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  • Springer  (669,031)
  • Institute of Physics  (129,244)
  • American Meteorological Society
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  • 1
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    Electronic Resource
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 137-144 
    ISSN: 1476-5535
    Keywords: Composting ; Explosives ; Propellants ; Thermophilic ; Mesophilic ; Bioremediation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Composting was investigated as a bioremediation technology for clean-up of sediments contaminated with explosives and propellants. Two field demonstrations were conducted, the first using 2,4,6-trinitrotoluene (TNT), octahydro-1,3,5,7-tetranitro-1,3,5,7-tetraazocine (HMX), hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), and N-methyl-N,2,4,6-tetranitroaniline (tetryl) contaminated sediment, and the second using nitrocellulose (NC) contaminated soil. Tests were conducted in thermophilic and mesophilic aerated static piles. Extractable TNT was reduced from 11840 mg/kg to 3 mg/kg, and NC from 13090 mg/kg to 16 mg/kg under thermophilic conditions. Under mesophilic conditions, TNT was reduced from 11 190 mg/kg to 50 mg/kg. The thermophilic and mesophilic half-lives were 11.9 and 21.9 days for TNT, 17.3 and 30.1 days for RDX, and 22.8 and 42.0 days for HMX, respectively. Known nitroaromatic transformation products increased in concentration over the first several weeks of the test period, but decreased to low concentrations thereafter.
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  • 2
    ISSN: 1476-5535
    Keywords: Fructo-oligosaccharide ; 1-Kestose ; Glycoprotein ; Fructosyl-transferring activity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Two extracellular β-fructofuranosidases (E-1 andE-2) fromAureobasidium sp. ATCC 20524, producing 1-kestose (1F-β-fructofuranosyl-sucrose) from sucrose, were purified to homogeneity. Molecular weights of the enzymes were estimated to be about 304000 (E-1) and 315000 (E-2) Da by gel filtration. The enzymes contained 33% (w/w) (E-1) and 27% (w/w) (E-2) carbohydrate. TheK m values for sucrose ofE-1 andE-2 andE-2 were 0.34 and 0.28 M, respectively. were 0.34 and 0.28 M, respectively. The enzymatic profiles of these enzymes were almost identical to intracellular enzymesP-1 andP-2 except for the differences in carbohydrate content andK m values ofE-2 andP-2.
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  • 3
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 149-161 
    ISSN: 1476-5535
    Keywords: Toxin ; Secondary plant metabolite ; Allelochemical ; Insecticide ; Mycotoxin ; Endocytobiont
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Many species of insects cultivate, inoculate, or contain symbiotic fungi. Insects feed on plant materials that contain plant-produced defensive toxins, or are exposed to insecticides or other pesticides when they become economically important pests. Therefore, it is likely that the symbiotic fungi are also exposed to these toxins and may actually contribute to detoxification of these compounds. Fungi associated with bark beetles, ambrosia beetles, termites, leaf-cutting ants, long-horned beetles, wood wasps, and drug store beetles can variously metabolize/detoxify tannins, lignins, terpenes, esters, chlorinated hydrocarbons, and other toxins. The fungi (Attamyces) cultivated by the ants and the yeast (Symbiotaphrina) contained in the cigarette beetle gut appear to have broad-spectrum detoxifying abilities. The present limiting factor for using many of these fungi for large scale detoxification of, for example, contaminated soils or agricultural commodities is their slow growth rate, but conventional strain selection techniques or biotechnological approaches should overcome this problem.
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  • 4
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 163-172 
    ISSN: 1476-5535
    Keywords: Biosensors ; Process control ; Enzyme thermistor ; Immunoassay ; Bio-field effect transistor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A short review about the biosensor research activities for bioprocess monitoring in the F.R.G. after its reunification is given. The principles of biosensor applications are presented. In situ sensors and sensors based on the principles of flow injection analysis are studied. Some applications of a four-channel enzyme thermistor, bio-field effect transistors, and immunoanalysis systems for real process monitoring are presented.
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  • 5
    ISSN: 1476-5535
    Keywords: Vibrio vulnificus ; Oyster ; Monoclonal antibody ; Most probable number ; Enzyme immunoassay
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Oysters, suspended particulate matter (SPM), sediment and seawater samples were collected from West Galveston Bay, Texas over a 16-month period and analyzed for the presence ofVibrio vulnificus, a naturally-occurring human marine pathogen. Detection and enumeration ofV. vulnificus was performed using a species-specific monoclonal antibody (mAb FRBT37) in an enzyme immunoassay (EIA)-most probable number (MPN) procedure capable of detecting as few as 2000 target organisms.V. vulnificus was not detected in seawater, oyster or SPM samples during the cold weather months, but was detected at low levels in several sediment samples during this time period. Increased levels of the organism were first observed in early spring in the sediment, and then in SPM and oysters. The major increase inV. vulnificus occurred only after the seawater temperature had increased above 20°C and the winter-spring rainfall had lowered the salinity below 16‰. The highestV. vulnificus levels at each site were associated with suspended particulate matter. These results are consistent with the hypothesis that (1)V. vulnificus over-winters in a floc zone present at the sediment-water interface, (2) is resuspended into the water column in early spring following changes in climatic conditions, (3) colonizes the surfaces of zooplankton which are also blooming during early spring and (4) are ingested by oysters during their normal feeding process.
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  • 6
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 235-238 
    ISSN: 1476-5535
    Keywords: Biodegradation ; Pseudomonas putida ; Immobilization ; Sodium cyanide
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Pseudomonas putida, isolated from contaminated industrial wastewaters and soil sites, was found to utilize sodium cyanide (NaCN) as a sole source of carbon and nitrogen. Cells, immobilized in calcium alginate beads (1–2 mm diameter) were aerated in air-uplift-type fluidized batch bioreactor containing 100–400 ppm of NaCN. Degradation of NaCN was monitored for 168 h by analyzing gaseous and dissolved ammonia (NH3), CO2, pH and optical density. The results indicated that the alginate-immobilized cells ofP. putida were able to degrade NaCN into NH3 and CO2 in a time-dependent manner.
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  • 7
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 229-234 
    ISSN: 1476-5535
    Keywords: Heat shock protein (HSP) ; Yeast ; Saccharomyces ; Viability ; Thermotolerance ; Ethanol tolerance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Heat shock and ethanol stress of brewing yeast strains resulted in the induction of a set of proteins referred to as heat shock proteins (HSPs). At least six strongly induced HSPs were identified in a lager brewing strain and four HSPs in an ale brewing strain. Four of these HSPs with molecular masses of approximately 70, 38, 26 and 23 kDa were also identified in two laboratory strains ofSaccharomyces cerevisiae. The appearance of HSPs correlated with increased survival of strains at elevated temperatures and high concentrations of ethanol. These results suggest that HSPs may play a role in the ethanol and thermotolerance of yeasts. The properties of these proteins and membrane fatty acids in relation to heat and ethanol shock are being investigated.
