ALBERT

Notizen: Abstract Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.

Notizen: Abstract The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.

Notizen: Abstract Galerkin's finite element-Laplace transform technique (GAFELTTE) has been used to study transient temperature distribution in human skin and subcutaneous tissues. This study incorporates heat conduction, heat carried by perfusion of blood in the capillary beds and metabolic heat generation in the tissues. Different values of various quantities have been considered in all three parts, namely epidermis, dermis and subcutaneous tissues, depending on physiological considerations. The GAFELTTE provides interface temperatures for a wide range of the values of skin surface temperatures. These values have been used to obtain temperature profiles in the region considered. Steady-state temperature distribution has been deduced from the solution obtained by GAFELTTE and has been compared with the results obtained by using different methods.

Notizen: Abstract Necessary and sufficient conditions are given for three equilibria to occur in a predatorprey model and conditions are given for two of these to be stable. The existence of two stable equilibria requires predator intraspecific competition for either space or food, and the lower the prey growth rate the stronger this predator self-regulation must be. A prey growth rate that is skewed to the right, the ability of a few predators to survive at low prey densities, and predators with high searching effectiveness, long handling times, and large maximum per capita rate of increase all make two stable equilibria more likely.

Notizen: Abstract Drawing evidence from a variety of cardiovascular studies on the heart rate in homeothermic animals, the author establishes the following thesis. The servocontrol (i.e. the autonomic and reflex control) by the medulla oblongata of the heart (rate) is a negative feedback dynamic which is isomorphic (i.e. ‘diffeomorphic’) to the dyamic underlying the heat rate control in those animals (cf. Kuyk,Bull. math. Biol. 46, 81–102, 1984). In fact, unlike in the heat rate case, the qualitative evidence supporting this thesis can not be fully complemented by quantitative data stemming from experiments, because of a lack of pertinent experiments—which, indeed, should measuresimultaneously the heart rate state parameter and thefour control parameters at the input side of the medulla. The results of some of the existing experiments on animal preparations can nevertheless be adduced to recognize that this dynamic can be graphed by the five-dimensional butterfly catastrophe type. The theory leads to new ways of looking at experiments in the field and/or setting up such experiments in the future.

Notizen: Abstract A model based upon minimization of surface energy is proposed as an explanation for compaction and internalization of cells during mammalian embryo development. The model is used to simulate and graphically display these phenomena on a computer.

Notizen: Abstract This paper describes a growth model for binary topological trees. The model defines the branching probability of all segments in the tree. The branching probability of a segment is formulated as a function of two variables, one indicating its type (intermediate or terminal), the other representing its order, i.e. the topological distance to the root segment. The function is determined by two parameters, namely the ratio of branching probabilities of intermediate and terminal segments and the strength of the order dependency, implemented in an exponential form. Expressions are derived for the calculation of symmetry properties of the partitions and it is indicated which part of the parameter domain results in predominantly symmetrical trees.

Notizen: Abstract The problem of cellular differentiation and consequent pattern generation during embryonic development has been mathematically investigated with the help of a reaction-diffusion model. It is by now a well-recognized fact that diffusion of micromolecules (through intercellular gap junctions), which is dependent on the spatial parameter (r), serve the purpose of ‘positional information’ for differentiation. Based on this principle the present model has been constructed by coupling the Goodwin-type equations for RNA and protein synthesis with the diffusion process. The homogeneous Goodwin system can exhibit stable periodic solution if the value of the cooperativity as measured by the Hill coefficient (ρ) is greater than 8, which is not biologically realistic. In the present work it has been observed that inclusion of a negative cross-diffusion can drive the system into local instability for any value of ρ and thus a time-periodic spatial solution is possible around the unstable local equilibrium, eventually leading to a definite pattern formation. Inclusion of a negative cross-diffusion thus makes the system biologically realistic. The cross-diffusion can also give rise to a stationary wave-like dissipative structure.

Notizen: Abstract A nes software system is described for building simulation programs on micro- and minicomputers. Model equations are written as C subroutines, compiled and linked to the SCoP package to produce a menu-driven, interactive program. The system maintains a database of names, values, and units for all model parameters and variables. Run-time options include several methods for interactive parameter modification and both graphic and tabular outputs, with output values presented as they are calculated. Simulation output values can be compared with experimental data graphically and a companion program SCoPFit is provided for formal optimization of parameter values.

Notizen: Abstract We consider the existence and global stability of aq-member equilibrium (1≤q≤n) in partially closed food-chains of lengthn having an abiotic component as resource. We observe that such existence demands bounds of resource supply rate and these bounds are weighted sums of interaction coefficients. Particular results of global sector-stability of partially feasible equilibria of simple food-chains obeying Lotka-Volterra dynamics are shown. Lastly the elasticity of such food-chains when a new species is introduced at the highest trophic level is investigated.

Notizen: Abstract Criteria are established for three classes of models of single-species dynamics with a single discrete delay to have a globally asymptotically stable positive equilibrium independent of the length of delay.

Notizen: Abstract The main concern of this paper is with survival or extinction of predators in models of predator-prey systems exhibiting group defence of the prey. It is shown that if there is no mutual interference among predators, enrichment could result in their extinction. However, if there is mutual interference, the predator population survives (at least deterministically).

Notizen: Abstract In this paper a general class of semi-Markov compartmental systems is studied. Two models for different input processes are analysed. Attention has been paid to the recurrence times associated with each compartment and to the distribution of the number of particles in each compartment. As an example, a three-compartment system is discussed to study the movement between three health states of patients with chronic diseases.

Notizen: Abstract A strategy is presented for searching the gene and protein sequence data banks which combines the use of two previously described algorthms. The implementation of this strategy is thoroughly evaluated with respect to sensitivity, specificity and speed. The establishment of standard benchmarks for comparing programs that rearch the sequence data banks for homology is proposed.

