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

Born-Infeld Corrections to the Entropy Function of Heterotic Black Holes

We use the black hole entropy function to study the effect of Born-Infeld terms on the entropy of extremal black holes in heterotic string theory in four dimensions. We find that after adding a set of higher curvature terms to the effective action, attractor mechanism works and Born-Infeld terms contribute to the stretching of near horizon geometry. In the alpha'--> 0 limit, the solutions of attractor equations for moduli fields and the resulting entropy, are in conformity with the ones for standard two charge black holes.Comment: 17 pages;v2:minor changes,added ref

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

Stability of naked singularities and algebraically special modes

We show that algebraically special modes lead to the instability of naked singularity spacetimes with negative mass. Four-dimensional negative-mass Schwarzschild and Schwarzschild-de Sitter spacetimes are unstable. Stability of the Schwarzschild-anti-de Sitter spacetime depends on boundary conditions. We briefly discuss the generalization of these results to charged and rotating singularities.Comment: 6 pages. ReVTeX4. v2: Minor improvements and extended discussion on boundary conditions. Version to appear in Phys. Rev.

The Bell-Szekeres Solution and Related Solutions of the Einstein-Maxwell Equations

A novel technique for solving some head-on collisions of plane homogeneous light-like signals in Einstein-Maxwell theory is described. The technique is a by-product of a re-examination of the fundamental Bell-Szekeres solution in this field of study. Extensions of the Bell-Szekeres collision problem to include light-like shells and gravitational waves are described and a family of solutions having geometrical and topological properties in common with the Bell-Szekeres solution is derived.Comment: 18 pages, Latex fil

Summing up Non-anti-commutative Kaehler potential

We offer a simple non-perturbative formula for the component action of a generic N=1/2 supersymmetric chiral model in terms of an arbitrary number of chiral superfields in four dimensions, which is obtained by the Non-Anti-Commutative (NAC) deformation of a generic four-dimensional N=1 supersymmetric non-linear sigma-model described by arbitrary Kaehler superpotential and scalar superpotential. The auxiliary integrations responsible for fuzziness are eliminated in the case of a single chiral superfield. The scalar potential in components is derived by eliminating the auxiliary fields. The NAC-deformation of the CP(1) Kaehler non-linear sigma-model with an arbitrary scalar superpotential is calculated as an example.Comment: 9 pages, LaTeX, no figures; section 5 and references adde