The identification of chemical intermediates in enzyme catalysis by the rapid quench-flow technique

Traditionally, enzyme transient kinetics have been studied by the stopped-flow and rapid quench-flow (QF) methods. Whereas stopped-flow is the more convenient, it suffers from two weaknesses: optically silent systems cannot be studied, and when there is a signal it cannot always be assigned to a particular step in the reaction pathway. QF is a chemical sampling method; reaction mixtures are aged for a few milliseconds or longer, ‘stopped’ by a quenching agent and the product or the intermediate is measured by a specific analytical method. Here we show that by exploiting the array of current analytical methods and different quenching agents, the QF method is a key technique for identifying, and for characterising kinetically, intermediates in enzyme reaction pathways and for determining the order by which bonds are formed or cleaved by enzymes acting on polymer substrates such as DNA. Received 24 May 2006; received after revision: 3 July 2006; accepted 19 July 2006     

Steady-state kinetic studies with the polysulfonate U-9843, an HIV reverse transcriptase inhibitor

The tetramer of ethylenesulfonic acid (U-9843) is a potent inhibitor of HIV-1 RT^* and possesses excellent antiviral activity at nontoxic doses in HIV-1 infected lymphocytes grown in tissue culture. Kinetic studies of the HIV-1 RT-catalyzed RNA-directed DNA polymerase activity were carried out in order to determine if the inhibitor interacts with the template: primer or the deoxyribonucleotide triphosphate (dNTP) binding sites of the polymerase. Michaelis-Menten kinetics, which are based on the establishment of a rapid equilibrium between the enzyme and its substrates, proved inadequate for the analysis of the experimental data. The data were thus analyzed using steady-state Briggs-Haldane kinetics assuming that the template:primer binds to the enzyme first, followed by the binding of the dNTP and that the polymerase is a processive enzyme. Based on these assumptions, a velocity equation was derived which allows the calculation of all the specific forward and backward rate constants for the reactions occurring between the enzyme, its substrates and the inhibitor. The calculated rate constants are in agreement with this model and the results indicated that U-9843 acts as a noncompetitive inhibitor with respect to both the template:primer and dNTP binding sites. Hence, U-9843 exhibits the same binding affinity for the free enzyme as for the enzyme-substrate complexes and must inhibit the RT polymerase by interacting with a site distinct from the substrate binding sites. Thus, U-9843 appears to impair an event occurring after the formation of the enzyme-substrate complexes, which involves either an event leading up to the formation of the phosphoester bond, the formation of the ester bond itself or translocation of the enzyme relative to its template:primer following the formation of the ester bond.     

Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well known that this account is problematic.This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.     

Fold-Hopf bifurcation in a simplified four-neuron BAM (bidirectional associative memory) neural network with two delays

The bidirectional associative memory (BAM) neural network with four neurons and two delays is considered in the present paper. A linear stability analysis for the trivial equilibrium is firstly employed to provide a possible critical point at which a zero and a pair of pure imaginary eigenvalues occur in the corresponding characteristic equation. A fold-Hopf bifurcation is proved to happen at this critical point by the nonlinear analysis. The coupling strength and the delay are considered as bifurcation par...     

Substrate specificity of bacterial DD-peptidases (penicillin-binding proteins)

The DD-peptidase enzymes (penicillin-binding proteins) catalyze the final transpeptidation reaction of bacterial cell wall (peptidoglycan) biosynthesis. Although there is now much structural information available about these enzymes, studies of their activity as enzymes lag. It is now established that representatives of two low-molecular-mass classes of DD-peptidases recognize elements of peptidoglycan structure and rapidly react with substrates and inhibitors incorporating these elements. No members of other DD-peptidase classes, including the high-molecular-mass enzymes, essential for bacterial growth, appear to interact strongly with any particular elements of peptidoglycan structure. Rational design of inhibitors for these enzymes is therefore challenging.     

Effect of pyrophosphate and orotidine monophosphate on cytosine deaminase regulatory properties

The maximal velocity of the reaction (Vmax) and the half-saturation constant (K0.5) values of the S. typhimurium cytosine deaminase were altered in the presence of its effectors, pyrophosphate and orotidine monophosphate. From the kinetics of orotidine monophosphate inhibition of cytosine deaminase, it was characterized as a mixed-type noncompetitive inhibitor.     

Kinetik der Reaktion von Imidazol-SH-Verbindungen mit Ellman Reagenz [5,5′-Dithio-bis-(-2-nitrobenzoesäure)]

Summary The rate of reaction of some derivatives and peptides of cysteine and a number of imidazole-SH-compounds with 5,5-Dithio-bis-(2-nitrobenzoic acid) (DTNB) as well as the dependence of the reaction rate upon pH were investigated; for several compounds an equation is given, by which the rate constants and half reaction times can be estimated for various pH values. For some of the imidazole-SH-compounds studied thepK of the SH-group is no criterion of their reactivity with DTNB.     

