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  • Springer  (57,589)
  • American Geophysical Union  (2,857)
  • Copernicus
  • 1985-1989  (60,504)
  • 1989  (60,504)
  • 1
    Electronic Resource
    Electronic Resource
    Memory but no suppression in low-dimensional symmetric idiotypic networks (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 223-246 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present a new symmetric model of the idiotypic immune network. The model specifies clones of B-lymphocytes and incorporates: (1) influx and decay of cells; (2) symmetric stimulatory and inhibitory idiotypic interactions; (3) an explicit affinity parameter (matrix); (4) external (i.e. non-idiotypic) antigens. Suppression is the dominant interaction, i.e. strong idiotypic interactions are always suppressive. This precludes reciprocal stimulation of large clones and thus infinite proliferation. Idiotypic interactions first evoke proliferation, this enlarges the clones, and may in turn evoke suppression. We investigate the effect of idiotypic interactions on normal proliferative immune responses to antigens (e.g. viruses). A 2-D, i.e. two clone, network has a maximum of three stable equilibria: the virgin state and two asymmetric immune states. The immune states only exist if the affinity of the idiotypic interaction is high enough. Stimulation with antigen leads to a switch from the virgin state to the corresponding immune state. The network therefore remembers antigens, i.e. it accounts for immunity/memory by switching beteen multiple stable states. 3-D systems have, depending on the affinities, 9 qualitatively different states. Most of these also account for memory by state switching. Our idiotypic network however fails to account for the control of proliferation, e.g. suppression of excessive proliferation. In symmetric networks, the proliferating clones suppress their anti-idiotypic suppressors long before the latter can suppress the former. The absence of proliferation control violates the general assumption that idiotypic interactions play an important role in immune regulation. We therefore test the robustness of these results by abandoning our assumption that proliferation occurs before suppression. We thus define an “escape from suppression” model, i.e. in the “virgin” state idiotypic interactions are now suppressive. This system erratically accounts for memory and never for suppression. We conclude that our “absence of suppression from idiotypic interactions” does not hinge upon our “proliferation before suppression” assumption.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458444
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  • 2
    Electronic Resource
    Electronic Resource
    Book reviews (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 287-291 
    Details
    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/BF02458448
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  • 3
    Electronic Resource
    Electronic Resource
    Editorial: Software survey section (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. I 
    Details
    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/BF02458449
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  • 4
    Electronic Resource
    Electronic Resource
    Upper and lower bounds from the maximum principle. Intracellular diffusion with Michaelis-Menten kinetics (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 325-335 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Analytical bounding functions for diffusion problems with Michaelis-Menten kinetics were recently presented by Anderson and Arthurs, 1985 (Bull. math. Biol. 47, 145–153). Their methods, successful to some extent for a small range of parameters, has the disadvantage of providing a weak upper bound. The optimal approach for the use of one-line bounding kinetics is presented. The use of two-line bounding kinetics is also shown, in order to give, sufficient accuracy in those cases where the one-line approach does not provide satisfactory results. The bounding functions provide excellent upper and lower bounds on the true solution for the entire range of kinetic and transport parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460111
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  • 5
    Electronic Resource
    Electronic Resource
    The threshold of survival for systems in a fluctuating environment (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 311-323 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Thresholds for survival and extinction are important for assessing the risk of mortality in systems exposed to exogeneous stress. For generic, rudimentary population models and the classical resource-consumer models of Leslie and Gallopin, we demonstrate the existence of a survival threshold for situations where demographic parameters are fluctuating, generally, in a nonperiodic manner. The fluctuations are assumed, to be generated by exogenous, anthropogenic stresses such as toxic chemical exposures. In general, the survival threshold is determined by a relationship between mean stress measure in organisms to the ratio of the population intrinsic growth rate and stress response rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460110
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  • 6
    Electronic Resource
    Electronic Resource
    Plant strategies and the dynamics and structure of plant communities (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 409-411 
    Details
    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/BF02460116
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  • 7
    Electronic Resource
    Electronic Resource
    Editorial: Viewpoint (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 415-415 
    Details
    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/BF02460080
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  • 8
    Electronic Resource
    Electronic Resource
    Stochastic models for subpopulation emergence in heterogeneous tumors (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 731-747 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A stochastic analog to a deterministic model describing subpopulation emergence in heterogeneous tumors is developed. The resulting system is described by the Fokker-Planck or forward Kolmogorov equation. A finite element approach for the numerical solution to this equation is described. Four biological and clinical scenarios are simulated (emergence of heterogeneity, exclusion of a subpopulation, and induction of drug resistance in both pure and heterogeneous tumors). The results of the simulations show that the stochastic model describes the same basic dynamics as its deterministic counterpart via a convective component, but that for each simulation a distribution of tumor sizes and mixes can also be derived from a diffusive component in the model. These distributions yield estimates for subpopulation extinction probabilities. The biological and clinical relevance of these results are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459658
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  • 9
    Electronic Resource
    Electronic Resource
    Algorithms for the optimal identification of segment neighborhoods (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 39-54 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two algorithms for the efficient identification of segment neighborhoods are presented. A segment neighborhood is a set of contiguous residues that share common features. Two procedures are developed to efficiently find estimates for the parameters of the model that describe these features and for the residues that define the boundaries of each segment neighborhood. The algorithms can accept nearly any model of segment neighborhood, and can be applied with a broad class of best fit functions including least squares and maximum likelihood. The algorithms successively identify the most important features of the sequence. The application of one of these methods to the haemagglutinin protein of influenza virus reveals a possible mechanism for conformational change through the finding of a break in a strong heptad repeat structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458835
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  • 10
    Electronic Resource
    Electronic Resource
    Approximate matching of regular expressions (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 5-37 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Given a sequenceA and regular expressionR, theapproximate regular expression matching problem is to find a sequence matchingR whose optimal alignment withA is the highest scoring of all such sequences. This paper develops an algorithm to solve the problem in timeO(MN), whereM andN are the lengths ofA andR. Thus, the time requirement is asymptotically no worse than for the simpler problem of aligning two fixed sequences. Our method is superior to an earlier algorithm by Wagner and Seiferas in several ways. First, it treats real-valued costs, in addition to integer costs, with no loss of asymptotic efficiency. Second, it requires onlyO(N) space to deliver just the score of the best alignment. Finally, its structure permits implementation techniques that make it extremely fast in practice. We extend the method to accommodate gap penalties, as required for typical applications in molecular biology, and further refine it to search for substrings ofA that strongly align with a sequence inR, as required for typical data base searches. We also show how to deliver an optimal alignment betweenA andR in onlyO(N+logM) space usingO(MN logM) time. Finally, anO(MN(M+N)+N 2logN) time algorithm is presented for alignment scoring schemes where the cost of a gap is an arbitrary increasing function of its length.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458834
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