ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Springer  (459,504)
  • 1985-1989  (267,449)
  • 1965-1969  (146,830)
  • 1950-1954  (34,810)
  • 1945-1949  (10,415)
Collection
Keywords
Publisher
Years
Year
  • 1
    Electronic Resource
    Electronic Resource
    Random walk with persistence and external bias (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 311-338 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The partial differential equation of the random walk problem with persistence of direction and external bias is derived. By persistence of direction or internal bias we mean that the probability a particle will travel in a given direction need not be the same for all directions, but depends solely upon the particle's previous direction of motion. The external bias arises from an anisotropy of the medium or an external force on the particle. The problem is treated by considering that the net displacement of a particle arises from two factors, namely, that neither the probability of the particle traveling in any direction after turning nor the distance the particle travels in a given direction need be the same for all directions. A modified Fokker-Planck equation is first obtained using the assumptions that the particles have a distribution of travel times and speeds and that the average time of travel between turns need not be zero. The fional equation incopporating the assumption of a persistence of direction and an external bias is then derived. Applications to the study of diffusion and to long-chain polymers are then made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476407
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Methods of statistical analysis (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 383-383 
    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/BF02476411
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    The transmission of excitation from the membrane to actomyosin (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 385-385 
    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/BF02476412
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    On the spread of information with time and distance (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 367-381 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The transmission of some information or behavior pattern is treated as a flow of “particles” which execute random motions over a population of individuals and which may multiply or disappear. Equations are derived for the number density of these “particles” and from this is calculated the number of individuals through which the “particles” have passed. The results are applied to a number of situations such as 1) uniform spatial distribution with multiplication factor decreasing with time because of loss of interest or confusion of the information, 2) multiplication factor constant but the rate of spreal decreasing with multiple hearings, 3) one-dimensional region with a small starting region with or without an absorbing barrier 4) two-dimensional region with absorbing barrier, 5) continous sources of information within a small region in one dimension, 6) uniform spatial distribution in which individuals do not respond to more than one hearing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476410
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 387-394 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A situation is considered in which a fluid containing a substance flows through a vessel at a constant rate, the substance being permeable to the vessel wall. In the region outside the vessel there is supposed to be rapid mixing in the direction perpendicular to the axis of the vessel but no mixing longitudinally. The solution for the spatial distribution at any time is given for the case of an arbitrary initial distribution along the vessel length in the absence of an input. The solution is also given for the case of a single impulsive input, the concentration being initially zero everywhere.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476432
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    A mathematical contribution to the study of orientation of organisms (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 431-476 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Organisms orient themselves to a stimulus by two general methods. One method is by directed orientation (taxis); the other is by undirected locomotory reaction (kinesis). An equation, and the methods for finding the necessary parameters of this equation, is derived for the distribution of organisms within a container, with the following limitations: (1) the organisms have no accommodation, (2) they are always active, and (3) the stimulus changes slowly with position. Necessary modifications of the equation are then derived, so that the last two limitations may be eliminated. The equation cannot be solved excatly because of its complexity; hence an approximation method must be used. This method is discussed, an approximate solution is found, and a time constant for equilibrium to be established is derived. Applications tovarious experiments in the literature are then made with fairly satisfactory results. A new interpretation of the theory of klino-kinesis with accommodation is found upon application of the equations developed to experimental work. Further limitations and uses of these equations are then discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476435
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Structural parameters of communication networks (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 501-507 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Certain parameters are defined which roughly characterize the internal structure of networks. A given network structure uniquely determines the values of the parameters, but the reverse is not true. The parameters therefore define certain classes of networks. One of the parameters, thedispersion D(S) gives an indication of the “compactness” of the internal structure. Addition theorems and inequalities are derived relating the dispersions of sub-systems to the dispersion of the complete structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476438
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Determination of diffusion and permeability coefficients in nerve trunks (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 489-500 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476437
