Autonomic energy conversion. I. The input relation: phenomenological and mechanistic considerations

The differences between completely and incompletely coupled linear energy converters are discussed using suitable electrochemical cells as examples. The output relation for the canonically simplest class of self-regulated incompletely coupled linear energy converters has been shown to be identical to the Hill force-velocity characteristic for muscle. The corresponding input relation (the “inverse” Hill equation) is now derived by two independent methods. The first method is a direct transformation of the output relation through the phenomenological equations of the converter; Onsager symmetry has no influence on the result. The second method makes use of a model system, a hydroelectric device with a regulator mechanism which depends only on the operational limits of the converter (an electro-osmosis cell operated in reverse) and on the load. The inverse Hill equation is shown to be the simplest solution of the regulator equation. An interesting and testable series of relations between input and output parameters arises from the two forms of the Hill equation. For optimal regulation the input should not be greatly different in the two limiting stationary states (level flow and static head). The output power will then be nearly maximal over a considerable range of load resistance, peak output being obtained at close to peak efficiency.     

Threshold for repetitive activity for a slow stimulus ramp: a memory effect and its dependence on fluctuations

We have obtained new insights into the behavior of a class of excitable systems when a stimulus, or parameter, is slowly tuned through a threshold value. Such systems do not accommodate no matter how slowly a stimulus ramp is applied, and the stimulus value at onset of repetitive activity shows a curious, nonmonotonic dependence on ramp speed. (Jakobsson, E. and R. Guttman. Biophys. J. 1980. 31:293-298.) demonstrated this for squid axon and for the Hodgkin-Huxley (HH) model. Furthermore, they showed theoretically that for moderately slow ramps the threshold increases as the ramp speed decreases, but for much slower ramp speeds threshold decreases as the ramp speed decreases. This latter feature was found surprising and it was suggested that the HH model, and squid axon in low calcium, exhibits reverse accommodation. We have found that reverse accommodation reflects the influence of persistent random fluctuations, and is a feature of all such excitable systems. We have derived an analytic condition which yields an approximation for threshold in the case of a slow ramp when the effect of fluctuations are negligible. This condition predicts, and numerical calculations confirm, that the onset of oscillations occurs beyond the critical stimulus value which is predicted by treating the stimulus intensity as a static parameter, i.e., the dynamic aspect of a ramp leads to a delay in the onset. The condition further demonstrates a memory effect, i.e., firing threshold is dependent on the initial state of the system. For very slow ramps then, fluctuations diminish both the delay and memory effects.(ABSTRACT TRUNCATED AT 250 WORDS)     

Performance of an iterated T-HMM for homology detection

MOTIVATION: Much information about new protein sequences is derived from identifying homologous proteins. Such tasks are difficult when the evolutionary relationships are distant. Some modern methods achieve better results by building a model of a set of related sequences, and then identifying new proteins that fit the model. A further advance was the development of iterative methods that refine the model as more homologs are discovered. These methods are generally limited by ad hoc methods of sequence weighting, neglect of underlying evolutionary relationships and the representation of the set with a single one-size-fits-all model. These limitations are avoided through the use of a Tree hidden Markov model (T-HMM) approach. Our previous work described how a non-iterative version of the T-HMM method could identify distant homologs with superior performance compared with other non-iterated approaches, and described how this method was particularly appropriate for being implemented as an iterative algorithm. RESULTS: We describe an iterative version of the T-HMM algorithm, and evaluate its performance for the detection of distant homologs. Significant improvement over other commonly used methods is found. AVAILABILITY: The software (C++, Perl) is available from the corresponding author.     

Application of adenylate energy charge to problems of environmental impact assessment in aquatic organisms

Various physiological and biochemical methods have been proposed for assessing the effects of environmental perturbation on aquatic organisms. The success of these methods as diagnostic tools has, however, been limited. This paper proposes that adenylate energy charge overcomes some of these limitations. The adenylate energy charge (AEC) is calculated from concentrations of adenine nucleotides ([ATP+½ADP]/[ATP+ADP+AMP]), and is a reflection of metabolic potential available to an organism. Several features of this method are: correlation of specific values with physiological condition or growth state, a defined range of values, fast response times and high precision. Several examples from laboratory and field experiments are given to demonstrate these features. The test organisms used (mollusc species) were exposed to a variety of environmental perturbations, including salinity reduction, hydrocarbons and low doses of heavy metal. The studies performed indicate that the energy charge may be a useful measure in the assessment of environmental impact. Its use is restricted, however, as several limitations exist which need to be fully evaluated. Further work relating values to population characteristics of multicellular organisms needs to be completed before the method can become a predictive tool for management.     