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  • 8
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 239-245 
    ISSN: 1476-5535
    Keywords: Novel polysaccharide ; Bacillus licheniformis ; Raffia venifera ; d-Glucose ; d-Mannose ; d-Xylose
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A polysaccharide producing strain ofBacillus licheniformis was isolated from exudate of raffia palm,Raffia vinifera. The optimum conditions for growth and polysaccharide production have been investigated and established. No appreciable polysaccharide was formed on glucose. It grew best in Czapek-Dox media with sucrose as the carbon source. The polysaccharide has been characterized as a heteropolymer containingd-glucose,d-mannose andd-xylose.
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  • 9
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 269-269 
    ISSN: 1476-5535
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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  • 10
    ISSN: 1476-5535
    Keywords: β-Fructofuranosidase ; Deglycosylation ; Aureobasidium ; Enzymatic stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Most of the carbohydrate moiety of β-fructofuranosidaseP-1 fromAureobasidium sp. ATCC 20524 was removed by endo-β-N-acetylglucosaminidase F. A subunit of 94000 Da was observed in SDS-PAGE after deglycosylation. TheK m value for sucrose was not changed by deglycosylation but the stability at pH 4–5 and 50°C was decreased. The deglycosylated enzyme was more sensitive to proteases such as pronase E and subtilisin than the native enzyme. It is considered that the carbohydrate moiety of β-fructofuranosidaseP-1 contributes to the stability of the enzyme but is not essential in its catalytic function.
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  • 11
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    Bulletin of mathematical biology 52 (1990), S. 153-197 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 12
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    Bulletin of mathematical biology 52 (1990), S. 319-334 
    ISSN: 1522-9602
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  • 13
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    Bulletin of mathematical biology 52 (1990), S. 335-337 
    ISSN: 1522-9602
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  • 14
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    Bulletin of mathematical biology 52 (1990), S. I 
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  • 15
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    Bulletin of mathematical biology 52 (1990), S. 335-348 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 16
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    Bulletin of mathematical biology 52 (1990), S. 349-358 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: 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.
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  • 17
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    Bulletin of mathematical biology 52 (1990), S. 509-525 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 18
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    Bulletin of mathematical biology 52 (1990), S. 527-534 
    ISSN: 1522-9602
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    Notes: 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.
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  • 19
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    Bulletin of mathematical biology 52 (1990), S. 535-547 
    ISSN: 1522-9602
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    Notes: 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.
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  • 20
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    Bulletin of mathematical biology 52 (1990), S. 583-596 
    ISSN: 1522-9602
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  • 21
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    Bulletin of mathematical biology 52 (1990), S. I 
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  • 22
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    Bulletin of mathematical biology 52 (1990), S. 549-582 
    ISSN: 1522-9602
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    Notes: 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.
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  • 23
    ISSN: 1522-9602
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    Notes: 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.
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  • 24
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    Bulletin of mathematical biology 53 (1991), S. 281-312 
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  • 25
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    Bulletin of mathematical biology 53 (1991), S. 253-279 
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  • 26
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    Bulletin of mathematical biology 53 (1991), S. 313-326 
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  • 27
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    Bulletin of mathematical biology 53 (1991), S. I 
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  • 28
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  • 29
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    Bulletin of mathematical biology 53 (1991), S. 345-353 
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    Notes: 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.
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    Bulletin of mathematical biology 53 (1991), S. 327-343 
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    Notes: 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.
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    Bulletin of mathematical biology 53 (1991), S. 579-589 
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    Notes: 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.
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  • 32
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    Notes: 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.
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  • 33
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    Bulletin of mathematical biology 53 (1991), S. 657-663 
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    Bulletin of mathematical biology 53 (1991), S. 881-899 
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    Notes: 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.
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    Bulletin of mathematical biology 53 (1991), S. 911-940 
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    Notes: 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.
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    Bulletin of mathematical biology 54 (1992), S. 1-20 
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    Notes: Abstract An organism persists only if it satisfies internal and external constraints. Within the organism networks of processes meet the constraints. In such networks a principle of matching often obtains: the pattern of coupling among processes matches the correlation among constraints. That is, a module—a cluster of coupled processes—meets a constraint. Dissociable modules meet dissociàble constraints. A hierarchy of modules meets a hierarchy of constraints. We have inquired whether such matching is predicted by an optimality criterion in a simple example. We find that in an ensemble of networks with unreliable processes, the networks that meet the constraints with highest reliability obey the principle of matching. The difference in reliability between modular and nonmodular networks that meet the same constraints is a function of the probability of success per process. Our results suggest that this difference is maximal at a probability of success that increases monotonically with the number of processes in the network.
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    Bulletin of mathematical biology 54 (1992), S. 59-75 
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    Notes: Abstract A method is described for estimating the distribution and hence testing the statistical significance of sequence similarity scores obtained during a data-bank search. Maximum-likelihood is used to fit a model to the scores, avoiding any costly simulation of random sequences. The method is applied in detail to the Smith-Waterman algorithm when gaps are allowed, and is shown to give results very similar to those obtained by simulation.
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    Bulletin of mathematical biology 54 (1992), S. 401-412 
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    Notes: Abstract We develop a theory for host seeking decisions in mosquitoes that explicitly considers the tradeoffs mosquitoes face in allocation to somatic and gametic function. Specifically, we consider conditions under which mosquitoes should seek out nectar and blood hosts upon encountering host odours. Results from development of a dynamic model that considers free and crop energy states suggest that mosquitoes should seek out blood hosts under a wide variety of conditions but that decisions to seek nectar depends upon crop volume, concentration and free energy. This pattern arises because mosquitoes carrying large crop loads are constrained in their ability to obtain large blood meals due to space limitations in the abdomen. The predicted patterns of behaviour are supported by published observations of mosquito behaviour.
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    Bulletin of mathematical biology 54 (1992), S. 413-422 
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    Notes: Abstract In behavioral ecology, diet selection is often predicted by using a theory in which it is assumed that behaviors have evolved to maximize the rate of intake of energy. In this theory, it is assumed that fitness is a monotonic function of energy intake. An alternative is to deal directly with fitness, measured in terms of expected reproduction, and thus connect short term behavior with reproduction. Following the usual assumptions of the theory of diet choice, fitness satisfies a partial differential-difference equation. Conditions under which rate maximizing and state variable theories of diet selection yield identical predictions are identified. When predation, as well as starvation, is a source of mortality, the identification is not as complete.
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    Bulletin of mathematical biology 54 (1992), S. 445-464 
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    Notes: Abstract Environmental uncertainty can be both a cause and consequence of chance variation in many of the phenotypic factors associated with the control of clutch size in birds. When such uncertainty inflates or otherwise influences the variance associated with expected reproductive success for any genotype, it will also influence the resulting phenotypic optima. Random variation that affects the evolution of clutch size optima explicitly may occur both within (intra-) and across (inter-) generations. Examples of intra-generational uncertainty could include chance variation in: (1) the quality and quantity of offspring, (2) parental quality, and (3) temporal resources like food. Inter-generational uncertainty would include chance variation in demographic and population characters. With respect to clutch (or litter) size, almost all forms of uncertainty tend to favor an optimum (genetic) strategy with a clutch that is smaller than the clutch associated with the apparent or actual maximal fitness of an individual parent. The overall effect of all the components of uncertainty can be evaluated through the integration of all this phenotypic variation: however each step of the integration is a conditional expectation of each component. Therefore, a single factor analysis may indicate a false optimum, and an integrated analysis of all components is necessary to evaluate the importance of their individual and joint effects on the adaptive evolution of clutch size.
