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  • Springer  (602,530)
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  • 1990-1994  (388,742)
  • 1980-1984  (273,095)
  • 1955-1959  (79,602)
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  • 1
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    Die Geschichte der Antarktisforschung (1984)
    Springer
    In:  EPIC3Naturwissenschaften, Springer, 71(12), pp. 599-608, ISSN: 0028-1042
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    Publication Date: 2014-06-04
    Repository Name: EPIC Alfred Wegener Institut
    Type: Article , notRev
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  • 2
    Electronic Resource
    Electronic Resource
    A contribution to the search of general mathematical principles in biology (1958)
    Springer
    Bulletin of mathematical biology 20 (1958), S. 71-93 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A somewhat different approach to the principle of biotopological mapping, discussed in previous publications, is given. The organism is considered as a set of properties, each of which is in its turn a set of numerous subproperties which are logically included in the corresponding properties. Topology is introduced by an appropriate definition of neighborhoods, and four postulates are stated which concern the mapping of the spaces corresponding to higher organisms on those of lower ones. A number of conclusions are drawn from the postulates. Some of them correspond to well-known facts. For example, in man and some higher organisms appropriate emotional stimuli should produce gastrointestinal or cardiovascular disturbances; or some microorganisms should produce substances harmful to other microorganisms (antibiotics). Some other conclusions are still awaiting verification. One of them is, for example, that there must exist unicellular organisms which produce antibodies to appropriate antigens.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476561
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  • 3
    Electronic Resource
    Electronic Resource
    Beitrag zur Theorie der Wirkung Mineralischer Nährstoffe (1958)
    Springer
    Bulletin of mathematical biology 20 (1958), S. 25-32 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Zusammenfassung Für die Praxis der Pflanzenernährung ist es wichtig, zu wissen, in welcher Weise die Ertragsbildung von der Konzentration eines mineralischen Nährstoffes in der Umgebung der Pflanze abhängt. Da nur diejenigen Nährstoffmengen das physiologische Geschehen in der Pflanze unmittelbar zu beeinflussen vermögen, die sich in der Pflanze befinden, wird angenommen, dass das Wachstum zum Zeitpunktt, d.h. die Geschwindigkeit der Trockensubstanzzunahme zu diesem Zeitpunkt, eine Funktion der zur Zeitt in der Pflanze enthaltenen Nährstoffmenge ist. Diese Nährstoffmenge wird natürlich im Intervall vor dem Zeitpunktt aufgenommen. Deshalb und auch noch aus anderen Gründen hängt das Wachstum zur Zeitt davon ab, wie die in der Umgebung der Pflanze herrschende Konzentration des betrachteten Nährstoffes in demjenigen Zeitintervall verläuft, das sich von der Aussaat bis zum Zeitpunktt erstreckt. Die angegebene Annahme fürhrt zusammen mit einigen weiteren naheliegenden Annahmen zu einem Ansatz, der Ergebnisse liefert, die in verschiedener Hinsicht gut mit der Erfahrung übereinstimmen. Jedoch gibt es auch noch Widersprüche zwischen Theorie und Erfahrung. Durch weitere Ausgestaltung der Theorie lassen sich diese Widersprüche beseitigen. Es wird angeregt, Versuche durchzuführen, deren Resultate Hinweise für die weitere Ausgestaltung der Theorie liefern.
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    URL: http://dx.doi.org/10.1007/BF02476559
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  • 4
    Electronic Resource
    Electronic Resource
    Kinetics of isotope incorporation into the desoxyribonucleic acid (DNA) of tissues: Life span and generation time of cells (1958)
    Springer
    Bulletin of mathematical biology 20 (1958), S. 33-70 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The dynamics of cell multiplication and differentiation in tissues in asteady state and the kinetics of isotope incorporation into the DNA have been theoretically analyzed. Equations have been derived, with the aid of which thegeneration time, thelife span, and the distribution or rate of death of the cells can be obtained if the tissue is in asteady state, i.e., if the number of cells is maintained constant by constant, equal rates of cell division and cell death and if the mean DNA content per cell is also constant. An equation has also been derived which gives thegeneration time in the case of logarithmic multiplication of cells. Two special cases have been analyzed: InCase 1, the isotope is considered as being introduced into the metabolic system at zero time only; inCase 2, the specific activity of the DNA precursor is considered as being maintained constant. The use of the method has been illustrated by an example in which thegeneration time and themean, themedian, and themode life span, as well as the curve of the rate of death of leukocytes in a patient with chronic leukemic granulocytic leukemia, have been obtained from the rate of P32 incorporation into the DNA. The merits and the limitations of the method are discussed.
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  • 5
    Electronic Resource
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    Announcement by perspectives in biology and medicine (1958)
    Springer
    Bulletin of mathematical biology 20 (1958), S. 95-95 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02476562
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  • 6
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    Mathematical formulation of cardiovascular dynamics by use of the laplace transform (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 1-11 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By means of the Laplace transform, the behavior of a simplified model of the cardiovascular system is mathematically formulated. This formulation allows mathematical expression of the periodicity of the cardiac output and the systemic response. With the cardiac output represented as half of a sine function cycle, the systolic aortic pressure becomes the sum of a sine term and exponential terms, while the sum of the exponential terms alone represents the diastolic pressure. The characteristics of the mathematical expressions for systole and diastole are analyzed, and some relationships of potentially practical value are derived. Variation in the parameters of the system yields mathematical results consistent with the expected physical ones.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476454
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  • 7
    Electronic Resource
    Electronic Resource
    A quasi-steady-state approximation method for diffusion problems: I. Concentration dependent diffusion coefficients (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 19-32 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A generalization of Landahl's approximation method (H. D. Landahl,Bull. Math. Biophysics,15, 49–61, 1953) for non-linear diffusion problems is suggested. The method is applied to sorption, desorption, and free diffusion problems involving concentration-dependent diffusion coefficients. With some limitations, the results compare favorably with those obtained by numerical methods.
