On the status of the Michaelis-Menten equation and its implications for enzymology

The Michaelis-Menten equation (MME) is considered to be the fundamental equation describing the rates of enzyme-catalysed reactions, and thus the 'physicochemical key' to understanding all life processes. It is the basis of the current view of enzymes as generally proteinaceous macromolecules that bind the substrate reversibly at the active site, and convert it to the product in a relatively slow overall sequence of bonding changes ('turnover'). The manifested 'saturation kinetics', by which the rate of the enzymic reaction (essentially) increases linearly with the substrate concentration ([S]) at low [S] but reaches a plateau at high [S], is apparently modelled by the MME. However, it is argued herein that the apparent success of the MME is misleading, and that it is fundamentally flawed by its equilibrium-based derivation (as can be shown mathematically). Thus, the MME cannot be classed as a formal kinetic equation _vis-a-vis_ the law of mass action, as it does not involve the 'incipient concentrations' of enzyme and substrate; indeed, it is inapplicable to the reversible interconversion of substrate and product, not leading to the expected thermodynamic equilibrium constant. Furthermore, the principles of chemical reactivity do not necessarily lead from the above two-step model of enzyme catalysis to the observed 'saturation kinetics': other assumptions are needed, plausibly the inhibition of product release by the substrate itself. (Ironically, thus, the dramatic graphical representation of the MME encrypts its own fundamental flaw!) Perhaps the simplest indictment of the MME, however, lies in its formulation that the rate of the enzymic reaction tends towards a maximum of k~cat~[E~o~] in the 'saturation regime'. This implies - implausibly - that the turnover rate constant k~cat~ can be known from the overall rate, but independently of the dissociation constant (K~M~) of the binding step. (Many of these arguments have been presented previously in preliminary form.

Kinetic resolution of racemates under chiral catalysis: connecting the dots

The current theory of the titled phenomenon is apparently based on an inconsistent use of concentration units, as employed in the derivation of the fundamental equations. Thus, manifestly, whilst the relation between extent of conversion and e.e. is derived with mole fractions, the succeeding kinetic equations employ units of molarity. This invalidates the derivation in the general case. Fortuitously, however, it is applicable in the majority of simple cases, wherein the total number of moles involved in the reaction remains constant. Herein is presented a rigorous approach which is generally valid

Non-linear Effects in Asymmetric Catalysis: Whys and Wherefores

It is argued that the titled non-linear effects (NLE) may arise whenever the order of the reaction in the chiral catalyst in greater than 1. In a fundamental departure from previous approaches, this is mathematically elaborated for the second order case. (NLE may also be observed if the chiral catalyst forms non-reacting dimers in a competing equilibrium; practically, however, this implies the in situ resolution of the catalyst.) The amplification of enantiomeric excess by NLE implies a relative (although modest) reduction in the entropy of mixing. The consequent increase in free energy apparently indicates a non-equilibrium process. It is suggested, based on arguments involving the chemical potential, that kinetically-controlled reactions lead to a state of “quasi-equilibrium”: in this, although overall equilibrium is attained, the product-spread is far from equilibrium. Thus, both the linear and NLE cases of chiral catalysis represent departures from equilibrium (which requires that the product e.e. = 0). Interesting similarities exist with models of non-equilibrium systems, the NLE cases apparently being analogs of open systems just after the bifurcation point has been crossed

A reassessment of the Carnot cycle and the concept of entropy

It is argued that the Carnot cycle is a highly inaccurate representation of a steam engine, and that the net work obtained in its operation would be zero. This conclusion is also supported by an elementary mathematical approach, which re-examines the work done in the four individual steps of the cycle. An important consequence of this is that the concept of entropy, originally proposed on the basis of the Carnot theorem, may not be a fundamentally valid thermodynamic quantity. Also, the experimental approach generally adopted in the determination of entropy is questionable, and the importance of increasing randomness in natural processes not universally valid. In fact, a more viable basis, at least vis-à-vis chemical reactions, appears to be the ratio of mass to energy, which is apparently maximized in the case of a spontaneous process

