Why do many Michaelian enzymes exhibit an equilibrium constant close to unity for the interconversion of enzyme-bound substrate and product?

Serine protease mechanism-based mimics. Direct evidence for a transition state bridge proton in stable potentials

We have synthesized 1-(2-hydroxyacetyl)piperidine-2-one (2) and 1-(2-hydroxyacetyl)azepan-2-one (3). Equilibrium (K(f)) between the free alcohol (open form) and the tetrahedral intermediate (cyclol) is readily established, and both forms are observed in the D(2)O (1)H NMR spectra of 2 and 3. Therefore, their interconversion can be considered as an almost thermoneutral non-identical one. Pseudo-first-order rate constants (k(obs)) were obtained by simulating the AB (1)H NMR system observed for the cyclol. By best fitting the experimental points of a k(obs) versus pD profile to the equation k(obs) = 0.5k(0r) + 0.5k(r) K(ac)/(K(ac) + [D(+)]) + 0.5k(f)K(ao)/(K(ao)+ [D(+)]), the parameters involved were obtained: rate constants of rupture and formation (k(0r) and k(0f) = K(f)k(0r)) catalyzed by water, rate constants of rupture (k(r)) and formation (k(f)) from the conjugated bases of the cyclol form and the open form, and their acidity equilibrium constants K(ac) and K(ao). The system studied mimics the serine alcohol attack on the peptide bond and its reverse reaction in serine protease enzymes. In fact, the reaction rates are similar or perhaps even faster than the ones obtained for enzymatic reactions. The results also show the participation of water molecules forming catalytic proton bridges in stable potentials with the two interconverted forms. The position change of the bridged proton is sensitive to lactam ring size, and it is manifested by considerable change in the pKa values of both cyclol and open forms. Other evidence such as kinetics, DeltaS degrees , DeltaS, and proton inventory experiments and semiempirical molecular calculations support this proposal.

Catalytic consequences of experimental evolution: catalysis by a 'third-generation' evolvant of the second beta-galactosidase of Escherichia coli, ebgabcde, and by ebgabcd, a 'second-generation' evolvant containing two supposedly 'kinetically silent' mutations

The kinetics of hydrolysis of a series of synthetic substrates by two experimentally evolved forms ('evolvants'), ebgabcd and ebgabcde, of the second beta-galactosidase of Escherichia coli have been measured. The ebgabcd enzyme differs from the wild-type (ebgo) enzyme by Asp92-->Asn (a) and Trp977-->Cys (b) changes in the large subunit, as well as two changes hitherto considered to have no kinetic effect, Ser979-->Gly in the large subunit (c) and Glu122-->Gly in the small subunit (d). The enzyme ebgabcde contains in addition a Glu93-->Lys change in the large subunit (e). Comparison of ebgabcd with ebgab [Elliott, K, Sinnott, Smith, Bommuswamy, Guo, Hall and Zhang (1992) Biochem. J. 282, 155-164] indicates that the c and d changes in fact accelerate the hydrolysis of the glycosyl-enzyme intermediate by a factor of 2.5, and also decrease the charge on the aglycone oxygen atom at the first transition state; the charge on the glycone, however, is unaltered [see K, Konstantinidis, Sinnott and Hall (1993) Biochem. J. 291, 15-17]. The e mutation causes a fall in the degalactosylation rate of about a factor of 3, and its occurrence only together with c and d mutations [Hall, Betts and Wootton (1989) Genetics 123, 635-648] suggests that degalactosylation of a hypothetical ebgabe enzyme would be so slow that the enzyme would have no biological advantage over the ancestral ebgab. The transfer products from galactosyl-ebgabcd and galactosyl-ebgabcde to high concentrations to glucose have been measured; the predominant product is allolactose, but significant quantities of lactose are also formed; however, at apparent kinetic saturation of the galactosyl-enzyme, hydrolysis rather than transfer is the preponderant pathway. A knowledge of the rates of enzyme-catalysed exchange of 18O from [1-18O]galactose to water permits the construction of the free-energy profiles for hydrolysis of lactose by begabcd and ebgabcde. As with the other evolvants, changes in the profile away from the rate-determining transition state are essentially random, and there is no correlation between the changes in the free energies of intermediates and of their flanking transition states. We consider the aggregate of our kinetic data on the ebg system to be telling experimental support for the theoretical objections of Pettersson [Pettersson (1992) Eur. J. Biochem. 206, 289-295 and previous papers] to the Albery-Knowles theory of the evolution of enzyme kinetic activity.

Optimal kinetic design of enzymes in a linear metabolic pathway

The rate equations for a sequence of enzymic reactions conforming to Michaelis-Menten kinetics have been analyzed in order to establish what kinetic design optimizes the steady-state reaction flux for a given total concentration of enzymes and a given average magnitude of true and apparent first-order rate constants in the reaction system. Analytical solutions are presented which have been derived with the assumptions that the concentration of the first substrate in the pathway represents a fixed parameter and that no diffusional constraints come into operation. The solutions prescribe that reaction flux in the examined system becomes optimal when all of the enzymes are present at equal active-site concentrations. The optimal kinetic design of each enzyme reaction is characterized by forward (true or apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. This means that the optimal kinetic design of the examined pathway is highly uniform, individual enzymes being likely to exhibit optimal V values differing by a factor less than 5 and optimal Km/[S] values falling within the range 0.3-2.

Large changes of transition-state structure during experimental evolution of an enzyme

The question of whether, during the evolution of an enzyme, the transition state of the catalysed reaction is largely unchanged, or whether transition state and protein change together, was examined using the egb beta-galactosidases of Escherichia coli. Charge development at the first chemical state was assumed [Konstantinidis and Sinnott (1991) Biochem. J. 279, 587-593] to be proportional to delta delta G++, the ratio of second-order rate constants for the hydrolysis of beta-D-galactopyranosyl fluoride and 1-fluoro-D-galactopyranosyl fluoride, expressed as a free-energy difference. delta delta G++ (kJ.mol-1) falls from 10.4 for wild-type enzyme to 6.8 and 7.2 as a consequence of two different single amino-acid changes (which arise from single evolutionary events), to 6.3 as a consequence of the two amino-acid changes together, and then increases slightly to 7.3 as a consequence of a third single evolutionary change involving three further amino-acid changes.

Evolutionary optimization of the catalytic efficiency of enzymes

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.