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  • 8
    Electronic Resource
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    Multipole representation of an eccentric dipole and an eccentric double-layer (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 33-60 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Recently a theorem for representing current generators in a volume conductor by the superposition of a central dipole, quadrupole, octopole, etc., has been established by G. C. K. Yeh, J. Martinek, and H. de Beaumont (Bull. Math. Biophysics,20, 203–16, 1958). This theorem makes possible the representation of any discrete or line, surface- or volume-distributed current source by a unique model which can be determined for each given case by surface potential measurements and closed form analysis. In this paper the multipole representations of an eccentric dipole and an eccentric double-layer are obtained in terms of the various parameters of the assumed singularities, and the contributions to surface potentials due to each of the multipoles are compared. Certain numerical results corresponding to those of E. Frank (Amer. Heart J.,46, 364–78, 1953) are carried out and compared. Furthermore, the multipole representation of a partially damaged double-layer is also determined and compared with that of an undamaged one. It is concluded that within the range of parameters corresponding to human subjects the higher-order multipoles can contribute significantly to the surface potentials compared with the dipole.
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    URL: http://dx.doi.org/10.1007/BF02476457
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  • 9
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    A note on topological biology (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 97-100 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In line with a recent suggestion by the author (Bull. Math. Biophysics,20, 267–73, September, 1958) that not only does the organism as a whole map on the primordial, but that each organ can also be thus mapped, it is shown that the previously introduced abstract spaces, which represent an organism, contain subspaces which map continuously on the space of the primordial. Several theorems about those subspaces are proven.
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  • 10
    Electronic Resource
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    The DNA-protein coding problem (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 71-95 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The DNA-protein coding problem is given a general algebraic formulation, the consequences of which are then explored by standard mathematical methods. To keep the treatment self-contained, the mathematical techniques to be used are explained in detail. It is demonstrated that there exista priori a countably infinite number of different abstract DNA-protein codes, thereby showing that inductive attempts to construct such a code will most likely be fruitless. A notion of ergodicity is then introduced, which imposes a number of restrictions on the admissible codes, and, in fact, these considerations enable us toderive a small portion of a code which, if our hypothesis of ergodicity is correct, must occur in nature. Finally, we discuss briefly the problem as to whether there can exist more than one DNA-protein code in nature.
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    URL: http://dx.doi.org/10.1007/BF02476459
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  • 11
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    The inconsistencies of present-day mathematical-physical methods pertaining to current generators in volume conductors used in electrocardiography (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 61-70 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The present-day practices of electrocardiography and vectorardiography are based upon the theory that the surface potential differences can be assumed to be due to a single dipole inside the body. It is shown in this paper that a dipole cannot account for all the surface potentials due to realistic current generators, and hence the determination of the current generator from surface potential measurements based upon such a theory will lead to inconsistent representations of the heart for one and the same subject. To demonstrate this point two eccentric dipoles of different strengths and locations representing two muscle fibers are taken to be the current generator in a homogeneous spherical conductor. The exact surface potentials are then expressed by means of the “interior sphere theorem” of the authors. With these expressions the magnitude, direction, and location of the resultant dipole are determined by the method of D. Gabor and C. V. Nelson (J. App. Physics,25, 413–16, 1954). The surface potentials due to this resultant dipole are again exactly expressed by means of the “interior sphere theorem” and compared with those due to the eccentric dipoles assumed. It can be seen that the differences can be considerable. It is suggested that the multipole model of the authors (Bull. Math. Biophysics,20, 203–16, 1958) be used as a more accurate and the only unique representation of the heart.
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  • 12
    Electronic Resource
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    A set-theoretical approach to biology (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 101-106 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a preceding paper (Bull. Math. Biophysics 20, 71–93, 1958) the principle of biotopological mapping was formulated in terms of a continuous mapping of an abstract space, made from the set of biological properties which characterize the organism, by an appropriate definition of neighborhoods. In this paper it is shown that we may consider directly the mappings of the different sets of properties which characterize different organisms without taking recourse to abstract spaces. All the verificable conclusions made in the preceding paper remain valid. A serious difficulty mentioned previously is, however, avoided and the possibility of more general predictions is established.
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  • 13
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    Statistical research monographs (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 107-107 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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  • 14
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    A relational theory of biological systems II (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 109-128 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The general Theory of Categories is applied to the study of the (M, R)-systems previously defined. A set of axioms is provided which characterize “abstract (M, R)-systems”, defined in terms of the Theory of Categories. It is shown that the replication of the repair components of these systems may be accounted for in a natural way within this framework, thereby obviating the need for anad hoc postulation of a replication mechanism. A time-lag structure is introduced into these abstract (M, R)-systems. In order to apply this structure to a discussion of the “morphology” of these systems, it is necessary to make certain assumptions which relate the morphology to the time lags. By so doing, a system of abstract biology is in effect constructed. In particular, a formulation of a general Principle of Optimal Design is proposed for these systems. It is shown under what conditions the repair mechanism of the system will be localized into a spherical region, suggestive of the nuclear arrangements in cells. The possibility of placing an abstract (M, R)-system into optimal form in more than one way is then investigated, and a necessary and sufficient condition for this occurrence is obtained. Some further implications of the above assumptions are then discussed.
