Effect of activation energy microheterogeneity on first-order enzyme deactivation

The influence of microheterogeneity on enzyme inactivation kinetics is examined. A continuous normal distribution of the thermal activation energy is assumed, and using this, a simple mathematical model is developed to find the activity-time trajectories for a microheterogeneous enzyme. Using an example, the model is used to show the quantitative effects of microheterogeneity such as increased order and stability observed during an enzyme inactivation. Experimental measurement of the extent of microheterogeneity in an enzyme sample is also discussed.     

The mean and standard deviation of development time

The variability in a population of the onset of a phenophase may be significantly great compared to the mean time or to a practical interest. This is illustrated by flowering of gladiolus and germination of tobacco seed andAlternaria spores. Mathematically, development is conceived to pass through a series of f stages at a rate P, the sum of P to the half-time equals f, and the variance of the times for individual completions is f divided by P² near the half-time.Presented at the Seventh International Biometeorological Congress, 17–23 August 1975, College Park, Maryland, USA.     

Dual stable point model of muscle activation and deactivation

Two dynamic models of muscle activation and deactivation based on the concepts of ion transport, reaction rates, and muscle mechanics are proposed. Storage release and uptake of calcium by the sarcoplasmic reticulum, and a two-step chemical reaction of calcium and troponin are included in the first model. This is a concise version of the complex chemical reactions of muscle activation and deactivation in sarcoplasm. The second model is similar to the first, but calcium-troponin reactions are simplified into two nonlinear rates functions. Due to these nonlinear dynamics, the second model can explain the catch-like enhancement of isometric force response. Simulation results which match experimental data are shown. Also, two new phenomena which need further experiment to verify are predicted by the second model.     

Estimating the probability that the sample mean is within a desired fraction of the standard deviation of the true mean

The use of small sample sizes in human and primate evolutionary research is commonplace. Estimating how well small samples represent the underlying population, however, is not commonplace. Because the accuracy of determinations of taxonomy, phylogeny, and evolutionary process are dependant upon how well the study sample represents the population of interest, characterizing the uncertainty, or potential error, associated with analyses of small sample sizes is essential. We present a method for estimating the probability that the sample mean is within a desired fraction of the standard deviation of the true mean using small (n < 10) or very small (n ≤ 5) sample sizes. This method can be used by researchers to determine post hoc the probability that their sample is a meaningful approximation of the population parameter. We tested the method using a large craniometric data set commonly used by researchers in the field. Given our results, we suggest that sample estimates of the population mean can be reasonable and meaningful even when based on small, and perhaps even very small, sample sizes.     

Different pathways for activation and deactivation in CaV1.2: a minimal gating model

Point mutations in pore-lining S6 segments of Ca_V1.2 shift the voltage dependence of activation into the hyperpolarizing direction and significantly decelerate current activation and deactivation. Here, we analyze theses changes in channel gating in terms of a circular four-state model accounting for an activation R–A–O and a deactivation O–D–R pathway. Transitions between resting-closed (R) and activated-closed (A) states (rate constants x(V) and y(V)) and open (O) and deactivated-open (D) states (u(V) and w(V)) describe voltage-dependent sensor movements. Voltage-independent pore openings and closures during activation (A–O) and deactivation (D–R) are described by rate constants α and β, and γ and δ, respectively. Rate constants were determined for 16-channel constructs assuming that pore mutations in IIS6 do not affect the activating transition of the voltage-sensing machinery (x(V) and y(V)). Estimated model parameters of 15 Ca_V1.2 constructs well describe the activation and deactivation processes. Voltage dependence of the “pore-releasing” sensor movement ((x(V)) was much weaker than the voltage dependence of “pore-locking” sensor movement (y(V)). Our data suggest that changes in membrane voltage are more efficient in closing than in opening Ca_V1.2. The model failed to reproduce current kinetics of mutation A780P that was, however, accurately fitted with individually adjusted x(V) and y(V). We speculate that structural changes induced by a proline substitution in this position may disturb the voltage-sensing domain.     

A model of enzyme adsorption and hydrolysis of microcrystalline cellulose with slow deactivation of the adsorbed enzyme

Reduction in the activity and the concentration of the adsorbed enzyme are noted in the experimental data. Two alternative mechanisms, inactivation of the adsorbed enzyme and mass transfer of the enzyme from the bulk solution to the solution within the cellulose fibril where the cellulase is assumed to be inactive, are used to represent the decline in activity. The decline in concentration of the adsorbed enzyme is represented by a modest product inhibition and, more importantly, the assumption that the concentration of the adsorption sites is proportional to the square of the remaining substrate concentration. Measurements of both adsorbed enzyme and product concentration over time are used in determining parameter values. The model is applied to a series of experiments having a 10-fold range of substrate concentration and to an experiment in which the product is removed continuously. For both deactivation mechanisms, a very good representation of product concentration (standard deviation 3.6%) is obtained over the full period (168 h) of hydrolysis; the representation of adsorbed enzyme is, however, less accurate (standard deviation 6.7-6.8%).     