Notizen: Abstract During functional linkage, ligand receptors are coupled to other receptors and to the cell's metabolic-transport apparatus. The linkage guides the cellular processing of matter, energy and information. Previous conceptions of functional linkage have used the ideas of classical physics appropriate to macroscopic objects. This study presents an initial quantum mechanical model of functional linkage in the case of ligands moving through lipid bilayers and hydrophilic transmembrane channels (‘pores’) of molecular dimensions. On the basis of permeability data, energy surfaces consisting of piecewise-constant potential regions are used to model the lipid bilayers and transmembrane channels. The centre-of-mass wavefunction for a ligand on such energy surfaces is analysed and the permeability coefficients calculated from the wavefunction's transmission characteristics. It is found that quasi-bound states in the several ligand-binding regions of a bilayer or pore system can functionally link to facilitate the passage of the molecule across the permeability barrier. Appearance of the linkage is a sensitive function of the ligand's energy. If the centre-of-mass energies are distributed as in a thermalized fluid, the flux via the quantum functional linkage can equal or exceed that of a classical flux for proton transport through rigid pores in which the intrasite barriers are relatively high (0.25–1 eV) and narrow (0.1–1 Å). The functional linkage plays a less important role in bilayer (rather than pore) energy surfaces and at higher molecular weights. If the ligand-receptor interaction is accompanied by energy transfer to or from ligands, the flux via the quantum functional linkage can equal or exceed the classically expected flux at all relevant ligand molecular weights. These findings are discussed in relation to earlier work and the limitations of the model emphasized.

Notizen: Abstract A new measure of subalignment similarity is introduced. Specifically, similaritys(l,c) is defined as the logarithm to the basep of the probability of findingc or fewer mismatches in a subalignment of lengthl, wherep is the probability of a match. Previous algorithms can not use this measure to find locally optimal subalignments because, unlike Needleman-Wunsch and Sellers similarities, this measure is nonlinear. A new pattern recognition algorithm is described for finding all locally optimal subalignments of two nucleotide sequences. The DD algorithm can uses(l, c) or any other reasonable similarity function to assess the relative interest of subalignments. The DD algorithm searches only the diagonal graph, which lacks insertions and deletions. This search strategy greatly decreases the computation time and does not require an arbitrary choice of gap cost. The paths of the resulting DD graph usually draw attention to likely locations for insertions and deletions. A heuristic formula is derived for estimating significance levels fors(l, c) in the context of the lengths of the two aligned sequences. The DD algorithm has been used to find interesting subalignments between the nucleotide sequences for human and murine interleukin 2.

Notizen: Abstract The entropy budget of a white-tailed deer (50kg) on a maintenance diet and a full-feed diet in a standing posture in an open field under clear nocturnal skies with an air temperature of −20°C is investigated based on the energetics given by Moen. Entropy inflow into a white-tailed deer due to infra-red radiation and entropy outflows from a deer due to infra-red radiation, convection, evaporation of water and conduction to ingested food are calculated. Also the entropy production due to metabolic heat production is estimated. Net entropy flow into a deer from its environment becomes negative. On the assumption that a white-tailed deer is in a steady state in entropy, the total entropy production in a deer on a maintenance diet becomes +0.46 J/sec/K. Positiveness of the entropy production shows that the Second Law of Thermodynamics certainly holds in a white-tailed deer. The entropy production per effective radiating surface area of a deer on a maintenance diet is 0.32×10−4 J/cm2/sec/K. On the other hand, the entropy production in a deer on a full-feed diet is 0.59 J/sec/K and that per effective surface area is 0.41×10−4 J/cm2/sec/K. Uptake of 1 g of food produces 22 J/K of entropy within the body of a white-tailed deer. Comparison is made with the results for entropy production in a lizard and in plant leaves.

Notizen: Abstract Biological adaptability has been proved to be analysable by means of the Maximum Entropy Formalism (MAXENT) in some cases of non-interacting systems. This formalism is extended to the biomass statistical structures of populations exhibiting internal interactions (i.e. predatorprey effects).

Notizen: Abstract The temporal behaviours of the nonlinear substructure of a self-organized compartmental model of calcium metabolism were investigated. The order-two autocatalytic process included in this simple two-dimensional model is compared to some secondary nucleation mechanisms which should take place at the extracellular fluid-bone interface. The model gives rise to complex dynamic behaviours, and multistability properties, involving up to two stable periodic regimes (birhythmicity), were established in different topological configurations. The bifurcations occurring on the boundaries between regions of different qualitative behaviour have been determined. These properties are discussed in relation to the dynamical behaviour of other two-variable models, especially those including the same nonlinearity.

Notizen: Abstract A linearized oscillation theorem due to Kulenović, Ladas and Meimaridou (1987,Quart. appl. Math. XLV, 155–164) and an extension of it are applied to obtain the oscillation of solutions of several equations which have appeared in population dynamics. They include the logistic equation with several delays, Nicholson's blowflies model as described by Gurney, Blythe and Nisbet (1980,Nature, Lond. 287, 17–21) and the Lasota-Wazewska model of the red blood cell supply in an animal. We also developed a linearized oscillation result for difference equations and applied it to several equations taken from the biological literature.

