Perturbance analysis of nuclear determination in Tetrahymena I: background, rationale, and illustrative example, employing temperature responses

A model based on comparative considerations, is presented for the nuclear determination of mating type in Tetrahymena thermophila. The model proposes a system of three binary control elements, each capable of stable persistence in one of two states. A general method is proposed for evaluating the model and for assigning particular mating types to particular compound states. Preliminary assignments of mating types are made from the responses of nuclei to temperature differentials.     

Modeling of self-sustained discharge-pumped,Ne-buffered XeCl laser kinetics

The aim of this work is to highlight some quantities characterizing the Ne/Xe/HCl gas mixture plasma at high pressure and under uniform preionization conditions. This mixture is used as excitation medium for XeCl excimer lasers. A comprehensive model of discharge kinetics is presented. The model combines the physical processes in the discharge with the chemistry of formation and destruction of the excimer molecule. It is based on an extensive reaction scheme including the major electronic and ionic processes. The importance of excited atomic and molecular states is demonstrated. A parametric study is presented.     

Peptide homologs, isosteres, and isomers: a general approach to structure-activity relationships

A general approach to study peptide structure is presented using three areas of ongoing research in our laboratories. The first involves the molecular basis for taste of peptide derivatives. We synthesized dipeptides based on L -aspartyl-α-aminocycloalkane carboxylic acid methyl ester. A homologous series of cycloalkane derivatives was studied. The cyclopropane, cyclobutane, and cyclopentane derivatives are sweet, the cyclohexane and cycloheptane peptides are bitter, and the cyclooctane homolog is tasteless. The related acyclic analog L -aspartyl-aminoisobutyric acid methyl ester is sweet, while the L -aspartyl diethyl glycine carboxylic acid methyl ester is tasteless. A model is presented to explain these experimental observations. The second area involves depsipeptides as isosteric replacements of α-hydroxy acids for amino acid residues in peptide chains. We have synthesized sequentially defined polydepsipeptides as model systems for polypeptides. A detailed analysis of the conformational order for these polydepsipeptides is presented. The third area involves partial retro–inverso peptide modifications of isomeric cyclic enkephalin analogs, which illustrate the relationship between the modification and biological activity. We are probing the intramolecular hydrogen-bonding features for these biologically active molecules. From such findings we are relating the structural and conformational preferences deduced from spectroscopy and molecular mechanics to biological activity.     

Thermal modeling of polymerizing polymethylmethacrylate, considering temperature-dependent heat generation.

A methodology for the modeling of unsteady heat conduction in polymethylmethacrylate (PMMA) during its exothermic polymerization is presented. The emphasis is on the formulation of a model for the volumetric rate of heat generation, including its temperature-dependent characteristics. Three parameters appear in the proposed model. The empirical determination of these parameters using Differential Scanning Calorimetry is demonstrated. The incorporation of the proposed model into finite volume methods is also demonstrated, in the context of unsteady, one-dimensional, radial heat conduction in cylindrical coordinates. In addition, the application of the proposed model to two test problems is presented and discussed. The results are encouraging, and the proposed methodology appears to be applicable to the thermal modeling of exothermic polymerization processes in general.     

Zero‐modified Poisson model: Bayesian approach,influence diagnostics,and an application to a Brazilian leptospirosis notification data

In this paper, a Bayesian method for inference is developed for the zero‐modified Poisson (ZMP) regression model. This model is very flexible for analyzing count data without requiring any information about inflation or deflation of zeros in the sample. A general class of prior densities based on an information matrix is considered for the model parameters. A sensitivity study to detect influential cases that can change the results is performed based on the Kullback–Leibler divergence. Simulation studies are presented in order to illustrate the performance of the developed methodology. Two real datasets on leptospirosis notification in Bahia State (Brazil) are analyzed using the proposed methodology for the ZMP model.     