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Enzyme localization as a mechanism of apparent active transport (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 509-522 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model based on enzyme localization is developed which gives rise to an apparent active transport of a metabolite into or out of cells. The model is applied to three simple situations, using Fick's equation and the Rashevsky approximation. It is shown that the apparent efficiency can be made as large as desired if, for constant reaction, the outer cell region is made sufficiently small, or, for autocatalytic reaction, if the metabolite concentration in the outer region is sufficiently small. The physical limitations imposed by this mechanism are developed for all three situations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476439
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Spread of information through a population with socio-structural bias: I. Assumption of transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 523-533 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A previously derived iteration formula for a random net was applied to some data on the spread of information through a population. It was found that if the axon density (the only free parameter in the formula) is determined by the first pair of experimental values, the predicted spread is much more rapid than the observed one. If the successive values of the “apparent axon density” are calculated from the successive experimental values, it is noticed that this quantity at first suffers a sharp drop from an initial high value to its lowest value and then gradually “recovers”. An attempt is made to account for this behavior of the apparent axon density in terms of the “assumption of transitivity”, based on a certain socio-structural bias, namely, that the likely contacts of two individuals who themselves have been in contact are expected to be strongly overlapping. The assumption of transitivity leads to a drop in the apparent axon density from an arbitrary initial value to the vicinity of unity (if the actual axon density is not too small). However, the “recovery” is not accounted for, and thus the predicted spread turns out to beslower than the observed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476440
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    Spread of information through a population with socio-structural bias: II. Various models with partial transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 535-546 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The assumption of transitivity treated in part I is modified in various ways to describe an information-diffusion process, in which a certain amount of randomness of contact does occur. In one model a parameter is introduced which is indicative of a tendency to go beyond one's immediate vicinity to spread the information as the vicinity becomes saturated with knowers. In another model the randomness appears in the assumption that new knowers are uniformly distributed among the knowers. Two of the equations thus derived, each with two free parameters are in good agreement with experimental results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476441
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    Coupling of a slow and a fast oscillator can generate bursting (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 1-21 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A general mechanism underlying bursting is proposed and described. It consists of two coupled nonlinear oscillators with different frequencies, where the slower oscillator alternatively switches the faster one on and off. This mechanism is shown to work in an extended Bonhoefer-van der Pol oscillator as well as in a modified version of the Hodgkin-Huxley equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459643
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 13
    Electronic Resource
    Electronic Resource
    A multidimensional birth process and its application to some problems in the dynamics of biological populations (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 333-345 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper is a sequel to a paper by the author entitled “Restricted Transition Probabilities and Their Applications to Some Problems in the Dynamics of Biological Populations” (Bull. Math. Biophysics, 1966,28, 315–331). The paper is divided into two parts. In part one some aspects of the maximum size attained by the population during a finite time interval are studied for the case the stochastic process underlying the evolution of the population is a birth process. Two interesting by-products emerge from the study presented in part one; namely a combinatorial method of finding solutions to the Kolmogorov differential equations in special cases, and secondly, a set of criteria for the optimum allocation of genotypes in the host population of a host-pathogen system. The optimum allocation of genotypes in the host population is a problem of practical importance in controlling plant pathogens. In part two the theory of restricted transition probabilities developed in the companion paper is applied in finding the distribution of the time to the appearance of the first mutation for the case of a two dimensional birth process. The distribution of the time to the appearance of the first mutation is of importance in understanding the role mutation plays in the evolution of a population, particularly in the pathogen population of a host-pathogen system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476814
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 14
    Electronic Resource
    Electronic Resource
    The motion of the left ventricle. I (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 355-362 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The complex arrangement of the muscle fibers in the ventricular wall and the nonsymmetric contraction and expansion of the ventricle preclude the writing of a differential equation of motion for the ventricle as a whole. We can, however, describe the motion of the ventricle by describing the motion of the dimensional parameters length and diameter; the radius, circumference, cross-sectional area, and volume following naturally from these. The ventricle is assumed to be an ellipsoid of revolution and the dimensional parameters to be periodic functions of time. Each of the parameters is expressed as a Fourier series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476816