Notizen: Abstract A theoretical approach to the explanation of the structural design of metabolic pathway is presented. It is based on the hypothesis that due to natural selection during evolution the cellular metabolism of present-day organisms may be characterized by optimal properties. Two cardinal terms enter the theory: (i) the efficiency of a metabolic pathway and (ii) the evolutionary effort for the change of the kinetic parameters of enzymes by mutations of the corresponding genes. For both quantities simple mathematical expressions are proposed. While the efficiency is related to the reaction rates of the enzymes constituting the metabolic pathway, the evolutionary effort is considered to be a monotonically increasing function of the parameter values. By maximizing the efficiency under the constraint of a fixed evolutionary effort the theory allows the calculation of the optimal parameter distribution as the outcome of evolution processes. The methods developed are applied to the following systems: (a) linear reaction sequences with very low affinities of the enzymes towards substrates, (b) linear sequences consisting of saturable enzymatic reactions, (c) branched metabolic pathways consisting of segments of linear chains and (d) glycolysis of erythrocytes. The conclusion is derived that the optimal distribution of kinetic constants depends strongly on the equilibrium constants of the reactions as well as on the total osmolarity of the metabolic intermediates. Without osmotic constraints the evolutionary effort is mainly spent on the enzymes at the beginning of the chain. Using Michaelis-Menten equations the optimal state is characterized by a decrease of the maximal activities of the enzymes towards the end of the chain. These results are modified if osmotic constraints are taken into account. At the investigation of branched pathways the following results were obtained: firstly, if a certain end product may be synthesized along different pathways those which are thermodynamically more unfavourable (e.g. characterized by a small change of free energy) are eliminated in the course of evolution; secondly, if a branched pathway leads to several important end products those reaction segments which are thermodynamically unfavourable are characterized by a higher evolutionary effort. The application of the theory to a realistic model of glycolysis of erythrocytes leads to a correct description of various functionally important properties of the system, such as the ratio between fluxes through different branches and the ATP/ADP ratio, whereas the theory cannot predict the strong separation of time constants observed in the real glycolytic system. It is concluded that the improvement of the predictive power of the theory necessitates the use of more complex functionals for the efficiency which take into account not only the fluxes but also other system properties such as the stability of the pathway or homoeostatic effects.

Notizen: Abstract Nonlinear similarity functions are often better than linear functions at distinguishing interesting subalignments from those due to chance. Nonlinear similarity functions useful for comparing biological sequences are developed. Several new algorithms are presented for finding locally optimal subalignments of two sequences. Unlike previous algorithms, they may use any reasonable similarity function as a selection criterion. Among these algorithms are VV-1, which finds all and only the locally optimal subalignments of two sequences, and CC-1, which finds all and only the weakly locally optimal subalignments of two sequences. The VV-1 algorithm is slow and interesting only for theoretical reasons. In contrast, the CC-1 algorithm has average time complexityO(MN) when used to find only very good subalignments.

Notizen: Abstract A resource-based competition model of two consumer species and one resource species is formulated in the form of a Lotka-Volterra system. The competition involves both exploitation and interference. By a method of asymptotic estimates, sufficient conditions are derived for the three species system to converge ast→∞ to an equilibrium point with all three species present; a generalization of the result forn≥2 and single resource species is indicated. The strong form of equilibrium perisistence of the three species consumer-resource system is achieved by the ability of each of the consumer species to exploit the resource and interfere with others in such a way which will avoid exclusion by the other.

Notizen: Abstract Bayesian image processing formalisms which incorporatea priori information about valued-uncorrelated and valued-correlated (patterned) source distributions are introduced and the corresponding iterative algorithms are derived using the EM technique. Striking improvement in image processing is demonstrated when applying these algorithms to Poisson and Gaussian randomized data in one-dimensional cases.

Notizen: Abstract This paper is a brief historical review of linear singular systems, followed by a survey of results on their solution and properties. The frequency domain and time domain approaches are discussed together to sketch an overall picture of the current status of the theory.

Notizen: Abstract For a broad class of interconnected nonlinear systems, this paper develops a complete design methodology for decentralized variable structure control. Specifically, the paper sets forth design schemes for local switching surfaces and the related local switched feedback gains which together force the original nonlinear interconnected system to behave as a reduced order interconnected equivalent system having a desired response such as stability, tracking, or prespecified eigenvalues. Also developed is a numerical algorithm for constructing the switched local feedback gains. A simple nonlinear example illustrates the control strategy.

Notizen: Abstract A new stabilization method of a large-scale dynamic system, consisting of a set of interconnected subsystems, is presented in this paper. The topology of the interconnected subsystems is given as a network containing nodes with only one ingoing link, and none, one, or more outgoing links. Here, when the notion “node” is used a subsystem is assumed, and the links stand for the subsystem interconnections. The stabilization method is made only by the use of local linear state feedback around each subsystem, in order to satisfy constraints given in the problem. The interconnections among the subsystems are assumed to be nonlinear, time-varying. According to the topology of the large-scale system, the method of stabilization is hierarchic, one proceeds from node to node, and is applicable from a computer standpoint. A design algorithm follows directly, and can be made using the Generate and Test method for each subsystem independently, thus enabling designers to use a computer which has a video terminal as a peripheral unit and providing a possibility for interactive applications.

Notizen: Abstract The estimation of covariance matrices which are structured, for example, of Toeplitz type, from measurement data is considered. The problem is considered in the context of array beamforming, and various methods of estimation are derived and compared, such comparison including consideration of the behavior of the estimate in beamforming applications.

Notizen: Abstract The planar least-squares inverse (PLSI) polynomials are used for stabilization of two-dimensional unstable recursive filters. In order to obtain the PLSI polynomials, the main work involved consists in forming a set of linear equations and then solving them. In this paper we present an efficient and simple method to form the necessary set of linear equations (i.e., the required coefficient matrix) for a chosen pattern and order of the desired PLSI polynomial, starting from the denominator polynomial of a two-dimensional unstable recursive filter.

Notizen: Abstract This paper shows how to use orthogonal functions to invert singular (i.e., generalized state-space) systems. The approach is to express the inverse system itself as a singular system, and then to apply the theory of orthogonal functions to convert that differential-algebraic system to a purely algebraicgeneralized Lyapunov equation whose solution yields the input of the original system given its output. Both left and right inversion are treated. Necessary and sufficient conditions for the existence and uniqueness of the generalized Lyapunov equation are derived, and a generalizedQZ algorithm is given for its efficient solution. It is also shown that the coefficients in the Walsh function expansion may be approximately found using an FFT-type butterfly network. These results provide both an extension in theory, by investigating the properties of a new Lyapunov equation, and an extension in the implementation of system inversion, by providing a scheme which applies to generalized state-space systems and uses an unconventional approach which may prove to be a useful contribution.

