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  • 1
    Digitale Medien
    Digitale Medien
    Random walk with persistence and external bias (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 311-338 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The partial differential equation of the random walk problem with persistence of direction and external bias is derived. By persistence of direction or internal bias we mean that the probability a particle will travel in a given direction need not be the same for all directions, but depends solely upon the particle's previous direction of motion. The external bias arises from an anisotropy of the medium or an external force on the particle. The problem is treated by considering that the net displacement of a particle arises from two factors, namely, that neither the probability of the particle traveling in any direction after turning nor the distance the particle travels in a given direction need be the same for all directions. A modified Fokker-Planck equation is first obtained using the assumptions that the particles have a distribution of travel times and speeds and that the average time of travel between turns need not be zero. The fional equation incopporating the assumption of a persistence of direction and an external bias is then derived. Applications to the study of diffusion and to long-chain polymers are then made.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476407
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  • 2
    Digitale Medien
    Digitale Medien
    Methods of statistical analysis (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 383-383 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476411
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  • 3
    Digitale Medien
    Digitale Medien
    The transmission of excitation from the membrane to actomyosin (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 385-385 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476412
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  • 4
    Digitale Medien
    Digitale Medien
    On the spread of information with time and distance (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 367-381 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The transmission of some information or behavior pattern is treated as a flow of “particles” which execute random motions over a population of individuals and which may multiply or disappear. Equations are derived for the number density of these “particles” and from this is calculated the number of individuals through which the “particles” have passed. The results are applied to a number of situations such as 1) uniform spatial distribution with multiplication factor decreasing with time because of loss of interest or confusion of the information, 2) multiplication factor constant but the rate of spreal decreasing with multiple hearings, 3) one-dimensional region with a small starting region with or without an absorbing barrier 4) two-dimensional region with absorbing barrier, 5) continous sources of information within a small region in one dimension, 6) uniform spatial distribution in which individuals do not respond to more than one hearing.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476410
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  • 5
    Digitale Medien
    Digitale Medien
    A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 387-394 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A situation is considered in which a fluid containing a substance flows through a vessel at a constant rate, the substance being permeable to the vessel wall. In the region outside the vessel there is supposed to be rapid mixing in the direction perpendicular to the axis of the vessel but no mixing longitudinally. The solution for the spatial distribution at any time is given for the case of an arbitrary initial distribution along the vessel length in the absence of an input. The solution is also given for the case of a single impulsive input, the concentration being initially zero everywhere.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476432
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  • 6
    Digitale Medien
    Digitale Medien
    A mathematical contribution to the study of orientation of organisms (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 431-476 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Organisms orient themselves to a stimulus by two general methods. One method is by directed orientation (taxis); the other is by undirected locomotory reaction (kinesis). An equation, and the methods for finding the necessary parameters of this equation, is derived for the distribution of organisms within a container, with the following limitations: (1) the organisms have no accommodation, (2) they are always active, and (3) the stimulus changes slowly with position. Necessary modifications of the equation are then derived, so that the last two limitations may be eliminated. The equation cannot be solved excatly because of its complexity; hence an approximation method must be used. This method is discussed, an approximate solution is found, and a time constant for equilibrium to be established is derived. Applications tovarious experiments in the literature are then made with fairly satisfactory results. A new interpretation of the theory of klino-kinesis with accommodation is found upon application of the equations developed to experimental work. Further limitations and uses of these equations are then discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476435
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  • 7
    Digitale Medien
    Digitale Medien
    Structural parameters of communication networks (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 501-507 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Certain parameters are defined which roughly characterize the internal structure of networks. A given network structure uniquely determines the values of the parameters, but the reverse is not true. The parameters therefore define certain classes of networks. One of the parameters, thedispersion D(S) gives an indication of the “compactness” of the internal structure. Addition theorems and inequalities are derived relating the dispersions of sub-systems to the dispersion of the complete structure.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476438
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  • 8
    Digitale Medien
    Digitale Medien
    Determination of diffusion and permeability coefficients in nerve trunks (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 489-500 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476437
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  • 9
    Digitale Medien
    Digitale Medien
    Enzyme localization as a mechanism of apparent active transport (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 509-522 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model based on enzyme localization is developed which gives rise to an apparent active transport of a metabolite into or out of cells. The model is applied to three simple situations, using Fick's equation and the Rashevsky approximation. It is shown that the apparent efficiency can be made as large as desired if, for constant reaction, the outer cell region is made sufficiently small, or, for autocatalytic reaction, if the metabolite concentration in the outer region is sufficiently small. The physical limitations imposed by this mechanism are developed for all three situations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476439
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  • 10
    Digitale Medien
    Digitale Medien
    Spread of information through a population with socio-structural bias: I. Assumption of transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 523-533 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A previously derived iteration formula for a random net was applied to some data on the spread of information through a population. It was found that if the axon density (the only free parameter in the formula) is determined by the first pair of experimental values, the predicted spread is much more rapid than the observed one. If the successive values of the “apparent axon density” are calculated from the successive experimental values, it is noticed that this quantity at first suffers a sharp drop from an initial high value to its lowest value and then gradually “recovers”. An attempt is made to account for this behavior of the apparent axon density in terms of the “assumption of transitivity”, based on a certain socio-structural bias, namely, that the likely contacts of two individuals who themselves have been in contact are expected to be strongly overlapping. The assumption of transitivity leads to a drop in the apparent axon density from an arbitrary initial value to the vicinity of unity (if the actual axon density is not too small). However, the “recovery” is not accounted for, and thus the predicted spread turns out to beslower than the observed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476440
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  • 11
    Digitale Medien
    Digitale Medien
    Spread of information through a population with socio-structural bias: II. Various models with partial transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 535-546 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The assumption of transitivity treated in part I is modified in various ways to describe an information-diffusion process, in which a certain amount of randomness of contact does occur. In one model a parameter is introduced which is indicative of a tendency to go beyond one's immediate vicinity to spread the information as the vicinity becomes saturated with knowers. In another model the randomness appears in the assumption that new knowers are uniformly distributed among the knowers. Two of the equations thus derived, each with two free parameters are in good agreement with experimental results.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476441
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  • 12
    Digitale Medien
    Digitale Medien
    The chemical basis of morphogenesis (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 153-197 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns onHydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459572
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  • 13
    Digitale Medien
    Digitale Medien
    Book reviews (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 319-334 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459577
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  • 14
    Digitale Medien
    Digitale Medien
    SIAM 1990 Annual Meeting and Short Course 15–20 July 1990 Hyatt Regency Hotel, Chicago, IL (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 335-337 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459578
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  • 15
    Digitale Medien
    Digitale Medien
    Editorial: Software survey section (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. I 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459579
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  • 16
    Digitale Medien
    Digitale Medien
    The cellular computer DNA: Program or data (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 335-348 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The classical metaphor of the genetic program written in the DNA nucleotidic sequences is reconsidered. Recent works on algorithmic complexity and logical properties of computer programs and data are used to question the explanatory value of that metaphor. Structural properties of strings are looked for which would be necessary to apply to DNA sequences if the metaphor is to be taken literally. The notion of sophistication is used to quantify meaningful complexity and to distinguish it from classical computational complexity. In this context, the distinction between program and data becomes relevant and an alternative metaphor of DNA as data to a parallel computing network embedded in the global geometrical and biochemical structure of the cell is discussed. An intermediate picture of an evolving network emerges as the most likely where the output of the cellular computing network can produce, at a different time scale, changes in the structure of the network itself by means of changes in the DNA activity patterns.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458575
