Computer-assisted indirect coulometric titrations of biological redox components

The optically coupled, indirect coulometric titration (ICT) method has been applied to assist in the characterization of several redox biocomponents such as heme proteins. This method has provided rapid and repetitive evaluation of redox stoichiometry and energeties with a high degree of precision. The usual manual ICT procedure requires operator control of the repetitive incremental additions of electrochemical charge, the on/off of the magnetic stirrer between such additions, and the recording of optical spectra after each addition. The sequence and timing of events in the above procedure can be fixed which then lends itself ideally to computer control. In this paper, a computer-controlled ICT intsrumentation is described. The hardware and software developed for the computerization permit versatility of displaying ICT data in various formats, i.e., conventional absorbance or derivative spectra and dual wavelength or differences between dual-wavelength spectra. Also, absorbance at a given wavelength could be obtained from the spectra as a function of the incremental addition of charge. The three-dimensional plots of spectral absorbance as a function of wavelength and incremental charge could also easily be obtained. To demonstrate the capability and versatility of the computer-controlled instrumentation, the ICT of the redox components, cytochrome c and cytochrome c oxidase, and of intact mitochondria is presented.     

A mathematical model of biological evolution

In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dN _n (t)/dt=(m _n (t-)N _n (t)+N _n-1(t) (n=0,1,2,3...), where N _n (t) and m _n (t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by is rigorously obtained for the case (i) m _n (t)=m _n is independent of t (constant fitness model), where m _n is essentially periodic with respect to n, and for the case (ii) (periodic fitness model), together with the long time average m of the average Malthusian parameter . The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.An early version of this study was read at the International Symposium on Mathematical Topics in Biological held in kyoto, Japan, on September 11–12, 1978, and was published in its Procedings.     

The mathematical modeling of entrained biological oscillators

In this paper perturbation methods are used for the mathematical analysis of coupled relaxation oscillators. This study covers entrainment by an external periodic stimulus as well as mutual entrainment of coupled oscillators with different limit cycles. The oscillators are of a type one meets in the modeling of biological oscillators by chemical reactions and electronic circuits. Special attention is given to entrainment different from 1∶1. The results relate to phenomena occurring in physiological experiments, such as the periodic stimulation of neural and cardiac cells, and in the non-regular functioning of organs and organisms, such as the AV-block in the heart.     

A generalized mathematical model of biological oscillators

Biological rhythms such as circadian rhythms, biochemical rhythms and neural oscillators are based on the mathematical model of the theory of harmonic oscillators. These are solutions of certain second-order differential equations. They can also be viewed as spherical harmonics on the circle in the two-dimensional Euclidean space. The spherical harmonics on (n-1)-spheres and, more generally, the Stiefel harmonics can represent oscillatory phenomena, and we expect that they can serve as models for more complex biological rhythms.     

Datac: A multipurpose biological data analysis program based on a mathematical interpreter

The use of a mathematical command interpreter combined with the structural facility of the C-language allowed us to design a data treatment program having considerable flexibility and being able to handle any types of data (electrophysiological, biochemical and theoretical data). Ensembles of data are treated by the interpreter as if they were simple variables so that an elaborate computation can be performed on the spot by simply writing the appropriate equation on the terminal. These facilities combined with the ability of editing macrocommands at run time provide the user with data treatment possibilities that extends far beyond the possibilities actually implemented in the program. The originality of this program is that the user can easily implement the commands he most often needs, writing them in a language that most scientists will know, algebra.     

Computer-assisted analysis of adenosine triphosphate data.

A computer program has been written to assist in the analysis of adenosine 5'-triphosphate data. The program is designed to calculate a dilution curve and to correct sample and adenosine 5'-triphosphate standard data for background and dilution effects. In addition, basic statistical parameters and estimates of biomass carbon are also calculated for each group of samples and printed in a convenient format. The versatility of the program to analyze data from both qauatic and terrestrial samples is noted as well as its potential use with various types of instrumentation and extraction techniques.     

Modelling and model-free mathematical description of biological relationships

The features of the modelling and the model free approaches for handling measured data of functional connections in respect to their advantages as well as to their troubles will be discussed theoretically and by means of morphometrical, histokinetical, and chronobiological examples.     

A realist approach to biological events

In this paper, I aim to show that the multiple realisability and the causal efficacy of biological events can best be explained by construing biological events as determinables of more determinate physical events. The determination relation itself is spelled out in terms of inclusive essence. In order to secure actual causation for biological events (in contrast to causal influence), two conditions are introduced such that for some events, biological events qualify as their cause. Finally, certain consequences of the presented theory are discussed, such as the question of how the biological token event can retain its identity across modal modifications of its realiser, and such as how the presented solution bears on the classical problem of biological causation.     