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    URL: http://dx.doi.org/10.1007/BF02476354
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  • 15
    Electronic Resource
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    A note on the transient stage of the random dispersal of logistic populations (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 141-151 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The transient stage of the random dispersal of logistic populations is investigated, using a Sturm-Liouville series leading to an infinite system of non-linear integral equations. These equations are then solved via a successive approximation scheme. R. A. Fisher's (steady-state) velocity of advance paradox is discussed. An illustrative example is worked to the second order of approximation.
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  • 16
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    A note on population growth under random dispersal (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 153-159 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An approximation method using a sine function is used to solve the second degree growth equation for the case in which an organism may simultaneously become dispersed throughout a uniform region. The resulting expression for a special case is compared with the expression obtained by R. Barakat (1959,Bull. Math. Biophysics,21, 141–51), giving the first two terms, by an iterative, procedure. The agreement is satisfactory.
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  • 17
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    A contribution to the study of diffusion of neutral particles through pores (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 129-140 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Diffusion through a flat pore into a large open region is proportional to the linear dimension of the pore and not to its area. This was first explained by Brown and Escombe (1900) for a circular pore and is here generalized, by means of a dimensional argument, to include any type of regular opening. The problem is further generalized to include diffusion through pores of finite thickness, finite distance apart, and into finite regions. Since this problem cannot be solved exactly, an approximation method is introduced. Reasons for the credibility of the approximation are presented. It is then shown, by means of the approximation method, that the diffusive flow through a pore is equal to the total concentration difference divided by the resistance of the system. The resistance, in turn, is the sum of the resistances of all portions of the system, each of which is calculated. The result is compared with results which have been calculated exactly for limiting cases and found to agree very well. The results are then applied to a standard method of computing pore size in membranes, and it is shown that the correction factor is negligible.
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  • 18
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    Some remarks on the mathematical theory of nutrition of fishes (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 161-183 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract V. S. Ivlev [Experimental Ecology of Nutrition of Fishes, 1955, Moscow (in Russia)] has shown that the food uptake by fishes during a fixed interval of time is an exponential function of the concentration of food. Ivlev's equation is derived here, and it is shown that it can hold only for non-stationary conditions, such as prevailed in Ivlev's experiments. For a stationary state, the rate of food uptake should tend asymptotically to a limiting value as the concentration increases, but the variation is not exponential. Different other aspects of the problem are investigated, and definite new experimental procedures suggested. The implications of Ivlev's findings on the effect of non-uniformity of food distribution upon the rate of food consumption are studied from a mathematical point of view. The conclusion is reached that whereas a fish does not, in the process of eating, move directly to an individual food particle which it perceives, it does move more or less directly to large aggregates of particles, if the latter are distributed nonuniformly.
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  • 19
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    A note on the nature and origin of life (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 185-193 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some relational aspects of the property of self-reproduction of biological systems are studied. If in addition to the requirement of the property of self-reproduction we add also the requirement of adaptability of the organism to changing environment, this imposes certain conditions on the topology of the graphs which represent such systems. A further study of the relational properties of such systems seems to offer the possibility of deriving the principle of biological mapping from the requirement of self-reproduction and adaptability. An examination of the problem of the original formation of such self-reproducing systems in connection with the established fact of impossibility of spontaneous generation leads to the conclusion that an organism must inhibit such processes which, in the absence of organisms, would lead to spontaneous generation.
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  • 20
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    Feedback in physiological systems: An application of feedback analysis and stochastic models to neurophysiology (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 195-216 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the human, the antagonistic, extensor-flexor system of the leg is an example of a common type of neurophysiological feedback system. After a brief introduction to the neuroanatomy and physiology of this feedback system, the paper formulates transfer functions from temporal response data available in the literature. A feedback stability analysis, based on the extension of Nyquist's stability criteria to multiple-loop systems and utilizing flow-graph techniques, demonstrates the stable behavior of the system. Expressions are given relating the sensitivity of the system to variations in muscle response and Golgi tendon organ (tension receptor) response. By considering the events taking place at synapses and end-plates during “isometric tension-small knee angle excursion” conditions as stationary stochastic processes, an external “noise” input to the system is given, whose spectrum is derived from the statistics of a shot-process representation of these events. The paper concludes with some correlations between the analytical results and clinical syndromes.
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  • 21
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    Further considerations on the statistical mechanics of biological associations (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 217-255 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this continuation of a previous report it is shown how the Volterra population dynamics, which underlies the statistical theory, can be based on a variational principle; how the dynamics can be generalized as regards both the behavior of total populations and migration phenomena; and how many directly observable data, such as amplitudes and frequencies of oscillation of a population, fit into the statistical theory and can test it. Such a test is carried out in some detail using the fox-catch data of Elton, with a clear indication that the theory is capable of comprehending the major statistical properties of population-time curves. A final section sketches an extension of the theory to cover secular variations of external conditions such as temperature of the environment.