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  • 17
    Digitale Medien
    Digitale Medien
    Distribution of the number of matches between nucleotide sequences (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 349-358 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract When two strings of symbols are aligned it is important to know whether the observed number of matches is better than that expected between two independent sequences with the same frequency of symbols. When strings are of different lengths, nulls need to be inserted in order to align the sequences. One approach is to use simple approximations of sampling for replacement. We describe an algorithm for exactly determining the frequencies of given numbers of matches, sampling without replacement. This does not lead to a simple closed form expression. However we show examples where sampling with, or without, replacement give very similar results and the simple approach may be adequate for all but the smallest cases.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458576
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  • 18
    Digitale Medien
    Digitale Medien
    Consistency of optimal sequence alignments (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 509-525 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Pairwise optimal alignments between three or more sequences are not necessarily consistent as a whole, but consistent and inconsistent residues are usually distributed in clusters. An efficient method has been developed for locating consistent regions when each pairwise alignment is given in the form of a “skeletal representation” (Bull. math. Biol. 52, 359–373). This method is further extended so that the combination of pairwise alignments that gives the greatest consistency is found when possibly many alignments are equally optimal for each pairwise comparison. A method for acceleration of simultaneous multiple sequence alignment is proposed in which consistent regions serve as “anchor points” limiting application of direct multi-way alignment to the rest of “inconsistent” regions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462264
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  • 19
    Digitale Medien
    Digitale Medien
    Conditions for the unlimited growth in multitype population size dependent galton-watson processes (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 527-534 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Sufficient conditions are given for the unlimited growth or otherwise in multitype population size dependent Galton-Watson processes. These conditions are given in terms of moments of offspring distributions and extend known conditions for processes with one type.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462265
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  • 20
    Digitale Medien
    Digitale Medien
    A deterministic model of the cell cycle (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 535-547 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The variability of the duration of the cell cycle is explained by the phenomenon of sensitive dependence upon initial conditions; as may occur in deterministic non-linear systems. Chaotic dynamics of a system is the result of this sensitive dependence. First a deterministic system is formulated that is equivalent to the Smith-Martin transition probability model of the cell cycle. Next the model is extended to a dynamic process that ranges over the cell generations. A deterministic non-linear relationship between the cycle time of the mother and daughter cell is established. It clarifies the variability of mother-daughter correlation for the different cell types. The model is fitted to two different cell cultures; it shows that the graph of the non-linear relation has the same shape for different cell types.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462266
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  • 21
    Digitale Medien
    Digitale Medien
    Book reviews (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 583-596 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462268
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  • 22
    Digitale Medien
    Digitale Medien
    Editorial: Software survey section (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. I 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462269
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  • 23
    Digitale Medien
    Digitale Medien
    Diffusion regulated growth characteristics of a spherical prevascular carcinoma (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 549-582 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Recently a mathematical model of the prevascular phases of tumor growth by diffusion has been investigated (S. A. Maggelakis and J. A. Adam,Math. Comput. Modeling, in press). In this paper we examine in detail the results and implications of that mathematical model, particularly in the light of recent experimental work carried out on multicellular spheroids. The overall growth characteristics are determined in the present model by four parameters:Q, γ, b, andδ, which depend on information about inhibitor production rates, oxygen consumption rates, volume loss and cell proliferation rates, and measures of the degree of non-uniformity of the various diffusion processes that take place. The integro-differential growth equation is solved for the outer spheroid radiusR 0(t) and three related inner radii subject to the solution of the governing time-independent diffusion equations (under conditions of diffusive equilibrium) and the appropriate boundary conditions. Hopefully, future experimental work will enable reasonable bounds to be placed on parameter values referred to in this model: meanwhile, specific experimentally-provided initial data can be used to predict subsequent growth characteristics ofin vitro multicellular spheroids. This will be one objective of future studies.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462267
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  • 24
    Digitale Medien
    Digitale Medien
    Synchronization of the behaviour within nests of the antleptothorax acervorum (fabricius)—I. Discovering the phenomenon and its relation to the level of starvation (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 597-612 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Workers of the speciesLeptothorax acervorum show age-polyethism, they start their life as broodworkers and later on they become nestworkers and foragers. Nestworkers and foragers of this ant species are inactive for 72% and 15% of the total time respectively. The short bursts of activity within the nest do not occur randomly but are synchronized so that the whole nest population exhibits nonperiodic pulses of activity: the ants were seen to wake each other actively. In addition starvation experiments were done to assess whether ants react upon food availability. In appeared that during a longlasting period of starvation the proportion of active ants in the nest is at a higher approximately constant level.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462100
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  • 25
    Digitale Medien
    Digitale Medien
    The economics of exhaustible resources (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 281-312 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02464433
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  • 26
    Digitale Medien
    Digitale Medien
    Some aspects of the dynamics of populations important to the management of the commercial Marine fisheries (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 253-279 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02464432
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  • 27
    Digitale Medien
    Digitale Medien
    Book reviews (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 313-326 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02464434
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  • 28
    Digitale Medien
    Digitale Medien
    Editorial: Software survey section (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. I 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02464436
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  • 29
    Digitale Medien
    Digitale Medien
    Resource management and behavioural ecology: A Conference in Celebration of the 60th Birthday of Colin Clark 24–26 July 1991 University of British Columbia, Cancouver, B.C. (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 327-327 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02464435
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  • 30
    Digitale Medien
    Digitale Medien
    The statistical correlation of nucleotides in protein-coding DNA sequences (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 345-353 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The statistical correlation of nucleotides in a DNA sequence is described by a set of redundanciesD 1,D 2,D 3,... By calculation of {D n} of 2341 coding regions of nucleic acid sequences it is demonstrated that about 2/3 of sequences has correlation length ≤2, 10% of sequences—correlation with 3-periodicity and others—long range aperiodic correlations. The implications of the results from the interactions of random mutation and natural selection are discussed briefly.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460722
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  • 31
    Digitale Medien
    Digitale Medien
    Autocatalytic membrane conductance and memory (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 327-343 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A basic characteristic of biological memory is that it has a graded duration, which, even for socalled short-term memory, can vary from minutes to days (i.e. over about three orders of magnitude), depending on the training protocol, which one can think of as determining the “strength” of the memory. Furthermore, the molecular analysis of simple learning in invertebrates has revealed many examples where “learning” is produced by adecrease in an appropriate membrane conductance. This paper provides a quantitative analysis of a simple kinetic scheme where by a conductance decrease can be produced by repetitive nerve impulses, with a duration that varies with stimulus frequency. The simplest model considered is based on the actual kinetics of the naturally-occurring ionophore Monazomycin. This model yields durations ranging only over a factor of about 10, for reasonable parameter values. However, a simple modification of the model yields memory durations ranging over three or more orders of magnitude. We also show that Monazomycin-like kinetics can appear as the result of a combination of simple uni- and bi-molecular reactions, thus making more plausible the possibility that the effects described here may operate in actual biological systems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460721
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  • 32
    Digitale Medien
    Digitale Medien