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 15
    Electronic Resource
    Electronic Resource
    Comparaison des modeles de neurone de Hodgkin-Huxley et de Nelson (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 347-354 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Le modèle de Nelson peut-être considéré comme une approximation du modèle de Hodgkin-Huxley. Moins précis, il est plus maniable. Le modèle de Nelson peut également être considéré comme une généralisation du modèle de Hodgkin-Huxley. En effet, il introduit des liaisons synaptiques localisées ou diffusantes, et un processus de facilitation. Le mécanisme des liaisons synaptiques ne se traduit pas facilement dans le langage de Hodgkin-Huxley. Par contre, le processus de facilitation s'interprète facilement. Nelson's model can be taken as an approximation of Hodgkin-Huxley's model. Its precision is lesser, but it is more usable. Nelson's model can also be taken as a generalization of Hodgkin-Huxley's one; for it introduces localized or diffusing synaptic connexions and a facilitating process. The mechanism of synaptic connexions cannot be easily translated into Hodgkin-Huxley's language. On the contrary, the facilitating process is easily interpreted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476815
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 16
    Electronic Resource
    Electronic Resource
    The theory of the left ventricular aneurysm (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 363-370 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A spherical model for the human left ventricle with two different types of aneurysms, circular and rectangular-square, is proposed and meaningful relations are derived between the parameters of the aneurysms and ventricle. Such ventricular parameters as stroke volume, end-diastolic volume, and end-systolic volume are given normal human values to compute values for end-systolic radius and percentage shortening of muscle for various sized circular and rectangular-square aneurysms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476817
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 17
    Electronic Resource
    Electronic Resource
    A note on crime control (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 375-378 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Volterra theory of two competing populations is extended to the contemporary social problem of crime control. Domains of stability for the time dependence of the numbers in the criminal and enforcement groups are exposed by a numerical example. Both augmentation and reduction of enforcement can produce a stable system. Average values of the ratio of members in each group show great sensitivity to the control policies adopted by the remaining sector of the total population.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476819
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 18
    Electronic Resource
    Electronic Resource
    Interactions in enzymatic reactions (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 379-390 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper deals with interactions of substances via an enzymatic reaction (Bull. Math. Biophysics,25, 141–154, 1963). The substances are the activators, inhibitors and/or substrates of the reaction. Due to the bimolecularity of the processes in the reaction, the quantitative relation between the steady state amount of complexes and the amounts of the substances assumes a typical form. In multiple enzymatic reactions this form is more complicated, though basically similar. Because the substances may influence the steady state amounts of the complexes in opposite directions, the compensation and blocking effects are the properties of enzymatic reactions. The substances with the same direction of influence may potentiate each other. In the enzymatic reaction here considered, the potentiation is always non-negative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476820
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 19
    Electronic Resource
    Electronic Resource
    Decay of cell synchronization: Solutions of the cell-growth equation (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 391-409 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Growth-rate functions in analytic form have been obtained for cell cultures in which the doubling times follow the Gaussian and Poisson distributions. The growth-rate functions are calculated by using Laplace transforms to solve an integral equation previously presented. Oscillatory solutions result if a substantial fraction of the cells in a culture are synchronized to divide at some particular time. The synchrony and, hence, the oscillatory character of the growth-rate function eventually disappear because of the non-zero variance of the doubling-time distribution. If their variances are sufficiently small, the Gaussian and Poisson doubling-time distributions lead to growth-rate functions that become identical in the limit of large time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476821
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 20
    Electronic Resource
    Electronic Resource
    On the derivation of a mean growth equation for cell cultures (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 411-416 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract IfN(t) is the expected number of cells in a culture at timet, $$\dot N(t)$$ the corresponding time derivative, andf(t−τ)dt the probability that a cell of aget−τ at timet will divide in the succeeding time intervaldt, then according to Hirsch and Engelberg (this issue) there obtains the integral equation $$\dot N(t) = 2\int_{ - \infty }^t {f(t - \tau )\dot N(\tau )d\tau }$$ for describing the dynamics of the cell population. It is the purpose of this note to give two alternative derivations of this equation, one based on the age density equation of Von Foerster, and the other based on a generalized form of the Harris-Bellman equation describing the first moment of an age dependent, branching process. In addition, a probability model is posed from which the Von Foerster equation and, hence, the Hirsch-Engelberg equation readily follows.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476822