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  • 22
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    Composting of explosives and propellant contaminated soils under thermophilic and mesophilic conditions (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 137-144 
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    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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  • 23
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    Purification and properties of extracellularβ-fructofuranosidases fromAureobasidium sp. ATCC 20524 (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 145-147 
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    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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  • 24
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    Insect fungal symbionts: A promising source of detoxifying enzymes (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 149-161 
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    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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    Biosensors for process monitoring (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 163-172 
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    Keywords: Biosensors ; Process control ; Enzyme thermistor ; Immunoassay ; Bio-field effect transistor
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    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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    Ecology ofVibrio vulnificus in Galveston Bay oysters, suspended particulate matter, sediment and seawater: Detection by monoclonal antibody — immunoassay — most probable number procedures (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 219-223 
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    Keywords: Vibrio vulnificus ; Oyster ; Monoclonal antibody ; Most probable number ; Enzyme immunoassay
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    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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    Conversion of sodium cyanide to carbon dioxide and ammonia by immobilized cells ofPseudomonas putida (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 235-238 
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    Keywords: Biodegradation ; Pseudomonas putida ; Immobilization ; Sodium cyanide
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    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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    Changes in protein composition ofSaccharomyces brewing strains in response to heat shock and ethanol stress (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 229-234 
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    Keywords: Heat shock protein (HSP) ; Yeast ; Saccharomyces ; Viability ; Thermotolerance ; Ethanol tolerance
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    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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    Isolation and characterization of a novel polysaccharide fromBacillus licheniformis NCIB 11634 (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 239-245 
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    Keywords: Novel polysaccharide ; Bacillus licheniformis ; Raffia venifera ; d-Glucose ; d-Mannose ; d-Xylose
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    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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    Announcement from the publisher (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 269-269 
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    Effect of deglycosylation on the properties of β-fructofuranosidaseP-1 fromAureobasidium sp. ATCC 20524 (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 251-255 
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    Keywords: β-Fructofuranosidase ; Deglycosylation ; Aureobasidium ; Enzymatic stability
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    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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    Comment on biomass diversity in ecology (1984)
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    Bulletin of mathematical biology 46 (1984), S. 967-969 
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    Notes: Abstract It is observed that a dynamical continuity equation for biomass distribution yields the asymptotic steady-state exponential dependencen=A exp( $$ - m/\bar m$$ ) exhibited by certain fishery data, wherem is the biomass of an individual,n is the number of individuals per unit biomass interval, andA, $$\bar m$$ are positive constants. This dynamical approach to biomass distribution is an alternative to the global maximization principle proposed recently by Lurié and Wagensberg.
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    Physik der Selbstorganization und Evolution (1984)
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    Bulletin of mathematical biology 46 (1984), S. 971-972 
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    Announcements (1984)
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    Bulletin of mathematical biology 46 (1984), S. 973-974 
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    Complementary variational principles for diffusion problems with Michaelis-Menten kinetics (1980)
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    Bulletin of mathematical biology 42 (1980), S. 131-135 
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    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for diffusion problems with Michaelis-Menten kinetics. In an illustrative calculation we obtain an extremely accurate variational solution in good agreement with the numerical solution of McElwain (1978).
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    Structural order and partial disorder in biological systems (1980)
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    Bulletin of mathematical biology 42 (1980), S. 137-141 
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    Primitivity of the product of two Leslie matrices (1980)
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    Bulletin of mathematical biology 42 (1980), S. 181-189 
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    Notes: Abstract Necessary and sufficient conditions for primitivity of a product of two Leslie matrices are given. Such a product could be used in modeling the growth of a population governed alternately by two different sets of fertility and survival parameters.
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    Frequency analysis of time-varying elastance model of the left ventricle (1980)
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    Bulletin of mathematical biology 42 (1980), S. 173-180 
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    Notes: Abstract Zadeh's transfer function method for linear time-variable systems is used to apply frequency-domain analysis to a periodically time-varying elastance model of the left ventricle. Left ventricular pressure computed from the system function of the time-varying elastance and the phasors of aortic flow shows a typical waveform of the measured ventricular pressure.
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    The 9th Annual Northeast Biomedical Engineering Conference (1980)
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    Bulletin of mathematical biology 42 (1980), S. 901-901 
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    Multibreath tracer species dynamics in the lung (1981)
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    Bulletin of mathematical biology 43 (1981), S. 1-19 
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    Notes: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.
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    Global stability of population models (1981)
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    Bulletin of mathematical biology 43 (1981), S. 47-58 
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    Notes: Abstract Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.
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    The logistic equation with a diffusionally coupled delay (1981)
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    Bulletin of mathematical biology 43 (1981), S. 125-140 
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    Notes: Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Layapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopf's bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.
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    Uncertainty in physiology and physics (1981)
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    Bulletin of mathematical biology 43 (1981), S. 141-149 
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    Notes: Abstract It was hypothesized in an earlier work that sensory perception can occur only when the perceiving system is uncertain about the nature of the event being perceived. In the absence of any uncertainty, perception will not take place. The response of the sensory afferent neuron (impulse transmission rate) was calculated using Shannon's measure of uncertainty or entropy. It will now be shown that when the event being perceived is the position and momentum of a particle, Shannon's measure of uncertainty leads to the Heisenberg Uncertainty relationship.
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    Consensusn-trees (1981)
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    Bulletin of mathematical biology 43 (1981), S. 239-244 
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    Notes: Abstract It is not unusual for several classifications to be given for the same collection of objects. We present a method, called majority rule, which can be used to define a consensus of these classifications. We also discuss some mathematical properties of this consensus tree.
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    Morphogen pattern formation and development in growth (1981)
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    Bulletin of mathematical biology 43 (1981), S. 259-270 
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    Notes: Abstract The dependence of the spatial concentration profiles of morphogens on a characteristic dimension is obtained by continuation techniques for Gierer and Meinhardt's activator-inhibitor model of morphogenesis. The study of the behaviour of the system during growth, where the linear and exponential increase of the characteristic dimension is considered, revealed that more complex patterns of morphogen spatial concentrations appear regularly in a reproducible way.