Notizen: Abstract In digital communication networks, a special class of complex biquad recursive digital filters called orthogonal filters is increasingly being used. The separate effects of the overflow and quantization nonlinearities on these orthogonal filters' responses have been investigated [5], [6]. In this paper we examine the zero-input stability properties of the actual orthogonal filter having both overflow and quantization nonlinearities. The overflow nonlinearities considered include saturation, bit-by-bit inversion, zeroing, and modulo 2 arithmetic. The quantization techniques used may be roundoff, magnitude, or value truncation. An example demonstrates the adverse coupling effect between the overflow and quantization nonlinearities. Two criteria are therefore derived to ensure asymptotic overflowstability of the filter in the presence of quantization. These criteria have been translated to the coefficient plane; various regions corresponding to different minimum wordlengths required to ensure decoupling of the overflow and quantization phenomena have been derived.

Notizen: Abstract The identification problem for electromagnetic objects excited by transients is discussed. Several classes of models are reviewed, and an output error model is selected. An algorithm for solving the transient identification problem using this model is presented, and some of the issues connected with its use are considered. Examples of the application of this algorithm to electromagnetic data are given.

Notizen: Abstract An understanding of the comparative statics of biological communities is important both as a means of explaining the long-term effects of changes in environmental conditions, and as a framework for viewing community time trajectories. A general formulation of community dynamics is presented here which, given full information about a particular community's dynamic behavior, describes the impact of a change in environmental conditions on the community steady state. However, since such full information is often lacking in studies of biological communities, various approaches to partial information analysis of comparative statics are presented and compared, including a generalized protocol for isocline analysis. The suggested isocline protocol is shown to be a useful tool for both full and partial information analyses, as well as for both general and partial equilibrium studies.

Notizen: Abstract Fujita's diagrams in phyllotaxis, showing the frequencies of divergence angles as a function of these angles for low phyllotactic patterns such as (2, 1) and (3, 2), which are approximately normal curves centered at the limitdivergence angle of 137.51°, are shown to be puzzling when compared to results and observations in the field. An analysis of these diagrams is proposed, in the context of Fujita's methodology, of data from other sources, of a mathematical theorem on lattices, and of the contact pressure theory of phyllotaxis.

Notizen: Abstract It is shown that a representative Fisher-Wright model withn(≥3) diallelic loci admits a necessary condition for existence of a time-independent steady-state probability distribution. This necessary condition states that a global integral depending on the phenotype fitness functions of natural selection must be larger than a certain quantity depending on the parameters associated with genetic drift.

Notizen: Abstract Equations for the time-dependent concentrations of all species involved in the general mechanism of human plasminogen activation proposed by Wohlet al. (J. biol. Chem. 255, 2005–2013, 1980) have been derived. These equations are valid for the whole course of the reaction: for both the transient phase and the steady state. In addition, we compare our results with the ones obtained by the above-mentioned authors for the steady state assuming rapid equilibrium conditions. Finally, we propose a method for the determination of all velocity constants.

Notizen: Abstract A special class of interval graphs is defined and characterized, and an algorithm is given for their construction. These graphs are motivated by an important representation of DNA called restriction maps by molecular biologists. Circular restriction maps are easily included.

Notizen: Abstract Over the past 25 years stepwise improvement in the cure of disseminated cancers has been good, fair or very poor depending on the particular cancer one is discussing. “Cancer chemotherapy provides variably effective treatment for the majority of forms of human cancer and curative treatment for some 12 categories.” We have been slow to gain and learn how to apply quantitative information on the biologic phenomena that underlie the responsiveness, or lack of responsiveness, of many different cancers to single drugs and combinations of drugs delivered in different ways. I am of the opinion that continuing development and integration of rational biomathematical models based on principles already identified, and testing them for compatibility with much already available experimental and clinical data, will lead to models that will help in planning more effective treatment regimens for cancers now classified as moderately refractory or very refractory to chemotherapy. Some of the critical variables are considered briefly. My advice, for what it is worth, is “try to be sure that the biologic concepts that you use in modeling are almost as good as the arithmetic.”

Notizen: Abstract A discussion of the bases of physiological pharmacokinetics is followed by a brief review of the fundamental mass balance equations of the models. Some examples are outlined, together with a listing of published reviews which give many more references and detailed examples. Finally, some thoughts on future research directions are presented.

Notizen: Abstract The use of stochastic simulation languages in cell kinetics research is discussed. Two special purpose simulation languages; CELLSIM and CELLGROW are described and example problems are presented.

Notizen: Abstract Mathematical models predicting tissue doses of chemical toxicants can be either highly complex or simple, depending upon the end results needed. As an example of a highly complex mathematical model, the Miller Model of the distribution of reactive gases in human and animal lungs is described. The Miller Model accounts for the convection, the radial and axial diffusion, and the chemical reactions of gases as an inhaled breath passes down the airways. The geometry and physiology of human and animal lungs are used to calculate the convection and diffusion likely in each generation or bifurcating series of airways commencing with the trachea and extending 24 generations in humans. The chemical reactivity of ozone, an air pollutant, is accounted for by simulating second-order chemical reactions with the fluid lining materials of the lung and tissue biological molecules. The flux of ozone into three compartments (pulmonary tissue, overlying liquid layer and capillary blood) in each generation of the lung is calculated to provide molecular doses of ozone reaching each region of the lung. These results of calculated molecular dose are then used to construct dose-response curves for a variety of biological endpoints. A much simpler model is also described which recognizes the saturable or Michaelis-Menten type of kinetics controlling the removal of nickelous ion (nickel) from the lung. This model is used to calculate the chronic lung burden of the human lung for occupational, environmental and cigarette smoking exposure scenarios. In both the complex Miller Model and the simpler nickel lung burden model, the results can be used to calculate molecular doses at the potential site of action of these environmental chemicals and to unify a wide variety of studies. The predictions made are more likely to be valid since multiple investigators using a variety of animal species have participated in generation of the primary data. As a methodology, mathematical modeling based on physiological, physicochemical and anatomical principles provides a means of eliminating non-scientific considerations from the important process of regulating and recognizing toxic or cancer causing chemicals in the human environment.