Solid-state enzyme deactivation in air and in organic solvents

Thermal deactivation of solid-state acid phosphates (E.C. 3.1.3.2, from potato) is analyzed, both in the presence and in the absence of organic solvents. The thermal deactivation profile departs from first order kinetics and shows an unusual activity. The process is described by a phenomenological equation, whose theoretical implications are also discussed. The total amount of buffer salts in the enzyme powder dramatically affects enzyme stability in the range 70xC to 105xC. The higher salt/protein ratio increases the rate of thermal deactivation. The deactivation rate is virtually unaffected by the presence of organic solvents, independent of their hydrophilicity. (c) 1994 John Wiley & Sons, Inc.     

Kinetics of a general model for enzyme activation through a limited proteolysis

The kinetics of a general model for enzyme activation through a limited proteoylsis has been studied, and equations which show the dependence on time of the concentration of the products have been deduced. A method for determination of rate constants is proposed, and several other mechanisms have been treated as particular cases of the general model.     

Effect of immobilized enzyme deactivation in fixed- and fluid-bed reactors

A two-parameter theoretical model is developed to evaluate the effect of immobilized enzyme deactivation on substrate conversion in fixed- and fluid-bed reactors under diffusion-free conditions. The method describes a simple reaction in which three different immobilized enzyme deactivation forms are considered, and an expression is developed to evaluate the effect of immobilized enzyme deactivation on yield in a consecutive reaction. Comparison of reactor performances for the two reactor types reduces to a comparison of the appropriate dimensionless parameters. The practical implications of the development are illustrated through an example.     

Application of MM/PBSA colony free energy to loop decoy discrimination: toward correlation between energy and root mean square deviation

Accurate free energy estimation is needed in many predictive tasks. The molecular mechanics/Poisson-Boltzmann solvent accessible surface area (MM/PBSA) approach has proven to be accurate. However, the correlation between the estimated free energy and the distance (e.g., root mean square deviation [RMSD]) from the most stable conformation is hindered by the strong free energy dependence on minor conformational variations. In this paper, a protocol for MM/PBSA free energy estimation is designed and tested on several loop decoy sets. We show that further integration of MM/PBSA free energy estimator with the colony energy approach makes the correlation between the free energy and RMSD from the native structure apparent, for the test sets on which it could be applied. Our results suggest that (1) the MM/PBSA free energy estimator is able to detect native-like structures for most decoy sets, and (2) application of the colony energy approach greatly hampers the MM/energy strong dependence on minor conformational changes.     

Comparing biomarker measurements to a normal range: when to use standard error of the mean (SEM) or standard deviation (SD) confidence intervals tests

This commentary is the second of a series outlining one specific concept in interpreting biomarkers data. In the first, an observational method was presented for assessing the distribution of measurements before making parametric calculations. Here, the discussion revolves around the next step, the choice of using standard error of the mean or the calculated standard deviation to compare or predict measurement results     

A rapid method for screening inhibitor effects: determination of I50 and its standard deviation.

A simple method has been developed for the rapid screening of potential effectors on enzymatic reactions. Use is made of the linear relationship between the inhibitor concentration I and the corresponding value $\text{I}\text{(I ? P)}$, where P is the fraction of inhibition given by I. This mode of representation permits the evaluation of half-inhibitory doses (I₅₀) and the calculation of their standard deviations S_I50. Theoretically, these parameters can be determined from the results of measurements carried out at a single inhibitor concentration. The method proved useful when applied to the study of a number of potential effectors of adrenal cortex cyclic AMP phosphodiesterase activity. This model system was used to assess the advantages and limitations of the procedure. This approach should be of value when dealing with the usual types of enzyme inhibition mechanisms and may be of interest in other biochemical fields, such as in the study of hormone-receptor interaction, provided that the biological and statistical limitations of the method are not overlooked.     

Oscillometric determination of diastolic, mean and systolic blood pressure--a numerical model

A theoretical model of oscillometric blood pressure measurement is presented. Particular emphasis is paid to the collapse behavior of the artery, and an exponential volume-pressure curve is used. The results of this study suggest that mean blood pressure can be accurately predicted from the peak of the oscillometric curve if corrections related to the cuff pressure waveform are applied. It is also shown, however, that systolic and diastolic pressure may not in general be accurately determined from fixed amplitude ratios based on the oscillometric peak due to the sensitivity of the method to variations in blood pressure waveform, pulse pressure, and arterial compliance. No simple procedures are found to correct for these effects.