Determination of the best-fit values of kinetic parameters of the Michaelis-Menten equation by the method of least squares with the Taylor expansion

The best-fit values of the Michaelis constant (Km) and the maximum velocity (V) in the Michaelis-Menten equation can be obtained by the method of least squares with the Taylor expansion for the sum of squares of the absolute residual, i.e., the difference between the observed velocity and the corresponding velocity by calculation. This method makes it possible to determine the values of Km and V not in a trial-and-error manner but in a deductive and unique manner after some iterative procedures starting from arbitrary approximate values of Km and V. These values can be said to be uniquely determined for a set of data as the finally converged values are no longer dependent upon the initial approximate values of Km and V. It is also very important to obtain initial approximate values of parameters for the application of the method described above. A simple method is proposed to estimate the approximate values of parameters involved in fractional functions. The method of rearrangement after canceling of denominator of a fractional function can be utilized to obtain approximate values, not only for cases of two unknown parameters such as the Michaelis-Menten equation, but also for cases with more than two unknowns.     

The estimation of population pharmacokinetic parameters using an EM algorithm

A questionnaire was mailed to locally trained Division One dental surgeons. The questionnaire was designed to assess the practice of orthodontics, the undergraduate orthodontic curriculum in relation to the dental practitioner and continuing orthodontic education. The results showed that the undergraduate orthodontic curriculum was of limited use to the practitioner and that there was a need for a continuing orthodontic education programme. Information pertaining to various aspects of orthodontic practice was presented.     

Constrained versus unconstrained estimation in structural equation modeling.

Recently, R. D. Stoel, F. G. Garre, C. Dolan, and G. van den Wittenboer (2006) reviewed approaches for obtaining reference mixture distributions for difference tests when a parameter is on the boundary. The authors of the present study argue that this methodology is incomplete without a discussion of when the mixtures are needed and show that they only become relevant when constrained difference tests are conducted. Because constrained difference tests can hide important model misspecification, a reliable way to assess global model fit under constrained estimation would be needed. Examination of the options for assessing model fit under constrained estimation reveals that no perfect solutions exist, although the conditional approach of releasing a degree of freedom for each active constraint appears to be the most methodologically sound one. The authors discuss pros and cons of constrained and unconstrained estimation and their implementation in 5 popular structural equation modeling packages and argue that unconstrained estimation is a simpler method that is also more informative about sources of misfit. In practice, researchers will have trouble conducting constrained difference tests appropriately, as this requires a commitment to ignore Heywood cases. Consequently, mixture distributions for difference tests are rarely appropriate. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing parameters in structural equation modeling: Every "one" matters.

A problem with standard errors estimated by many structural equation modeling programs is described. In such programs, a parameter's standard error is sensitive to how the model is identified (i.e., how scale is set). Alternative but equivalent ways to identify a model may yield different standard errors, and hence different Z tests for a parameter, even though the identifications produce the same overall model fit. This lack of invariance due to model identification creates the possibility that different analysts may reach different conclusions about a parameter's significance level even though they test equivalent models on the same data. The authors suggest that parameters be tested for statistical significance through the likelihood ratio test, which is invariant to the identification choice. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Logistic regression analysis of twin data: estimation of parameters of the multifactorial liability-threshold model

This study with the rat evaluated the contribution of omega-conotoxin GVIA-(omega-CgTx) and verapamil-sensitive Ca2+ channels in behavioural, antinociceptive and thermoregulatory responses to intracerebroventricular (i.c.v.) injection of [D-Ala2,NMePhe4,Gly-ol5]enkephalin (DAMGO), [D-Pen2,D-Pen5]enkephalin (DPDPE) and dynorphin A-(1-17), which are selective agonists for putative mu, delta and kappa-opioid receptors, respectively. The rats treated with omega-CgTx (8-32 pmol i.c.v.) showed transient, dose-dependent shaking behaviour, hyperalgesia and hypothermia which gradually disappeared within 4 h. The behaviour of the rats was normal by 24 h. Histological examination of brain sections showed morphological alterations of neurons in the hippocampus, medial-basal hypothalamus and pyriform cortex. antinociception, catalepsy and thermoregulatory responses elicited by DAMGO (0.4 and 2.0 nmol) were significantly prolonged and potentiated by verapamil (20 pmol i.c.v. 15 min before) or omega-CgTx (8 pmol 24 h before). Antinociception and hypothermia induced by DPDPE were antagonized by verapamil and omega-CgTx, whereas only omega-CgTx prevented the behavioural arousal observed after DPDPE. Similarly, hypothermia induced by dynorphin A-(1-17) (5.0 nmol) and by the kappa-opioid receptor agonist U50,488H (215 nmol) was antagonized by the two Ca2+ channel blockers but only omega-CgTx prevented the barrel rolling and bizarre postures caused by the opioid peptide.     