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    Bulletin of mathematical biology 54 (1992), S. 503-519 
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    Notes: Abstract A difference equation model for the dynamics of a semelparous size-structured species consisting of juvenile and adult individuals is derived and studied. The adult population consists of two size classes, a smaller class and a larger more fertile class. Negative feedback occurs through slowed juvenile growth due to increased total population levels during the developmental period and consequently a smaller adult size at maturation. Intra-specific competition coefficients are size dependent and measure the strength of intra-specific competition between juveniles and adults. It is shown that equilibrium states in which adults and juveniles occur together at all times are in general destabilized by significantly increased juvenilevs adults competition with the result that stable periodic cycles appear, in which the generations alternate in time and hence avoid competition. This result supports the tenet that intra-specific competition between juveniles and adults is destabilizing. Exceptions to this destabilization principle are found, however, in which populations exhibiting non-equilibrium, aperiodic dynamics can be equilibrated by increase competition between juveniles and adults. This occurs, for example, when adult fertility and competition coefficients are significantly size class dependent.
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    Bulletin of mathematical biology 54 (1992), S. 537-561 
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    Notes: Abstract An epithelial cell is modeled as a single compartment, bounded by apical and basolateral cell membranes, and containing two nonelectrolyte solute species, nominally NaCl and KCl. Membrane transport of these species may be metabolically driven, or it may follow the transmembrane concentration gradients, either singly (a channel) or jointly (a cotransporter). To represent the effect of stretch-activated channels or shrinkage-activated cotransporters, the membrane permeabilities and cotransport coefficients are permitted to be functions of cell volume. When this epithelium is considered as a dynamical system, conditions are indicated which guarantee the uniqueness and stability of equilibria. Experimentally, many epithelial cells can regulate their volume, and such volume regulatory capability is defined for this model. It is clearly distinct from dynamical stability of the equilibrium and requires more stringent conditions on the volume-dependent permeabilities and cotransporters. For a previously developed model of the toad urinary bladder (Strieteret al., 1990,J. gen. Physiol. 96, 319–344) the uniqueness and stability of its equilibria are indicated. The analysis also demonstrates that under some conditions a second stable equilibrium may appear, along with a saddle-node bifurcation. This is illustrated numerically in a modified model of the epithelium of the thick ascending limb of Henle.
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    Bulletin of mathematical biology 54 (1992), S. 687-694 
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    Bulletin of mathematical biology 54 (1992), S. 649-672 
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    Notes: Abstract Models of the dynamical interactions important in generating immune reactivity have generally assumed that the immune system is a single well-stirred compartment. Here we explicitly take into account the compartmentalized nature of the immune system and show that qualitative conclusions, such as the stability of the immune steady state, depend on architectural details. We examine a simple model idiotypic network involving only two types of B cells and antibody molecules. We show, for model parameters used by De Boeret al. (1990,Chem. Eng. Sci. 45, 2375–2382), that the immune steady state is unstable in a one compartmental model but stable in a two compartment model that contains both a lymphoid organ, such as the spleen, and the circulatory system.
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    Bulletin of mathematical biology 54 (1992), S. 839-873 
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    Notes: Abstract Using the chromium release assay and the single cell assay in agarose, we study the cytotoxic reaction of the MHC-restricted T lymphocyte clones P89:15 and P1:3, which recognize distinct but specific tumour antigens on the surface of syngeneic P815 mastocytoma cells. We propose a mathematical model which describes these experiments, accounts for the strongly non-Michaelian behaviour of the reaction and permits us to estimate the kinetic parameters characterizing effector-target conjugation and lethal hit delivery. The results show that the binding and lytic activity of effector cells is modulated by the number of targets bound to them. The binding of a second target by an effector having already a target bound is facilitated; on the other hand, an effector having bound two targets delivers a lethal hit more slowly than one with a single target bound. We investigate the role of these kinetic properties in the competition between the process of tumour progression due to cancer cell replication and the process of tumour regression due to T lymphocyte cytotoxic activity. For both clones, we estimate the effector-target ratio beyond which rejection prevails. This ratio is nine times larger for P1:3 than for P89:15. Furthermore, our analysis suggests that there exists an optimal specificity minimizing this ratio. Deviations from this optimum, be it in the sense of an increase or decrease of specificity, tendsto stabilize the tumoural state: a situation which in the broader context of the immune response evolution and regulation can be viewed as animmune response dilemma.
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    Bulletin of mathematical biology 54 (1992), S. 929-938 
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    Notes: Abstract In this paper a stochastic model for a two-compartment system which incorporates Erlang residence time distributions (i.e. the residence times have the gamma distribution where the shape parameters assume integer values only) into each compartment is generalized to include random rate coefficients. Analytical forms of the model are derived for the case where the rate coefficients have gamma densities. A relationship is established between the new models and existing models that are in current practical usage.
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    Bulletin of mathematical biology 54 (1992), S. 939-955 
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    Notes: Abstract Oscillations and chaos can be modelled and observed in a realistic simulation model of interacting prey-predator populations based on Monte Carlo simulation methods. These nonlinear phenomena are linked with some biological and physical bifurcation parameters and mathematical tools from dynamical systems theory may be used in order to characterize this behaviour. Chaotic dynamics are therefore, in our simulation, more the rule than the exception, and are related to delays associated with spatial degrees of freedom.
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    Bulletin of mathematical biology 54 (1992), S. 1023-1038 
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    Notes: Abstract Cells displaying the classic multidrug resistant (MDR) phenotype possess a transmembrane protein (p170 or P-glycoprotein) which can actively extrude cytotoxic agents from the cytoplasm. A mathematical model of this drug efflux pump has been developed. Outward transport is modeled as a facilitated diffusion process. Since energy-dependent efflux of cytotoxic agents requires that ATP also bind to p170, the model includes a dynamic calculation for efflux rate which considers Michaelis-Menten kinetics for both the substrate agent and ATP. The final system consists of one partial differential equation (PDE) for the facilitated diffusion of substrate agents out of the cell a 2×2 ordinary differential equation (ODE) system for the dynamic calculation of the ATP-ADP pool, and a dynamic algebraic calculation of the efflux rate given substrate levels at the interior cell membrane interface and ATP levels in the cell. A stability analysis of the ATP-ADP pool distribution and a simplistic closed form solution of the linearized PDE are included. Numerical simulations are also provided.
