01½S 0 .…”

Enzyme Kinetics at High Enzyme Concentration

“…Lim (1973) showed that expression (8) is not the substrate mass balance, it is only a definition for the sum of C and S. The correct conservation law is…”

“…Therefore, the general rate equation is equivalent to the MM equation. In addition, Lim (1973) has analysed the discrepancies between the numerical solution of S and the sQSSA solution. The agreement between the sQSSA solution and the numerical solution is quite good when…”