    Statistical evaluation of dendritic growth models (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 579-589 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model (Kliemann, W. 1987.Bull. math. Biol. 49, 135–152.) that predicts the quantitative branching pattern of dendritic tree was evaluated using the apical and basal dendrites of rat hippocampal neurons. The Wald statistics for χ2-test was developed for the branching pattern of dendritic trees and for the distribution of the maximal order of the tree. Using this statistic, we obtained a reasonable, but not excellent, fit of the mathematical model for the dendritic data. The model's predictability of branching patterns was greatly enhanced by replacing one of the assumptions used for the original model “splitting of branches for all dendritic orders is stochastically independent”, with a new assumption “branches are more likely to split in areas where there is already a high density of branches”. The modified model delivered an excellent fit for basal dendrites and for the apical dendrites of hippocampal neurons from young rats (30–34 days postpartum). This indicates that for these cells the development of dendritic patterns is the result of a purely random and a systematic component, where the latter one depends on the density of dendritic branches in the brain area considered. For apical dendrites there is a trend towards decreasing pattern predictability with increasing age. This appears to reflect the late arrival of afferents and subsequent synaptogenesis proximal on the apical dendritic tree of hippocampal neurons.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458630
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  • 33
    Digitale Medien
    Digitale Medien
    Computer simulations of cell-target encounter including biased cell motion toward targets: Single and multiple cell-target simulations in two dimensions (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 591-621 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In order for immune cells to carry out many of their functions, including clearance of infectious agents from tissue, they must first encounter their targets in the tissue. This encounter process is often the rate-limiting step in the overall function. Most immune cells exhibit chemotactic ability, and previous continuum models for encounter rates and dynamics have shown that chemotaxis can be a great advantage to cells by greatly increasing encounter rates relative to those for randomly moving cells. This paper describes computer simulations of discrete cell-target encounter events in two dimensions, for the two cases considered by the continuum models: where only a single cell and a single target are present, and where many cells and targets are present. The results of these simulations verify our previous model predictions that a small amount of chemotactic bias dramatically decreases the encounter time, while further increases in the amount of bias have a much smaller effect. Chemotactic ability is shown to be an important determinant of the kinetics of target clearance, and its effects depend on the initial cell-target ratio and the initial distributions of cells and targets. To the best of our knowledge, this work provides the first computer simulations of particle-target encounter in which there is biased motion of particles toward their targets, and is therefore of general interest beyond specific application to immune cell function.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458631
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  • 34
    Digitale Medien
    Digitale Medien
    Book reviews (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 657-663 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458634
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  • 35
    Digitale Medien
    Digitale Medien
    One-way blocks in cardiac tissue: A mechanism for propagation failure in purkinje fibres (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 881-899 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The concept of a one-way block, arising from a region of depressed tissue, has remained central to theories for cardiac arrhythmias. We show that both the geometry of a depressed region and spatial heterogeneities in depression are key factors for inducing such a block. By using an asymptotic approximation, known as the eikonal equation, to model qualitatively the movement of a depolarization wave-front down a Purkinje fibre bundle, we show how a one-way block in conduction may result from asymmetric constriction in the width of a depressed bundle. We demonstrate that this theory is valid for biologically relevant parameters and simulate a one-way block by numerically solving the eikonal approximation. We consider the case of non-uniform depression, where the planar travelling wave speed is spatially dependent. Here, numerical simulations indicate that such a spatial dependency may, in itself, be sufficient to produce a one-way block.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461489
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  • 36
    Digitale Medien
    Digitale Medien
    A system dynamics model of island biogeography (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 911-940 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The MacArthur-Wilson equilibrium theory of island biogeography has been one of the more influential concepts in modern biogeography and ecology. In this paper, we synthesize the theory and examine effects of different immigration/extinction rate-species diversity curves on original predictions from the theory by using the System Dynamics simulation modeling approach. Moreover, we develop a comprehensive and generic System Dynamics model to incorporate a variety of recent modifications and extensions of the theory, including area effect, distance effect, competition effect, habitat diversity effect, target effect, and rescue effect. Through computer simulation with STELLA, a more profound understanding of the theory of island biogeography can be gained. The System Dynamics modeling approach is especially appropriate for such a study because it maximizes the utilization of the ecological data by incorporating qualitative information so that a complex, imprecisely-defined ecological system can be studied quantitatively, effectively, and comprehensively. Our simulation results show that different monotonic rate-species diversity curves do not affect the essence of the theory of island biogeography, while the magnitude of equilibrium species diversity may be greatly affected. Non-monotonic rate-species diversity curves may result in potential multiple equilibria of species diversity. In addition, our model suggests that a non-monotonic relationship may exist between the equilibrium turnover rate and island area and between the equilibrium turnover rate and distance.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461491
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  • 37
    Digitale Medien
    Digitale Medien
    The estimation of the Kolmogorov entropy from a time series and its limitations when performed on EEG (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 665-678 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A method to estimate a lower bound of the Kolmogorov entropy—the so calledK 2-entropy—from a time series is presented which avoids use of the generalized correlation integral. The influence of the norm is studied. The method is demonstrated on some standard examples. The entropy of the attractor apparent in the EEG of the foetal sheep is estimated and the results are compared with results obtained from synthesized data featuring some basic properties of EEG. This gives an insight into the limitations of the procedure.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461547
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  • 38
    Digitale Medien
    Digitale Medien
    Analysis of oscillations in yeast continuous cultures by a new simplified model (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 685-700 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The autonomous oscillations in yeast continuous cultures are investigated analytically and related to the behaviour of the single cell by means of a suitable modified version of Monod’s classical chemostat model. Two main cell phases or states are considered to account for the experimentally observed changes occurring in the cell growth course: the budded phase and the unbudded one. Thus, a sort of two compartment structure is given to the total biomass. The model so far obtained allows one to analyse the local properties of the predicted steady states under various assumptions, both on the yield coefficients and the specific growth rates. Necessary conditions for the local instability are derived and the existence of stable limit cycles is shown by computer simulation. With respect to the qualitative changes in the metabolic parameters, this analysis agrees with the results obtained by simulation of complex structured and segregated models. However, the oscillation period is too long compared with the experimental one and this fact may be mainly due to the strong simplifying assumptions on the dynamic evolution of the transfer rates between the two compartments. The model’s usefulness seems until now restricted to the identification of the relationships between the cell cycle regulation and the oscillation triggering.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461549
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  • 39
    Digitale Medien
    Digitale Medien
    Analysis of chemotactic bacterial distributions in population migration assays using a mathematical model applicable to steep or shallow attractant gradients (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 721-749 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The mathematical model developed by Riveroet al. (1989,Chem. Engng Sci. 44, 2881–2897) is applied to literature data measuring chemotactic bacterial population distributions in response to steep as well as shallow attractant gradients. This model is based on a fundamental picture of the sensing and response mechanisms of individual bacterial cells, and thus relates individual cell properties such as swimming speed and tumbling frequency to population parameters such as the random motility coefficient and the chemotactic sensitivity coefficient. Numerical solution of the model equations generates predicted bacterial density and attractant concentration profiles for any given experimental assay. We have previously validated the mathematical model from experimental work involving a step-change in the attractant gradient (Fordet al., 1991Biotechnol. Bioengng.37, 647–660; For and Lauffenburger, 1991,Biotechnol. Bioengng,37, 661–672). Within the context of this experimental assay, effects of attractant diffusion and consumption, random motility, and chemotactic sensitivity on the shape of the profiles are explored to enhance our understanding of this complex phenomenon. We have applied this model to various other types of gradients with successful intepretation of data reported by Dalquistet al. (1972,Nature New Biol. 236, 120–123) forSalmonella typhimurum validating the mathematical model and supportin the involvement of high and low affinity receptors for serine chemotaxis by these cells.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461551
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  • 40
    Digitale Medien
    Digitale Medien
    Book reviews (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 797-804 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461554
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  • 41
    Digitale Medien
    Digitale Medien
    Rook’s tour representation of the genetic code (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 845-851 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Disconnected recurrences of the stop signal, serine and arginine appear in the original representation of the genetic code, and of the stop signal, arginine, serine and leucine in the codon ring representation. To achieve connectedness along with structural continuity, arook’s tour representation is presented here. On the basis of structural similarities and disparities in their side groups, each of the 20 amino acids is associated with a domain comprised of from one to six contiguous squares on the chess board. As the rook moves on the chess board, it reaches all 64 squares in the ordering of the codon numbers, which prescribe the codons by a simple formula based on the position and size of the nucleotides in a triplet. Recurrences of the stop signal, arginine and serine occur naturally on the tour as the rook enters each of the latter domains for the second time. A mathematical equivalent of the rook’s tour may enter as a programming device in the implementation of the code by the RNAs.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461487