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    Bulletin of mathematical biology 54 (1992), S. 1039-1056 
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    Notes: Abstract Reentry in the heart is the repeated excitation of the same tissue by a single excitation wave; it is responsible for several types of cardiac arrhythmia. The simplest model which permits the phenomenon of reentry is two laterally coupled excitable fibers; in this paper we examine such a model in order to establish a basis for the understanding of the fundamental physical processes underlying the process of reentry. Two versions of the FitzHugh-Nagumo equations are used to develop complementary numerical and analytical results for the coupled fiber model. On the basis of numerical studies, regions of qualitatively different behaviour are mapped in the parameter space of excitation threshold and coupling strength between the fibers, and the effect of the rate of recovery is explored. Some of these regions are also obtained analytically, in good agreement with the numerical results. Finally, the results are discussed in the light of recent work on the role of the anisotropy of cardiac tissue in the initiation of reentrant activity in the heart.
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    Bulletin of mathematical biology 54 (1992), S. 1069-1081 
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    Notes: Abstract A sigmoid curve with three fitting parameters is proposed as a descriptive model for the spatial velocity field in one-dimensional growth of plant organs. Analytic expressions are derived for the relative elemental growth (REG) rate, the position and value of the REG rate maximum, the length of the growth zone, the inverse of the growth trajectory and cell length in the “elongation only” zone. The expressions are fit to published data to characterize the effects of environmental variation on growth of monocotyledonous roots. The simple expressions for growth may prove useful in mechanistic models. The fitted curves summarize more than a decade of observations and thus provide a challenge to theorists.
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    Bulletin of mathematical biology 55 (1993), S. 1-13 
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    Notes: Abstract A simple one-dimensional model of single-species populations is studied by means of computer simulations. Although the model has a rich spectrum of dynamics including chaotic behavior, the introduction of survival thresholds makes the chaotic region so small that it can be hardly observed. Stochastic fluctuations further reduce the chaotic region because they accidentally lead populations to extinction. The model thus naturally explains the observation that the majority of natural populations do not show chaotic behavior but a monotonic return to a stable equilibrium point following a disturbance.
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    Notes: Abstract Current understanding of the pattern of proliferation within intestinal crypts involves the notion of a cutoff region introduced by Cairnieet al. (Exp. Cell. Res. 39, 539–553, 1965b). (Cells produced above the cutoff are non-cycling, whereas cells produced below the cutoff are cycling.) They contrasted the predicted distribution of proliferation in the extreme cases of a cutoff of width 0 (a sharp cutoff) with one eight cells wide (a slow cutoff) and concluded that the data were better explained by the latter. We have shown that crypt size variation artificially broadens the apparent distribution of proliferating cells in the crypt (Totafurnoet al., Biophys. J. 54, 845–858, 1988). Here we show that the measurement and analysis of crypts of a specified height reduces this artifact. This work introduces the use of distance from the crypt base (in microns) to specify the location of cells within the crypt as an improvement over the cell position ordering traditionally used in the determination of the distribution of proliferating cells. We also show how to explicitly correct for several artifacts in the measurement of the labelling index. We conclude that cell proliferation within the crypt is more localized than previously realized; in fact, a cutoff as slow as eight cells wide is rejected.
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    Bulletin of mathematical biology 55 (1993), S. 141-154 
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    Notes: Abstract Multiple string (sequence) alignment is a difficult and important problem in computational biology, where it is central in two related tasks: finding highly conserved subregions or embedded patterns of a set of biological sequences (strings of DNA, RNA or amino acids), and inferring the evolutionary history of a set of taxa from their associated biological sequences. Several precise measures have been proposed for evaluating the goodness of a multiple alignment, but no efficient methods are known which compute the optimal alignment for any of these measures in any but small cases. In this paper, we consider two previously proposed measures, and given two computationaly efficient multiple alignment methods (one for each measure) whose deviation from the optimal value isguaranteed to be less than a factor of two. This is the novel feature of these methods, but the methods have additional virtues as well. For both methods, the guaranteed bounds are much smaller than two when the number of strings is small (1.33 for three strings of any length); for one of the methods we give a related randomized method which is much faster and which gives, with high probability, multiple alignments with fairly small error bounds; and for the other measure, the method given yields a non-obviouslower bound on the value of the optimal alignment.
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    Bulletin of mathematical biology 55 (1993), S. 197-212 
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    Notes: Abstract The kinematics of helical motion are descirbed for an organism treated as a rigid body with six degrees of freedom relative to the organism's frame of reference, i.e. the organism can translate in the direction of, or rotate around any of, three orthogonal axes fixed to its body. Equations are derived that express the unit vectors of the Frenet trihedron and the torsion and curvature of the trajectory in terms of the organism's translational and rotational velocities. These equations permit description of the radius, pitch, angular velocity and axis of a helical trajectory in terms of the translational and rotational velocities of the organism swimming along that trajectory. The results of this analysis are then used in two later papers that describe how organisms can orient to an external stimulus.
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    Bulletin of mathematical biology 55 (1993), S. 257-257 
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    Bulletin of mathematical biology 55 (1993), S. 231-255 
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    Notes: Abstract Organisms that move along helical trajectories change their net direction of motion largely by changing the direction, with respect to the body of the organism, of their rotational velocity (Crenshaw and Edelstein-Keshet, 1993,Bull. math. Biol. 55, 213–230). This paper demonstrates that an organism orients to a stimulus field, such as a chemical concentration gradient or a ray of light, if the components of its rotational velocity, with respect to the, body of the organism, are simple functions of the stimulus intensity encountered by the organism. For example, an organism can orient to a chemical concentration gradient if the rate at which it rotates around its anterior-posterior axis is proportional to the chemical concentration it encounters. Such an orientation can be either positive or negative. Furthermore, it is true taxis—orientation of the axis of helical motion is direct. It is neither a kinesis nor a phobic response—there is no random component to this mechanism of orientation.
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    Bulletin of mathematical biology 55 (1993), S. 277-294 
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    Notes: Abstract A basic but neglected property of neuronal trees is their finite length. This finite length restricts the length of a segment to a certain maximum. The implications of the finite length of the tree with respect to the segment length distributions of terminal and intermediate segments are shown by means of a stochastic model. In the model it is assumed that branching is governed by a Poisson process. The model shows that terminal segments are expected to be longer than intermediate segments. Terminal and intermediate segments are expected to decrease in length with incrasing centrifugal order. The results are compared with data fromin vivo pyramidal cells from rat brain and tissue cultured ganglion cells from chicken. A good agreement between data and model was found.
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    Bulletin of mathematical biology 55 (1993), S. 345-364 
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    Notes: Abstract Shape and size of elongating cells were examined in three plant tissues: the adaxial epidermis of the petiole ofZebrina pendula L., the abaxial epidermis ofAnacharis densa L. leaves and the abaxial epidermis of the scale leaf ofAllium cepa L. Based on a few simple assumptions, the expected probability distribution frequencies (pdf) for cell length and number of adjacent walls were calculated. Actual data of cell lengths closely approximated those expected with the pdfs being asymmetrical since there are more younger, shorter cells than older, longer cells. Data for number of lateral walls of real cells were similar to that expected and these walls increase in compensating mechanism exists to maintain a constant range of cell lengths through many cell generations. It is expressed by longer than average new daughter cells dividing relatively soon while shorter than average new daughter cells divide after a relatively long cycle.