Degradation of DNA in haemophilus influenzae cells after X-ray irradiation. II. Comparison with theoretical models.

Differential equations, describing time development of local sensitivity and that of ensemble average of firing, are obtained from a digital equation in a neural network. Theoretical structure giving the differential equation of the first order is found to be such that a slowly varying part of stimulus affects the variation of the averaged firing and its relaxation time non-linearly. High frequency part of stimulus with variation of about 1kHz is taken into account by being included in “effective threshold”, which is shown to contribute transmission probability between cells in division form. Effective threshold is also used to take into account rising phase of post synaptic potential firstly in theoretical neurology. The importance of effective threshold generated in a network with apt connections of inhibitory synapses is discussed as a future problem of information processing in a brain.     

Application of Different Variants of the BEM in Numerical Modeling of Bioheat Transfer Problems

Heat transfer processes proceeding in the living organisms are described by the different mathematical models. In particular, the typical continuous model of bioheat transfer bases on the most popular Pennes equation, but the Cattaneo-Vernotte equation and the dual phase lag equation are also used. It should be pointed out that in parallel are also examined the vascular models, and then for the large blood vessels and tissue domain the energy equations are formulated separately. In the paper the different variants of the boundary element method as a tool of numerical solution of bioheat transfer problems are discussed. For the steady state problems and the vascular models the classical BEM algorithm and also the multiple reciprocity BEM are presented. For the transient problems connected with the heating of tissue, the various tissue models are considered for which the 1st scheme of the BEM, the BEM using discretization in time and the general BEM are applied. Examples of computations illustrate the possibilities of practical applications of boundary element method in the scope of bioheat transfer problems.     

A contribution to the mathematical biophysics of psychophysical discrimination III

The neural mechanism previously discussed is further generalized. The case is considered in which a random variation is associated with each stimulus. The mechanism is generalized and equations are derived for discriminations between stimuli differing in several modalities. The latter indicates an analysis by the factor method. Suggestions are made in connection with the use of triads and with the problem of a multidimensional psychophysics.     

A structured model for simulation of cultures of the cyanobacterium Spirulina platensis in photobioreactors: I. Coupling between light transfer and growth kinetics

The study of the interactions between physical limitation by light and biological limitations in photobioreactors leads to very complex partial differential equations. Modeling of light transfer and kinetics and the assessment of radiant energy absorded in photoreactors require an equation including two parameters for light absorption and scattering in the culture medium. In this article, a simple model based on the simplified, monodimensional equation of Schuster for radiative transfer is discussed. This approach provides a simple way to determine a working illuminated volume in which growth occurs, therefore allowing indentification of kinetic parameters. These parameters might then be extended to the analysis of more complex geometries such as cylindrical reactors. Moreover, this model allows the behavior of batch or continuous cultures of cyanobacteria under light and mineral limitations to be predicted. (c) 1992 John Wiley & Sons, Inc.     

Mathematical biophysics of the galvanic skin response

Beginning with Rashevsky's equation for the development of the excitatory state in a nerve fiber, an equation for the change in skin resistance upon the presentation of an instantaneous stimulus is derived. The mechanism assumed is in conformity with the existing evidence of neuro-physiology. Certain deductions from the equations are made and experimental problems suggested for testing the theory.     

A "two-objective, one-area" procedure in absorption microphotometry and its application using an inverted microscope

A 'two-objective, one-area' method and related equations are suggested to measure absorbance of microscopic stained objects. In such work, the measuring field invariably includes an image of the object and some clear area surrounding the image. The total intensity in the two areas is measured photometrically, using two different objectives, and substituted in the equation for absorbance. The equation is independent of the term representing intensity from the clear area and hence the error in the measurement of absorbance is reduced. The limitations of the 'two-objective, one-area' method are discussed and its pragmatic operation described with an experimental setup involving an inverted microscope. The method permits measurement of intensity in a part of a stained cell while the rest of the cell remains in the field of view. The method is applied to measure absorbance in Giemsa stained ascites cells and Feulgen stained liver and Human Amnion cells.     