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 21
    Electronic Resource
    Electronic Resource
    A mathematical theory of enamel solubility and the onset of dental caries: I. The kinetics of dissolution of powdered enamel in acid buffer (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 417-432 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model of the dissolution kinetics of powdered enamel is developed based on the kinetic rate termq, $$q = K'H - k'C \cdot P_1$$ , whereH=[H +],C=[Ca ++] andP 1=[HPO 4 = ]. The differential equations describing the rate of mineral dissolution (and the linearly related rate of appearance of calcium and phosphate in solution) have been derived and solved for three basic cases: (1) when thepH of the solution and surface area of the enamel are considered constant, (2) when thepH is assumed constant, but the reduction in surface area during dissolution is considered, and (3) when the rise ofpH resulting from the buffering effect of the dissolved enamel is considered along with the change in surface area. Analytical solutions have been obtained for cases (1) and (2), while a numerical solution has been found for case (3). Data from a study on enamel dissolution are presented that agree with the theory of case (3), and it is noted that apH rise as large as 0.5 can occur, as has been shown elsewhere in the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476823
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 22
    Electronic Resource
    Electronic Resource
    Analytical bounding functions for diffusion problems with michaelis-menten kinetics (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 145-153 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Pointwise upper and lower bounds for the solution of a class of nonlinear diffusion problems with Michaelis-Menten kinetics are presented. Simple analytical bounding curves are obtained and for an illustrative case the calculated values bound the recent numerical solution of P. Hiltmann and P. Lory, 1983.Bull. math. Biol. 45, 661–664.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459650
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 23
    Electronic Resource
    Electronic Resource
    Reward and punishment in learning with possible reference to punishment for crime (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 477-481 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract On the basis of Landahl's theory of two-choice learning it is shown that application of punishment for wrong responses, without giving award for correct ones, does not lead to complete learning, no matter how many trials are used. If initially a “wrong response” was learned, then an attempt to inhibit it by punishment alone will in a class of cases lead only to a 50% suppression of that wrong response. Possible connection with the problem of effectiveness of punishment as a deterrent for crime is mentioned.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476827
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 24
    Electronic Resource
    Electronic Resource
    The use of two radiotracers for transfer-rate determinations in closed two compartment systems (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 483-483 
    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/BF02476828
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 25
    Electronic Resource
    Electronic Resource
    Cooperative specific adsorption of iona at charged sites in an electric field (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 483-483 
    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/BF02476829
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 26
    Electronic Resource
    Electronic Resource
    Operations research around the world meetings (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 485-485 
    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/BF02476830
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 27
    Electronic Resource
    Electronic Resource
    Dimensional anlaysis and the equations of electrophoresis (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 501-510 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A set of characteristic parameters is given for electrophoresis accompanied by diffusion, followed by a method of simplification of the transport equation. The concept of electrophoretic similarity is introduced in connection with the presentation of solutions and the final section contains some dimensional considerations of the potential equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476857
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 28
    Electronic Resource
    Electronic Resource
    Categories of (ℓ, ℛ)-systems (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 511-517 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We show that when we represent (ℓ, ℛ)-systems with fixed genome as automata (sequential machines), we get automata with output-dependent states. This yields a short proof that ((ℓ, ℛ)-systems from a subcategory of automata—and with more homomorphisms than previously exhibited. We show how ((ℓ, ℛ)-systems with variable genetic structure may be represented as automata and use this embedding to set up a larger subcategory of the category of automata. An analogy with dynamical systems is briefly discussed. This paper presents a formal exploration and extension of some of the ideas presented by Rosen (Bull. Math. Biophyss,26, 103–111, 1964;28, 141–148;28 149–151). We refer the reader to these papers, and references cited therein, for a discussion of the relevance of this material to relational biology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476858
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 29
    Electronic Resource
    Electronic Resource
