An on-line method for the collection and analysis of quasi-steady-state kinetic data for enzyme-catalyzed reactions.

A special mixing device for initiating enzyme-catalyzed reactions is used to rapidly achieve an unperturbed quasi-steady state. An on-line computer is employed to sample the initial conditions, the mixing time, and concentrations that change as a function of time during this quasi-steady state phase. A statistical method for estimating initial, quasi-steady state rates from the time course of the enzyme-catalyzed reaction is described. Practical considerations for using this parameter estimation system lead to the conclusion that for the enzyme-catalyzed reaction tested, the extent overall reaction should be above .2% for high initial substrate concentrations, and above 1% for initial substrate concentrations in the range of the Michaelis constant. Application of this method to a typical enzyme-catalyzed reaction suggests that objective estimates of initial rates from a given set of concentrations and corresponding times can be obtained with a standard error in the range of 2–3%, but that reproducibility is not better than about 10%. When this procedure was used to estimate initial rates for the glycerol dehydrogenase-catalyzed oxidation of glycerol by NAD, it was found that this enzyme did not behave according to the classical “Michaelis-Menten” mechanism of enzyme action.     

Classical cumulant dynamics for statistical chemical physics

Abstract

We developed classical cumulant dynamics for statistical mechanics in order to evaluate thermal equilibrium properties of a given system. The equations of motion (EOMs) for momentum and position were formulated together with those for second-order cumulant variables, which are functions of second-order moments. From the Kramers equation, and simplified EOMs were obtained by assuming a stationary state limit. The present method combined with the umbrella integration method was applied to evaluate free energy surface of a seven-particle Morse cluster. With low computational costs, the present approach gave almost equivalent free energy barrier those by conventional classical molecular dynamics.     

A method to describe enzyme-catalyzed reactions by combining steady state and time course enzyme kinetic parameters

Background

Complete analysis of single substrate enzyme-catalyzed reactions has required a separate use of two distinct approaches. Steady state approximations are employed to obtain substrate affinity and initial velocity information. Alternatively, first order exponential decay models permit simulation of the time course data for the reactions. Attempts to use integrals of steady state equations to describe reaction time courses have so far met with little success.

Methods

Here we use equations based on steady state approximations to directly model time course plots.

Results

Testing these expressions with the enzyme β-galactosidase, which adheres to classical Michaelis–Menten kinetics, produced a good fit between observed and calculated values.

General significance

This study indicates that, in addition to providing information on initial kinetic parameters, steady state approximations can be employed to directly model time course kinetics.Integrated forms of the Michaelis–Menten equation have previously been reported in the literature. Here we describe a method to directly apply steady state approximations to time course analysis for predicting product formation and simultaneously obtain multiple kinetic parameters.     

An optimizing start-up strategy for a bio-methanator

This paper presents an optimizing start-up strategy for a bio-methanator. The goal of the control strategy is to maximize the outflow rate of methane in anaerobic digestion processes, which can be described by a two-population model. The methodology relies on a thorough analysis of the system dynamics and involves the solution of two optimization problems: steady-state optimization for determining the optimal operating point and transient optimization. The latter is a classical optimal control problem, which can be solved using the maximum principle of Pontryagin. The proposed control law is of the bang–bang type. The process is driven from an initial state to a small neighborhood of the optimal steady state by switching the manipulated variable (dilution rate) from the minimum to the maximum value at a certain time instant. Then the dilution rate is set to the optimal value and the system settles down in the optimal steady state. This control law ensures the convergence of the system to the optimal steady state and substantially increases its stability region. The region of attraction of the steady state corresponding to maximum production of methane is considerably enlarged. In some cases, which are related to the possibility of selecting the minimum dilution rate below a certain level, the stability region of the optimal steady state equals the interior of the state space. Aside its efficiency, which is evaluated not only in terms of biogas production but also from the perspective of treatment of the organic load, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are, respectively, characterized by Monod and Haldane kinetics.     

Schematic methods for probabilistic enzyme kinetics.