Notizen: Abstract This paper presents a brief review of applications of kinetic simulation of multi-enzyme networks to the study of antimetabolite drugs used as anticancer agents. Kinetic models consist of systems of nonlinear differential equations that describe changes in concentrations of cellular metabolites with respect to time. Such models have been used to predict the effect of changes in activity of enzymes, or changes in enzyme kinetic parameters, on sensitivity to inhibition. Kinetic simulation has provided insight into several aspects of the biochemical pharmacology of antimetabolites, including drug sensitivity and resistance, and drug-drug interactions. Two specific studies are described in detail. The first concerns the importance of the ratio of competing enzymes in determining the selectivity of inhibitors of one of the competing enzymes, studied by a simple model. The second case study examines the effect of alternative biosynthetic pathways, thede novo and salvage pathways of pyrimidine nucleotide biosynthesis, on the selectivity of antipyrimidine drugs, as studied by a detailed model of 27 reactions of pyrimidine metabolism.

Notizen: Abstract General (deterministic) ordinary differential equations for the representation of cancer growth are presented when the growth is perturbed due to the action of a chemotherapeutic agent. The Verhulst-Pearl equation is introduced as a particular example of a growth equation applicable to human tumors. An optimal control problem with general performance criterion and state equation is formulated and shown to possess a novel feedback control relationship. This relationship is used in two continuous drug delivery problems involving the Verhulst-Pearl equation.

Notizen: Abstract Complex networks of biological processes are analogous to electrical circuits. For each step in a biological or electrical network, flow is dependent on the driving force and the conductivity of the step. The relationship between biological flows and their driving forces can therefore be expressed as relationships between analogous currents and voltages. The time dependence of approach to equilibrium or a steady state is determined by the rates of depletion of material in various compartments. Electrical capacitance is therefore analogous to compartment volume. Once these generalized concepts of flow, force and capacitance are recognized, it becomes clear that computer programs designed for analysis of electrical circuits may be used for simulation of biological networks. A set of simple mathematical descriptions of the individual steps and a diagram showing how the steps are arranged with respect to each other are all that is necessary to perform a simulation; there is no need for computer programming skills or differential equations. The use of SPICE2 for simulation of the cellular and plasma pharmacokinetics of cytosine arabinoside (araC) is described as an example. A network model is developed which considers cellular pharmacokinetics (membrane transport, intracellular phosphorylation and dephosphorylation), and plasma pharmacokinetics following infusions of araC.

Notizen: Abstract Developments in computer hardware and software are making significant improvements in the availability of simulation for biomedical researchers. This paper reviews past and present techniques for digital computer simulation and looks at improvements likely in the near future. In the area of hardware, personal computers are making computing and simulation more widely available and at the same time, supercomputers and special-purpose numerical processors are making it possible to solve larger problems. Software developments for simulation are reducing the time, effort and special skills required to produce a simulation program. A new hierarchical linker is proposed to make it easy to synthesize a global model by combining existing submodels. In the more distant future, computer models may be constructed graphically and with the assistance of intelligent programs capable of analysis and information retrieval.

Notizen: Abstract Modeling is a ubiquitous and often misunderstood enterprise in which data from diverse disciplines are analyzed by techniques from other diverse disciplines in an attempt to confirm or falsify a set of hypotheses about the real world. Guidelines are offered for designing models to match the goals of modeling biological systems. Techniques for the construction and interpretation of models are discussed. The requirements for credibility of models are detailed, and tests are suggested for their validation.

Notizen: Abstract Presentations and discussions at the symposium illustrate some general issues in biomedical modeling for cancer research. Given the motivations for modeling and assumptions concerning who should be involved in the modeling process, one can identify some basic needs to be met in supports to modelers. These concern both the models themselves and ways of presenting them to users. In conclusion, some thoughts are offered on economic and educational issues that may affect the infusion of modeling into biomedical research.

Notizen: Abstract A stochastic model for the population regulated by logistic growth and spreading in a given region of two-or three-dimensional space has been introduced. For many-species population the interactions among the species have also been icorporated in this model. From the random variables that describe stochastic processes of a Wiener type the space-dependent random population densities have been formed and shown to satisfy the Langevin equations. The Fokker-Planck equation corresponding to these Langevin equations has been approximately solved for the transition probability of the population spreading and it has been found that such approximate expressions of the transition probability depend on the solutions of the deterministic equations of the diffusion model with logistic growth and interactions. Also, the stationary or equilibrium solutions of the Fokker-Planck equation together with the special discussion on the pattern of single-species population spreading have been made.

Notizen: Abstract The notion of an evolutive hierarchical system proposed in this paper is a mathematical model for systems, like organisms, with more or less complex objects. This model, based on category theory, retains the following characteristics of natural systems: they have an internal organization consisting of components with interrelations; they maintain their organization in time though their components are changing; their components are divided into several levels corresponding to the increasing complexity of their own organization, and the system may be studied at any of these levels (e.g. molecular, cellular...). The state of the system at a given instant is modeled by a category whose objects are its components, the state transition by a functor, a complex object by the (direct) limit of a pattern of linked objects (which describes its internal organization). The properties of limits in a category make it possible to ‘measure’ the emergence of properties for a complex object with respect to its components, and to reduce the study of a hierarchical system to that of its components of the lowest degree and their links. Categorical constructions describe the formation of a hierarchical evolutive system stepwise, by means of the operations: absorption of external objects, destruction of some components, formation of new complex objects.

Notizen: Abstract An algorithmic formulation is presented for the inference procedure concerning lineage models. The problem is to find lineage rules from observed sequences of tree structures under the assumption that no interactions take place in the course of development and that sufficiently frequent observations are available at equal time intervals. The underlying structural pattern is taken to be a OL system, and the goal is to find propagating and deterministic OL schemes with minimal properties satifsying certain biological reliance criteria. Upper bounds have been found for the complexity of the inference algorithms.

Notizen: Abstract A statistical theory of non-equilibrium fluctuation in Volterra-Lotka systems has been presented on the basis of the technique of statistical linearization of non-linear coupled stochastic differential equations.