The impact of nonnormality on full information maximum-likelihood estimation for structural equation models with missing data.

A Monte Carlo simulation examined full information maximum-likelihood estimation (FIML) in structural equation models with nonnormal indicator variables. The impacts of 4 independent variables were examined (missing data algorithm, missing data rate, sample size, and distribution shape) on 4 outcome measures (parameter estimate bias, parameter estimate efficiency, standard error coverage, and model rejection rates). Across missing completely at random and missing at random patterns, FIML parameter estimates involved less bias and were generally more efficient than those of ad hoc missing data techniques. However, similar to complete-data maximum-likelihood estimation in structural equation modeling, standard errors were negatively biased and model rejection rates were inflated. Simulation results suggest that recently developed correctives for missing data (e.g., rescaled statistics and the bootstrap) can mitigate problems that stem from nonnormal data. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Michaelis-Menten analysis of immobilized enzyme by affinity capillary electrophoresis

Michaelis constant of enzymatic reaction was evaluated by affinity capillary electrophoresis using beta-galactosidase as a model enzyme and o- and p-isomers of nitrophenyl-beta-galactoside as substrates. The enzyme was immobilized on the inner surface of a fused-silica capillary by the covalent bonding through a bridging group, and the substrates were introduced into the capillary. The reaction products migrated electrophoretically toward the detection side (anodic side), while the unreacted substrates moved toward the injection side (cathodic side) on a slow electroosmotic flow generated by the weak negative charge of the immobilized enzyme. The initial velocity of the enzymatic reaction was estimated from the peak height of the product, and the Michaelis constant was calculated according to Lineweaver-Burk equation. The results (Km, 2.34 mM for o-isomer and 1.09 mM for p-isomer) were reproducible (RSD < 11.8%, n = 5). Although the estimated Michaelis constants were larger than the reported values measured in homogeneous solution, the ratio of the Michaelis constants of o-/p-isomers was in good agreement with the literature value. The present method required as low as a few microgram amount of enzyme and nanogram amount of substrate which is far smaller than those required in a conventional affinity HPLC.     

Interpretation of simulation studies for efficient estimation of population pharmacokinetic parameters

OBJECTIVE: To develop new approaches for evaluating results obtained from simulation studies used to determine sampling strategies for efficient estimation of population pharmacokinetic parameters. METHODS: One-compartment kinetics with intravenous bolus injection was assumed and the simulated data (one observation made on each experimental unit [human subject or animal]), were analyzed using NONMEM. Several approaches were used to judge the efficiency of parameter estimation. These included: (1) individual and joint confidence intervals (CIs) coverage for parameter estimates that were computed in a manner that would reveal the influence of bias and standard error (SE) on interval estimates; (2) percent prediction error (%PE) approach; (3) the incidence of high pair-wise correlations; and (4) a design number approach. The design number (phi) is a new statistic that provides a composite measure of accuracy and precision (using SE). RESULTS: The %PE approach is useful only in examining the efficiency of estimation of a parameter considered independently. The joint CI coverage approach permitted assessment of the accuracy and reliability of all model parameter estimates. The phi approach is an efficient method of achieving an accurate estimate of parameter(s) with good precision. Both the phi for individual parameter estimation and the overall phi for the estimation of model parameters led to optimal experimental design. CONCLUSIONS: Application of these approaches to the analyses of the results of the study was found useful in determining the best sampling design (from a series of two sampling times designs within a study) for efficient estimation of population pharmacokinetic parameters.     