The theory of steady-state enzyme processes which avoids using the mass action law of chemical kinetics and consistently describes catalytic mechanisms by probabilistic concepts has recently been proposed (Mazur, 1991, J. theor. Biol. 148, 229-242). To facilitate the analysis of complex reaction graphs by this theory the possibility of constructing schematic rules similar to those used in classical kinetics is studied. It is found that due to the similarity of algebraic procedures the popular method of King & Altman can be applied in probabilistic kinetics in addition to the earlier proposed rule based on enumeration of cycles of the reaction graph. This similarity also allows one to adapt many other shortcut methods of classical kinetics for probabilistic reaction graphs. The paper considers separately the possibility of transforming reaction mechanisms so that the initial graph is replaced by a simpler but equivalent one. It is shown that there are few cases when a group of states can be replaced by one united state, with earlier known rules such as the rule of Cha for equilibrium stages being particular cases of a more general procedure. In addition a novel method is proposed which performs step-by-step reduction of any reaction graph. All the new methods can be adapted for traditional kinetics as well. The results obtained demonstrate that many schematic rules of classical kinetics are of probabilistic origin.     

Multidimensional spectroscopy of β-carotene: Vibrational cooling in the excited state

Pump-degenerate four wave mixing (Pump-DFWM) is used for investigating the vibrational dynamics in the excited state of β-carotene in solution. In this 2D technique, an initial pump pulse promotes the system to the excited state, which is then probed by the succeeding DFWM sequence. We focus particularly on the internal conversion between the S₂ and S₁ state with high temporal and spectral resolution. The frequency shift of the excited state vibrations is measured and is explained as mode-specific vibrational cooling. Our results suggest an internal conversion in a time range between 260 and 500 fs without any intermediate states.     

Studies on the initial phase of dynein ATPase activity.

Kinetic measurement of the reaction of dynein ATPase (ATP phosphohydrolase, EC 3.6.1.3) extracted from the gills of Mytilus edulis shows that in the presence of Mg2+ there is a very rapid initial liberation of Pi from the dynein-ATP system, followed by a slower liberation in the steady state. In view of following results, we have confirmed that this phenomenon is not due to the accumulation of end products, a fall in substrate concentration, nor to the presence of labile impurities in ATP but is due to the catalytic activity of dynein ATPase. 1. The replacement of native dynein by heat denatured dynein or other kinds of Mg2+-ATPase could not produce such a burst phenomenon under the same condition. 2. Both the rate of initial burst and that of steady state were proportional to enzyme content over a wide range under our standard condition. 3. Initial burst was also observed under the constant ATP level by using a ATP generate system. 4. Preincubation of dynein with Pi prior to initiation of the reaction did not eliminate the initial burst. Some properties of the initial rapid liberation of dynein ATPase were also examined. These are shown below. 5. The free ADP liberation did not show any initial burst though the Pi liberation did in the initial phase and the rate of free ADP liberation was almost equal to that of Pi liberation of the steady state. 6. Mg2+ was more effective than Ca2+ for the appearance of the initial burst while the liberation of Pi in the steady state was activated more by Ca2+ than by Mg2+. The addition of K+ in the presence of Mg2+ resulted in a marked increase of Pi liberation in the steady state but not in the initial state. 7. The activation energy of the initial burst was 9.7 kcal, which is slightly smaller than that of myosin ATPase.     

Strategies for Manipulating Metabolic Fluxes in Biotechnology

Strategies for biotechnologically manipulating metabolic fluxes are critically examined in relation to a model system. The common idea of first identifying the rate-limiting enzyme in the biosynthetic pathway to a desired end-product, and then increasing its activity, is shown to be completely ineffective; such manipulation typically produces only trivial changes in flux. Manipulating the activities of all of the enzymes in a biosynthetic pathway by amounts calculated to increase a desired flux while leaving all other fluxes and all concentrations unchanged is potentially effective, and can be applied to any system without regard to its regulatory design. however, it requires accurate knowledge of the initial state of the system and the ability to make precise changes to numerous activities. The classical information about the regulatory mechanisms that exist in living organisms suggests that one can make much simpler manipulations, involving only the steps that remove the desired end-product, with almost equally satisfactory results.     