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    Simulation experiments with a model for cellular growth (1981)
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    Bulletin of mathematical biology 43 (1981), S. 271-278 
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    Notes: Abstract Computer models have been used by various authors to simulate both the growth of normal cellular tissue and the development of cancerous cells within normal tissue. As these models were the result of considerable idealization, the purpose of the present paper is to propose a model in which the degree of simplification is relaxed: the features of simultaneous growth, and cell growth whose rate depends on the free absorbing periphery of the cell are introduced. Simulation experiments have been conducted using the model, and the results are presented.
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    Complementary extremum principles for a nonlinear model of heat conduction in the human head (1981)
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    Bulletin of mathematical biology 43 (1981), S. 341-346 
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    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for a nonlinear model of heat conduction in the human head. Accurate variational solutions are obtained in illustrative calculations. The effect of nonlinearity is seen to be significant from a comparison with the linearized model.
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    On Zeeman's equations for the nerve impulse (1981)
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    Bulletin of mathematical biology 43 (1981), S. 279-325 
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    Notes: Abstract A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.
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    Asymptotic analysis of the Michaelis-Menten reaction equations (1981)
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    Bulletin of mathematical biology 43 (1981), S. 375-388 
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    Notes: Abstract The irreversible Michaelis-Menten reaction is studied by the use of the method of multiple scales. Three stages of the reaction are identified, one of which is studied in detail. The results are compared with those of two earlier analyses.
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    Pulse evolution on coupled nerve fibres (1981)
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    Bulletin of mathematical biology 43 (1981), S. 389-400 
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    Notes: Abstract A numerical study of the coupled nerve fibre problem is given which verifies and extends the perturbation theory of Luzader. Pulses on adjacent fibres can couple together with two possible stable pulse separations.
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    Field-induced forces at dielectric interfaces as a possible mechanism of RF hearing effects (1981)
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    Bulletin of mathematical biology 43 (1981), S. 401-413 
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    Notes: Abstract A possible mechanism for effects of microwave radiation on the auditory system is the generation of field-induced forces at interfaces that divide materials of dissimilar electrical properties. A general expression for these “Maxwell stresses” is derived and then used to calculate the approximate magnitude of field-induced force within the organ of Corti during microwave exposure. Comparison of the results with data on the force needed to excite cochlear hair cells indicates auditory responses could be evoked by this mechanism at power densities near the threshold of rf hearing sensations.
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    The construction of homogeneous nets (1981)
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    Bulletin of mathematical biology 43 (1981), S. 415-426 
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    Notes: Abstract A definition of homogeneity for neural networks is given which permits their construction as group quotients. The significance of this for neural dynamics is discussed.
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    Contractile analysis and kinetic energy of the myocardium (1981)
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    Bulletin of mathematical biology 43 (1981), S. 447-461 
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    Notes: Abstract The left ventricle is represented as a cylinder contracting both radially and longitudinally. A simple method is indicated to derive an expression for the rate of change of the kinetic energy of this three-dimensional model, which quantity can be used as an index for the study of the contractile behaviour of the myocardium. An application to the study of muscle mechanics is also indicated.
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    Limit cycles in periodically perturbed population systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 463-485 
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    Notes: Abstract A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.
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    On a unified approach to pattern generation (1981)
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    Bulletin of mathematical biology 43 (1981), S. 513-516 
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    An equivalence result for integral equations with application to branching processes (1982)
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    Bulletin of mathematical biology 44 (1982), S. 1-15 
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    Notes: Abstract A theorem is proved, concerning expected values of a multitype branching process in a varying environment. The consequence of the theorem is that the branching process can be treated (in the sense of expected values) as a dynamical system with control terms. This is of importance in situations where the process serves as an abstract model of the dynamics of malignant cells for use in chemotherapy. A simple example of this kind is given.
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    General solution for flow and stress phenomena in elastic vessles (Navier-Stokes) (1982)
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    Bulletin of mathematical biology 44 (1982), S. 29-42 
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    Notes: Abstract A method is developed for a full nonlinear evaluation of all velocities and stresses represented in the Navier-Stokes equations and in the general stress tensor. The information required is essentially that for solution of linearized forms. The solution is analytical except for the calculation of the axial velocity, which requires computer assistance to step through time and space. The treatment of the problem, although directed towards solutions involving fluid flow in elastic vessels, is also adaptable to solid deformations (strain vs rate of strain) where the general stress tensor applies. A special case for the distorting ellipse is presented as well as a limited, spatially analytic, solution.
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    Spatially localized interactive neural populations—II: Stability and dynamics of excitatory sets (1982)
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    Bulletin of mathematical biology 44 (1982), S. 43-56 
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    Notes: Abstract The stability characteristics and dynamical behavior of a system of mutually excitatory neurons in close spatial proximity are investigated with a mathematical model. The model predicts the existence of uniform, intermediate levels of activity other than those of no activity and maximal activity. The model also, yeilds a good explanation of data obtained from periglomerular neurons in the olfactory bulb of the cat.
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    Stochastic compartmental models with banching and immigrant particles (1982)
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    Bulletin of mathematical biology 44 (1982), S. 75-86 
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    Notes: Abstract A multicompartmental model in which particles enter the system from the environment and reproduce according to a Markov branching process has been considered. Explicit expressions have been obtained for the mean vector and the correlation structure for the numbers of particles in different compartments in different time points of the system. Growth rates of the mean vector and some special cases of the system are also discussed.