Comparison of three methods of estimating the parameters of the Naka-Rushton equation

The Naka-Rushton equation empirically describes the amplitude R of the dark-adapted electroretinogram b-wave, as a function of stimulus luminance L, as R/Rmax = Ln/(Ln + Kn). Estimating the three parameters Rmax, n, and K of this function from electroretinogram data is of both experimental and clinical interest. Several different approaches have been developed to accomplish this analysis, but these approaches may derive different estimates of the three parameters. To examine this possibility, we compared the results of three methods of fitting the Naka-Rushton equation to data sets obtained from 30 normal subjects. Two methods were nonlinear curve-fitting programs; the third method involved fitting a regression line to transformed data. The results indicate that solutions provided by these methods have consistent differences, which may be an important consideration when comparing results reported in studies that used different curve-fitting methods.     

Latent variable interaction and quadratic effect estimation: A two-step technique using structural equation analysis.

The author proposes an alternative estimation technique for latent variable interactions and quadratics. Available techniques for specifying these variables in structural equation models require adding variables or constraint equations that can produce specification tedium and errors or estimation difficulties. The proposed technique avoids these difficulties and may be useful for EQS, LISREL 7, and LISREL 8 users. First, measurement parameters for indicator loadings and errors of linear latent variables are estimated in a measurement model that excludes the interaction and quadratic variables. Next, these estimates are used to calculate values for the indicator loadings and error variances of the interaction and quadratic latent variables. Then, these calculated values are specified as constants in the structural model containing the interaction and quadratic variables. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Capillary zone electrophoresis of interconverting cis-trans conformers of peptidyl-proline dipeptides: estimation of the kinetic parameters

Peptides containing proline residues, except at the N-terminus, exist in cis and trans forms due to the rigidity of the peptidyl-proline bond. Computer-simulated and experimental electropherograms have been used to study the interplay of the electrophoretic migration and the kinetics of the cis-trans interconversion. The measure of the interference by the reaction is the dimensionless Damk?hler number (Da) which is the ratio of the migrant's residence time to the characteristic time of reaction in the capillary. The fraction of the trans conformer that is not separable with 90% purity is employed to quantify the extent of overlap between the concentration profiles of the two interconverting migrants and the effect of the various operational variables was examined by simulation. The deterioration of separation, as measured by the degree of overlap, is a quasi sigmoidal function of Da with the selectivity and the intrinsic efficiency of the system as the parameters. At sufficiently low temperatures the interference by reaction kinetics may vanish and the two conformers are separated. At high enough temperatures, when the rate of interconversion is very fast, the two conformers are not separated at all. A simple and rapid method is proposed for estimation of kinetic parameters for the cis-trans isomerization on the basis of data obtained with phenylalanyl-proline dipeptide. The procedure involves determination of the equilibrium constant by measuring equilibrium concentrations of the two conformers using nuclear magnetic resonance (NMR) or capillary zone electrophoresis (CZE) at very low temperature, correlation of the peak shapes in the electropherograms with the Da, and finally, evaluation of the forward rate constants from the assigned Da values in the domain: 0.01 < Da < 0.5. Separations using CZE were performed in the temperature range of 1-40 degrees C by using the Beckman P/ACE unit equipped with an auxiliary cooling system. The kinetic data thus obtained showed good agreement (average error less than 5%) with those measured by NMR.     

Baseband velocity estimation for second-harmonic signals exploiting the invariance of the Doppler equation

Molecular chaperones differ in their ability to stabilize nonnative polypeptides and to mediate protein folding, defining 'holding' and 'folding' systems. Here we show that the mammalian cytosolic and nuclear chaperone Hsc70 can act as both, as a 'holding' and a 'folding' system, depending on the chaperone cofactors which associate with Hsc70. In conjunction with the cofactor Hsp40, Hsc70 stabilizes heat-denatured firefly luciferase. The stabilizing activity turns into a folding activity in the additional presence of the Hsc70-interacting protein Hip. In contrast, the cofactor BAG-1 abrogates the 'holding' function of the Hsc70/Hsp40 system and blocks the action of Hip on Hsc70. Our study sheds light on the molecular mechanisms that determine the functional specificity of Hsc70 in the mammalian cell.     