Theoretical Characterization of Slurry Fermentation

This is an extensive study of the three classical fermentation systems (emerged, submerged and solid‐state fermentations), thus uncovering, a system that is an intrinsically concomitant overlap of submerged and solid‐state fermentations – slurry fermentation. It is a convenient method of fermentation with hardly any theoretical characterization. This paper details the specifics of this system and its potential fields of application.     

Differential interferometry in the analytical ultracentrifuge. II. General applications

Various ways of applying differential interferometry to ultracentrifugal analyses are examined and several analytical techniques are established. In transport and moving boundary methods, the sedimentation coefficient is more precisely determined in the differential interference system than in the schlieren optical system because fringe measurement accuracy is much higher in the former system. Compared to interference and absorption optics, the differential interferometer provides a more exact s value in the transport method since an accurate calculation procedure can be adopted. Moreover, the following advantages of differential interferometry are noted. Determination of the initial solute concentration, which must be done in the usual interference method, is unnecessary in this sedimentation equilibrium method. Regardless of the partial loss of solute from the observed system due to rapid precipitation or adsorption to the cell wall during centrifugation, the molecular weight of the rest of the solute can be determined exactly. The diffusion coefficient can be determined accurately by fringe displacement analysis at the hinge point during the transient state. Together with the molecular weight and diffusion coefficient, the partial specific volume and sedimentation coefficient of a solute can be obtained from the result of a single low-speed centrifugation when the sample solutions in H₂O and D₂O are compared.     

Possibility of X-ray spectral diagnostics of a plasma in the tracks of fast multicharged ions

A plasma model of the relaxation of a medium within the tracks of heavy ions in condensed matter is proposed that is based on solving time-dependent radiative collisional kinetic equations with the initial condition corresponding to a medium’s state described by the classical model of multiple ionization of the target atoms by the field of fast multicharged ions. It is shown that the plasma model allows one to describe X-ray spectra recorded in the interaction of ion beams with condensed targets. An X-ray spectral method for plasma diagnostics is proposed that is based on the plasma model. The results obtained can also be used to study the initial stage of the formation of defects in solid bodies under the action of individual fast heavy ions.     

A Simple Self-Maintaining Metabolic System: Robustness,Autocatalysis, Bistability

A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts.     

Robust thermoregulatory overcompensation, rather than tolerance, develops with serial administrations of 70% nitrous oxide to rats

Changes in typical whole-animal dependent variables following drug administration represent an integral of the drug's pharmacological effect, the individual's autonomic and behavioral responses to the resulting disturbance, and many other influences. An archetypical example is core temperature (T_c), long used for quantifying initial drug sensitivity and tolerance acquisition over repeated drug administrations. Our previous work suggested that rats differing in initial sensitivity to nitrous oxide (N₂O)-induced hypothermia would exhibit different patterns of tolerance development across N₂O administrations. Specifically, we hypothesized that rats with an initially insensitive phenotype would subsequently develop regulatory overcompensation that would mediate an allostatic hyperthermic state, whereas rats with an initially sensitive phenotype would subsequently compensate to a homeostatic normothermic state. To preclude confounding due to handling and invasive procedures, a valid test of this prediction required non-invasive thermal measurements via implanted telemetric temperature sensors, combined direct and indirect calorimetry, and automated drug delivery to enable repeatable steady-state dosing. We screened 237 adult rats for initial sensitivity to 70% N₂O-induced hypothermia. Thirty highly sensitive rats that exhibited marked hypothermia when screened and 30 highly insensitive rats that initially exhibited minimal hypothermia were randomized to three groups (n=10 each/group) that received: (1) twelve 90-min exposures to 70% N₂O using a classical conditioning procedure, (2) twelve 90-min exposures to 70% N₂O using a random control procedure for conditioning, or (3) a no-drug control group that received custom-made air. Metabolic heat production (via indirect calorimetry), body heat loss (via direct calorimetry) and T_c (via telemetry) were simultaneously quantified during N₂O and control gas administrations. Initially insensitive rats rapidly acquired (3rd administration) a significant allostatic hyperthermic phenotype during N₂O administration whereas initially sensitive rats exhibited classical tolerance (normothermia) during N₂O inhalation in the 4th and 5th sessions. However, the sensitive rats subsequently acquired the hyperthermic phenotype and became indistinguishable from initially insensitive rats during the 11th and 12th N₂O administrations. The major mechanism for hyperthermia was a brisk increase in metabolic heat production. However, we obtained no evidence for classical conditioning of thermal responses. We conclude that the degree of initial sensitivity to N₂O-induced hypothermia predicts the temporal pattern of thermal adaptation over repeated N₂O administrations, but that initially insensitive and sensitive animals eventually converge to similar (and substantial) magnitudes of within-administration hyperthermia mediated by hyper-compensatory heat production.     

