William P. Jencks

Statistical Time Events in Enzymes: A Physical Assessmen

Author(s): Careri, G; Fasella, P; Gratton, E | Abstract: Enzyme action is the result of a large number of discrete steps involving a great variety of processes such as cooperative conformational changes, acid-base catalysis, nucleophylic and/or electrophylic attack from properly positioned groups, etc.; it is widely recognized that in order to be useful for catalysis, the various elementary processes must be space- and time-controlled during enzyme function. In the past decade great progresses have been made in understanding the chemistry and the stereochemistry of enzyme action, with particular emphasis on the role of the spatial effects. Obviously, an analysis of the temporal aspects of enzyme action is equally important. The ultimate goal is the description of the concomitance and/or sequence of individual elementary steps in the catalytic act. This ambitious but difficult goal can be approached by focusing the attention on the time constants of the various elementary processes and assessing their microscopic mechanism by comparative studies on representative model systems. This approach was introduced in enzymology with the development of fast relaxation methods and will be followed in this paper, with the understanding that it suffers from the same intrinsic limitations as an analysis of a musical piece restricted to a list of the sound frequencies occurring in it but devoid of any information about their temporal sequence and relative intensity. Our aims are: l. To review time events detected in enzymes using a proper physical framework, i.e., the theory of the random processes. 2. To identify these events at a molecular level by comparison with processes occurring in appropriate model systems. 3. To discuss the statistical significance of the detected events. We shall start with the simpler model systems and shall then proceed to analyze situations of increasing complexity and eventually consider enzyme-substrate complexes. For each class of events some data will be critically reviewed and their relevance to enzyme catalysis stressed. All data will then be comparatively discussed according to their time scale and some mechanistic conclusions will be derived. The representative enzymes considered in this review were chosen among those which can work as separate entities in an aqueous medium because they are simpler and better known.

[7] Utilization of binding energy and coupling rules for active transport and other coupled vectorial processes

Publisher Summary This chapter describes the utilization of binding energy and coupling rules for active transport and other coupled vectorial processes. The primary role of binding energy is kinetic. Binding energy is utilized to avoid high- or low-energy intermediates along the reaction path under physiological conditions. High-energy intermediates are likely to introduce a barrier to rapid turnover of the system, while low-energy intermediates cause the enzyme to fall into an energy well from which escape is difficult. The energies of the intermediates in the reaction cycle of the Ca 2+ -ATPase from sarcoplasmic reticulum illustrate how the energies are balanced in a system of this kind to avoid high- or low-energy intermediates. The utilization of binding energies to avoid high- or low-energy intermediates is described by interaction energies. The coupling process is described by a set of rules. These rules generally represent enzyme specificities for catalysis that change in different states of the enzyme.

The denaturation of crustacyanin

Abstract The shell pigments of the lobster have been separated into three fractions, α-crustacyanin, β-crustacyanin, and a yellow pigment, by chromatography on DEAE-cellulose. The prosthetic group of all three pigments is the red carotenoid, astaxanthin. α-Crustacyanin is converted to a red product in the presence of “hydrophobic” denaturing agents and to a yellow product in the presence of denaturing agents of the urea-guanidinium class. Urea itself gives first a yellow and then a red product. Acid and base cause reversible transformations to red and yellow products.

Different forms of pig liver esterase

Abstract Trimeric molecules of pig liver esterase of low, intermediate, and high isoelectric point do not give molecules with significantly different isoelectric points upon dissociation and reassociation. The heterogeneity of esterase preparations, therefore, cannot be explained by random combinations of a small number of different subunits to form trimeric molecules. There is an increase with increasing isoelectric point of activity toward ethyl thiolacetate, as well as for the reaction with methanol of the acetyl-enzyme intermediate formed from phenyl acetate. The high-isoelectric point fraction dissociates more easily into subunits. A different type of heterogeneity is responsible for nonlinear first-order kinetics in the inactivation of esterase by bis( p -nitrophenyl) phosphate monoanion. Phenol causes a timedependent decrease in the amount of the slowly reacting form, presumably by inducing a change to a different conformer. Ethyl thiolacetate protects against inactivation and causes an increase in slowly reacting enzyme. The enzyme is not inactivated by bisphenyl phosphate, but is an excellent catalyst for the hydrolysis of bisphenyl carbonate. The enzyme is resistant to complete denaturation by 8 m urea. Circular dichroism and infrared spectra indicate that the protein contains a large amount of β-sheet structure.

Orbital steering, entropy, and rate accelerations

Abstract Some important conceptual and quantitative differences are described between the “orbital steering” and entropy descriptions of the rate accelerations in intramolecular and enzymic reactions that may be brought about by geometric constraints other than distortion. The treatments differ by a factor of 10 3 – 10 4 in the maximum rate acceleration that may be obtained from these constraints. The estimation of a “proximity factor” without taking adequate account of the translational and overall rotational entropy terms gives a misleading value for this factor. The conclusion is reaffirmed that increasing the probability of reaction by restricting the free translational and rotational movement of reacting groups can play a large role in the catalytic power of enzymes.