Notizen: Abstract Under certain basic assumptions the branching pattern of dendrites can be modeled as a Galton-Watson process in varying environment. Using results from graph theory we compute the probability distributions, expectations and variances for biologically significant variables such as the number of (intermediate and terminal) branches, the maximum number of orders, etc., together with the limit behavior of these quantities. Furthermore, the probability measure induced by the Galton-Watson process on the set of all trees is calculated. The measure assigns to any set of branching patterns the probability that it is realized by a certain process, which is completely described through the bifurcation probabilities.

Notizen: Abstract Theoretical models for DNA repair mechanisms are constructed. Reliability studies considering the living cell as a repairable system are done. The DNA repair process is discussed along with applications and comparison with available experimental data.

Notizen: Abstract A mathematical model has been developed to simulatein vivo transmural accumulation of an intravenously injected tracer in the aortic wall of experimental animals. Parameters have been included to represent the following processes that affect tracer distribution: permeation of the blood-tissue interface, diffusion through the layers of the artery wall,convective solute drag through the same, and degradation. Of particular interest for thein vivo situation situation is the inclusion of boundary conditions that account for the variation in the plasma concentration of injected tracer as a function of time. Two analytical solutions are presented. The first describes a system in which two boundaries must be delineated; it pertains if the tracer is allowed to circulate until it enters the avascular media of the artery wall both across its luminal boundary and from the capillaries in its outer layer. The second applies to shorter duration experiments in which entry across only the luminal boundary is considered. A limiting case of the solution for short circulation times is presented, compared with a previously published solution, and examined for its potential utility in parameter estimation. Because of its treatment of time-dependent boundary conditions, the model has unique application toin vivo experiments related to macromolecular transport in atherosclerosis that may otherwise elude proper interpretation.

Notizen: Abstract Several current reaction-diffusion mechanisms have been proposed as models for morphogenesis in the Turing (1952,Phil. Trans. R. Soc. Lond. B 237, 37–72) sense. We introduce and exploit a quantity, we have termed heterogeneity, which allows us to elaborate the differences between the various models with regard to spatial pattern formation. It is shown that this quantity provides a concise view for the comparison of theoretical models with experimental observations. Two model mechanisms are treated explicitly both for linear and for biased diffusion.

Notizen: Abstract The optimum number of total capillaries in the whole human body was estimated from the analysis of the efficiency for oxygen (O2) transport in the vascular-tissue system. We used a tissue model composed of uniform spheres in which O2 diffuses from the capillary located at the centre of each sphere towards the surrounding tissue consuming O2 at a constant rate. The tissue mass supplied by a single capillary was estimated as the area of positive O2 concentration under a given condition of capillary flow and O2 consumption rate. Total tissue mass was determined as the function of the capillary numbern and the total blood flow. On the other hand, the energy cost required to maintain the vascular system withn terminals was assessed by using the minimum volume model (Kamiya and Togawa,Bull. math. Biophys. 34, 431–438, 1972). The efficiency of the entire vascular-tissue system was evaluated by calculating the ratio of total tissue mass/cost function. The result of the calculation using physiological data of cardiac output and O2 consumption for an average human adult during a heavy exercise revealed the maximum efficiency occurring at the capillary number 3.7×1010 which coincided well with its normal range of physiological estimates (3.2×1010–4.2×1010). We concluded that the entire vascular-tissue system is constructed so as to attain the highest efficiency in O2 transport at its maximum activity.

Notizen: Abstract A kinetic model involving synthesis of proinsulin in the rough endoplasmic reticulum, maturation through the Golgi apparatus and granules, with conversion to insulin, is proposed to account for data on the amount of insulin and of proinsulin both secreted during various time intervals and remaining in islets. Introducing three compartments for granules makes it possible to account for the measurement of both hot (pulse labeled with tritiated leucine) and cold proinsulin and insulin over a period of 21/2 hr under constant glucose. Data from islets from animals pretreated with tolbutamide are also presented and modeled. The model is then expanded so that it can be successfully applied to available data on the effects of a period of glucose deprivation on secretion of both hot and cold hormone. Parameters have essentially the same values, where they overlap, as were obtained (Landahl and Grodsky, 1982Bull. math. Biol. 44, 399–410) from insulin secretion by perfused rat pancreas stimulated by a variety of temporal patterns of glucose concentration.

Notizen: Abstract Two models of binary tree growth are examined in terms of the Strahler order branching ratio (Rb) and the types of vertex produced during growth, and their inter-relationship. The sequential growth model is that described by Van Pelt and Verwer (1985,Bull. math. Biol. 47, 323–336) in which random growth occurs according to attributed probabilities on terminal or internal segments, one branch at a time. This model generates values ofRb≥3. The synchronous growth model is new and permits more than one segment to branch at a time, again randomly with attributed probabilities. This model generates values ofRb≥2 and in particular, when only terminal branching is permitted, gives 2≤Rb〈3. Such a model might explain the branching in the human bronchial tree, in which 2.5≤Rb≤2.8. Our synchronous model is an alternative to the centrifugal-order-dependent sequential model of Van Pelt and Verwer.

Notizen: Abstract From an energy budget of a deciduous plant leaf in moderate conditions, entropy fluxes into or out of the leaf due to solar radiation, infrared radiation, evaporation of water and heat conduction are calculated. Net entropy flow into the leaf is negative. On the assumption that the entropy in the leaf is in a steady state, the entropy production in the typical deciduous leaf in moderate conditions [the solar energy absorbed by both sides of the leaf isE solar=0.0602 (J cm−2 s−1)] becomesS prod=1.8×10−4 (J cm−2 s−1 K−1). The positiveness of the entropy production shows that the Second Law of Thermodynamics certainly holds in the plant leaf. Entropy productions in other conditions are also calculated. The entropy production in the leafS prod becomes a linear function of the solar energy absorbed by the leafE solar:S prod≈-(29.5E solar)×10−4. A theorem is presented: the entropy production in plant leaves oscillates during the period of one day, paralleling the daily solar energy absorbed by leaves.