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    Mode analysis of physiological oscillators intercoupled via pure time delays (1982)
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    Bulletin of mathematical biology 44 (1982), S. 57-74 
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    Notes: Abstract The study of bi-directionally coupled oscillators is relevant in biological modelling of such systems as gastro-intestinal electrical activity, cardiac pacemarkers, cardiovascular and respiratory interactions and circadian rhythms. Interconnecting pathways in biological systems often exhibit pure time-delay characteristics. In this paper the multiple-mode limit-cycle behaviour of such systems is analysed using the method of harmonic blance. It is shown that the coupling time delay radically affects the number, frequency and amplitudes of entrained limit-cycles.
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    Bifurcation, stability diagrams, and varying diffusion coefficients in reaction-diffusion equations (1982)
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    Bulletin of mathematical biology 44 (1982), S. 87-102 
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    Notes: Abstract The effect of keeping all the parameters constant, except the diffusion coefficients, in a pair of reaction-diffusion equations is studied. It is shown that the stability of the constant solution and the bifurcation points can be easily established by constructing a simple stability diagram. The possible qualitatively different diagrams are enumerated.
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    Random ecological systems with structure: Stability-complexity relationship (1982)
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    Bulletin of mathematical biology 44 (1982), S. 103-117 
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    Notes: Abstract We have numerically examined more than one million Large Complex Systems (LCS) of interacting variables (interpretable as interacting populations) governed by Generalized Lotka-Volterra Equations (GLV), with self-regulation term. The scope was to have some insight on the stability-complexity relationship. We considered systems of prey-predator type, and we gave appropriate rules for constructing the model systems, rules that specify the behaviour of model systems in order to put them near the biological reality. The results show, among other things, a strict correlation between the stability and the prey-predator ratio (which, in our model, uniquely determines the connectedness of the system).
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    Remark on the article, “Applied catastrophe theory in the social and biological sciences” by M. A. B. Deakin (1980) (1982)
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    Bulletin of mathematical biology 44 (1982), S. 149-150 
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    Transient effects on the initial rate of oxygenation of red blood cells (1982)
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    Bulletin of mathematical biology 44 (1982), S. 119-134 
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    Notes: Abstract The rate-controlling process in the oxygenation of red blood cells is investigated using a Roughton-like model for oxygen diffusion and reaction with hemoglobin. The mathematical equations describing the model are solved using two independent techniques, numerical inversions of the Laplace transform of the equations and numerical solutions via an implicit-explicit finite difference form of the equations. The model is used to re-examine previous theoretical models that incorporate either a red cell membrane that is resistive to oxygen diffusion or an unstirred layer of water surrounding the cell. Although both models have been postulated to be equivalent, the results of the computer simulations demonstrate significant differences between the two models in the rate of oxygenation of the red cells, depending upon the values chosen for the diffusion coefficient for O2 in the membrane and the thickness of the water layer. The difference is apparently due to differences in the induction and transient periods of the water layer model relative to the membrane model.
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    Energy and biological evolution—II. The mathematical structure of equilibrium states (1982)
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    Bulletin of mathematical biology 44 (1982), S. 537-547 
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    Notes: Abstract We examine certain mathematical structures presented in Part I. The most important of these are the energy structures determined by the couple (ω×E, ψ) the space of causality defined by ψ-1(0) and the notion of collapsibility, i.e., the descent of a species from a higher to a lower equilibrium configuration as a result of energy loss.
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    A stochstic model for a two-compartment reversible system (1982)
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    Bulletin of mathematical biology 44 (1982), S. 557-570 
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    Notes: Abstract This paper discusses a general stochastic model for a two-compartment reversible system with non-homogeneous Poisson inputs, arbitrary residence times at each of the compartments and time-dependent transition probabilities. The probability distributions of the number of particles in each compartment and in the system are obtained together with the number of particles which depart from the system. In addition, various covariance functions with a time lag are obtained. Some of the above obtained results are deduced for time-independent arrivals, exponential residence times and time-independent transition probabilities. Fluctuations of the particles present in the system are also analysed. Similar analysis is provided for the model into which some particles are initially introduced at the system. Some possible applications are discussed at the end.
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    Effects of dispersion on stability of multispecies prey-predator systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 571-578 
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    Notes: Abstract The general multispecies prey-predator system with Gompertz's antisymmetric interactions is nonlinearly stable in the absence of dispersion and continues to remain stable with dispersion under both homogeneous reservoir and zero flux boundary conditions in a region containing the equilibrium state. It is proved that a general multispecies food-web model without antisymmetric interactions is stable in the absence of dispersion and remains stable with dispersion in the above-mentioned region.
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    Repeatability of experiments (1982)
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    Bulletin of mathematical biology 44 (1982), S. 593-593 
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    Graph theoretical criteria for stability and boundedness of predator-prey systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 579-585 
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    Notes: Abstract We introduce a graphical approach in the study of the qualitative behavior ofm species predator-prey systems. We prove that tree graphs imply global stability for Volterra models and local stability for general models; furthermore, we derive sufficient conditions so that loop graphs imply stability and boundedness of the solutions.