Effects of changes in the capacity for photosynthetic electron transfer and photophosphorylation on the kinetics of fluorescence induction in isolated chloroplasts

Chlorophyll fluorescence, 9-aminoacridine fluorescence and O₂ evolution have been measured in a chloroplast system reconstituted to simulate the induction kinetics observed in leaves. Transients in redox state and energy state, both of which control the yield of fluorescence, were seen to depend upon (a) light intensity, (b) electron-transfer rate as controlled by ferredoxin level, (c) the initial levels of ADP and phosphate and (d) the initial level of NADP. These factors were shown to interact to produce a range of fluorescence patterns. It is suggested that in vivo fluorescence transients in part are due to reduction and phoshorylation of the finite NADP and ADP pools that exist in the chloroplast prior to illumination.     

Biological models: measuring variability with classical and quantum information

This essay proposes methods to analyse the variability of biological data. The idea is to express the state of a biological system as a linear combination of base states in a Hilbert space. Coefficients of the linear combination can be interpreted as probabilities and informational entropy is associated to each state allowing the definition of a classical variability measure. Besides, state transition matrices can also be calculated and their norms express the dynamics of the system organization and a quantum variability measure. As the examples show, the classical measure expresses a structural variability and the quantum measure expresses a functional variability.     

Internal apparatus of neuropil in coelomata: Reconstruction of the earlier stages of its evolution

Based on previously obtained data on structural organization and evolution of neuropil in annelids and phoronids, reconstruction of their internal apparatus has been performed. Four structural types are identified: the first—the initial, the most primitive state characteristic of neuropil of articulates (polychaetes with intraepidermal nervous system); the second—peculiar to neuropil of polychaetes in the beginning of the exit of the nervous system from epidermis; the third—the specific state of neuronal interrelations in leeches, when the internal apparatus contains no local interneurons, but is formed by intensive local arborization of associative neurons with intersegmental connections; the fourth—the initial state of the internal apparatus peculiar to Tentaculata, which is structurally incomparable with that in the primitive articulates. It has been shown that the initial state of neuronal structure of the internal apparatus of primitive polychaetes oweniids and phoronids, although has externally similar basiepidermal position, is incomparable architectonically. Therefore, at present, determination of the internal apparatus can be achieved only in general as a system of local interneurons, which provides to an extent of precision the afferent—efferent connections in neuropil and contributes to integration of these connections with the cerebropetal and cerebrofugal pathways. Complication of the internal apparatus structure in jointed Trochozoa with the ganglionic type of the nervous system has its own specific features. Four levels of its differentiation have been identified: (1) start of exit of the abdominal ganglion from epidermis (polychaetes nephthyds); (2) complete or partial exit of the nervous system form epidermis (most of polychaetes, oligochaetes); (3) replacement of local interneurons of the internal apparatus by a morphologically rearranged system of intersegmental associative neurons of the functionally similar nature (with exception of leeches, this process is typical to different extent of crustacean and arachnids); (4) intensive development of the system of local interneurons, which is peculiar to the internal apparatus of insects.Translated from Zhurnal Evolyutsionnoi Biokhimii i Fiziologii, Vol. 40, No. 6, 2004, pp. 546–555.Original Russian Text Copyright © 2004 by Lagutenko.To the 100-Anniversary of A. K. VoskresenskayaThis revised version was published online in April 2005 with a corrected cover date.     