Ligand binding systems at equilibrium: specificity, heterogeneity, cross-reactivity, and site-site interactions

The simplest ligand binding model that can account for systems which consist of heterogeneous receptors that show site-site interactions and can react with several types of ligands was presented. This model was based on the grand canonical partition function whose properties and potentialities for obtaining binding functions are briefly illustrated. A computer simulation of this model was carried out in order to examine the contributions of site-site interactions on the shape of binding isotherms and on specificity curves. The shape of the binding isotherms was shown to be independent regardless of whether the path of binding was considered. However, the shape of the specificity curves was strongly dependent on site-site interactions and on the particular sequence of ligand-receptor configurations formed during the ligand binding process, leading to the conclusion that site-site interactions may influence the specificity of a system more than even very strong cross-reactions. A method based on the Ising model of statistical mechanics was also described and was used for obtaining binding functions applicable to infinite lattices which show site-site interactions and competitive binding. The results presented here point out possible errors that can arise if standard statistical methods are used to fit binding data in order to prove a given binding model.     

Plasmid-bearing,plasmid-free organisms competing for two complementary nutrients in a chemostat

A model of competition for two complementary nutrients between plasmid-bearing and plasmid-free organisms in a chemostat is proposed. A rigorous mathematical analysis of the global asymptotic behavior of the model is presented. The work extends the model of competition for a single-limited nutrient studied by Stephanopoulos and Lapidus [Chem. Engng. Sci. 443 (1988) 49] and Hsu, Waltman and Wolkowicz [J. Math. Biol. 32 (1994) 731].     

A finite-element model of blood flow in arteries including taper, branches, and obstructions

A nonlinear mathematical model of arterial blood flow, which can account for tapering, branching, and the presence of stenosed segments, is presented. With the finite-element method, the model equations are transformed into a system of algebraic equations that can be solved on a high-speed digital computer to yield values of pressure and volume rate of flow as functions of time and arterial position. A model of the human femoral artery is used to compare the effects of linear and nonlinear modeling. During periods of rapid alternations in pressure or flow, the nonlinear model shows significantly different results than the linear model. The effect of a stenosis on pressure and flow waveforms is also simulated, and the results indicate that these waveforms are significantly altered by moderate and severe stenoses.     

A Biophysical Model for Integration of Electrical, Osmotic, and pH Regulation in the Human Bronchial Epithelium

A dynamical biophysical model for the functioning of an epithelium is presented. This model integrates the electrical and osmotic behaviors of the epithelium, taking into account intracellular conditions. The specific tissue modeled is the human bronchial epithelium, which is of particular interest, as it is the location of the most common lethal symptoms of cystic fibrosis. The model is implemented in a modular form to facilitate future application of the code to other epithelial tissue by inputting different transporters, channels, and geometric parameters. The model includes pH regulation as an integral component of overall regulation of epithelial function, through the interdependence of pH, bicarbonate concentration, and current. The procedures for specification, the validation of the model, and parametric studies are presented using available experimental data of cultured human bronchial epithelium. Parametric studies are performed to elucidate a), the contribution of basolateral chloride channels to the short-circuit current functional form, and b), the role that regulation of basolateral potassium conductance plays in epithelial function.     

Decomposition of the Transmembrane Action Potential into Sodium, Calcium, and Potassium Constituents

A scheme is presented for decomposition of the transmembrane action potential into sodium, calcium, and potassium constituents. The scheme is based on an earlier, qualitatively innovative model of the activity of the cardiovascular system during the cardiac cycle. The model takes account not only of the active systolic work of the myocardium, but also of its active (energy-dependent) diastolic work. The scheme was collated with the ECG pattern.     

Mathematical model for apical growth, septation, and branching of mycelial microorganisms

A mathematical model for apical growth, septation, and branching of mycelial microorganisms is presented. The model consists of two parts: the determinstic part of the model is based on fundamental cellular and physical mechanisms; it represents the kinetics for growth of hyphal tips and septation of apical as well as intercalary compartments. In regard to random occurrences of hyphal growth and branching, the stochastic part deals with branching processes, tip growth directions, and outgrowth orientations of branches. The model can explain the morphological development of mycelia up to the formation of pellets. The results, as predicted by the model, correspond very closely to those observed in experiments. In addition, some unmeasured states can be ascertained, such as the distribution functions of hyphal length (biomass) and tips along pellet radii.     