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    A reply to “repeatability of experiments” by R. B. Campbell (1982)
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    Bulletin of mathematical biology 44 (1982), S. 594-595 
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    An epizootic model of an insect-fungal pathogen system (1982)
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    Bulletin of mathematical biology 44 (1982), S. 731-739 
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    Notes: Abstract A system of integro-differential equations is derived to describe epizootics of a fungal pathogen in an insect population. Because of piecewise continuous behavior under some parametric conditions, it is concluded that standard phase orbits can be misleading. Using a different analytic approach yields a simple system of finite difference equations. Both the continuous and discrete versions are compared to classical forms. The continuous version differs from a classical one in possessing a second derivative dependent on population density. The discrete version differs in maintaining positive, non-zero populations of both infectives and susceptibles in finite time.
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    On feedback control of gonadotropin secretion (1982)
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    Bulletin of mathematical biology 44 (1982), S. 741-748 
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    Notes: Abstract This note is an attempt to demonstrate that hypothalamic pulsatile GnRH secretion is not the result of a short-term, negative steroid hormone feedback. Clarification of this point is of importance for further modelling the control of gonads.
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    The development of largangians for biological models (1982)
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    Bulletin of mathematical biology 44 (1982), S. 749-760 
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    Notes: Abstract A modern theory of the calculus of variations is used to form necessary and sufficient conditions for the existence of a Lagrangian representation of a system of first-order ordinary differential equations. There exists a theorem to the effect that when a system of ordinary differential equations is variationally self-adjoint, the fulfillment of such conditions is guaranteed. In addition, self-adjointness, allows establishement of an algorithm by which a Lagrangian for the system may be explicitly constructed. Examples in mathematical biology are given to illustrate the use of the stated theorem.
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    An optimal control model of diabetes mellitus (1982)
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    Bulletin of mathematical biology 44 (1982), S. 793-808 
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    Notes: Abstract Engineering optimal control theory is applied to equations describing insulin and glucose interactions. The nature of the optimal controller is established. It is shown how the results can be utilized in a closed loop feedback control system.
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    Biological optimality: Comparison of generalized feasibility and optimality conditions for linear, error-minimizing systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 777-791 
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    Notes: Abstract An attempt is made to compare the conditions for the general error-optimality of linear systems developed by Kalman with the conditions for feasibility of linear models of neuromuscular and physiological control systems. Models of three actual physiological systems are tested for both the above criteria. Theoretical analysis presented here shows that there are no simple relationships between the two sets of conditions. Analysis carried out on the physiological systems models suggests the need for a general set of conditions for other optimality criteria, such as time and energy minimization, similar to Kalman's condition for error minimization.
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    The development of anoxia following occlusion (1982)
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    Bulletin of mathematical biology 44 (1982), S. 851-877 
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    Notes: Abstract Following arteriolar occlusion, tissue oxygen concentration decreases and anoxic tissue eventually develops. Although anoxia first appears in the region most distal to the capillary at the venous end, it eventually spreads throughout the entire region of supply. In this paper the changing oxygen concentration, from the time of occlusion until the tissue is entirely anoxic, is examined mathematically. The equations governing oxygen transport to tissue are solved by iterating a nonlinear integral equation. This solution is valid until anoxia first appears. After anoxia develops it is necessary to solve a moving boundary problem. This is done using the method of matched asymptotic expansions, and accurate solutions are obtained for a wide range of physiological conditions.
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    Announcements (1982)
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    Bulletin of mathematical biology 44 (1982), S. 899-900 
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    On biomass diversity in ecology (1983)
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    Bulletin of mathematical biology 45 (1983), S. 287-293 
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    Notes: Abstract We postulate that the biomass distribution function for an ecological population may be derived from the condition that the biomas diversity functional is maximal subject to an energetic constraint on the total biomass. This leads to a biomass distribution of the form $$p(m) = \bar m^{ - 1} \exp ( - m/\bar m)$$ , where $$\bar m$$ is the mean biomass per individual. The same condition yields a unique value for the biomass diversity functional. These predictions are tested against fishery data and found to be in good agreement. It is argued that the existence of a unique value for biomass diversity may provide a preliminary theoretical foundation for the observed upper limit to species diversity.
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    A model for hydranth regeneration inTubularia (1983)
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    Bulletin of mathematical biology 45 (1983), S. 311-321 
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    Notes: Abstract Pigment distribution presages hydranth regeneration in the marine hydroidTubularia. We suggest that such a distribution could result from a reaction-diffusion system. A model system based on a practical reaction scheme is studied and spatial structures found which closely resemble this pigment distribution. Finite-amplitude spatial structures in reaction-diffusion systems are considered. Whereas in one spatial dimension the final structures are normally very similar to the transient patterns which emerge from a linear analysis, it is shown that in more than one dimension this is not necessarily the case. The reasons for this are discussed.