    The origin of lift forces in fluttering flight (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 487-500 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A two-dimensional nonlinear integro-differential equation with time-varying coefficients describing the behavior of the fluttering wing-body systems typical of natural flight mechanisms has been deduced from the Navier-Stokes equation which generalizes local pressure and velocity distributions in the externally oscillating air field. The resulting equation for the wing forces is combined with an analogous expression for the forces of gravitation and acceleration associated with the body. The air acceleration force, not previously considered in bio-physical models of insect and bird flight, is shown to arise from a formal analysis of unsteady or time-varying contributions to the velocity field, while the square form of the conventional steady state aerodynamic forces is derived from the intertial terms in the Navier-Stokes equation with the aid of the approximations of Newtonian impact theory. Previous calculations (Houghton, 1964) have indicated that the contribution to gravitational stability of air acceleration and aerodynamic life are roughly in the ratio of 3:1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476856
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 30
    Electronic Resource
    Electronic Resource
    Evoked potentials arising from neural population elements excited at different times on a warped surface (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 519-536 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Certain types of cortical electrical events are non-propagated so that the associated electric fields must have standing wave characteristics. However, cortical electric events typically are generated by neurone populations which cannot be activated simultaneously on impulse driving. Hence the sum of the standing wave fields due to asynchronous activation of adjoining regions of cortical neurones must give the appearance of a traveling wave. Analysis of cortical waveforms is further complicated by curvature in cortical surfaces. A model is presented that shows the effects of curvature and time lag in activation on the form of the potential at points in space around a laminar array of elements simulating a population of cortical neurones. The results are compared with waveforms evoked by single-shock stimulation of the prepyriform cortex in cats.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476859
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 31
    Electronic Resource
    Electronic Resource
    A continuity equation for cell populations (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 545-554 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A continuity equation for cell-number density in a population of cells is derived, and a system of equations for eliminating parameters between the general solution and the initial distribution obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476861
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 32
    Electronic Resource
    Electronic Resource
    The behavior of the weakening and failing myocardium (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 537-544 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Use of an electrical model of the left ventricle of the heart and the arterial system permits analysis of the changes which take place as the capacity of the myocardium for generation of force decreases. The model is simple in structure, and its construction and practical testing would not be difficult. It demonstrates that, as the heart muscle weakens, the peak of intracardiac force occurs later in systole, and the difference between the intracardiac pressure and the aortic pressure in the second half of systole is much greater than for the normal heart. The feedback mechanisms which are proposed to affect myocardial contractility would affect this compensation for cardiac weakening. Indices to categorize the behavior of the normal, compensated though weakened, and decompensated myocardium are proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476860
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 33
    Electronic Resource
    Electronic Resource
    The frequency distribution of chromosome constituents in cells with chromosome-number dispersion (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 555-566 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The frequency distribution in a population of cells of the quantityCD (defined as the amount of some chromosomal substance in a cell which containsC chromosomes) is calculated using the distribution in the population of the amount per chromosome,D, and the distribution of chromosome number,C.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476862
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 34
    Electronic Resource
    Electronic Resource
    Calculation of rate of synthesis of chromosomal DNA in cells with chromosome-number dispersion (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 567-574 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The rate of chromosomal DNA synthesis in an exponentially growing population of cells having chromosome-number dispersion is calculated using DNA histogram data, chromosome-number distribution data, and the assumptions that the synthesis rate is constant and DNA double exactly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476863
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 35
    Electronic Resource
    Electronic Resource
    Estimation of rate of synthesis of chromosomal DNA in ehrlich ascites tumor cells (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 575-584 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An estimate is made of the rate coefficient for linear DNA synthesis with exact doubling in an exponentially growing population of Ehrlich ascites tumor cells having chromosome-number dispersion. Comparison of calculated and experimental results suggest that the assumptions used in the calculation are tenable, but further experimental evidence is needed to prove this.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476864
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 36
    Electronic Resource
    Electronic Resource
    A sociological approach to biology (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 655-661 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper develops further some suggestions made previously (Bulletin of Mathematical Biophysics,28, 283–308, 1966) that certain biological phenomena may be more easily interpreted from a “sociological” point of view by considering the organism as a social aggregate of cells and a cell as a social aggregate of genes. In this light the problems of origin of life on earth, of aging, and of parasitism and symbiosis are discussed. The notion of social aggregates of different orders is introduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476867