Flexibility, diversity, and cooperativity: pillars of enzyme catalysis

This brief review discusses our current understanding of the molecular basis of enzyme catalysis. A historical development is presented, beginning with steady state kinetics and progressing through modern fast reaction methods, nuclear magnetic resonance, and single-molecule fluorescence techniques. Experimental results are summarized for ribonuclease, aspartate aminotransferase, and especially dihydrofolate reductase (DHFR). Multiple intermediates, multiple conformations, and cooperative conformational changes are shown to be an essential part of virtually all enzyme mechanisms. In the case of DHFR, theoretical investigations have provided detailed information about the movement of atoms within the enzyme-substrate complex as the reaction proceeds along the collective reaction coordinate for hydride transfer. A general mechanism is presented for enzyme catalysis that includes multiple intermediates and a complex, multidimensional standard free energy surface. Protein flexibility, diverse protein conformations, and cooperative conformational changes are important features of this model.     

Conditioning, attention, and the CS-US interval. A theoretical statement of relations

A revised version of the Rescorla-Wagner (1972) mathematical model is presented. A metatheoretical assumption of an attentional process, the added revision, is conceived as an independent alpha-salience growth factor determining both rate of association and performance. Conditioned stimulus-unconditioned stimulus (CS-US) correlation, and CS-US interval (two primary conditioning parameters) are incorporated in the mathematical model as alpha-salience growth rate and as alpha-salience and association asymptote factors, respectively. In this manner, the long-standing issue of necessary and sufficient factors in classical conditioning is resolved. An empirical assessment of the model's parameters has been included.     

Analysis of shape, fluctuations, and dynamics in intermembrane junctions

A dynamic-elastic model for weakly adhered intermembrane junctions is presented. Helfrich membrane energetics coupled to hydrodynamic modes of the surrounding solvent reproduce the average shape, fluctuations, and dynamics of these junctions as measured experimentally. Comparison between numerical results and experimental data provides the first direct measure of surface tension in these systems (0.01-0.06 dyn/cm). The measurements suggest bilayer-bilayer adhesion energetics as the dominant source of surface tension in the experimental systems.     

Extended monod kinetics for substrate, product, and cell inhibition

A generalized form of Monod kinetics is proposed to account for all kinds of product, cell, and substrate inhibition. This model assumes that there exists a critical inhibitor concentration above which cells cannot grow, and that the constants of the Monod equation are functions of this limiting inhibitor concentration. Methods for evaluating the constants of this rate form are presented. Finally the proposed kinetic form is compared with the available data in the literature, which unfortunately is very sparse. In all cases, this equation form fitted the data very well.     

A kinetic study of analyte-receptor binding and dissociation, and dissociation alone, for biosensor applications: a fractal analysis

A fractal analysis is presented for (a) analyte-receptor binding and dissociation kinetics and (b) dissociation kinetics alone for biosensor applications. Emphasis is placed on dissociation kinetics. Data taken from the literature may be modeled, in the case of binding, using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis represents a change in the binding mechanism as the reaction progresses on the surface. A single-fractal analysis is adequate to model the dissociation kinetics in the examples presented. Predictive relationships developed for the dissociation rate coefficient(s) as a function of the analyte concentration are of particular value since they provide a means by which the dissociation rate coefficients may be manipulated. Relationships are also presented for the binding and dissociation rate coefficients as a function of their corresponding fractal dimension, D(f), or the degree of heterogeneity that exists on the surface. When analyte-receptor binding or dissociation is involved, an increase in the heterogeneity on the surface (increase in D(f)) leads to an increase in the binding and in the dissociation rate coefficient.