Vacuolar symplast and methodological approach to monitoring water self-diffusion between vacuoles of contacting root cells

New concepts of structural-functional organization of the transport system in higher plants were evolved at the current stage of investigations. In addition to the classical (cytoplasmic) symplast, another supra-cellular continuum was supposed to exist in the plant tissue, which interconnects vacuoles of neighboring cells through desmotubules and represents the second transport pathway within the plasmodesmata. This study describes and experimentally validates the method for monitoring the self-diffusion of water molecules between vacuoles of contacting cells in the maize (Zea mays L.) root by means of NMR method with a pulsed magnetic field gradient. The method is based on the fact that, at long period of self-diffusion observation, when water molecules in the apoplast and cytoplasm had already completed their relaxation and did not contribute significantly to the proton echo signal, the slope of the initial portion of the diffusional decay is independent of water permeability of the vacuolar membrane and is determined exclusively by water permeability of intervacuolar pathway through the desmotubules.     

Multidimensional spectroscopy of beta-carotene: vibrational cooling in the excited state

Pump-degenerate four wave mixing (Pump-DFWM) is used for investigating the vibrational dynamics in the excited state of beta-carotene in solution. In this 2D technique, an initial pump pulse promotes the system to the excited state, which is then probed by the succeeding DFWM sequence. We focus particularly on the internal conversion between the S(2) and S(1) state with high temporal and spectral resolution. The frequency shift of the excited state vibrations is measured and is explained as mode-specific vibrational cooling. Our results suggest an internal conversion in a time range between 260 and 500 fs without any intermediate states.     

Computing the transition state populations in simple protein models

We describe the master equation method for computing the kinetics of protein folding. We illustrate the method using a simple Go model. Presently most models of two-state fast-folding protein folding kinetics invoke the classical idea of a transition state to explain why there is a single exponential decay in time. However, if proteins fold via funnel-shaped energy landscapes, as predicted by many theoretical studies, then it raises the question of what is the transition state. Is it a specific structure, or a small ensemble of structures, as is expected from classical transition state theory? Or is it more like the denatured states of proteins, a very broad ensemble? The answer that is usually obtained depends on the assumptions made about the transition state. The present method is a rigorous way to find transition states, without assumptions or approximations, even for very nonclassical shapes of energy landscapes. We illustrate the method here, showing how the transition states in two-state protein folding can be very broad ensembles. © 2002 Wiley Periodicals, Inc. Biopolymers 68: 35–46, 2003     

Modeling protein conformational changes by iterative fitting of distance constraints using reoriented normal modes

Recently we have developed a normal-modes-based algorithm that predicts the direction of protein conformational changes given the initial state crystal structure together with a small number of pairwise distance constraints for the end state. Here we significantly extend this method to accurately model both the direction and amplitude of protein conformational changes. The new protocol implements a multisteps search in the conformational space that is driven by iteratively minimizing the error of fitting the given distance constraints and simultaneously enforcing the restraint of low elastic energy. At each step, an incremental structural displacement is computed as a linear combination of the lowest 10 normal modes derived from an elastic network model, whose eigenvectors are reorientated to correct for the distortions caused by the structural displacements in the previous steps. We test this method on a list of 16 pairs of protein structures for which relatively large conformational changes are observed (root mean square deviation >3 angstroms), using up to 10 pairwise distance constraints selected by a fluctuation analysis of the initial state structures. This method has achieved a near-optimal performance in almost all cases, and in many cases the final structural models lie within root mean square deviation of 1 approximately 2 angstroms from the native end state structures.