Interpretation of Nonhyperbolic Behavior in Enzymic Systems. I. Differentiation of Model Mechanisms

1971 ◽  
Vol 49 (5) ◽  
pp. 568-580 ◽  
Author(s):  
J. Tze-Fei Wong ◽  
Laszlo Endrenyi
Keyword(s):  
Steady State ◽  
Relative Velocity ◽  
General Scheme ◽  
Binding Constants ◽  
Rate Function ◽  
Quasi Equilibrium ◽  
Subunit Interactions ◽  
Binding Data ◽  
Good Discriminator ◽  
Sheep Hemoglobin

Mechanistic interpretation of nonhyperbolic rate and binding responses of enzymic reactions involves interlaced distinctions between steady-state and quasi-equilibrium kinetics, between the effects of K, V, and KV types of subunit interactions, and between the effects of different model mechanisms. Therefore (a) the steady-state and quasi-equilibrium predictions of selected kinetic models were analyzed. In most instances the degree of the rate function is a good discriminator between the two types of kinetics. (b) Sensitive detection of K effects in quasi-equilibrium is possible by observing the dependence of the ratio (relative velocity/fractional binding) on the substrate concentration, (c) Relationships between Adair binding constants and constants of models proposed by Pauling, by Monod et al., and by Koshland et al. permit testing the validity of these models to experimental binding data. For illustration the results of Roughton on the binding of oxygen to sheep hemoglobin have been analyzed, which appear to exclude the applicability of models of Pauling and Koshland, but may admit the mechanism of Monod et al. These criteria have been discussed in terms of a general scheme of presently feasible model differentiations.

Correction for Unequal Intensities of Left and Right Circularly Polarized Light in Steady-State and Lifetime-Resolved Fluorescence-Detected Circular Dichroism

1994 ◽  
Vol 48 (2) ◽  
pp. 167-175 ◽  
Author(s):  
Lei Geng ◽  
Linda B. McGown
Keyword(s):  
Circular Dichroism ◽  
Steady State ◽  
General Scheme ◽  
Multicomponent System ◽  
Polarized Light ◽  
Circularly Polarized Light ◽  
Circularly Polarized ◽  
Experimental Approaches ◽  
Total Absorbance ◽  
Circular Dichroïsm

A major difficulty in fluorescence-detected circular dichroism (FDCD) and lifetime-resolved fluorescence-detected circular dichroism (LRFDCD) is the generation of equal excitation intensities of left circularly polarized light (LCPL) and right circularly polarized light (RCPL). In the presence of unequal intensities, the observed FDCD signal of an optically active sample, or the resolved FDCD signals of a multicomponent system in the case of LRFDCD, will be contaminated by a factor that is the ratio of the two unequal intensities. For optically inactive samples, a sample-independent, artifactual, nonzero signal of constant magnitude is observed. A general scheme is presented for the correction of these inaccuracies caused by unequal intensities of LCPL and RCPL. Large differences between LCPL and RCPL excitation intensities were artificially introduced in steady-state FDCD measurements, and the artifact was accurately corrected by the scheme. Corrected results for the different experimental approaches that have been described for LRFDCD showed similarly good accuracy. In a related consideration, inclusion of the total absorbance and absorption circular dichroism of the sample in the calculation of the FDCD signal is shown to be essential for samples with high absorbances.

Structure formation mechanisms of low-dimensional porous titanium systems condensed under quasi-equilibrium steady-state conditions

Vacuum ◽  
2011 ◽  
Vol 86 (1) ◽  
pp. 111-118 ◽  
Author(s):  
V.I. Perekrestov ◽  
Yu.O. Kosminska ◽  
A.A. Mokrenko ◽  
I.N. Kononenko ◽  
A.S. Kornyushchenko
Keyword(s):  
Steady State ◽  
Structure Formation ◽  
Porous Titanium ◽  
Formation Mechanisms ◽  
Quasi Equilibrium ◽  
Low Dimensional