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    Bulletin of mathematical biology 55 (1993), S. 365-384 
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    Notes: Abstract Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism for pattern formation in numerous embryological and ecological contexts. However, the possible effects of environmental inhomogeneities has received relatively little attention. We consider a general two species reaction-diffusion model in one space dimension, with one diffusion coefficient a step function of the spatial coordinate. We derive the dispersion relation and the solution of the linearized system. We apply our results to Turing-type models for both embryogenesis and predator-prey interactions. In the former case we derive conditions for pattern to be isolated in one part of the domain, and in the latter we introduce the concept of “environmental instability”. Our results suggest that environmental inhomogeneity could be an important regulator of biological pattern formation.
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    Notes: Abstract The particular dynamics of the previously proposed model of a catalytic network formed byn error-prone self-replicative species without and with superimposed competition is analysed. In the first case, two situations are studied in detail: a uniform network in which all the species are inter-coordinated in the same way, and a network with a species differentiated in its catalytic relation with the remaining elements. In the second case, the superimposed competition is introduced at two levels: first, as an asymmetry in one of the network species amplification factor considering a null self-catalytic vector, and secondly, as a non-null self-catalytic vector with no asymmetry in the other propertics of the species. This kind of system does not present complex behaviour and can be adequately deseribed by performing a standard linear analysis, which gives direct information on the asymptotic behaviour of the sytem. Finally, the biological implications of this analysis within the framework of biological evolution are discussed.
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    Bulletin of mathematical biology 55 (1993), S. 451-464 
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    Notes: Abstract A theoretical model is proposed for the formation of cell distribution patterns in the slug stage of the cellular slime moldDictyostelium discoideum. The equilibrium distribution of two types of cells, prestalk and prespore, is obtained by minimizing the free energy, which is defined in terms of differential chemotaxis, differential cell adhesion and randomness of cell movement. Resulting distributions show various segregation patterns of cell types. The condition for cell sorting is obtained from stability analysis of the set of diffusion equations governing the evolution of cell type distribution and the concentration of chemoattractant. The intensities of differential chemotaxis and random cell movement are quantitatively evaluated from experimental data to show that two cell types can sort themselves completely by these forces.
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    Bulletin of mathematical biology 55 (1993), S. 655-674 
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    Notes: Abstract Multicell spheroids, small spherical clusters of cancer cells, have become an importantin vitro model for studying tumour development given the diffusion limited geometry associated with many solid tumour growths. Spheroids expand until they reach a dormant state where they exhibit a grossly static three-layered structure. However, at a cellular level, the spheroid is demonstrably dynamic with constituent cells migrating from the outer well-nourished region of the spheroid toward the necrotic central core. The mechanism that drives the migrating cells in the spheroid is not well understood. In this paper we demonstrate that recent experiments on internationalization can be adequately described by implicating pressure gradients caused by differential cell proliferation and cell death as the primary mechanism. Although chemotaxis plays a role in cell movement, we argue that it acts against the passive movement caused by pressure differences.
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    Bulletin of mathematical biology 55 (1993), S. 675-691 
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    Bulletin of mathematical biology 55 (1993), S. 693-693 
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    Bulletin of mathematical biology 55 (1993), S. 695-713 
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    Notes: Abstract In recent years, methods of consensus, developed for the solution of problems in the social sciences, have become widely used in molecular biology. Westudy a method of consensus originally due to Watermanet al. (Waterman, Galas and Arratia. 1984. Pattern recognition in several sequences: consensus and alignment.Bull. math. Biol. 46, 515–527) which is used to identify patterns or features in a molecular sequence where a pattern can vary in position within a given window. We show that some well-known consensus methods of the social sciences, the median and the mean, are special cases of this method for certain choices of the parameters used in it and give a precise account of the parameters for which these special cases arise. We also show that the specific parameters used in the method of Watermanet al. make their method equivalent to the median procedure which is widely used in the social sciences.
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    Bulletin of mathematical biology 55 (1993), S. 745-780 
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    Notes: Abstract We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation, B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis, how each of the processes influences the model's behavior. After appropriate nondimensinalization, the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-tye equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior.
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    Bulletin of mathematical biology 55 (1993), S. 781-816 
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    Notes: Abstract Two types of behavior have been previously reported in models of immune networks. The typical behavior of simple models, which involve B cells only, is stationary behavior involving several steady states. Finite amplitude perturbations may cause the model to switch between different equilibria. The typical behavior of more realistic models, which involve both B cells and antibody, consists of autonomous oscillations and/or chaos. While stationary behavior leads to easy interpretations in terms of idiotypic memory, oscillatory behavior seems to be in better agreement with experimental data obtained in unimmunized animals. Here we study a series of models of the idiotypic interaction between two B cell clones. The models differ with respect to the incorporation of antibodies, B cell maturation and compartmentalization. The most complicated model in the series has two realistic parameter regimes in which the behavior is respectively stationary and chaotic. The stability of the equilibrium states and the structure and interactions of the stable and unstable manifolds of the saddle-type equilibria turn out to be factors influencing the model's behavior. Whether or not the model is able to attain any form of sustained oscillatory behavior, i.e. limit cycles or chaos, seems to be determined by (global) bifurcations involving the stable and unstable manifolds of the equilibrium states. We attempt to determine whether such behavior should be expected to be attained from reasonable initial conditions by incorporating an immune response to an antigen in the model. A comparison of the behavior of the model with experimental data from the literature provides suggestions for the parameter regime in which the immune system is operating.
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    Bulletin of mathematical biology 55 (1993), S. 865-867 
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    Bulletin of mathematical biology 55 (1993), S. 869-889 
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    Notes: Abstract We show that the existence of diffusional resistance due to the presence of a solid phase can have a positive effect on the metabolic reactions of plant cells. In this case the efficiency of metabolic reactions, defined as the ratio of rate of production of biomass of aggregated cells/rate of production of biomass of dispersed cells, can be greater than unity for a certain range of aggregate sizes for both solid spheres (common plant cell aggregates) and hollow spheres (e.g.Volvox aggregates). This means that, under appropriate conditions, plant cells tend to stay in the aggregated form to improve the efficiency of their metabolic reactions. The result of the present analysis provides an explanation as to why aggregates of plant cells are observed under typical culture conditions.
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    Bulletin of mathematical biology 55 (1993), S. 937-952 
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    Notes: Abstract The Hodgkin and Huxley equations model action potentials in squid giant axons. Variants of these equations are used in most models for electrial activity of excitable membranes. Computational tools based upon the theory of nonlinear dynamical systems are used here to illustrate how the dynamical behavior of the Hodgkin Huxley model changes as functions of two of the system parameters.