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  • 42
    Digitale Medien
    Digitale Medien
    Hypnosis modelling in neural networks (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 1-20 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In the framework of the neural network theory effects similar to hypnotic displays are constructed. They are based on the associative paradigm involving non-linear interaction of excitatory and inhibitory channels with synaptic memory. The non-linearity of long-term memorizing processes may cause effects exhibited by blind spots, which are interpreted as the first stage of hypnosis. More complicated phenomena are discussed in terms of a two-layer network.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458314
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  • 43
    Digitale Medien
    Digitale Medien
    Dynamics of small autocatalytic reaction networks—II. Replication, mutation and catalysis (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 21-61 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Mutation is introduced into autocatalytic reaction networks. The differential equations obtained are neither of repliator-type nor can they be transformed straightway into a linear equation. Examples of low dimensional dynamical systems —n=2, 3 and 4 — are discussed and complete qualitative analysis is presented. Error thresholds known from simple replication-mutation kinetics with frequency independent replication rates occur here as well. Instead of cooperative transitions or higher order phase transitions the thresholds appear here as supercritical or subcritical bifurcations being analogous to first-order phase transitions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458315
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  • 44
    Digitale Medien
    Digitale Medien
    Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 63-76 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The non-linear behavior of a differential equations-based predator-prey model, incorporating a spatial refuge protecting a consant proportion of prey and with temperature-dependent parameters chosen appropriately for a mite interaction on fruit trees, is examined using the numerical bifurcation code AUTO 86. The most significant result of this analysis is the existence of a temperature interval in which increasing the amount of refuge dynamically destabilizes the system; and on part of this interval the interaction is less likely to persist in that predator and prey minimum population densities are lower than when no refuge is available. It is also shown that increasing the amount of refuge can lead to population outbreaks due to the presence of multiple stable states. The ecological implications of a refuge are discussed with respect to the biological control of mite pests.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458316
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  • 45
    Digitale Medien
    Digitale Medien
    Optimal root/shoot-partitioning of carbohydrates in plants (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 99-107 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In many applications of control theory on plant growth models biomass maximization is postulated to avoid analytically unsolvable problems while fruit maximization is commonly considered to be a more realistic criterion. In a special case, we are able to compare these criteria. Iwasa and Roughgarden (1984,Theor. Pop. Biol. 25, 78–105) have investigated a certain class of plant growth models using a fruit maximization criterion. They proved that, in the vegetative growth period, the organs follow a certain path of balanced growth. We show that this path remains optimal when biomass maximization is postulated. This underlines the importance of the balanced growth path found by Iwasa and Roughgarden. Furthermore, our result suggests that in the vegetative growth period the biomass maximization criterion is a good approximation of fruit maximization. In another theoretical control investigation, Schultzeet al. (1983,Oecologia 58, 169–177) derived a different type of balanced growth path. We apply the theory of Iwasa and Roughgarden to an improved version of the model of Schulzeet al. This leads to a new description of balanced growth between root and shoot that reflects non-linearities in the water uptake process and constitutes an interesting hypothesis for further experimental testing.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458318
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  • 46
    Digitale Medien
    Digitale Medien
    Ion induced deformation of soft tissue (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 77-98 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Laiet al. (1990,Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myerset al. (1984,ASME J. biomech. Engng,106, 151–158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to acount for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility, of approximate analytic solutions in certain cases.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458317
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  • 47
    Digitale Medien
    Digitale Medien
    Memory capacity in large idiotypic networks (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 109-136 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Many models of immune networks have been proposed since the original work of Jerne [1974,Ann. Immun. (Inst. Pasteur) 125C, 373–389]. Recently, a limited class of models (Weisbuchet al., 1990,J. theor. Biol. 146, 483–499) have been shown to maintain immunological memory by idiotypic network interactions. We examine generalizations of these models when the networks are both large and highly connected to study their memory capacity, i.e. their ability to account for immunization to a large number of random antigens. Our calculations show that in these minimal models, random connectivities with continuously distributed affinities reduce the memory capacity to essentially nil.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458319
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  • 48
    Digitale Medien
    Digitale Medien
    A kinetic model of coronary reactive hyperemic response to transient ischemia (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 137-156 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A kinetic model is proposed to delineate the factors that determine the coronary reactive hyperemic response (RHR) to transient ischemia. The model comprises of myocardial-interstitial (M) and vascular (V) compartments. Vasodilator metabolites (VM) are produced in the M compartment during the interval of coronary occlusion. The rate of VM production is dependent on the flow rate during the ischemic period, the ratio of excess flow above the control level (R) to the loss of flow during occlusion period (D), the amount of oxygen stored and the degree of vasodilation in the V compartment prior to occlusion. Following a complete release of occlusion, VM are transported from the M to V compartment and are washed out or degraded with time. The time course of RHR is determined by the coronary patency which is proportional to VM concentration in the V compartment. Based on a set of numerical constants, the model is tested by simulating RHR to the various occlusion manoeuvres: a pair of 10 sec occlusions separated by brief release, a 15 sec release followed by a second brief occlusion, a brief release of an occlusion followed by restriced inflow and a period of restricted inflow after occlusion. The simulated results fit the experimental R/D and RH durations data of canine hearts. Factors that determine the impairment of RH capacity in coronary stenosis are suggested in terms of the model scheme.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458320
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  • 49
    Digitale Medien
    Digitale Medien
    Kinetic study of an enzyme-catalysed reaction in the presence of novel irreversible-type inhibitors that react with the product of enzymatic catalysis (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 157-168 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In the present paper a kinetic study is made of the behaviour of a Michaelis-Menten enzyme-catalysed reaction in the presence of irreversible inhibitors rendered unstable in the medium by their reaction with the product of enzymatic catalysis. A general mechanism involving competitive, non-competitive, uncompetitive and mixed irreversible inhibition with one or two steps has been analysed. The differential equation that describes the kinetics of the reaction is non-linear and computer simulations of its dynamic behaviour are presented. The results obtained show that the systems studied here present kinetic co-operativity for a target enzyme that follows the simple Michaelis-Menten mechanism in its action on the substrate, except in the case of an uncompetitive-type inhibitor.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458321
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  • 50
    Digitale Medien
    Digitale Medien
    Book reviews (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 169-173 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458322
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  • 51
    Digitale Medien
    Digitale Medien
    On the estimation of alternative pathways of fatty acid oxidation in the liverIn vivo (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 191-203 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The relative contributions of mitochondrial β-oxidation and peroxisomal β-oxidation and peroxisomal ω-oxidation to the oxidation of a given fatty acidin vivo can be quantitated by an isotopic method. The approach requires infusion of a fatty acid labelled on two specific carbon atoms (e.g. [1-14C] and [11-14C] palmitate) to an isotopic steady state, with subsequent isolation and degradation of an acetylated conjugate as a product of the liver cytosolic acetyl CoA pool and of ketone bodies as a product of the liver mitochondrial acetyl CoA pool.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460615
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  • 52
    Digitale Medien
    Digitale Medien
    Correlations of rates of insulin release from islets and plateau fractions for β-cells (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 229-246 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Pancreatic β-cells in intact islets of Langerhans perfused with various glucose concentrations exhibit periodic bursting electrical activity (BEA) consisting of active and silent phases. The fraction of the time spent in the active phase is called the plateau fraction and appears to be strongly correlated with the rate of release of insulin from islets as glucose concentration is varied. Here this correlation is quantified and a theoretical development is presented in detail. Experimental rates of insulin release are correlated with “effective” plateau fractions over a range of glucose concentrations. There are a number of different models for BEA in pancreatic β-cells and a method is developed here to quantify the dependence of a glucose dependent parameter on glucose concentration. As an example, the plateau fractions computed from the Sherman-Rinzel-Keizer model are matched with experimental plateau fractions to obtain a relationship between the model's glucose-dependent parameter, β, and glucose concentration. Knowledge of the relationships between β and glucose concentration and between experimental measurements of rates of insulin release and plateau fractions permits the determination of theoretical rates of insulin release from the model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460617
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  • 53
    Digitale Medien
    Digitale Medien