The reaction of aspirin with base

a b s t r a c t Aspirin anion appears to exist only fleetingly, rearranging via acetyl transfer to the ortho carboxylate group, as indicated by IR, UV and NMR. The resulting mixed anhydride cyclises to the more stable bicyclic orthoacetate isomer, a process facilitated by time and increasing pH. Mechanistic possibilities are discussed to explain these intriguing observations. Ó 2011 Elsevier Ltd. All rights reserved. Acetylsalicylic acid (1b, Scheme 1) is an over-the-counter pharmaceutical that has acquired the status of a household remedy, its generic term 'aspirin' having passed into common parlance. 1 Its well-known analgesic effect has now been supplemented by the recognition of its anti-coagulant and anti-inflammatory properties. The simplicity of its molecular structure, however, belies the rather complex mechanisms mediating its chemical reactivity and pharmacological action. 2,3 A chemical reaction of particular relevance to aspirin's stability in biological fluids is hydrolysis. Early work by Edwards, 4 later extended by Garrett, 5 indicated that aspirin was unstable in nearly all pH regions, the pH-rate profile being characterised by a minimum at pH $2.2 and a broad plateau region at pH$ 5-10. An initial mechanistic proposal based on intramolecular nucleophilic catalysis by carboxylate was later overturned by the extensive work of Fersht and Kirby, 6a in favour of mechanistic general base catalysis. It is noteworthy, however, that the balance between the two alternatives is a subtle one: the former mechanism, which is perhaps 'deceptively obvious' in the case of the parent aspirin, is actually preferred in the 3,5-dinitro derivative. Furthermore, aspirin hydrolysis has been studied by UV spectroscopy, but it is particularly intriguing that the deprotonation of aspirin is accompanied by a decrease in absorption intensity. The difference in the behaviour of salicylic acid and aspirin towards base is indeed striking. In order to gain further insight, we have studied the changes in the 1 H NMR spectrum of aspirin in D 2 O at various pH values, as described below There was also insignificant hydrolysis (if any), as 1b could be recovered in 80% yield upon acidification of the mixture at pH 8.0 after 12 h. NMR also did not indicate the formation of acetic acid. These changes in the high field region were accompanied by changes in the aromatic region. The pK a of aspirin is 3.5, so it would be practically completely deprotonated at neutral pH. The above-apparently straightforward-explanation, however, does not account for the intensification of the d 1.76 resonance, with both time and increasing pH. An alternative explanation would be that the resonance at d 2.36 is due not to carboxylate anion 2, but to some other species that interconverts with 3b at basic pH. An intriguing possibility is that aspirin anion (2) initially forms the mixed anhydride 4a (possibly the source of the d 2.36 resonance). On this basis 2 has only a fleeting existence. Also, the relatively high pK a of the phenolic hydroxyl group in 4a ($9) ensures 0040-4039/$ -see front matter

Pseudoasymmetry: A final twist?

The original definition of "pseudoasymmetry" conveyed the apparent paradox that a tetrahedral center with four different groups did not result in overall chirality. However, there are problems in applying the concept to cyclic systems that do not contain chirotopic centers. Pseudoasymmetry appears most appropriate to acyclic systems with chirotopic carbon centers, e.g. the meso trihydroxyglutalic acids. Analogous cyclic cases, e.g. the isomeric 1,4-dimethylcyclobutanes, are best treated as diastereomers, and may indeed be described by an interesting extension of the like-unlike notation. Remarkably, in several tri- and tetramethylcyclohexanes, CIP descriptors cannot be applied even to chirotopic centers, which can only be described by the modified 1-u notation

Molecular homochirality and the parity-violating energy difference. A critique with new proposals

Previous proposals for the origin of molecular homochirality, based on the effect of the weak neutral current (W-NC) on enantiomers, and the amplification of the resultant parity-violating energy difference (PVED), are possibly flawed. The additive amplification of PVED in crystals and polymers ("Yamagata hypothesis") cannot lead to detectable levels of optical activity, the original theory apparently overestimating PVED by a factor equal to Avogadro's number. An alternative theory based on the irreversible and spontaneous evolution of a dynamically fluctuating system is apparently impractical. However, the nonlinear amplification of PVED via autocatalytic polymerization may be possible as indicated by a simplified physico-chemical approach. This may also occur during crystallization and melting, and form the basis of the second order asymmetric transformation. (Thus, reported differences in the melting points of enantiomers in several cases may well be real). Also, the preponderance of racemic compounds over conglomerates may be based on the destabilization of the conglomerate by the action of the WNC on the crystalline lattice. The WNC may also be involved in the anomalous scattering of X-rays, which possibly arises from their circular polarization: the current theory would need to be revised accordingly

Critical Reflections on the Hydrophobic Effect, its Origins and Manifestation: Water Structure, Chemical Reactivity, Micelles and Gels.

The origins of the Hydrophobic Effect (HE), its biological significance and its experimental basis are critically addressed in this brief review. It is argued that the mechanistic work reported on the HE in recent decades needs to be reassessed, as its conclusions are apparently debatable. Essentially, it is highly inaccurate to view the HE as a repulsive interaction, which is rather an attractive one. It appears inevitable that the HE is indeed a manifestation of the perturbation of the structure of water upon the introduction of hydrocarbon molecules into its interior. There appears to be no other satisfactory explanation for the formation of micellar aggregates and the existence of the critical micelle concentration. Also, the practical significance of the HE on the reactivity of organic compounds (e.g. cycloadditions) is severely limited by their minuscule solubility levels, itself a manifestation of the HE! Other related phenomena apparently include the formation of gels and the occurrence of certain esterification reactions in water, which are briefly reviewed from a conceptual viewpoint