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    Bulletin of mathematical biology 55 (1993), S. 919-936 
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    Notes: Abstract The description of the “microbial loop” has led to some major changes in our understanding of nutrient cycling within aquatic ecosystems. It now appears that in many settings it is not uncommon for some 50% of phytoplankton production to be diverted into microbial pathways rather than passing up to higher trophic levels. As a result the microbial loop is responsible for enhanced and rapid nutrient cycling at the very base of the food web. Since tight recycling is often associated with unstable positive feedback, we use a model to examine the possible repercussions in more detail. The model simulates the dynamics of the microbial loop and finds it to greatly affect the way in which aquatic primary production responds to nutrient pulses.
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    Bulletin of mathematical biology 55 (1993), S. 953-971 
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    Notes: Abstract The maintenance activity of plants is investigated in terms of a simple model. Maximization of a certain biomass fraction we refer to asnonactive biomass is postulated. Optimal behaviour of plants according to this principle is explicitly derived and expressed depending on environmental conditions. Several interesting hypotheses result, e.g. a quadratic law relating specific growth rate and gross rate of photosynthesis. A qualitative comparison with data from the literature is performed, with a special emphasis on the question whether plants stressed by air pollutants repair optimally. Regarding long-term constant environmental conditions, no data were found that contradict optimal behaviour. Exact quantitative testing of the theory is desirable, appropriate experiments are suggested.
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    Bulletin of mathematical biology 55 (1993), S. 993-1011 
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    Notes: Abstract In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocrine and paracrine growth factors in tumor growth.Bull. math. Biol. 53, 639–656). The target population, a generic tumor, was modeled as a single, homogeneous population using the standard Verhulst equation of logistic growth. Mitogenic signals were represented by modifications to the Malthusian growth parameter and adaptational signals were represented by modifications to the carrying capacity. Three growth scenarios were described: (1) normal tissue wound healing, (2) unperturbed tumor growth, and (3) tumor growth in a radiation damaged environment, a phenomenon termed the Tumor Bed Effect (TBE). In this paper, we extend those results to include a “triad” of growth factor controls (autocrine, paracrine and endocrine) and heterogeneity of the target population. The heterogeneous factors in the model represent either intrinsic, epigenetic or environmental differences in both normally differentiating tissues and tumors. Three types of growth are modeled: (1) normal tissue differentiation or wound healing, assuming no communication between differentiated and undifferentiated cell compartments; (2) normal wound healing with feedback inhibition, due to signalling from the differentiated compartment; and (3) the development of hypoxia in a spherical tumor. The signal processing within the triad is discussed for each model and biologically reasonable constraints are defined for limits on growth control.
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    Bulletin of mathematical biology 55 (1993), S. 1039-1061 
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    Notes: Abstract A transient multispecies model for quantifying microbial space competition in biofilm is derived from existing models, introducing a new approach to biomass detachment modelling. This model includes inert biomass, substrate diffusion and utilization rate within the biofilm and diffusional layers. It predicts the evolution of biofilm thickness, bulk substrate concentration, species distribution and substrate concentration within the biofilm. A zero-dimensional transient model is described. Its steady-state solution is used to set up initial conditions of the one-dimensional model and case computation towards steady-state solution. Some numerical tools have been developed, enabling fast computation on microcomputers. Simulations show the validity of a zero-dimensional model and perturbated systems are also simulated. Simulations with experimental data give acceptable results.
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    Bulletin of mathematical biology 55 (1993), S. 1025-1038 
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    Notes: Abstract Recently, we proposed a new model of DNA sequence evolution (Arquès and Michel. 1990b.Bull. math. Biol. 52, 741–772) according to which actual genes on the purine/pyrimidine (R/Y) alphabet (R=purine=adenine or guanine, Y=pyrimidine=cytosine or thymine) are the result of two successive evolutionary genetic processes: (i) a mixing (independent) process of non-random oligonucleotides (words of base length less than 10: YRY(N)6, YRYRYR and YRYYRY are so far identified; N=R or Y) leading to primitive genes (words of several hundreds of base length) and followed by (ii) a random mutation process, i.e. transformations of a base R (respectively Y) into the base Y (respectively R) at random sites in these primitive genes. Following this model the problem investigated here is the study of the variation of the 8 R/Y codon probabilities RRR,..., YYY under random mutations. Two analytical expressions solved here allow analysis of this variation in the classical evolutionary sense (from the past to the present, i.e. after random mutations), but also in the inverted evolutionary sense (from the present to the past, i.e. before random mutations). Different properties are also derived from these formulae. Finally, a few applications of these formulae are presented. They prove the proposition in Arquès and Michel (1990b.Bull. math. Biol. 52, 741–772), Section 3.3.2, with the existence of a miximal mean number of random mutations per base of the order 0.3 in the protein coding genes. They also confirm the mixing process of oligonucleotides by excluding the purine/pyrimidine contiguous and alternating tracts from the formation process of primitive genes.
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    Bulletin of mathematical biology 55 (1993), S. 1199-1210 
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    Notes: Abstract It is believed that the native folded three-dimensional conformation of a protein is its lowest free energy state, or one of its lowest. It is shown here that both a two-and three-dimensional mathematical model describing the folding process as a free energy minimization problems is NP-hard. This means that the problem belongs to a large set of computational problems, assumed to be very hard (“conditionally intractable”). Some of the possible ramifications of this results are speculated upon.
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    Bulletin of mathematical biology 55 (1993), S. 1133-1182 
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    Notes: Abstract A model employing separate dose-dependent response functions for proliferation and differentiation of idiotypically interacting B cell clones is presented. For each clone the population dynamics of proliferating B cells, non-proliferating B cells and free antibodies are considered. An effective response function, which contains the total impact of proliferation and differentiation at the fixed points, is defined in order to enable an exact analysis. The analysis of the memory states is restricted in this paper to a two-species system. The conditions for the existence of locally stable steady states with expanded B cell and antibody populations are established for various combinations of different field-response functions (e.g. linear, saturation, log-bell functions). The stable fixed points are interpreted as memory states in terms of immunity and tolerance. It is proven that a combination of linear response functions for both proliferation and differentiation does not give rise to stable fixed points. However, due to competition between proliferation and differentiation saturation response functions are sufficient to obtain two memory states, provided proliferation preceeds differentiation and also saturates earlier. The use of log-bell-shaped response functions for both proliferation and differentiation gives rise to a “mexican-hat” effective response function and allows for multiple (four to six) memory states. Both a primary response and a much more pronounced secondary response are observed. The stability of the memory states is studied as a function of the parameters of the model. The attractors lose their stability when the mean residence time of antibodies in the system is much longer than the B cells' lifetime. Neither the stability results nor the dynamics are qualitatively chanbed by the existence of non-proliferating B cells: memory states can exist and be stable without non-proliferating B cells. Nevertheless, the activation of non-proliferating B cells and the competition between proliferation and differentiation enlarge the parameter regime for which stable attractors are found. In addition, it is shown that a separate activation step from virgin to active B cells renders the virgin state stable for any choice of biologically reasonable parameters.