    The development of concentration gradients in a suspension of chemotactic bacteria (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 299-344 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract When a suspension of bacterial cells of the speciesBacillus subtilis is placed in a chamber with its upper surface open to the atmosphere complex bioconvection patterns are observed. These arise because the cells: (1) are denser than water; and (2) usually swim upwards, so that the density of an initially uniform suspension becomes greater at the top than the bottom. When the vertical density gradient becomes large enough, an overturning instability occurs which ultimately evolves into the observed patterns. The reason that the cells swim upwards is that they are aerotactic, i.e. they swim up gradients of oxygen, and they consume oxygen. These properties are incorporated in conservation equations for the cell (N) and oxygen (C) concentrations, and these are solved in the pre-instability phase of development whenN andC depend only on the vertical coordinate and time. Numerical results are obtained for both shallow- and deep-layer chambers, which are intrinsically different and require different mathematical and numerical treatments. It is found that, for both shallow and deep chambers, a thin boundary layer, densely packed with cells, forms near the surface. Beneath this layer the suspension becomes severely depleted of cells. Furthermore, in the deep chamber cases, a discontinuity in the cell concentration arises between this cell-depleted region and a cell-rich region further below, where no significant oxygen concentration gradients develop before the oxygen is fully consumed. The results obtained from the model are in good qualitative agreement with the experimental observations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460620
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  • 54
    Digitale Medien
    Digitale Medien
    Topological and phenomenological classification of bursting oscillations (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 413-439 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (inMathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the phenomenological character of different types of bursting, addressing the issue of how well the bursting can be characterized given the limited amount of information often available in experimental settings.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460633
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  • 55
    Digitale Medien
    Digitale Medien
    Book reviews (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 499-506 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460637
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  • 56
    Digitale Medien
    Digitale Medien
    Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 461-486 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract To ensure its sustained growth, a tumour may secrete chemical compounds which cause neighbouring capillaries to form sprouts which then migrate towards it, furnishing the tumour with an increased supply of nutrients. In this paper a mathematical model is presented which describes the migration of capillary sprouts in response to a chemoattractant field set up by a tumour-released angiogenic factor, sometimes termed a tumour angiogenesis factor (TAF). The resulting model admits travelling wave solutions which correspond either to successful neovascularization of the tumour or failure of the tumour to secure a vascular network, and which exhibit many of the characteristic features of angiogenesis. For example, the increasing speed of the vascular front, and the evolution of an increasingly developed vascular network behind the leading capillary tip front (the brush-border effect) are both discernible from the numerical simulations. Through the development and analysis of a simplified caricature model, valuable insight is gained into how the balance between chemotaxis, tip proliferation and tip death affects the tumour's ability to induce a vascular response from neighbouring blood vessels. In particular, it is possible to define the success of angiogenesis in terms of known parameters, thereby providing a potential framework for assessing the viability of tumour neovascularization in terms of measurable quantities.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460635
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  • 57
    Digitale Medien
    Digitale Medien
    The transmission of excitation from the membrane to actomyosin (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 1-13 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The impressed field, “Window Field” (WF), due to a half-wave action potential on a muscle fiber, has been calculated on the basis of potential theory. It has been shown that in spite of the small intensity of the field, its integrated action can transfer the energy needed to induce, contraction from the membrane to the interior of the fiber. The energy of polarization has been found to be sufficient to exceed the energy of, thermal agitation on that length of fiber, which can be identified as the length of a sarcomere. The changes of ion concentration, caused by the WF, if calculated on the assumption of the semipermeability of theZ membranes, was found to be equal to the changes necessary to induce contraction of actomyosinin vitro.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476362
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  • 58
    Digitale Medien
    Digitale Medien
    Nonlinear diffusion in metabolic systems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 15-21 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Some general properties of the solution of the diffusion equation are deduced for the steady-state, spherically symmetric system. On the basis of these developments some results of N. Rashevsky (Bull. Math. Biophysics,11, 15, 1949) are discussed and the results of a previous investigation (Hearon,Bull. Math. Biophysics,12, 135, 1950b) are extended to more general conditions. In particular these extensions apply to the flow of a soluteagainst its concentration gradient, the nonzero gradient of an inert metabolite, and theaccumulation or exclusion of an inert metabolite in a metabolic system.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476363
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  • 59
    Digitale Medien
    Digitale Medien
    Comments on the approximate solution of the diffusion equation: I (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 23-31 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The approximation method of N. Rashevsky is discussed and reviewed. It is shown that in addition to theexplicit assumptions and approximations there is involved the assumption that the rate of metabolism is the same at every point in the cell and that theaverage rate of metabolism is different from zero. An expression is given for the error in the approximate method when the rate of metabolism is any function of the concentration. It is also shown that a solution in theform of that obtained by the approximate method is not possible if the generalized laws of diffusion are assumed to apply.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476364
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  • 60
    Digitale Medien
    Digitale Medien
    The kinetics of the succinoxidase (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 33-42 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Rate equations for the enzymatic oxidation of succinic acid are derived on the assumption that when a single molecule of substrate combines with an enzyme molecule, it can do so with either one or two sites on the enzyme, and that oxidation occurs only in the second case. In addition it is assumed that the product of the reaction, fumaric acid, combines reversibly with the enzyme. With certain enzyme preparations the data fitted such an equation satisfactorily. In others the rate was that of a first-order reaction, but addition of cytochrome changed it to the former type. It was concluded that the transfer of hydrogen to oxygen was a first-order reaction and dominated the whole rate when enzyme preparations were used which had been washed relatively free of cytochrome. When the limiting factor was succino-dehydrogenase the rates followed the new equation. Criteria for recognizing noncompetitive inhibition are given, and inhibition by di-tertiary butyl peroxide was shown to be of this type.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476365
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  • 61
    Digitale Medien
    Digitale Medien
    The interpretation of exponential dose-effect curves (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 43-47 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper deals with the following question: Which distributions of radiosensitivity in a population can lead to an exponential survival curve? The problem is solved exactly, with statistical fluctuations in dose fully accounted for. It is shown that only an exponential distribution of sensitivities can give rise to an exponential survival curve.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476366
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  • 62
    Digitale Medien
    Digitale Medien
    An approximation method for the solution of diffusion and related problems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 49-61 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An approximation method is introduced which enables a number of diffusion-type problems to be solved in an approximate but simple manner. Many cases require only the solution of a simple first-order differential equation. The method is applied to a number of cases in which the exact solutions are available. A comparison shows that the method is quite satisfactory in these cases. The method is applied to diffusion problems with rate of consumption proportional to concentration or to the square of the concentration. In the latter case, the result obtained is essentially the same as that found by H. G. Landau (1950) after elaborate calculations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476367
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  • 63
    Digitale Medien
    Digitale Medien
    On spontaneous discharge obtained from a physicochemical model of excitation (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 83-91 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is shown that a slight modification of a model of excitatory phenomena in irritable tissues, which has been treated before, exhibits spontaneous oscillations. The frequency of these oscillations and the time-course of the potential across the model membrane have been determined, together with the dependence of some of their characteristics on some important parameters, particularly (Ca++).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476370
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  • 64
    Digitale Medien
    Digitale Medien
    Cell division by swelling stresses (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 73-81 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is demonstrated that, if the variations of viscosity throughout a cell are considered, swelling stresses may produce elongation and division. To do this it is necessary to generalize Betti's theorem to cover systems containing viscosity gradients and such a generalization is presented. On the basis of two special assumptions it is shown that most of the results of the diffusion drag theory of cell division may be duplicated by the present theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476369
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  • 65
    Digitale Medien
    Digitale Medien