On geometric objects,the non-existence of a gravitational stress-energy tensor,and the uniqueness of the Einstein field equation

The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the inception of the theory. Folklore has it that no adequate definition of a localized gravitational stress-energetic quantity can be given. Most arguments to that effect invoke one version or another of the Principle of Equivalence. I argue that not only are such arguments of necessity vague and hand-waving but, worse, are beside the point and do not address the heart of the issue. Based on a novel analysis of what it may mean for one tensor to depend in the proper way on another, which, en passant, provides a precise characterization of the idea of a “geometric object”, I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of the bundle of Lorentz metrics over spacetime. I conclude by showing that my results also imply that, under a few natural conditions, the Einstein field equation is the unique equation relating gravitational phenomena to spatiotemporal structure, and discuss how this relates to the non-localizability of gravitational stress-energy. The main theorem proven underlying all the arguments is considerably stronger than the standard result in the literature used for the same purposes (Lovelock's theorem of 1972): it holds in all dimensions (not only in four); it does not require an assumption about the differential order of the desired concomitant of the metric; and it has a more natural physical interpretation.     

Microbial energetics applied to waste repositories

Summary Through their catalytic abilities microbes can increase rates of chemical reactions which would take a very long time to reach equilibrium under abiotic conditions. Microbes also alter the concentration and composition of chemicals in the environment, thereby creating new conditions for further biological and chemical reactions. Rates of degradation and possible indirect consequences on leaching rates in waste repositories are a function of the presence or absence of microbes and of the conditions which allow them to become catalytically active.Microbially mediated reactions are no exception to the rule that all chemical processes are basically governed by thermodynamic laws. Naturally occurring processes proceed in the direction that leads to the minimal potential energy level attained when equilibrium is reached. A continuous supply of energy to an ecosystem in the form of biochemically unstable compounds maintains non-equilibrium conditions, a prerequisite for all chemotrophic life. Energy is released as a chemical reaction progresses towards equilibrium. Microbes scavenge that portion of the free energy of reaction (G_r) which can be converted into biochemically usable forms during the chemical oxidation processes. As electrontransfer catalysts, the microorganisms mediate reactions which are thermodynamically possible thereby stimulating reaction rates. Decomposition and mineralization in systems without a continuous supply of substrates and oxidants will lead to equilibria with minimal free energy levels at which point further microbial action would cease. The differences in the free energy levels of reactions (G_r), represent the maximal energy which is available to microorganisms for maintenance and growth. How much of the released free energy will be conserved in energy-rich bonds, compounds (e.g. ATP), and chemical potentials (e.g. emf) useful for biosynthesis and biological work is characteristic for the microbes involved and the processes and metabolic routes employed.Materials whose elements are not present in the most oxidized form attainable in the oxic environment of our planet are potentially reactive. Microbial activities are associated only with chemical reactions whose free energy changes are exergonic. This should be kept in mind for all investigations related to the role of microbes in repositories or in the layout of proper waste storage conditions. Rigorous application of thermodynamic concepts to environmental microbiology allows one to develop models and design experiments which are often difficult to conceive of in complex natural systems from physiological information alone. Thermodynamic considerations also aid in selecting proper deposition conditions and in carrying out thoughtful experiments in areas related to microbial ecology of waste repositories.     

On the origins and foundations of Laplacian determinism

In this paper I examine the foundations of Laplace’s famous statement of determinism in 1814, and argue that rather than derived from his mechanics, this statement is based on general philosophical principles, namely the principle of sufficient reason and the law of continuity. It is usually supposed that Laplace’s statement is based on the fact that each system in classical mechanics has an equation of motion which has a unique solution. But Laplace never proved this result, and in fact he could not have proven it, since it depends on a theorem about uniqueness of solutions to differential equations that was only developed later on. I show that the idea that is at the basis of Laplace’s determinism was in fact widespread in enlightenment France, and is ultimately based on a re-interpretation of Leibnizian metaphysics, specifically the principle of sufficient reason and the law of continuity. Since the law of continuity also lies at the basis of the application of differential calculus in physics, one can say that Laplace’s determinism and the idea that systems in physics can be described by differential equations with unique solutions have a common foundation.     

Physical aspects of biophotons

By comparing the theoretically expected results of photon emission from a chaotic (thermal) field and those of an ordered (fully coherent) field with the actual experimental data, one finds ample indications for the hypothesis that 'biophotons' originate from a coherent field occurring within living tissues. A direct proof may be seen in the hyperbolic relaxation dynamics of spectral delayed luminescence under ergodic conditions. A possible mechanism has to be founded on Einstein's balance equation and, under stationary conditions, on energy conservation including a photochemical potential. It is shown that the considered equations deliver, besides the thermal equilibrium, a conditionally stable region far away from equilibrium, which can help to describe both 'biophoton emission' and biological regulation.     

Modeling eBay price using stochastic differential equations

Online auctions have become increasingly popular in recent years. There is a growing body of research on this topic, whereas modeling online auction price curves constitutes one of the most interesting problems. Most research treats price curves as deterministic functions, which ignores the random effects of external and internal factors. To account for the randomness, a more realistic model using stochastic differential equations is proposed in this paper. The online auction price is modeled by a stochastic differential equation in which the deterministic part is equivalent to the second‐order differential equation model proposed in Wang et al. (Journal of the American Statistical Association, 2008, 103, 1100–1118). The model also includes a component representing the measurement errors. Explicit expressions for the likelihood function are also obtained, from which statistical inference can be conducted. Forecast accuracy of the proposed model is compared with the ODE (ordinary differential equation) approach. Simulation results show that the proposed model performs better.     