Passive Membrane Potentials: A Generalization of the Theory of Electrotonus

The theory of electrotonus, which has been well developed for small cylinders, is extended: the fundamental potential equations for a membrane of arbitrary shape are derived, and solutions are found for cylindrical and spherical geometries. If two purely conductive media are separated by a resistance-capacitance membrane, then Laplace's equation describes the potential in either medium, and two boundary equations relate the transmembrane potential to applied currents and to currents flowing into the membrane from each medium. The core conductor model, on which most previous work on cylindrical electrotonus has been based, gives rise to a one dimensional diffusion equation, the cable equation, for the transmembrane potential in a small cylinder. Under the assumptions of the core conductor model the more general equations developed here are shown to reduce to the cable equation. The two theories agree well in predicting the transmembrane potential in a small cylinder owing to an applied current step, and the extracellular potential for this cylinder is estimated numerically from the general theory. A detailed proof is given for the isopotentiality of a spherical soma membrane.     

Mathematical biophysics of abstraction and logical thinking

Developing further a recent suggestion of H. D. Landahl, equations are derived which give the probability for an individual to judge two stimulus patterns as similar or dissimilar. The possibility of experimental verification of those equations is discussed. Next, a mechanism is described which provided for abstraction by responding only to “essential” components of a stimulus pattern. Equations, verifiable in principle experimentally, are derived. Finally, a mechanism is suggested for logical inferences, and equations are derived which give the probability of making an error in a reasoning consisting of a chain of syllogisms, as well as the probability of being unable to complete the chain of reasoning at all.     

Some nutritional and excretional interactions and the growth of an organ or colony

Following the general form for the differential equation of organism and colonial growth, there is derived a rational formulation for the growth of a bounded cell community (e.g., an organ) equipped with a food supply and a waste removal mechanism. It is shown how, from the integral form and an empirical curve, the vital coefficients of the equation can be derived. Changes to be expected in these coefficients are discussed, and the analytic methods for assessing them are set forth. It is hoped that these equations and similar ones will make it possible to relate empirical curves to the mathematico-biophysical theory of the cell. The opinions or assertions contained herein are the private ones of the writers, and are not to be construed as official or reflecting the views of the Navy Department or the Naval Service at large.     

Methods for Fitting the Right-Truncated Weibull Distribution to Life-Test and Survival Data

This paper develops mathematical and computational methods for fitting, by the method of maximum likelihood (ML), the two-parameter, right-truncated Weibull distribution (RTWD) to life-test or survival data. Some important statistical properties of the RTWD are derived and ML estimating equations for the scale and shape parameters of the RTWD are developed. The ML equations are used to express the scale parameter as an analytic function of the shape parameter and to establish a computationally useful lower bound on the ML estimate of the shape parameter. This bound is a function only of the sample observations and the (known) truncation point T. The ML equations are reducible to a single nonlinear, transcendental equation in the shape parameter, and a computationally efficient algorithm is described for solving this equation. The practical use of the methods is illustrated in two numerical examples.     

An Analysis and Comparison of Convergence and Uniqueness of Time-Independent Bone Adaptation Models

Several stimuli are proposed in the bone remodeling theory. It is not clear, if a unique solution exists and if the result is convergent using a certain stimulus. In this study, the strain stimulus, strain energy stimulus and the von Mises stress stimulus for bone remodeling are compared and applied to a square plate model using the finite element method. In the plane stress state, the remodeling equilibrium equations are transformed into functions of only the principal strains and the graphs of these functions are drawn in a diagram using the principal strains as the variables of two coordinate axes. The equation of the sum of principal strain squared equal to a constant is a circle in the diagram. The remodeling equilibrium equation of the strain stimulus is a quadrangle fitting into the circle, the remodeling equilibrium equation of the strain energy stimulus is an ellipse and the remodeling equilibrium equation of the von Mises stress stimulus is also an ellipse close to the principal strains circle when we take the same constants in the above equations. Using the finite element method, two models are performed with the uniform initial elastic properties and with the semi-random initial distribution of the elastic properties. The principal strains as the final finite element results converge within 2% of the objective constant for all the different stimuli. The obtained Young's moduli of two models as the adaptation object are different but in equilibrium, i.e. the equilibrium solution of adaptation model is not unique. The principal strains can not be used to examine the uniqueness of solution, since two different solutions can have the same results of principal strains. Using a certain stimulus, certain initial properties and a certain iterative equation, the solution is unique in equilibrium. The results using the model in this study show also that the same results can be obtained using any of the three stimuli when a proper constant in each remodeling equilibrium equation is chosen.     