What is a Coupled Vectorial Process

Publisher Summary The reversible transformation of chemical energy or potential into mechanical, osmotic, and other kind of work through coupled vectorial processes represents one of the most interesting frontiers of biochemistry today. Many models have been proposed to “explain” the active transport of ions and small molecules and the synthesis of adenosine transport (ATP) from proton transport in oxidative phosphorylation and photophosphorylation. Some of these proposals have included—(1) mechanisms in which a change from tight binding on one side to weak binding on the other side of a membrane is responsible for coupled transport of a ligand, (2) particular steps in which coupling or energy transfer occurs, (3) “energized states,” and (4) hydrogen-bonded or other channels for ion transport. The coupling process itself can be described by a set of rules. Understanding coupling then represents an understanding of these rules and how they are enforced. The rules often represent enzyme specificities for catalysis that are strictly comparable to the specificities of ordinary enzymes. They differ from the specificities of most enzymes, however, in that they are turned on and off, or change in different states of the enzymes.

Interactions of salts and denaturing agents with a polyacrylamide gel

Abstract The relative elution volumes of urea, phenol and a series of salts, including guanidine hydrochloride and tetramethylguanidine hydrochloride, from polyacrylamide and dextran gel columns have been determined. The elution positions reflect an interaction with the primary amide groups of the gel and, except for salts containing di- or trianions, are correlated with the strength of the interaction of the same compounds with acetyltetraglycine ethyl ester. The results provide further support for the hypothesis that these compounds affect the physical state of proteins by interactions with amide groups, but they shed no light on the question of whether this interaction represents a specific site binding or a less direct activity coefficient effect.

Acid and base catalysis of urea synthesis: nonlinear Brønsted plots consistent with a diffusion-controlled proton-transfer mechanism and the reactions of imidazole and N-methylimidazole with cyanic acid

Bronsted plots for general acid and general base catalysis of the synthesis of phenylurea from aniline and cyanic acid are nonlinear. The maximum values of the rate constants for general acid and for general base catalysis are similar and the value of βnuc for the buffer catalysed reaction is ca. 1·0. The data are consistent with a mechanism involving a zwitterionic intermediate and a rate-limiting proton-transfer step that is close to diffusion controlled in the thermodynamically favourable direction. Proof that proton transfer to the leaving nitrogen is complete before C–N bond breaking takes place in the cleavage of a substituted urea is provided by the similar rate and equilibrium constants for the reversible reaction of imidazole and N-methylimidazole with cyanic acid.

The vectorial specificity for calcium binding to the CaATPase of sarcoplasmic reticulum is controlled by phosphorylation, not by an E—E* conformational change

The E-E* model for calcium pumping by the CaATPase of sarcoplasmic reticulum includes two distinct conformational states of the enzyme, E and E*. Exterior Ca2+ binds only to E and interior Ca2+ binds only to E*. Therefore, it is expected that there will be competition between the binding of calcium to the unphosphorylated enzyme from the two sides of the membrane. The equilibrium concentration of cECa2, the enzyme with Ca2+ bound at the exterior site, was measured at different Ca2+ concentrations with empty sarcoplasmic reticulum vesicles (SRV) and with SRV loaded with 40 mM Ca2+ by reaction with 0.5 mM [gamma-32P]ATP plus 20 mM EGTA for 13 ms (100 mM KCl, 5 mM MgSO4, 40 mM Mops/KOH, pH 7.0, 25 degrees C). The sigmoidal dependence on free exterior calcium concentration of the concentration of cECa2, measured as [32P]phosphoenzyme, is identical with empty and loaded SRV, within experimental error. The value of K0.5 is 2.8 microM, and the Hill coefficient is 2. This result shows that there is no competition between binding of Ca2+ to the outside and the inside of the membrane. This is consistent with a model in which the vectorial specificity for calcium binding is controlled by the chemical state of the enzyme, rather than a simple conformational change. It is concluded that there are not two interconverting forms of the free enzyme, E and E*, instead the vectorial specificity for binding and dissociation of Ca2+ is determined by the state of phosphorylation of the CaATPase.

The calcium ATPase of sarcoplasmic reticulum is inhibited by one Ca2+ ion

Inhibition by calcium of the steady‐state turnover of the calcium ATPase from sarcoplasmic reticulum of rabbit muscle follows a Hill slope of 0.8 ± 0.2 (pH 7.0, 0.1 M KCl, varying [Mg2+] and 2 μM A23187 ionophore). It is concluded that dissociation of the two Ca2+ ions from E‐P·Ca2 is sequential and that the inhibition arises from the binding of one Ca2+ to A‐P·Ca1.