Analytical Investigation of Hopf Bifurcations Occurring in a 1DOF Sliding-Friction Oscillator With Application to Disc-Brake Vibrations

2005 ◽  
Author(s):  
Hartmut Hetzler ◽  
Wolfgang Seemann ◽  
Daniel Schwarzer
Keyword(s):  
Fixed Point ◽  
Steady State ◽  
Limit Cycle ◽  
Relative Velocity ◽  
Sliding Friction ◽  
Analytical Investigation ◽  
Stable Region ◽  
Stable Steady State ◽  
Disc Brake ◽  
Stick Slip

This article deals with analytical investigations on stability and bifurcations due to declining dry friction characteristics in the sliding domain of a simple disc-brake model, which is commonly referred to as “mass-on-a-belt”-oscillator. Sliding friction is described in the sense of Coulomb as proportional to the normal force, but with a friction coefficient μS which depends on the relative velocity. For many common friction models this latter dependence on the relative velocity can be described by exponential functions. For such a characteristic the stability and bifurcation behavior is discussed. It is shown, that the system can undergo a subcritical Hopf-bifurcation from an unstable steady-state fixed point to an unstable limit cycle, which separates the basins of the stable steady-state fixed point and the self sustained stick-slip limit cycle. Therefore, only a local examination of the eigenvalues at the steady-state, as is the classical ansatz when investigating conditions for the onset of friction-induced vibrations, may not give the whole picture, since the stable region around the steady state fixed point may be rather small. The analytical results are verified by numerical simulations. Parameter values are chosen for a model which corresponds to a conventional disc-brake.

scholarly journals Reversible enzyme-catalysed reactions: the quasi steady state as a a quasi-equilibrium, and a correction to Haldane's kinetic constants and to secondary relationships involving kinetic constants.

2021 ◽  
Author(s):  
Eric A Barnsley
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Rate Of Change ◽  
Kinetic Constants ◽  
Rate Equations ◽  
Quasi Equilibrium ◽  
Quasi Steady State ◽  
Enzyme Substrate ◽  
State Approximation ◽  
Specificity Constant

For reversible enzyme-catalysed reactions obeying Henri-Michaelis-Menten kinetics, theoretical solution of the rate equations for the enzyme-substrate intermediate are generally incorrect when the quasi-steady state approximation, equating the rate of change of the concentration of the enzyme-substrate intermediate to zero, is used.  For the simplest kinetic model used by Haldane, such a procedure does not reveal that in one direction, that starting with the reactant having the lower binding constant, the quasi-steady state is one of quasi-equilibrium, and Haldane’s structure of the Km written in terms of rate constants is incorrect. This is probably also true of more complex mechanisms in which the structure of kcat may also be in error.  Modern methods of numerical integration for the solution of rate equations, if applied to reversible reactions to obtain rate constants from measured catalytic constants, will require the correct expressions for kcat and Km. Furthermore, the (now called) Haldane relationship, relating the kinetic constants kcat and Km for the forward and reverse reactions to the equilibrium constant of a reaction, is now seen to be generally incorrect, and in addition another exception for a the theoretical validation of kcat /Km as a specificity constant arises.

Design of Pressurized Cylinders for High-Temperature Applications

1960 ◽  
Vol 82 (2) ◽  
pp. 477-481
Author(s):  
J. F. Traexler
Keyword(s):  
Steady State ◽  
High Temperature ◽  
Creep Rate ◽  
Plane Strain ◽  
Material Properties ◽  
Rate Function ◽  
Specific Form ◽  
Steady State Creep ◽  
Numerical Examples ◽  
Walled Cylinder

General equations for the stresses in a thick-walled cylinder in a state of plane strain are derived considering “steady-state” creep. A specific form of the creep-rate function is assumed and numerical examples are included to show the effect of geometry and material properties.