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    Bulletin of mathematical biology 56 (1994), S. 129-146 
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    Notes: Abstract More than 20 years after its proposal, Keller and Segel's model (1971,J. theor. Biol.,30, 235–248) remains by far the most popular model for chemical control of cell movement. However, before the Keller-Segel equations can be applied to a particular system, appropriate functional forms must be specified for the dependence on chemical concentration of the cell transport coefficients and the chemical degradation rate. In the vast majority of applications, these functional forms have been chosen using simple intuitive criteria. We focus on the particular case of eukaryotic cell movement, and derive an approximation to the detailed model of Sherrattet al. (1993,J. theor. Biol.,162, 23–40). The approximation consists of the Keller-Segel equations, with specific forms predicted for the cell transport coefficients and chemical degradation rate. Moreover, the parameter values in these functional forms can be directly measured experimentally. In the case of the much studied neutrophil-peptide system, we test our approximation using both the Boyden chamber and under-agarose assays. Finally, we show that for other cell-chemical interactions, a simple comparison of time scales provides a rapid check on the validity of our Keller-Segel approximation.
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    Bulletin of mathematical biology 56 (1994), S. 1-64 
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    Notes: Abstract The formal structure of evolutionary theory is based upon the dynamics of alleles, individuals and populations. As such, the theory must assume the prior existence of these entities. This existence problem was recognized nearly a century ago, when DeVries (1904,Species and Varieties: Their Origin by Mutation) stated. “Natural selection may explain the survival of the fittest, but it cannot explain the arrival of the fittest.” At the heart of the existence problem is determining how biological organizations arise in ontogeny and in phylogeny. We develop a minimal theory of biological organization based on two abstractions from chemistry. The theory is formulated using λ-calculus, which provides a natural framework capturing (i) the constructive feature of chemistry, that the collision of molecules generates specific new molecules, and (ii) chemistry's diversity of equivalence classes, that many different reactants can yield the same stable product. We employ a well-stirred and constrained stochastic flow reactor to explore the generic behavior of large numbers of applicatively interacting λ-expressions. This constructive dynamical system generates fixed systems of transformation characterized by syntactical and functional invariances. Organizations are recognized and defined by these syntactical and functional regularities. Objects retained within an organization realize and algebraic structure and possess a grammar which is invariant under the interaction between objects. An organization is self-maintaining, and is characterized by (i) boundaries established by the invariances, (ii) strong self-repair capabilities responsible for a robustness to perturbation, and (iii) a center, defined as the smallest kinetically persistent and self-maintaining generator set of the algebra. Imposition of different boundary conditions on the stochastic flow reactor generates different levels of organization, and a diversity of organizations within each level. Level 0 is defined by selfcopying objects or simple ensembles of copying objects. Level 1 denotes a new object class, whose objects are self-maintaining organizations made of Level 0 objects, and Level 2 is defined by self-maintaining metaorganizations composed of Level 1 organizations. These results invite analogy to the history of life, that is, to the progression from self-replication to self-maintaining procaryotic organizations to ultimately yield self-maintaining eucaryotic organizations. In our system self-maintaining organizations arise as a generic consequence of two features of chemistry, without appeal to natural selection. We hold these findings as calling for increased attention to the structural basis of biological order.
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    Bulletin of mathematical biology 56 (1994), S. 249-273 
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    Notes: Abstract A model is developed to describe neuronal elongation as a result of the polymerization of microtubules and elastic stretching of the neurites by force produced by the growth cone. The model for a single segment with a single growth cone revealed a constant elongation rate, while the concentration of tubulin in the soma rises, and the concentration of tubulin becomes constant in the growth cone. Extending the model to a neurite with a single branch point and two growth cones revealed the same results. When the assembly or the disassembly rate of microtubules is unequal in both growth cones, transient retraction of one of the terminal segments occurs, which results in complete retraction of the segment when the difference in (dis)assembly rate between the two growth cones is large enough. When the model is applied to large trees, a maximal sustainable number of terminal segments as a function of the production rate of tubulin appears. Mechanisms to stop outgrowth are discussed in relation to the establishment of synaptical contacts between cells.
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    Bulletin of mathematical biology 56 (1994), S. 225-247 
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    Notes: Abstract We have developed a new model describing the relationship between plasma and red cell tracers flowing through the lung. The model is the result of an analysis of the transport of radiolabeled plasma albumin between two flowing phases and shows that differences between red cell and plasma tracer curves are related to microvascular hematocrit. The model was tested in an isolated, blood-perfused dog lung preparation in which we injected51Cr-labeled red cells and125I-labeled plasma albumin into the pulmonary artery. From the tracer concentration-time curves at the venous outflow, we calculatedh r, the ratio of microvascular hematocrit to large-vessel hematocrit. In 18 baseline experiments,h r=0.92±0.01 (mn±sem) at a blood flow rate of 10.7±0.3 ml s−1. We determined the effects of (a) glass bead embolization, (b) alloxan, and (c) lobe ligation onh r. Embolization attenuated the separation between plasma and red cells (increasedh r), probably as a consequence of passive vasodilation. Alloxan enhanced separation of plasma and red cells (decreasedh r), possibly as a result of arteriolar vasoconstriction. Ligation of a fraction of the perfused tissue at constant flow did not cause significant change inh r in the remaining perfused tissue. The model assumes that large-vessel transit times are uniform and that all dispersion occurs in the microvasculature. A theoretical analysis apportioning dispersion between large and small vessels disclosed that the error associated with these assumptions is likely to be less than 15% of the measuredh r. We conclude from this study that the microvascular hematocrit model describes experimental plasma and red cell curves. The results imply thath r can be readily deduced from tagged red cells and plasma and can be accounted for in calculating permeability-surface area in diffusing tracer experiments.
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    Notes: Abstract We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seenin vivo, including immunostimulation of tumor growth, “sneaking through” of the tumor, and formation of a tumor “dormant state”. The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measuredin vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.
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    Bulletin of mathematical biology 56 (1994), S. 275-294 
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    Notes: Abstract We present a new, practical algorithm to resolve the experimental data in restriction site analysis, which is a common technique for mapping DNA. Specifically, we assert that multiple digestions with a single restriction enzyme can provide sufficient information to identify the positions of the restriction sites with high probability. The motivation for the new approach comes from combinatorial results on the number of mutually homeometric sets in one dimension, where two sets ofn points are homeometric if the multiset ofn(n−1)/2 distances they determine are the same. Since experimental data contain errors, we propose algorithms for reconstructing sets from noisy interpoint distances, including the possibility of missing fragments. We analyse the performance of these algorithms under a reasonable probability distribution, establishing a relative error limit ofr=Θ(1/n 2) beyond which our technique becomes infeasible. Through simulations, we establish that our technique is robust enough to reconstruct data with relative errors of up to 7.0% in the measured fragment lengths for typical problems, which appears sufficient for certain biological applications.