    Imitative behavior in nonuniformly spatially distributed populations (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 63-71 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The theory of imitative behavior, developed previously, is applied to the case of two social groups which are separated spatially. If the information of each group as to the behavior of the other is complete, the case reduces to that of a single group. When any information is lacking at all, the two groups are independent. If we have two mutually exclusive behaviorsA andB, all four combinationsAA, AB, BA, andBB are possible. If the mutual information gradually increases from zero, then for a certain value of it, the group which is more informed about the behavior of the other will change to that behavior if it did not already exhibit it. If for constant information the size of the group increases, then above a certain threshold value, the larger group imposes its behavior on the smaller.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476368
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  • 66
    Digitale Medien
    Digitale Medien
    Note on a theory of membrane permeability (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 103-104 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476372
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  • 67
    Digitale Medien
    Digitale Medien
    The limiting information capacity of a neuronal link (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 107-107 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476374
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  • 68
    Digitale Medien
    Digitale Medien
    Heredity in uterine cancer (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 105-106 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476373
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  • 69
    Digitale Medien
    Digitale Medien
    Some considerations on capillary adjustment to changing metabolism of tissue (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 93-101 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Local regulation of blood flow as determined by capillary diameter and the number of open capillaries in a region is considered. The local changes in capillary diameter and in the number of open capillaries are assumed to be due to concentration changes of a diffusible, nonspecified metabolite. This metabolite is produced in the tissue and carried away by the blood stream. Using these assumptions and applying pertinent data on capillaries, deductions are made concerning: (a) the law of blood flow as a function of temperature and capillary radius for the hyperemia of high temperature, (b) high flow as it depends on metabolism during strenuous exercise of muscle, and (c) a first approximation to the time duration of occlusion hyperemia.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476371
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  • 70
    Digitale Medien
    Digitale Medien
    Some Contributions to the Mathematical Biology of Blood Circulation. Reflections of pressure waves in the arterial system (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 109-109 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476375
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  • 71
    Digitale Medien
    Digitale Medien
    On dominance relations and the structure of animal societies: III The condition for a score structure (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 143-148 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The necessary and sufficient condition is given forn integers to be the score structure of a society with a dominance relation. A proof is also given for a theorem showing that there are members who dominate every other member either directly or indirectly through a single intermediate member.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476378
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  • 72
    Digitale Medien
    Digitale Medien
    Comments on the approximate solution of the diffusion equation: II (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 111-119 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract On the basis of a previous general formulation (Bull. Math. Biophysics,15, 21–29, 1953a) a discussion is given of the error in the approximation method of N. Rashevsky. This error, inherent in the method when the metabolic rate is different at each point in the cell, is discussed in detail and numerical values are presented for two particular cases: the rate proportional to the concentration and the rate a prescribed function of the spatial coordinates. It is shown that the formulation for the first case also applies to several other cases, that the error is negligible provided the rate is sufficiently small, and that the error is fairly sensitive to the cell size. If the rate depends upon the coordinatesalone a small rate is not sufficient to insure a negligible error. The relations between the exact method, the standard approximate method, an earlier approximate method (Physics,7 260, 1936), and a more recent refinement (Bull. Math. Biophysics,10, 201, 1948) of the standard method are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476376
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  • 73
    Digitale Medien
    Digitale Medien
    The kinetics of linear systems with special reference to periodic reactions (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 121-141 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is shown on the basis of (1) conservation of mass, (2) positive concentrations, and (3) the principle of detail balancing that periodic reactions cannot occur in a closed system described bylinear differential equations. The matrix,A, of the rate equations must be such that |A|=0,a ij〉0 fori≠j,a ii〈0, andVAV −1=B, whereV is diagonal andB is symmetric. These properties ofA imply that the latent roots are real and non-positive and that neither catalysis nor inhibition can be described bylinear equations. It is further shown that periodic reactions cannot occur in anopen system for which the matrix associated with the chemical reactions has the above properties and in which thesimple law of diffusion is obeyed. The relation of these results to Onsager's reciprocal relations and to previous work on periodic and cyclic chemical reactions is discussed. The utility of certain of these results for the treatment of isotope kinetics is indicated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476377
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  • 74
    Digitale Medien
    Digitale Medien
    A note on the flow of blood in capillary tubes (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 149-152 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is demonstrated that an explanation of the small radius effect or the so-called sigma phenomenon may be obtained by noting that one of the effects of the presence of suspended particles in a flowing fluid is to increase the velocity of flow near the wall over that existing in the absence of particles. This effect may be considered equivalent to relaxing the boundary conditions at the wall. An expression for the viscosity is compared with data and fit is found to be good.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476379
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  • 75
    Digitale Medien
    Digitale Medien
    Note on the Donnan equilibrium (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 153-159 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The solution for the spatial distribution of ions in a Donnan equilibrium has been given by J. H. Bartlett and R. A. Kromhout (1952). The present note gives an explicit solution for the case in which the length of the region containing the membrane is large; in biological situations this requires only that the length considered should be greater than a few hundred Ångstrom units. The Donnan equilibrium may be considered to be a special case of a situation in which forces other than electrical act upon the ions; in particular, it represents the case in which only one ion is acted upon and the energy difference on the two sides of the membrane is infinite. An expression is given for the difference in energy of theith in terms of the electrical potential and of the ion concentrations. As an illustration, the results are applied to nerve membrane potentials.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476380
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  • 76
    Digitale Medien
    Digitale Medien
    Some considerations on a carrier mechanism as a model for ion accumulation (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 161-165 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mechanism is described which accounts for the active transport of Na+ ions through a membrane. It is assumed that at one side of the membrane the ion combines with a carrier ion, the resulting carrier compound then diffuses through the membrane and decomposes at the other side of the membrane. The free diffusion of the ions is also taken into account. The time rate of accumulation of the ion in question at the latter side of the membrane is calculated in terms of the concentrations of the ion at both sides of the membrane.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476381
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  • 77
    Digitale Medien
    Digitale Medien
    Approximate treatment of the formation of a difference in the concentrations of an ion at the two sides of a membrane (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 167-171 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The recent extension of the approximation method is applied to enable us to arrive at the time course of the concentrations at both sides of a membrane. From the differential equations which govern these, the steady-state solution is obtained in terms of the parameters, which are determined by the thickness of the diffusion layers, the chemical composition and reactions, and the diffusion constant of the membrane.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476382
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  • 78
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    Digitale Medien
    Contribution to the mathematical theory of contagion and spread of information: I. Spread through a thoroughly mixed population (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 173-183 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An equation is derived from the spread of a “state” by contact through a thoroughly mixed population, in which the probability of transmission depends both on the over-all duration of the process and on the time an individual has been in the “state.” Cases in which this probability is a function of only one or the other of the two “times” are worked out. It is shown that in the case of dependence on “private time” alone the asymptotic value of the fraction of the population effected is the same as that derived by the random net approach.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476383
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  • 79
    Digitale Medien
    Digitale Medien
    Comments on the approximate solution of the diffusion equation: I (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 235-235 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476386
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  • 80
    Digitale Medien
    Digitale Medien
    Contributions to the mathematical biophysics of the cardiovascular system (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 185-195 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The reflection of pressure waves in a fluid enclosed within a tube with an elastic wall is studied for the case of a localized change in diameter of the tube. The concept of impedance is introduced. The relation of the reflection characteristics of the parts of the tube at either side of the change is derived on the basis of the continuity of pressure and mass flow at the site of the change. This relations is used to derive the expression for the ratio of the pressure oscillations measured in front of, and behind, the constriction in terms of the constants of the system. As a result, a method is indicated to locate the coarctation from measurements of the pressures in front of, and behind it.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476384
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  • 81
    Digitale Medien
    Digitale Medien