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    The chemical basis of morphogenesis (1990)
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    Bulletin of mathematical biology 52 (1990), S. 153-197 
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    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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    Book reviews (1990)
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    Bulletin of mathematical biology 52 (1990), S. 319-334 
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    SIAM 1990 Annual Meeting and Short Course 15–20 July 1990 Hyatt Regency Hotel, Chicago, IL (1990)
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    Bulletin of mathematical biology 52 (1990), S. 335-337 
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    Editorial: Software survey section (1990)
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    Bulletin of mathematical biology 52 (1990), S. I 
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    The cellular computer DNA: Program or data (1990)
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    Bulletin of mathematical biology 52 (1990), S. 335-348 
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    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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    Distribution of the number of matches between nucleotide sequences (1990)
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    Bulletin of mathematical biology 52 (1990), S. 349-358 
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    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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    On the fate of inhaled particles in the human: A comparison of experimental data with theoretical computations based on a symmetric and asymmetric lung (1983)
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    Bulletin of mathematical biology 45 (1983), S. 409-424 
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    Notes: Abstract An analytical model is used to described the behavior of inhaled particulate matter in the human respiratory tract. Three different geometries, symmetric and asymmetric, are utilized to simultate the tracheobronchial (TB) tree. The suitability of each geometry for representing the human is evaluated by comparing calculated aerosol deposition probabilities with experimental data from inhalation exposure tests. A symmetric, dichotomously branching pattern is found to be a reliable description of the TB tree for studies of factors affecting aerosol deposition in the human lung. Calculations with the theoretical model are in excellent agreement with measured aerosol deposition efficiencies. Furthermore, the model accurately predicts experimentally observed features of inhalation exposure data, such as effects of inter-subject lung morphology differences and relative efficiencies of specific deposition mechanisms, on aerosol deposition patterns in the TB tree.
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    Reply to letter by Jane Cronin (1982) (1983)
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    Bulletin of mathematical biology 45 (1983), S. 436-436 
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    Foreword (1983)
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    Bulletin of mathematical biology 45 (1983), S. 437-437 
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    Consistency of optimal sequence alignments (1990)
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    Bulletin of mathematical biology 52 (1990), S. 509-525 
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    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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    URL: http://dx.doi.org/10.1007/BF02462264
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    Conditions for the unlimited growth in multitype population size dependent galton-watson processes (1990)
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    Bulletin of mathematical biology 52 (1990), S. 527-534 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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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    URL: http://dx.doi.org/10.1007/BF02462265
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    A deterministic model of the cell cycle (1990)
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    Bulletin of mathematical biology 52 (1990), S. 535-547 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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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    URL: http://dx.doi.org/10.1007/BF02462266
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    Book reviews (1990)
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    Bulletin of mathematical biology 52 (1990), S. 583-596 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462268
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    Editorial: Software survey section (1990)
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    Bulletin of mathematical biology 52 (1990), S. I 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02462269
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    Diffusion regulated growth characteristics of a spherical prevascular carcinoma (1990)
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    Bulletin of mathematical biology 52 (1990), S. 549-582 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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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    Synchronization of the behaviour within nests of the antleptothorax acervorum (fabricius)—I. Discovering the phenomenon and its relation to the level of starvation (1990)
    Springer
    Bulletin of mathematical biology 52 (1990), S. 597-612 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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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    URL: http://dx.doi.org/10.1007/BF02462100
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    Invariant probabilities for systems in a random environment—With applications to the Brusselator (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 579-590 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper we are concerned with problems of the long-term behavior for nonlinear systems in random environment. The general model is assumed to be given by an ordinary differential equation with random parameters or random input. The disturbance process can be taken from a fairly general class of Markov processes having a bounded state space. In terms of the system’s dynamics we give sufficient conditions for the existence and uniqueness of invariant probabilities. Finally, we apply these results to the two-dimensional biochemical model which is known as the Brusselator.
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    URL: http://dx.doi.org/10.1007/BF02459589
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    Non-linear filtering with discontinuous observations and applications to life sciences (1983)
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    Bulletin of mathematical biology 45 (1983), S. 571-577 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In various applications one faces the problem of estimating a signal from discontinuous observations. For example, in biomedical applications the signal may be the ‘state’ of a given organ and one observes through an external counter the amount of radioactivity sequestered by the organ after injection of a radioactive tracer. Here the problem is studied in the context of nonlinear filtering when the signal can be modelled as either a random variable or a diffusion process, and the observations have a continuous and a purely discontinuous component; both components may be affected by the signal. When the signal is a random variable an explicitly computable solution is obtained; for the diffusion case the solution is given as a sequence of approximating filters that can be computed recursively.
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    URL: http://dx.doi.org/10.1007/BF02459588
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    Lateral diffusion and eigenvalue estimates (1983)
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    Bulletin of mathematical biology 45 (1983), S. 627-634 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Eigenvalue problems arise in various biological models. We outline a useful comparison method and a technique using Lyapunov functions that can be applied in many cases. An application to lateral diffusion is discussed.
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    URL: http://dx.doi.org/10.1007/BF02459594
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    Recent views on the cell cycle structure (1983)
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    Bulletin of mathematical biology 45 (1983), S. 605-616 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper reviews, up to their recent developments, two types of models of the cell cycle: those considering the size controls over the cycle events and the transition probability models. The distribution of inter-mitotic time and the sister-sister and motherdaughter correlations implied by the two approaches are discussed in view of some relevant experimental data.
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    URL: http://dx.doi.org/10.1007/BF02459592
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    Controlled branching processes and their applications to normal and malignant haematopoiesis (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 617-626 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The development of a blood cell line originating from a pluripotent stem cell pool is modelled by a chain of multidimensional branching processes in which the sojourn times of the cells in certain resting states depend on the size of the following subpopulation. The stability of such a model is discussed qualitatively and some considerations concerning a possible malignant degeneration are presented. The behaviour of models for normal and malignant cell production are illustrated by stochastic stimulations. The model presented here describes the development of a certain line of blood cells (e.g. erythrocytes, monocytes or granulocytes) originating from the pluripotent stem cell up to the functional cell in the blood (for related models see, e.g., Rubinow and Lebowitz,J. math. Biol. 1, 87–225;Biophys. J. 16, 897–910).
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    URL: http://dx.doi.org/10.1007/BF02459593
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