The Path Integral Formulation of Climate Dynamics

The chaotic nature of the atmospheric dynamics has stimulated the applications of methods and ideas derived from statistical dynamics. For instance, ensemble systems are used to make weather predictions recently extensive, which are designed to sample the phase space around the initial condition. Such an approach has been shown to improve substantially the usefulness of the forecasts since it allows forecasters to issue probabilistic forecasts. These works have modified the dominant paradigm of the interpretation of the evolution of atmospheric flows (and oceanic motions to some extent) attributing more importance to the probability distribution of the variables of interest rather than to a single representation. The ensemble experiments can be considered as crude attempts to estimate the evolution of the probability distribution of the climate variables, which turn out to be the only physical quantity relevant to practice. However, little work has been done on a direct modeling of the probability evolution itself. In this paper it is shown that it is possible to write the evolution of the probability distribution as a functional integral of the same kind introduced by Feynman in quantum mechanics, using some of the methods and results developed in statistical physics. The approach allows obtaining a formal solution to the Fokker-Planck equation corresponding to the Langevin-like equation of motion with noise. The method is very general and provides a framework generalizable to red noise, as well as to delaying differential equations, and even field equations, i.e., partial differential equations with noise, for example, general circulation models with noise. These concepts will be applied to an example taken from a simple ENSO model.     

The effect of turbulent motion on the diffusion of microorganisms

The effect of turbulent fluid motion on the diffusion of simple organisms is discussed. The net reproduction rate and the turbulent flow are assumed to be Gaussian-correlated random variables. For homogeneous istropic turbulence, simple equations for the average concentration of the organisms are derived in terms of the energy density of the fluid. It is shown that the effective diffusivity generated by the motion is positive-definite, and is independent of the helicity of the flow.     

Invariance of least squared-error estimation under some commonly used neurophysiological data pre-processing methods

The relationship of least squared-error estimation to the commonly used data pre-processing method of stimulus locked signal averaging is discussed. First, a generalized squared-error estimate is derived. Second, two data pre-processing methods are introduced and shown analytically to be equivalent with respect to subsequent least squared-error estimation. The first method consists of fitting known functions directly to unaltered data while the second method fits to the same data after it has been time-averaged. A third method of less utility is also demonstrated to be equivalent. It consists of first fitting to sub-blocks of the unaltered data and then averaging the resulting estimates. Finally, a numerical example is presented. It substantiates the analytical contentions and points out practical considerations which might arise in the course of implementation of the estimation procedure.     

Modeling the electrophoresis of lysozyme. II. Inclusion of ion relaxation.

In this work, boundary element methods are used to model the electrophoretic mobility of lysozyme over the pH range 2-6. The model treats the protein as a rigid body of arbitrary shape and charge distribution derived from the crystal structure. Extending earlier studies, the present work treats the equilibrium electrostatic potential at the level of the full Poisson-Boltzmann (PB) equation and accounts for ion relaxation. This is achieved by solving simultaneously the Poisson, ion transport, and Navier-Stokes equations by an iterative boundary element procedure. Treating the equilibrium electrostatics at the level of the full rather than the linear PB equation, but leaving relaxation out, does improve agreement between experimental and simulated mobilities, including ion relaxation improves it even more. The effects of nonlinear electrostatics and ion relaxation are greatest at low pH, where the net charge on lysozyme is greatest. In the absence of relaxation, a linear dependence of mobility and average polyion surface potential, (lambda zero)s, is observed, and the mobility is well described by the equation [formula: see text] where epsilon 0 is the dielectric constant of the solvent, and eta is the solvent viscosity. This breaks down, however, when ion relaxation is included and the mobility is less than predicted by the above equation. Whether or not ion relaxation is included, the mobility is found to be fairly insensitive to the charge distribution within the lysozyme model or the internal dielectric constant.     

The distribution of allelic effects under mutation and selection

The Price (1970, 1972) equation is applied to the problem of describing the changes in the moments of allelic effects caused by selection, mutation and recombination at loci governing a quantitative genetic character. For comparable assumptions the resulting equations are the same as those obtained by different means by Barton & Turelli (1987; Turelli & Barton, 1989). The Price equation provides a natural framework within which to examine certain kinds of non-additive allelic effects, recombination and assortative mating. The use of the Price equation is illustrated by finding the equilibrium genetic variance under multiplicative dominance and epistasis and under assortative mating at an additive locus. The limitations of the use of recursion equations for the moments of allelic effects are also discussed.