    On the subnormal variance in the counts of randomly distributed particles: I. Approximate treatment of the three-dimensional case and discussion of experiments (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 237-244 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The question is raised concerning the possible causes of abnormally small standard deviations found in counting samples in which particles are distributed at random (e.g., blood cells, fat globules in milk, etc.). The effect of discarding abnormal samples is discounted inasmuch as small standard deviations occur even when all samples are counted. An approximation method is used to calculate the effect of finite particle size, of known repulsive forces between particles and of convection currents. This calculation shows that neither finite size nor the known repulsive forces are sufficient to account for the observed abnormality of standard deviation, but that convection currents can possibly account for it. The possible presence of long-range repulsive forces cannot, however, be excluded.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476399
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  • 82
    Digitale Medien
    Digitale Medien
    On the subnormal variance in the counts of randomly distributed particles: II. Exact treatment of the one-dimensional case (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 245-250 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The effect of finite particle size on the standard deviation in sample counts is computed for the one-dimensional case. To a first order of approximation the correction is found to be identifical with that found by H. de Vries (1953) using a general approximation method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476400
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  • 83
    Digitale Medien
    Digitale Medien
    Outlines of a new theory of photoreception (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 251-260 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A critical examination of the “classical” theories of photoreception in view of more recent experimental findings yields the result that these theories do not possess the property to describe all the more significant phenomena of photoreception correctly, and to some extent suffer the lack of more general applicability. The basis for a new and presumably more general theory of photoreception based on dynamical aspects is laid out. Emphasis is put on the time course of afferent and efferent excitation in the photoreception model, consisting of a receptor element, an afferent and an efferent neuron of the one-factor Rashevsky-type, and an effector organ.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476401
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  • 84
    Digitale Medien
    Digitale Medien
    Outline of a mathematical approach to history (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 197-234 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model for the development of human society, beginning with the earliest stages of urban cultures, is outlined. In the early stages of history, behavior was characterized largely by adherence to a number of beliefs and prejudices of diffeirent kinds, which were accepted on faith and not subject to critical rational analysis. Due to psychobiological variability a very small number of individuals spontaneously appear at all times who challenge the accepted beliefs and prejudices and do not follow the accepted patterns of social behavior. The effect of these individuals upon the rest of the society, especially upon the younger generation, depends on the facilities with which information spreads in society. In earliest societies, when modern methods of mass communication were unknown, the channels of communication were practically identical with the channels of economic transport. The latter in its turn depended on the nature of the roads, and especially on the presence of waterway, which facilitated transportation. The sizes of the earliest cities and the distances between them were largely determined by relative ease of transporation. Expressions are derived for the average size of the earliest cities and for the average distance between them. The calculated average populations of the earliest cities are of the order of 103; the distance of the order of 102 km. Both are in agreement with some archaeological findings. An expression for the time spaon required for the development from the earliest stages of urban cultures to the present time is derived and shown to depend on the specific shoreline of the country, that is, the length of the shorline divided by the area of the country. It is pointed out that western Europe's specific shoreline, including land bordering both seas and rivers, is ten times as large as the shoreline area of other parts of the world. It is shown that this greater specific shoreline may account quantitatively for the faster social and technological development of western Europe in the last few centuries. The calculated total span of time of development from earliest urban cultures to our days is found to be of the order of magnitude of ten thousand years. It is shown that the model accounts for the existence at the present time of primitive cultures. A number of suggestions is made in regard to other possible applications of mathematics to history.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476385
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  • 85
    Digitale Medien
    Digitale Medien
    A note on the integral-equation description of metabolizing systems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 269-276 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The assumptions latent in the derivation of the integral equation of Branson are rendered explicit and discussed. It is shown that the equation is valid only for systems in which the substance disappears according to a linear rate law.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476403
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  • 86
    Digitale Medien
    Digitale Medien
    A critical investigation of the integral description of metabolizing systems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 261-268 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is shown that the validity of Branson's integral description of metabolizing systems is subject to severe limitations. The validity is insured only in cases where the reaction is of first order, or quasi of first order. In all other cases Branson's equation has to be modified to insure general applicability. The consequences of a different definition of the metabolizing functionF have also been investigated. With the new definitionF describes the pure effect of metabolization. It is found that in this case the integral equation is only capable of describing first-order reactions. With a slight modification of the integral equation it is possible to describe metabolites “with age”, which do not have reactions of definite order, but which satisfy the superposition principle.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476402
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  • 87
    Digitale Medien
    Digitale Medien
    On the statistical distribution of mutant bacteria (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 277-292 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A problem in probability is stated with included the problem of the distribution of bacterial mutants as a special case. This problem is solved exactly but since the resulting expressions are too complicated for practical use, various approximate expressions for the distribution are considered, especially for the bacterial mutation case.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476404
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  • 88
    Digitale Medien
    Digitale Medien
    Note on the neurobiophysical interpretation of imitative behavior (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 293-300 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Simple reaction and discrimination reaction, under the influence of imitation, are considered for the situation in which the stimulus or the stimuli vary slowly with time. The result is analogous to hysteresis under certain conditions. The calculations are facilitated by the solution of $$x = \int_{ - \infty }^{a + \beta x} {g\left( \xi \right)d} \xi ,$$ g(ξ) being the normal error function. Values ofx(α, β) are given in a table.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476405
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  • 89
    Digitale Medien
    Digitale Medien
    Blood flow in branching circulatory systems during rest and activity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 301-309 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract On the basis of simple physical considerations the blood flow in a branching circulatory system is studied. The case of two groups of parallel vessels is treated. The vessels of the same group are supposed to be identical. The resistance of each group is determined by the resistance of each vessel in the group and by the number of vessels in the group. From the dependence of the resistance of each vessel on its radius an expression is obtained for the blood flow through each group of vessels in terms of the numbers and sizes of the vessels in each group. The number of open vessels in an organ and the radius of each of those vessels are assumed to depend on the metabolic rate of that organ. The relations so obtained, together with the expression above, are applied to derive the blood flow through an organ as a function of the metabolic rate of that organ. It is indicated that the relations obtained might describe the shifting of blood from one organ to another if the activity of one of them changes. A way is pointed out to treat neural regulation of this phenomenon.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476406
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  • 90
    Digitale Medien
    Digitale Medien
    An age-dependent stochastic model of population growth (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 361-365 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A stochastic model of population growth is treated using the Bellman-Harris theory of agedependent stochastic branching processes. The probability distribution for the population size at any time and the expectation are obtained when it is assumed that there is probability (1−σ), 0≤σ〈1, of the organism dividing into two at the end of its lifetime, and probability σ that division will not take place.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476409
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  • 91
    Digitale Medien
    Digitale Medien
    Some quantitative aspects of history (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 339-359 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In a previous paper, in which a possible mathematical approach to history was outlined, it was shown that urbanization plays an important part in the propagation of new ideas. The rate of such propagation influences the rate of historical developments. The present paper deals in more detail with possible mechanisms of formation of earliest cities. Equations are derived which give the limiting size of such cities and their rate of growth. Of particular importance for the spread of new ideas is the spread of information. The latter largely depends on the fraction of individuals who travel between city and country. Expressions for this quantity are derived. An approach is outlined to the mathematical study of the earliest social classes, which may have been formed as a result of military, religious, or economic stratifications.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476408
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  • 92
    Digitale Medien
    Digitale Medien