Superefficient enzymes

Diffusion-controlled enzymes are characterized by second-order rate constants in the range 10(8)-10(10) M(-1)s(-1). These values are at the upper end of the observed rates of many enzyme-substrate reactions and have been predicted by theoretical studies on bimolecular reaction in solution. Such enzymes are considered to be perfect, since their rate-limiting step is not due to any chemical event but to the diffusional association rate between the enzyme and the substrate. Often the enzyme-substrate encounter is facilitated either through the presence of a strong attractive electric field, produced by charges on the enzyme surface, or through the reduction in the dimension of the search process. Here we provide a brief review of some of the enzymes characterized by a very fast second-order constant, focusing attention on triose phosphate isomerase and Cu,Zn superoxide dismutase taken as typical examples of such highly tuned enzymes.     

Direct observation of enzyme substrate complexes by stopped-flow fluorescence: mathematical analyses

The fluorescence changes which occur upon the interaction of enzyme and substrate under stopped-flow conditions can provide a sensitive means to directly observe ES complexes. The interconversion of the intermediates during catalysis causes changes in fluorescence, signaling directly their existence, and allowing their quantitation. We have studied extensively an approach which measures radiationless energy transfer (RET) between enzyme tryptophanyl residues and a fluorescent peptide or ester substrate. Our studies of a number of proteolytic enzymes have validated the approach, which is sensitive and applicable to a variety of enzymes under a wide range of experimental conditions, including subzero temperatures. Direct excitation of fluorescent substrates can also be used to observe ES complex formation and breakdown and is complementary to the RET approach. Here we review both the RET and direct excitation kinetic approaches, with particular emphasis on the mathematical foundations we have developed which are critical to the successful interpretation of these or any other spectroscopic approach which yields a signal that is unique to the ES complex.     

Eine Bemerkung zur Frage der Verwendung Lagrangescher Koordinaten in der Physik nichtlinearer Schwingungen

Summary For the Cartesian coordinates of the elements of a vibrating string, which are introduced as functions of time and a parameter (similar to the Lagrangean method in hydrodynamics), a general, non-linear system of differential equations is offered. The behaviour of the freely vibrating string corresponding to this system agrees, approximately, with the behaviour of a string put in motion in a certain way, which string, if moving freely, would act according to the linear differential equation of the elementary theory.     

质子传导陶瓷膜在催化脱氢反应中的应用

有机化合物催化脱氢是一种吸热、体积增大的可逆反应过程,通过特定的膜将反应过程中生成的氢气不断地移出反应区,可促使反应向产物方向移动,从而提高反应转化率、减少副反应并最终达到降低反应温度、提高产率的目的。质子传导陶瓷膜可以以质子传递方式选择性透过氢,具有成本低、选择高,耐高温、热稳定及化学稳定性能好、不易中毒等特点,非常适合于脱氢膜反应器。本文对质子传导陶瓷膜材料、透氢机理、膜制备、膜反应器及其用于脱氢反应的研究现状与进展情况进行了综述。     

Simple integrated rate equations for reversible bimolecular reactions

Summary If the complete rate equations for reversible, one-step, bimolecular reactions are written withP _e–P as the concentration variable (whereP _e is the equilibrium, andP is the instantaneous, product concentration), the 3 possible stoichiometries can be reduced to a single straightforward differential equation. This can be solved very economically. For each stoichiometry, weret is time,k ₁ is the forward rate constant,K _e is the equilibrium constant, and P isP–P _o. The termsP _c–P _o andD+P _c–P _o are the physically possible and physically impossible roots of the quadratic equation forP _e–P _o in terms of the initial concentrations andK _c.D is the discriminant in this equation. All 3 quantities can be calculated if the equilibrium constant is known. A plot oft against ln{[1–P/(D+P _c–P _o)]/[1–P/(P _c–P _o)]} should be a straight line for any second order reaction. For each stoichiometry,P _c–P _o approachesA _o, the initial concentration of the first reactant, as the equilibrium constant increases. When a second reactant is present,D+P _e–P _o approachesB _o. The limiting equation is then that of an irreversible bimolecular reaction. For AP+Q,D approaches –K _e as the equilibrium constant becomes large, and the value of the second logarithmic term in the integrated equation approaches zero. The limiting equation is that of an irreversible, unimolecular reaction.Acknowledgments. I thank Dr. Athel Cornish-Bowden for many helpful discussions. This work was partially supported by a grant from Utah State University.     

OV or TOV?

The well-known equation for hydrostatic equilibrium in a static spherically symmetric spacetime supported by an isotropic perfect fluid is referred to as the Oppenheimer–Volkoff (OV) equation or the Tolman–Oppenheimer–Volkoff (TOV) equation in various General Relativity textbooks or research papers. We scrutinize the relevant original publications to argue that the former is the more appropriate terminology.