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    Bulletin of mathematical biology 56 (1994), S. 323-336 
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    Notes: Abstract A simple chemical model of the idiotypic network of immune systems, namely the AB model, has been developed by De Boeret al. The complexity of the system, such as the steady states, periodic oscillations and chaotic motions, has been examined by the authors mentioned above. In the present paper, the periodic motions and chaotic behaviours exhibited by the system are intuitively described. To clarify in which parameter domains concerned the system exhibits periodic oscillations and in which parameter domains the system demonstrates chaotic behaviours the Lyapounov exponent is explored. To characterize the strangeness of the attractors, the fractal dimension problem is worked out.
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    Bulletin of mathematical biology 56 (1994), S. 359-363 
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    Bulletin of mathematical biology 56 (1994), S. 337-357 
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    Notes: Abstract We consider a stochastic mechanism of the loss of resistance of cancer cells to cytotoxic agents, in terms of unstable gene amplification. Two models being different versions of a time-continuous branching random walk are presented. Both models assume strong dependence in replication and segregation of the extrachromosomal elements. The mathematical part of the paper includes the expression for the expected number of cells with a given number of gene copies in terms of modified Bessel functions. This adds to the collection of rare explicit solutions to branching process models. Original asymptotic expansions are also demonstrated. Fitting the model to experimental data yields estimates of the probabilities of gene amplification and deamplification. The thesis of the paper is that purely stochastic mechanisms may explain the dynamics of reversible drug resistance of cancer cells. Various stochastic approaches and their limitations are discussed.
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    Bulletin of mathematical biology 56 (1994), S. 365-368 
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    Bulletin of mathematical biology 56 (1994), S. 369-389 
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    Notes: Abstract Dextran has been the most commonly employed test molecule for probing the selectivity of glomerular filtration to macromolecules of varying size. The usual theories for hindered transport of solid spheres through pores have limited utility in interpreting clearance data for dextran or other linear polymers because such polymers in solution more closely resemble random, solvent-filled coils than solid spheres. To provide a model for glomerular filtration of random-coil macromolecules, the equilibrium partitioning of random coils between cylindrical pores and bulk solution was simulated using Monte Carlo calculations, and those results were combined with a hydrodynamic theory for restricted motion of solvent-filled polymer coils in pores. The rates of transport predicted for either neutral random coils or for solid spheres of the same Stokes-Einstein radius were significantly lower than observed transport rates of dextran through the glomerular capillary wall or across synthetic porous membranes. This facilitation of dextran transport was modeled by postulating weak, attractive interactions between dextran monomers and the pore wall. The random-coil model with attractive interactions, modeled using a short-range, square-well potential, was found to adequately represent dextran sieving data in normal rats. Various limitations of this approach are discussed.
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    Bulletin of mathematical biology 56 (1994), S. 567-586 
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    Notes: Abstract Method-dependent mechanisms that may affect dynamic numerical solutions of a hyperbolic partial differential equation that models concentration profiles in renal tubules are described. Some numerical methods that have been applied to the equation are summarized, and ways by which the methods may misrepresent true solutions are analysed. Comparison of these methods demonstrates the need for thoughtful application of computational mathematics when simulating complicated time-dependent phenomena.
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    Bulletin of mathematical biology 56 (1994), S. 587-616 
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    Notes: Abstract The regulation of the interactions between the actin binding proteins and the actin filaments are known to affect the cytoskeletal structure of F-actin. We develop a model depicting the formation of actin cytoskeleton, bundles and orthogonal networks, via activation or inactivation of different types of actin binding proteins. It is found that as the actin filament density increases in the cell, a spontaneous tendency to organize into bundles or networks occurs depending on the active actin binding protein concentration. Also, a minute change in the relative binding affinity of the actin binding proteins in the cell may lead to a major change in the actin cytoskeleton. Both the linear stability analysis and the numerical results indicate that the structures formed are highly sensitive to changes in the parameters, in particular to changes in the parameter ϕ, denoting the relative binding affinity and concentration of the actin binding proteins.
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    Bulletin of mathematical biology 56 (1994), S. 633-664 
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    Notes: Abstract To investigate morphogenesis and in particular circularization mechanisms in young mycelia, we observe cultures of the zygomyceteMucor spinosus and develop discrete models of two-dimensional filamental branching growth. The models are based on the hypothesis that the fungus secretes a regulatory substance that diffuses into the surrounding medium and is detected by the growing hyphae. We also present a simple Markovian growth model without such a feedback, but yielding to analytical computations.
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    Bulletin of mathematical biology 56 (1994), S. 617-631 
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    Notes: Abstract In vivo volume growth of two murine tumor cell lines was compared by mathematical modeling to their volume growth as multicellular spheroids. Fourteen deterministic mathematical models were studied. For one cell line, spheroid growth could be described by a model simpler than needed for description of growthin vivo. A model that explicitly included the stimulatory role for cell-cell interactions in regulation of growth was always superior to a model that did not include such a role. The von Bertalanffy model and the logistic model could not fit the data; this result contradicted some previous literature and was found to depend on the applied least squares fitting method. By the use of a particularly designed mathematical method, qualitative differences were discriminated from quantitative differences in growth dynamics of the same cells cultivated in two different three-dimensional systems.
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    Bulletin of mathematical biology 56 (1994), S. 665-686 
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    Notes: Abstract This paper develops and applies a dynamic mathematical model for optimal scheduling of nitrogen fertilization and irrigation that minimizes nitrogen leaching subject to a target level of yield. The analysis assumes a single crop grown during a single growing season of a given length. It is shown that substitution of water for nitrogen along a given plant growth path decreases nitrogen leaching and, therefore, groundwater contamination. It is proved that a minimum leaching solution to the optimization problem is obtained with a single nitrogen application at the beginning of the season and irrigation scheduling that maintains a wet soil throughout the growing period. A numerical example utilizing experimental data for an irrigated summer corn in Israel confirms and quantifies the analytical findings.
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    Bulletin of mathematical biology 53 (1991), S. 665-678 
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    Notes: 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.
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  • 95
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    Bulletin of mathematical biology 53 (1991), S. 685-700 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 96
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    Topics: Biology , Mathematics
    Notes: 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.
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  • 97
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    Bulletin of mathematical biology 53 (1991), S. 797-804 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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  • 98
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    Bulletin of mathematical biology 53 (1991), S. 845-851 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 99
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    Bulletin of mathematical biology 56 (1994), S. 875-898 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We analyse the stochastic properties of dynamical systems with finite populations of a few differentreplicator species. Our main interest is to evaluate the typicallifetime, i.e. the time for the extinction of the first species in the network, for different catalytic structures, as a function of the population size.
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  • 100
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    Bulletin of mathematical biology 56 (1994), S. 899-921 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The capacity of a model immune network in terms of the number of different antigens that can be vaccinated against without any memory lost is computed and tested by numerical simulations. We also investigate memory loss and failure to vaccinate due to overcrowding the network with too many antigens. The computations are done for two different strategies for proliferation, one implying all the antigen specific clones and the second one being more thrifty.
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