Steady-state parameters

Of all existing methods to monitor electrical properties while using semiconductor sensors, only two [5] have become widely implemented both in experimental practice and in industrial conditions. These are kinetic method, i.e. measurement of various electrical parameters under kinetic conditions, and stationary (equilibrium) method based on the measurement of steady-state parameters (conductivity, work function. Hall s electromotive force, etc.). 

Wypych and Arnold (1985b) and hence, only a brief description is presented here. The test procedure basically consists of three different types of experiments which are applied to the material until sufficient data have been collected for the determination of conveying characteristics. The steady-state parameters generated specifically for this purpose are... 

The program THERMFF solves the same dynamic process model equations as THERM, where it was shown that all the parameters, including the inlet temperature and concentration will influence the steady state. In the case of multiple steady states the values of the steady state parameters cannot be set, because they are not unique. This example should, therefore, be mn under parameter conditions that will guarantee a single steady state for all expected values of the CA0 and T0. These can be selected with the aid of the programs THERMPLOT and THERM. 

In a multiple dosing regimen involving oral medication, the following equations are useful to find the steady-state parameters ... 

Rigorous adherence of enzymes to the Haldane relation is well illustrated by the case of wild-type and Glu -to-Asp triose-phosphate isomerases. These enzymes differ only with respect to a single methylene in the side-chain carboxyl group of residue 165. The steady-state parameters for the wild-type enzyme are kcat,forward, 430 s" ... 

The ratio of the turnover number (i.e., Emax/[Etotai]) to the Xn, value of a substrate in a particular enzyme-catalyzed reaction. When kcat and are the true steady-state parameters, this ratio (or the ratio Emax/T m) is an excellent gauge of the specificity of the enzyme for that substrate. The larger the ratio, the more effective that substrate is used by the enzyme under study. In addition, the effects of a number of mechanistic probes of enzyme action on this ratio (for example, pH effects, isotope effects, temperature effects, the influence of various modifiers, etc.) can provide much information on the catalytic and binding mechanism. See... 

Effect of Alcohol. Table IV and Figure 4 show the effect of 1-octanol. It is evident that the alcohol does affect k0. The steady-state parameter,... 

For the middle steady state, Figure 7.12(b) shows that the increase in the gas oil feed temperature Yqj from 450 K to 527 K and to 539 K causes the dimensionless reactor temperature to decrease from 1.76 to 1.56 and to 1.07. This increase in Yaf in turn causes a decrease in conversion and an increase in gasoline yield from 0.314 to 0.3875 and to 0.3971, see Figure 7.11(b). The opposite response directions for these middle steady state parameters is again evident. 

Although V)/ ss is a steady-state parameter, it can be calculated using non-steady-state data as... 

Application of the theory of Markov chains to model steady-state parameters of complex circuits... 

Takahashi K. Klinman J. P. Relationship of stopped flow to steady state parameters in the dimeric copper amine oxidase from Hansenula polymorpha and the role of zinc in inhibiting activity at alternate copper-containing subunits. Biochemistry 2006, 45, 4683 1694. 

Knowles JR (1976) The intrinsic pKa-values of functional groups in enzymes improper deductions from the pH-dependence of steady-state parameters. CRC Crit Rev Biochem 4 165-173... 

Despite the short half-time of Zn-69m which limited the data collection period such that the model could only analyze the rapid processes of zinc metabolism (approximately 10% of total body zinc), a number of fundamental steady state parameters were derived as shown In Table I. 

Besides steady-state and djmamic simulation, CHEOPS supports a number of further applications like solving steady-state parameter identification and optimization problems for open-form models. It also supports a hybrid model formulation, where only one model is explicitly formulated in an open form, while the other one is represented in a closed form, and the full problem requires transformation to a single representation. The framework supports the addition of further application components. 

Depending on the mechanism every substrate A, B, P and Q requires one or two kinetic constants (designated as K and Km) in order to describe its reciprocal action with the enzyme. According to the steady -state derivation of these rate equations, Ki and Km are no longer simple dissociation constants (compare discussion about Ks and KM). In some cases Ki is identical to a dissociation constant as described before, but most often these steady state parameters are defined by three and more rate constants. A verbal distinction between an inhibition constant a Michaelis constant and a dissociation constant does not have a corresponding mechanistic scenario in all cases. 

The performance of the EMR may be calculated by means of the measured kinetics and the simultaneous calculation of mass balances of each reactant. The steady-state parameters of the reactor can be estimated by numerical integration of the differential mass-balance equations by means of the Runge-Kutta method. 

The kinetic analysis of an enzyme mechanism often begins by analysis in the steady state therefore, we first consider the conclusions that can be derived by steady-state analysis and examine how this information is used to design experiments to explore the enzyme reaction kinetics in the transient phase. It has often been stated that steady-state kinetic analysis cannot prove a reaction pathway, it can only eliminate alternate models from consideration (5). This is true because the data obtained in the steady state provide only indirect information to define the pathway. Because the steady-state parameters, kcat and K, are complex functions of all of the reactions occurring at the enzyme surface, individual reaction steps are buried within these terms and cannot be resolved. These limitations are overcome by examination of the reaction pathway by transient-state kinetic methods, wherein the enzyme is examined as a stoichiometric reactant, allowing individual steps in a pathway to be established by direct measurement. This is not to say that steady-state kinetic analysis is without merit rather, steady-state and transient-state kinetic studies complement one another and analysis in the steady state should be a prelude to the proper design and interpretation of experiments using transient-state kinetic methods. Two excellent chapters on steady-state methods have appeared in this series (6, 7) and they are highly recommended. 

The two kinetic constants, and itcat. are most often misinterpreted as the substrate dissociation constant and the rate of the chemical reaction, respectively. However, this is not always the case, and /Cm can be greater than, less than, or equal to the true substrate dissociation constant, K. The steady-state kinetic parameters only provide information sufficient to describe a minimal kinetic scheme. In terms of measurable steady-state parameters, a reaction sequence must be reduced to a minimal mechanism (Scheme I),... 

The form of the equation exactly parallels that for Michaelis-Menten kinetics and for a similar reason. The increase in rate as a function of concentration reflects the saturation of the E S collision complex at the upper limit, the rate approaches the maximum rate of reaction. There are three important differences that distinguish these kinetic measurements from steady-state parameters (1) the hyperbola is a function of the true dissociation constant, = VKt, because only a single turnover is measured (2) the maximum rate provides a direct measure of the sum of the rate constants, k2 + k.2 < and (3) the intercept on the y axis is equal to the rate constant, k-2, defining the dissociation rate. 

In Table IV we list the temperature-dependent steady-state parameters static permittivity 8S density p Debye relaxation time td second-Debye relaxation time tD2 the contribution Aes to 8S due to fast vibrating HB molecules and the dipole-moment factor k involved in Eq. (3). 

Transient state and equilibrium measurements have led to a complete kinetic scheme for dihydrofolate reductase which accounts for the steady-state parameters and predicts the full time course kinetics under a variety of substrate concentrations and at various pH values. The pH-independent pathway is shown in... 

By means of Eqn. 17 and stopped-flow studies at various values of Sq, k2, and kj, can be separately determined and studied. For carboxypeptidase Y, which also shows such burst kinetics with 4-nitrophenyl trimethylacetate (I), enzyme preparations with differing amounts of attached carbohydrate, reacted with closely similar steady-state parameters K, k ) but differences were apparent for presteady-state parameters (k2> [14]. 

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