Notizen: Abstract Molecular biologists strive to infer evolutionary relationships from quantitative macromolecular comparisons obtained by immunological, DNA hybridization, electrophoretic or amino acid sequencing techniques. The problem is to find unrooted phylogenies that best approximate a given dissimilarity matrix according to a goodness-of-fit measure, for example the least-squares-fit criterion or Farris'sf statistic. Computational costs of known algorithms guaranteeing optimal solutions to these problems increase exponentially with problem size; practical computational considerations limit the algorithms to analyzing small problems. It is established here that problems of phylogenetic inference based on the least-squares-fit criterion and thef statistic are NP-complete and thus are so difficult computationally that efficient optimal algorithms are unlikely to exist for them.

Notizen: Abstract Certain properties of solutions similar to set invariance, set attractivity, boundedness, BIBO stability, etc. are investigated for the semistate model $$P(t)\dot x = M(t,x)x + D(t,x)u,y = q(t,x,u).$$ For systems considered, it is assumed that the reduction to a normal form of lower order is not possible. Using the direct method of Liapunov, the properties of solutions are investigated without actual knowledge of solutions.

Notizen: Abstract In this paper we extend the results on the multiple time-scale structure for linear autonomous systems of the form $$\dot x = A( \in )x$$ (cf. Coderchet al. [1]) to nonlinear autonomous systems. Our main result is in obtaining conditions under which the linearized system and the nonlinear system around an equilibrium point have the same time-scale structure.

Notizen: Abstract The process of cooperative binding of ligands to DNA has been classified into different modes. An additional mode of cooperative interaction amongst ligands binding at sites on complementary strands has been emphasised. A statistical mechanical method has been applied to obtain an analytical expression for the fraction of nucleotide sites bound. Theoretical Scatchard plots have been drawn and analysed.

Notizen: Abstract Suspensions of chemotactic bacteria develop spatial and temporal structures in response to an initial inhomogeneity in the medium. A theoretical model is presented for the analysis of spatial and temporal evolution of bacterial bands in response to several attractants. Applications of the model to various experimental cases give good agreement between theory and observation. The theoretical analysis provides further insight to the mechanisms governing band formation and band migration.

Notizen: Abstract The theory of maximum principles is applied to a nonlinear differential equation representing a heat conduction model of the human head to obtain accurate analytical upper and lower bounding curves.

Notizen: Abstract This paper is a general introduction to the field of biomathematical modeling. Biomathematical modeling is divided into three parts: the derivation of models, the fitting of models to data, and the simulation of data from models. This paper focuses on the simulation of data from models. The uses of simulation, the potential users of simulation, and simulation software are described.

Notizen: Abstract A stochastic model for the chemotherapy of experimental tumors is presented. The focus of this model is on the presence of drug-resistant mutants and their influence on eventual treatment outcome. Equations are derived for the joint probability-generating function for the number of chemo-sensitive and chemo-resistant cells. The model is extended to two drugs and it is shown how the model may be used to make deductions regarding the optimum scheduling of therapy.

Notizen: Abstract Earlier and some recent ideas about the possible modes of specification of the wiring-in of nervous systems are reviewed in the light of older and several recent experiments, and some new ideas are suggested. It is argued that certain general principles, notably the postulated ‘principle of alternative matching’ (PALMA) and a suggested and related ‘kaleidoscopic effect’ (KALEF), as well as the notion of an ‘extracellular guidance network’ (ECGN), are in good agreement with recent and older findings concerning axonal guidance during neural wiring-in. It seems possible that by means of genetically programmed processes, neurons become systematically combinatorially labelled to such a degree that possibly all neurons areuniquely specified, as regards the combination oftypes of cell labels they make. Yet, there remains considerable freedom as regards the modes of arrangements of cell labels within cell surface membranes and the KALEF permits to overcome apparent difficulties that confronted earlier versions of the cell labelling hypotheses (cf. Edelman,Science 219, 450–457, 1983, for mention of such difficulties). Apart from label specification, neural development seems to depend on trophic factors, which are also essential for the maintenance of the developed nervous system. The systematic programmes for cell labelling, apart from generating all the required neurons, also produces inappropriate neurons and synaptic connections. These are got rid of by systematic cell death and/or atrophy of inappropriate synapses and/or elimination of inappropriate axon collaterals. The resulting neural net seems then very specifically wired-in for each species, apparently without redundant neurons.

Notizen: Abstract In order to understand the abnormal flow conditions of blood in a locally constricted blood vessel, the analytical results are obtained for the oscillatory flow of blood which behaves as a Newtonian fluid. It is here assumed that the surface roughness is cosine-shaped and the maximum height of the roughness is very small compared with the radius of the unconstricted tube. Numerical solutions are presented for the instantaneous flow rate, resistive impedance, wall shear stress and phase lag.

Notizen: Abstract In order to better understand the effect of initial stress in blood flow in arteries, a theoretical analysis of wave propagation in an initially inflated and axially stretched cylindrical thick shell is investigated. For simplicity in the mathematical analysis, the blood is assumed to be an incompressible inviscid fluid while the arterial wall is taken to be an isotropic, homogeneous and incompressible elastic material. Employing the theory of small deformations superimposed on a large initial field the governing differential equations of perturbed solid motions are obtained in cylindrical polar coordinates. Considering the difficulty in obtaining a closed form solution for the field equations, an approximate power series method is utilized. The dispersion relations for the most general case of this approximation and for the thin tube case are thoroughly discussed. The speeds of waves propagating in an unstressed tube are obtained as a special case of our general treatment. It is observed that the speeds of both waves increase with increasing inner pressure and axial stretch.

Notizen: Abstract A model of a predator-prey interaction, where the prey population consists of three genotypes with random mating and continuous, nonlinear birth and death processes with fertility differences, is proposed. Sufficiency conditions giving the existence of a globally stable equilibrium on one of the coordinate planes are given. This extends results of Freedman and Waltman [J. Math. Biol. 6, 367–374 (1978) andRocky Mountain J. Math. 12, 779–784 (1982)]. In addition, conditions are derived which guarantee the persistence of all components of the populations.