    On the propagation of a disturbance through a viscous liquid flowing in a distensible tube of appreciable mass (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 395-409 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The velocity of propagation of a disturbance wave in a liquid flowing in a distensible tube is computed. The mathematical model is more general than those used in previous analyses: the tube wall properties are realistic; the convective part of the axial inertia forces is taken into account; radial inertia forces of both the fluid and tube wall are present; viscous stresses are present. Four parameters influencing the velocity of propagation are obtained and discussed. Curves are plotted illustrating the effects of the parameters. Contrary to the results of previous analyses, viscous effects are shown to be appreciable in blood flow. It is also shown that radial inertia effects can be important in laboratory set-ups.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476433
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  • 93
    Digitale Medien
    Digitale Medien
    Theory of the vacuum drying of frozen tissues (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 411-429 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A general theory of the drying of frozen tissue is developed and applied to the measurement of the drying rate of frozen guinea pig liver. It is shown that for a given temperature of the subliming ice crystals the mininum drying time of a piece of guinea pig liver is greater than the minimum sublimation time of a piece of ice of the same size and shape by a factor of the order of one thousand. This fact has many implications in the design of freeze-dry apparatus which will be developed in a following paper.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476434
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  • 94
    Digitale Medien
    Digitale Medien
    The time course of capillary exchange (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 477-488 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The equations governing the time course of the exchange of substances between the blood in the capillaries and the extracellular space are solved for the case of substances which do not penetrate the cells. The equations given relate the time course of the exchange process to the various tissue and circulation parameters such as the specific capillary wall area, the pore area, the inter-capillary distance, the size of the extra-vascular, extra-cellular space, the diffusion coefficient in this space, and the velocity of blood in the capillaries. Some experimental work on capillary exchange is discussed in relation to the theory and estimates are made of the relative importance of the various tissue and circulation parameters in the exchange of substances in different tissues.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476436
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  • 95
    Digitale Medien
    Digitale Medien
    Bioconversion of the sodium salt of Simvastatin (MK-733) to 6-desmethyl-6-α-hydroxymethyl Simvastatin (1991)
    Springer
    Journal of industrial microbiology and biotechnology 8 (1991), S. 157-164 
    Details
    ISSN: 1476-5535
    Schlagwort(e): Actinomycete ; Biotransformation ; pH control ; Magnesium sulfate ; MK-733 ; Simvastatin
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Summary An actinomycete (MA 6474, ATCC 53828) isolated from a soil sample (Mutare, Zimbabwe) was found to biotransform the sodium salt of Simvastatin (MK-733) to 6-α-hydroxymethyl MK-733, 6-β-hybroxymethyl MK-733, and 6-ring-hydroxy MK-733. The bioconversion efficiency to the desired compound, 6-α-hydroxymethyl MK-733, was enhanced by optimizing the physico-chemical parameters of the process. In shake flask cultures, addition of magnesium (0.125 mg/l Mg SO4·7H2O) to the medium resulted in a five-fold increase in the rate of bioconversion to the α diastereomer. The ratio of bioconversion products (6-α-hydroxymethyl, 6-β-hydroxymethyl, and 6-ring-hydroxy MK-733) was regulated by pH. Process improvements and scale up in 23-1 fermentors, which consisted of a controlled addition of substrate (MK-733), resulted in a 2-fold increase in alpha diastereomer Production (42 vs. 79 U/ml) and a 23-fold rate increase in the formation of α-diastereomer. A high diastereomeric ratio (α: β=9∶1) facilitated downstream processing.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01575848
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  • 96
    Digitale Medien
    Digitale Medien
    Fermentation study for the production of hepatitis B virus pre-S2 antigen by the methylotrophic yeastHansenula polymorpha (1991)
    Springer
    Journal of industrial microbiology and biotechnology 8 (1991), S. 147-156 
    Details
    ISSN: 1476-5535
    Schlagwort(e): Methanol ; Yeast extract ; Two-phase process ; Periplasmic antigen ; Intracellular antigen
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Summary Various physico-chemical parameters have been studied in order to improve the production of hepatitis B virus pre-S2 antigen (middle surface antigen) by the methylotrophic yeastHansenula polymorpha. Antigen production was done in two steps: first, production of cells on glycerol (Phase 1), followed by induction of antigen expression with methanol (Phase 2). Dense cultures ofH. polymorpha, equivalent to 35–40 g/l (dry weight), were readily obtained in small fermenters using minimal medium containing glycerol as carbon source. Antigen expression in this minimal medium, after induction with methanol, was however low and never exceeded 1.6 mg/l of culture. Antigen production was greatly enhanced by adding complex organic nitrogen sources along with methanol at induction time; yeast extract was the best of all the sources tested. In shake flasks, antigen production was proportional to yeast extract concentration up to 7% (w/v) yeast extract. it became clear that the nutritional conditions for good antigen expression were different from those for good biomass production. The effects of yeast extract were reproduced in small fermenters: antigen levels reached 8–9 mg/l in medium containing 6% (w/v) yeast extract during induction with methanol. The mechanisms of yeast extract's effects are still unknown but are probably nutritional. The recombinantH. polymorpha strain produced both periplasmic and intracellular antigen. The periplasmic antigen was shown to be present as 20–22-nm particles and was therefore immunogenic. Immunoblotting indicated that part of the pre-S2 antigen was present as a 24-kDa degradation product. These studies have led to a 140-fold increase in volumetric productivity of antigen and to a 4.6-fold increase in specific production.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01575847
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  • 97
    Digitale Medien
    Digitale Medien
    Effect of cultural conditions on production of eicosapentaenoic acid byPythium irregulare (1991)
    Springer
    Journal of industrial microbiology and biotechnology 8 (1991), S. 171-178 
    Details
    ISSN: 1476-5535
    Schlagwort(e): EPA ; Omega-3 ; Arachidonic acid ; Polyunsaturated fatty acid
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Summary The effect of culture conditions upon lipid content and fatty acid composition of mycelia ofPythium irregulare was investigated with particular attention to increasing the yield of 5,8,11,14,17-eicosapentaenoic acid (20∶5; ω−3) (EPA). All experiments were done by shake flask culture using a yeast extract + malt extract medium. The maximum growth rate was obtained at 25°C, but maximum EPA production was obtained at 12°C. The highest EPA production was 76.5 μg EPA/ml 13 days fermentation at 12°C. Addition of glucose during fermentation increased the yield considerably. The highest yield was 112 μg/ml, obtained at 13 days fermentation with spiking on day 11. Fermentation time could be shortened by initial incubation at 25°C for 2 days, followed by incubation at 12°C for 6 days. The culture also produced arachidonic acid and other ω-6 polyunsaturated fatty acids. EPA production was also obtained with lactose or sweet whey permeate, a by-product of cheese manufacture that contains lactose as the main carbohydrate.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01575850
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  • 98
    Digitale Medien
    Digitale Medien
    Production of arachidonic acid byMortierella alpina ATCC 32222 (1991)
    Springer
    Journal of industrial microbiology and biotechnology 8 (1991), S. 179-185 
    Details
    ISSN: 1476-5535
    Schlagwort(e): Mortierella alpina ; Arachidonic acid ; Polyunsaturated fatty acid ; Fungal lipid
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Summary WhenMortierella alpina ATCC 32222 was incubated in a glucose salts medium at 25°C the biomass (17.5 g/l) contained 9.62% arachidonic acid which amounted to 54% (w/w) of total biomass lipids. When the glucose concentration in the medium was varied from 0 to 150 g/l, the percentage of arachidonic acid in biomass and in lipids was highest at a glucose concentration of 30 g/l, but highest yield of arachidonic acid per litre of culture broth was observed at a glucose concentration of 100 g/l. While production of biomass reached a plateau of 17 g/l after a 3-day incubation at 25°C, the percentage of arachidonic acid in lipids and biomass increased dramatically from 3 to 6 days with a concurrent arachidonic acid yield increase from 0.89 to 1.63 g/l. Optimum initial culture pH for arachidonic acid production was in the range 6.0–6.7. By increasing the concentration of the glucose salts medium three-fold, yields of biomass and arachidonic acid were increased to 35.8 g/l and 3.73 g/l, respectively.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01575851
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  • 99
    Digitale Medien
    Digitale Medien
    Sch 42029, a naturally produced dopamine receptor ligand: Taxonomy, fermentation, isolation and structure (1991)
    Springer
    Journal of industrial microbiology and biotechnology 8 (1991), S. 187-192 
    Details
    ISSN: 1476-5535
    Schlagwort(e): Dopamine receptor ; Agonist and antagonist ; Ligand ; Dihydroxy acetanilide
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Summary A natural product, Sch 42029, isolated from the fermentation of anActinoplanes sp. (SCC 1971) was found to displace Sch 23390 from the dopamine-1 (D1) receptor. The compound was isolated from the fermentation broth by adsorption of the filtrate on XAD-16 resin, elution with water-methanol, followed by purification by gel-permeation chromatography and HPLC. Using spectroscopic analysis, the structure was determined to be 2,5-dihydroxy acetanilide. The pure compound displaced Sch 23390, a D1-selective ligand, at aK i of 1.6 μm and spiperone, a D2-selective ligand, at aK i of 200 μm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01575852
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  • 100
    Digitale Medien
    Digitale Medien
    The assimilation of organic hazardous wastes by municipal solid waste landfills (1991)
    Springer
    Journal of industrial microbiology and biotechnology 8 (1991), S. 193-199 
    Details
    ISSN: 1476-5535
    Schlagwort(e): Organic hazardous waste ; Leachate ; Landfill management
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Summary Co-disposal of 12 compounds representing major organic classes (aromatic hydrocarbons, halogenated hydrocarbons, pesticides, phenols, and phthalate esters) with shredded municipal solid waste was tested using a laboratory-scale column and pilot-scale lysimeter to characterize transport and transformation phenomena including sorption, volatilization and bioassimilation. Leachate and gases emitted from the lysimeters were examined for identifiable products of biotransformation. The results of this investigation provided a mechanistic evaluation of the attenuating and assimilative capacity of municipal solid waste landfills for specific organic compounds. Physical/chemical organic compound characteristics were related to refuse characteristics and composition to predict compound fate. Such knowledge is useful in developíng landfill management and operational strategies consistent with the need for control of pollutant releases.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01575853
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