Computer-assisted sperm analysis of canine spermatozoa motility measurements

Computer-assisted sperm analysis (CASA) allows for the determination of specific motion characteristics of sperm cells in vitro. This study was designed to develop a system for the use of CASA to objectively evaluate canine sperm motility, and specifically to determine whether motility characteristics vary between individual dogs. Ejaculates from 10 dogs were collected weekly. Sperm cells were extended in a glucose-free TALP medium, placed on slides and videotaped at 200x. Videotaped samples were then analyzed by the Hamilton-Thorn Motility Analyzer, with 100 cells evaluated per slide. Two slides were made from each ejaculate. Motility characteristics that were evaluated included lateral head displacement, beat cross frequency, path velocity, path linearity, path straightness, percentage of motile cells, and percentage of progressively motile cells. Sperm cell morphology was also evaluated. Canine spermatozoa maintained good overall motility (mean +/- SD, 73 +/- 9%) during the procedure. Mean sperm motility and morphology measurements differed significantly between dogs (P<0.01). There was no difference (P>0.05) between the mean measurements of different ejaculates for an individual dog, or for different slides made from the same ejaculate. Mean motility values for the 10 dogs are reported. There was a significant but not strong correlation (r=0.44) between the percentage of progressively motile sperm cells and the percentage of sperm cells with normal morphology.     

Computer-assisted structural analysis of oligosaccharides using CASPER.

The computer program CASPER for structural analysis has been tested on some oligosaccharides. The program is shown to predict the correct structure of five linear or branched tri- to hexasaccharides using information on components and linkage positions and NMR chemical shifts. Theoligosaccharides are either reducting or methyl glycosides.     

The statistical dynamics of recurrent biological events

In this paper we develop a general modeling framework within which many models for systems which produce events at irregular times through a combination of probabilistic and deterministic dynamics can be comprehended. We state and prove new sufficient conditions for the global asymptotic behaviour of the density evolution in these systems, and apply our results to many previously published models for the cell division cycle. In addition, we develop a new interpretation for the statistics of action potential production in excitable cells.To whom correspondence should be sent     

Integrated mathematical models for describing complex biological processes

This review describes integrated mathematical models of processes, such as calcium homeostasis, pathogen–host interaction (with hepatitis C virus as a pathogen), and the response of the human brain to a stimulating event. It is shown that integrated mathematical models provide a deeper insight into the mechanisms and conditions that lead to the development of diseases of different natures (musculoskeletal disorders, viral infections, and various impairments in brain function) and aid identification of the key targets and conditions for a directed effect of new generation drugs, as well as the interpretation of the results of state-of-theart CT imaging.     

Stable oscillations in mathematical models of biological control systems

Summary Oscillations in a class of piecewise linear (PL) equations which have been proposed to model biological control systems are considered. The flows in phase space determined by the PL equations can be classified by a directed graph, called a state transition diagram, on anN-cube. Each vertex of theN-cube corresponds to an orthant in phase space and each edge corresponds to an open boundary between neighboring orthants. If the state transition diagram contains a certain configuration called a cyclic attractor, then we prove that for the associated PL equation, all trajectories in the regions of phase space corresponding to the cyclic attractor either (i) approach a unique stable limit cycle attractor, or (ii) approach the origin, in the limitt→∞. An algebraic criterion is given to distinguish the two cases. Equations which can be used to model feedback inhibition are introduced to illustrate the techniques.     

Computer-assisted motion analysis of sperm from the common carp

Computer-assisted semen analysis (CASA) technology was applied to the measurement of sperm motility parameters in the common carp Cyprinus carpio. Activated sperm were videotaped at 200 frames s⁻¹ and analysed with the CellTrak/S CASA research system. The percentage of motile cells and both sperm head curvilinear velocity and straight-line velocity were measured following exposure of carp sperm to three predilution conditions and activation in media of differing ionic strengths and osmotic pressures. The highest percentage of motile sperm was obtained following predilution of sperm in seminal plasma and activation in Na-HEPES buffer pH 8.0. This level of motility was equalled after predilution in 200 m m KCl for 2 h. Straight-line velocities and curvilinear velocities of 130 μm s⁻¹ and 210 μm s⁻¹, respectively, were observed. Duration of motility was higher under seminal plasma predilution conditions (over 50% motile sperm at 55 s post-activation). The application provides a sound basis for the assessment of Sperm Characteristics in fish.