Notizen: Abstract A theoretical study is made of three organ flow models with heterogeneity of capillary transit times. A new parametrization of Rose and Goresky's Model III facilitates in many cases a reduction to Goresky's Model II, accomplished by a special time shift. The shift parameter $$\tau _{c_z } = \tau _{c_m } - t_{APP} /b$$ defined here is critical in this analysis of Model III. A new expression of the series for outflow concentration in Model III is given and proves useful in examining the model as an operator and in relating it to Models I and II. A result on parameter optimization is given: if $$\tau _{c_z } \geqslant 0$$ then Model III cannot fit better than Model II. This is applied to some data from Rose and Goresky [Circulation Res. 39, 541–544 (1976)] and raises a new question about their model. A heart model of Levin and Bassingthwaighte based on regional flow measurement is shown to be a discretized generalization of Model II.

Notizen: Abstract This paper analyses the diffusion effect on stability in Lotka-Volterra systems for a patch-type environment. Applying the extended stability theorem of LaSalle, some classes of patches for which the diffusion does not affect the system's stability are drawn. Further, complicated dynamical behaviours in two-prey, one-predator diffusion models are given when the patch does not belong to the above classes.

Notizen: Abstract When comparing two biological sequences, it is often desirable for a gap to be assigned a cost not directly proportional to its length. If affine gap costs are employed, in other words if opening a gap costsv and each null in the gap costsu, the algorithm of Gotoh (1982,J. molec. Biol. 162, 705) finds the minimum cost of aligning two sequences in orderMN steps. Gotoh's algorithm attempts to find only one from among possibly many optimal (minimum-cost) alignments, but does not always succeed. This paper provides an example for which this part of Gotoh's algorithm fails and describes an algorithm that finds all and only the optimal alignments. This modification of Gotoh's algorithm still requires orderMN steps. A more precise form of path graph than previously used is needed to represent accurately all optimal alignments for affine gap costs.

Notizen: Abstract A series of Bayesian image processing algorithms which incorporate various classes ofa priori source information in treating data which obeys Poisson and Gaussian statistics is derived using maximum entropy considerations. The standard maximum likelihood equations are shown to be a special case of Bayesian image processing when thea priori information about a source distribution φ j is solely that a non-vanishing probability for each element value φ j exists only in some finite interval,a j ≤φ j ≤φ j . Bayesian image processing equations for thea priori source information that all φ j are finite -∞〈φ j 〈∞ and each φ j distribution has a defined mean φ j and a defined variance σ j are derived. The Bayesian image processing equations are also derived when thea priori source information is that all φ j ≥0 and that each φ j distribution has a defined mean φ j and a defined variance σ j . The a priori source distribution constraint that a correlation exists among nearby elements is also considered. The results indicate improvement over standard methods.

Notizen: Abstract The superficial capillary network of the gastric mucosa can be monitored for red blood cell velocity measurements by a microscopic technique. This network, however, reflects the blood flow in capillaries of more physiological interest, namely those passing by the acid-producing cells and emptying into the superficial network. It is, however, not possible to study these capillaries directly and therefore the problem is to determine in what way and to what degree blood flow measurements in the superficial network reflect the capillary flow of interest. A probabilistic approach where the movements of the red blood cells have been analysed, gives indications of determinable relations between observations on the superficial network flow and the flow passing the acid-producing cells.

Notizen: Abstract The present paper describes a calculation technique to determine a value of Young's modulus for the cornea when the intraocular pressure, the shape of the cornea and the thickness variation along the cornea are known fromin vivo measurements. Twenty-eight persons were examined in both eyes and a mean value of Young's modulus for the cornea was calculated to 2.45×104±0.57×104 N/m2 (S.D.).

Notizen: Abstract It is pointed out that the asymptotic general solution to the ϕ-model equation for a periodic carrying capacityK(t) andt≳r −1 is identical in form to the generalized logistic equation solution with a built-in developmental time delay τ(≲r −1) and associated parameter ranges of primary biological interest. In the case of the ϕ-model equation, the time delay is a purely dynamical consequence of the nonlinear form featured by the population growth rate.

Notizen: Abstract The pulsatile flow of blood through arteries is investigated in this paper by treating the blood vessel as a thin-walled anisotropic, non-linearly viscoelastic, incompressible circular cylindrical shell; nonlinearities of the flow of blood are also paid due consideration. The displacement components of the vessel wall are obtained from the equations of equilibrium which have been linearized by employing the principle of superimposition of a small deformation on a state of known finite deformation. The influence of the wall deformation on the flow properties of blood, has been accounted for by considering suitably formulated continuity conditions. A finitedifference scheme is employed for solving the flow equations together with the boundary and initial conditions by using the locally measured values of pressure and pressure gradient. Numerical results obtained for the velocity profile of blood flowing in a canine middle descending thoracic aorta have been presented through figures.

Notizen: Abstract The “protocell” is a mathematical model of a self-maintaining unity based on the dynamics of simple reaction-diffusion processes and a self-controlled dynamics of the surface. In this paper its spatio-temporal behaviour far from the stationary structure is investigated by means of a boundary layer approximation. It is shown in detail how a simplified and mathematically feasible equation can be derived from the original parabolic problem. It turns out that the known instability which is initiated in the linear region around the stationary structure is continued further in the direction to a division by nonlinear dynamics.

Notizen: Abstract To describe stationary-state kinetics of solute clearance from an interstitial space with an initial uniform concentration, an explicit solution of the Sangren-Sheppard model and a stratagem for an explicit solution of the Johnson-Wilson model are presented. In both cases expressions for computing the exact intravascular and extravascular concentrations at any time and location are complicated and inconvenient. Simpler and far more convenient formulae for determining upper and lower bounds on solute concentrations and on the pseudo-first-order clearance rate ‘constant’ (k) are derived. For the Johnson-Wilson model, the bounds are so tight thatk, for example, can be estimated with considerable accuracy whenever the capillary blood flow exceeds the permeability-surface area product.