Kinematics of Enzyme Action

2018 ◽  
pp. 81-121
Author(s):  
Giovanni Zocchi
Keyword(s):  
Steady State ◽  
Elastic Energy ◽  
Control Function ◽  
Nonequilibrium State ◽  
The Other ◽  
Quasi Equilibrium ◽  
Post Translational Modifications ◽  
Allosteric Control ◽  
Individual Enzyme ◽  
Specific Ligand

Enzymes are catalysts as well as the molecular machines that generate and maintain the nonequilibrium state of the cell. There are roughly two main mechanisms by which enzymes provide the control function for the network of chemical reactions in the cell. One is the presence or absence of the enzyme, controlled by gene expression. The other is allosteric control: the modulation of the activity of an individual enzyme caused by binding of a specific ligand, often a small metabolite, or else caused by so-called post-translational modifications. This chapter addresses what could be variously called the quasi-equilibrium aspects, or steady state, or kinematics, of enzyme operation, and what one learns from time-independent perturbations of this steady state. Topics discussed include Michaelis–Menten kinetics, the method of the DNA springs, force and elastic energy in the enzyme–DNA chimeras, injection of elastic energy vs. activity modulation, and connection to nonlinear dynamics.

STUDY OF THE CROSSOVER FROM NON-EQUILIBRIUM STATIONARY STATES TO QUASI-EQUILIBRIUM STATES IN A DRIVEN DIFFUSIVE SYSTEM UNDER THE INFLUENCE OF AN OSCILLATORY FIELD

2002 ◽  
Vol 16 (27) ◽  
pp. 4165-4174 ◽  
Author(s):  
ROBERTO A. MONETTI ◽  
EZEQUIEL V. ALBANO
Keyword(s):  
Steady State ◽  
Lattice Gas ◽  
Thermal Bath ◽  
Quasi Equilibrium ◽  
Stationary States ◽  
Driving Field ◽  
Driven Diffusive System ◽  
Crossover Behavior ◽  
Diffusive System ◽  
Non Equilibrium

A driven diffusive system (DDS) is a lattice-gas in contact with a thermal bath in the presence of an external field. Such DDS constantly gains (losses) energy from (to) the driving field (thermal bath) and therefore, for long enough time, it reaches a non-equilibrium steady-state (NESS) with a generally unknown statistical distribution. It is found that if the constant driving is replaced by an oscillatory field of magnitude E and period τ, the system exhibits a crossover from NESS to a quasi-equilibrium state (QES) driven by τ. The crossover behavior is characterized by a typical crossover time which is proportional to the lattice side and consequently relevant to confined systems.

STEADY-STATE THEORY OF ADSORPTION PSEUDOCAPACITANCE IN ELECTROCHEMICAL RADICAL-ION REACTIONS

1964 ◽  
Vol 42 (1) ◽  
pp. 90-106 ◽  
Author(s):  
B. E. Conway ◽  
E. Gileadi
Keyword(s):  
Steady State ◽  
Adsorption Isotherms ◽  
Rate Constants ◽  
State Theory ◽  
Electrochemical Reactions ◽  
Recombination Reaction ◽  
Quasi Equilibrium ◽  
Adsorbed Species ◽  
Heterogeneity Parameter ◽  
State Case

The theory of adsorption pseudocapacity behavior is developed for a sequence of electrochemical reactions involving an ion discharge step which produces an adsorbed radical, followed by an "ion–atom" recombination reaction with or without desorption of the product of this step. The adsorption pseudocapacity behavior is deduced analytically particularly for the steady-state case and distinguished from the results obtained for assumed quasi-equilibrium in the ion discharge step when the succeeding step is rate-controlling. The effect of variation of the relative values of the rate constants of the discharge and of succeeding steps is investigated. It is shown that the capacity-potential behavior is sensitively dependent on the ratio of these rate constants, particularly for the case of adsorption isotherms involving a large value for the "heterogeneity parameter", r, defining the variation of energy of adsorption of the intermediates with coverage. Under the latter conditions, limiting coverages of the electrode by the adsorbed species are reached with increasing potential, depending on the relative values of the rate constants and the value of r.

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