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.     

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.     

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.     

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.     

A novel method of determination of the internal enzyme distribution within porous solid supports and the deactivation rate constant

This article presents a method for determining the rate constant for deactivation and the internal distribution of immobilized enzyme. This method makes use of the parallel deactivation process in a diffusion-controlled regime, in which the internal activity profile behaves like a penetration front. This front basically traces through the initial active enzymatic profile, and one can determine the internal profile and the rate constant for deactivation from the experimentally observable bulk concentration versus time. This method is applied to the experimental data of the system of hydrogen-peroxide-immobilized catalase on controlled pore glass and Si-Al particles.     

Effect of membrane microheterogeneity and domain size on fluorescence resonance energy transfer

Studies of multicomponent membranes suggest lateral inhomogeneity in the form of membrane domains, but the size of small (nanoscale) domains in situ cannot be determined with current techniques. In this article, we present a model that enables extraction of membrane domain size from time-resolved fluorescence resonance energy transfer (FRET) data. We expand upon a classic approach to the infinite phase separation limit and formulate a model that accounts for the presence of disklike domains of finite dimensions within a two-dimensional infinite planar bilayer. The model was tested against off-lattice Monte Carlo calculations of a model membrane in the liquid-disordered (l(d)) and liquid-ordered (l(o)) coexistence regime. Simulated domain size was varied from 5 to 50 nm, and two fluorophores, preferentially partitioning into opposite phases, were randomly mixed to obtain the simulated time-resolved FRET data. The Monte Carlo data show clear differences in the efficiency of energy transfer as a function of domain size. The model fit of the data yielded good agreement for the domain size, especially in cases where the domain diameter is <20 nm. Thus, data analysis using the proposed model enables measurement of nanoscale membrane domains using time-resolved FRET.     

Unstable electron pairing and the energy loan model of enzyme catalysis

A theory of enzyme catalysis is described which utilizes a thermodynamically consistent construction of a free energy diagram with different pathways for complex formation and decomposition. The switch to the decomposition pathway occurs when downward uncertainty and thermal fluctuations make possible a short-lived potential energy dominance in which parallel spin electrons are paired and thus free to drop below the energy floor normally maintained by the Pauli exclusion principle. Such pairing is possible if van der Waal's and other weak interactions holding the complex together impose confinement constraints on parallel spin electrons, thereby both increasing uncertainty fluctuations in their kinetic energy and weakly favoring a phase correlation in their motion (which can be interpreted in terms of an exchange of virtual particles). The paired configuration is highly unstable and thus energy released by pair falling is either immediately recaptured to re-establish a normal orbital structure or, if the pair persists long enough to produce a nuclear motion, recaptured at the end of this motion. In the latter case the release of energy can be thought of as an energy loan which finances the switch to the lower activation energy pathway without compromising an energy-balanced regeneration of the enzyme. The advantage is that the complex (because of its instability) has a real free energy which is lower than the free energy which would be assigned to it on the basis of its equilibrium concentration. This increases the specificity and speed of complex formation without decreasing the speed of decomposition. The theory predicts that the magnetic moment which marks the pair should accompany the nuclear (e.g. allosteric) motion and that the pair formation stage of the enzymatic process should have an anomalous temperature dependence. Variations of the model may be constructed to deal with a number of processes involving macromolecular motions, including sequential processes in catalysis, allosteric control, persistent molecular motions, self-assembly, energy transfer, channeled transport, and protection against inhibitors.     

Theme and variations on kinetics of GPCR activation/deactivation

G protein-coupled receptors (GPCRs) initiate intracellular signaling pathways in response to physiologically and medically important extracellular ligands such as peptide and large glycoprotein hormones, neurotransmitters, sensory stimuli (odorant and taste molecules, light), calcium, l-amino acids, and are the target of many clinical drugs. The conversion of these extracellular stimuli into intracellular signals involves sequential and reversible reactions that initially take place at the plasma membrane. These reactions are mediated not only by dynamic interactions between ligands, receptors and heterotrimeric G proteins, but also by conformational changes associated with the activation/deactivation process of each protein. This review discusses the kinetic characteristics and rate-limiting reactions engaged in signal propagation that are involved in systems as diverse as neurotransmitter and hormonal signaling, and that have been recorded in live cells by Förster resonance energy transfer (FRET) approaches.     

Structural basis of blocking integrin activation and deactivation for anti-inflammation

Integrins mediate leukocyte accumulation to the sites of inflammation, thereby enhancing their potential as an important therapeutic target for inflammatory disorders. Integrin activation triggered by inflammatory mediators or signaling pathway is a key step to initiate leukocyte migration to inflamed tissues; however, an appropriately regulated integrin deactivation is indispensable for maintaining productive leukocyte migration. While typical integrin antagonists that block integrin activation target the initiation of leukocyte migration, a novel class of experimental compounds has been designed to block integrin deactivation, thereby perturbing the progression of cell migration. Current review discusses the mechanisms by which integrin is activated and subsequently deactivated by focusing on its structure-function relationship.     

Structural aspects of AMPA receptor activation, desensitization and deactivation

Glutamate mediates most of the excitatory neurotransmission in the mammalian central nervous system by activating ionotropic glutamate receptors. Structural and functional studies of ionotropic glutamate receptors have offered detailed insight into the mechanism by which these integral membrane proteins function. In particular, advances in our understanding of the atomic structure of the agonist-binding domain have provided new opportunities to consider the conformational changes that take place in a functioning ligand-gated ion channel. Several recent studies have turned up important new ideas about the structural determinants of channel activation, deactivation and desensitization of AMPA receptors. Working hypotheses derived from this structural insight offer a rare opportunity to enrich and guide functional studies.