Michaelis-Menten kinetics determine cyclosporine steady-state concentrations: a population analysis in kidney transplant patients

Dosage adjustments of cyclosporine are confounded with an unexpected degree of variability, thus invalidating a direct proportionality between the oral dose rate and the steady-state concentration. In 1033 observations of dose rate and average steady-state concentration collected during therapeutic monitoring (area under the curve method) in 134 adult kidney transplant patients, a population pharmacokinetic analysis showed that a Michaelis-Menten model fitted the data better than a linear clearance model. It was further shown that the Michaelis-Menten constant (Km) parameter of the Michaelis-Menten model (the average steady-state concentration at half-maximal dose rate) increased during the first 4 months after transplantation whereas the maximal dose rate of the Michaelis-Menten model (Vmax) remained constant. The following parameters with interindividual variation in parenthesis were estimated: Vmax = 852 mg/24 hr (43%) and Km at 114 days after transplantation = 349 ng/ml (117%). An algorithm was derived from this population model that guides the clinician during the adjustment of oral cyclosporine dose rates.     

The other half of the expectancy equation: Pygmalion.

The central position of this study is that both expectancy research and compensatory educational theory have reached an impasse because expectancy manipulation has largely been confined to the teacher. 45 inner-city 5-6 yr old Blacks enrolled in a compensatory program were exposed to different positive expectancy inductions in order to assess the effects of manipulating Ss' expectations alone, teacher's alone, and the 2 simultaneously on reading achievement test scores (Metropolitan Reading Readiness Test, Form A). Results show that postexperimental scores improved significantly for all 3 expectancy conditions. Moreover, inducing positive expectations in Ss was more effective than the conventional teacher manipulation and was as successful as the group in which both teachers and Ss were given controlled feedback. It is concluded that perhaps the focus of educational programs should be the potentially malleable child rather than the sometimes intransigent teacher. (26 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Michaelis-Menten kinetics model of oxygen consumption by rat brain slices following hypoxia

In the present study, we have measured partial pressure of oxygen (pO2) profiles through rat brain slices before and after periods of hypoxia (5 and 10 min) to determine its effect on tissue oxygen demand. Tissue pO2 profiles were measured through rat cerebral cortex slices superfused with phosphate buffer using oxygen (O2)-sensitive microelectrodes at different times in controls [40% O2 balance nitrogen (N2)], and at different times before and after 5 or 10 min of hypoxia (100% N2). A one-dimensional, steady-state model of ordinary diffusion with a Michaelis-Menten model of O2 consumption where the maximal O2 consumption (Vmax) and the rate at half-maximal O2 consumption (Km) were allowed to vary was used to determine the kinetics of O2 consumption. Actual pO2 profiles through tissue were fitted to theoretical profiles by a least-squares method. Vmax varied among penetrations in a control slice and among slices. Vmax seemed to decrease after hypoxic insult, but the change was not statistically significant. The Km value measured before hypoxia was lower than the first Km value measured after the end of hypoxia, indicating that hypoxia induced a compensatory change in the metabolic state of the tissue. Km increased immediately after both 5- and 10-min hypoxic insults and returned to normal after recovery for each case. It seems that during and immediately after short periods of hypoxia, Km increases from near zero but returns to normal values within a few minutes.     

Measurement and estimation system for monitoring physiologic parameters of man and biological feedback training

A flexible instrumental programmed system realizing the biological feedback (BFB) method and permitting an easy tuning of the channels and parameters for treatment and reflection of physiological information is designed. A measurement and estimation real-time medical system for monitoring and BFB training is described, based on visual programming. An example of practical clinical application of the system to BFB training for the EEG rhythms is offered.