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 37
    Electronic Resource
    Electronic Resource
    Theorems on random evolution (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 663-663 
    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/BF02476868
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 38
    Electronic Resource
    Electronic Resource
    A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of intraocular pressure (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 585-643 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theoretical and experimental study was made of the mechanical behavior of the cornea. The theoretical analysis included an analytical solution for the symmetrical constraint of a thin, shallow, spherical shell by a rigid indenter. The experimental study investigated the rheology of the cornea with particular emphasis on its compliance with the requirements of the Boltzmann Superposition Principle. Representative results of tests on twenty enucleated hog eyes and two human eyes have been reported. The corneas of the human and hog eyes behaved as linear viscoelastic solids; the human eyes differed from the hog eyes in having a long term creep component. Several eyes were tested at the site of procurement, six to seven minutes after the animal's death, and it was established that creep is not an artifact due to aging or enucleation. The analytical and experimental results were combined to study some instruments used to detect the level of pressure in the eye. The theoretical analysis predicted that a type of elastic instability occurs during the process of flattening a small portion of the cornea; this is discussed with reference to the Goldmann and Mackay-Marg tonometers. The role of corneal creep was considered with reference to the response of the Schiøtz indentation tonometer during the time dependent process known as tonography.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476865
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 39
    Electronic Resource
    Electronic Resource
    Further studies on the shape of the tracking curve of an automobile and its dependence on biological parameters of the driver (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 645-654 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Following previous studies, differential equations are established which determine the variation of the stimulus towards a corrective turn of the steering wheel and its effect on the excitation of the centers in the brain which results in the production of the corrective turn. The equations are derived under the highly oversimplified assumption that all excitation thresholds are so small that they can be neglected. Under these assumptions it is found that the tracking curve of a car is a sinusoid with negative damping, that is, with an ever increasing amplitude. Driving under these assumptions is imposible since the car will always eventually jump off the road. The possible effects of the threshold as well as stimuli towards corrective turns other than the distance from the edge of the lane are very briefly discussed. In spite of the negative results of the paper, its interest lies in the circumstance that with the complication of the model, we find that driving depends not only on the reaction times as the only “purely biological” parameter, but on three other neurobiophysical constants. In a subsequent paper (Rashevsky, 1967) it is shown how the introduction of one or more purely biological parameters of the driver makes a stable driving regime possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476866
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 40
    Electronic Resource
    Electronic Resource
    The motion of thhe left ventriele: I (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 663-663 
    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/BF02476869
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 41
    Electronic Resource
    Electronic Resource
    Bimolecular systems: I. Linear systems of complexes (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 1-16 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A vast number of biologically important processes are based upon bimolecular systems. In these systems intermediate complexes are formed. Bimolecular systems in which no complex-complex interactions occur are called linear systems of complexes. A definition and some characteristic properties of these systems are given here. There may exist a contradiction of Onsager's principle of detailed balancing in these systems; however, no principal differences are found between the steady state behavior of an open system and that of a closed system. It is shown that the steady state behavior of a linear system of complexes of arbitrary complexity has some similarities with the steady state behavior of a simple bimolecular system, e.g., Michaelis-Menten enzymatic reaction. Multiplicity of action of the substances participating in biomolecular processes may produce some qualitative differences in the steady state behavior of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476958
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 42
    Electronic Resource
    Electronic Resource
    DNA histograms of irradiated cells: The case of prophase-trapping (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 17-32 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A time-dependent DNA histogram is calculated for an irradiated population of cells under the limiting assumption that the cells cannot pass through prophase due to the effects of the radiation. The population is assumed to increase exponentially prior to irradiation, but after irradiation to neither gain nor lose cells. Chromosome-number dispersion is taken into account in the calculation. The qualitative behavior of the calculated and experimental histograms are in reasonable agreement. The quantitative agreement between the two is relatively good at short post-irradiation times but is poor at long post-irradiation times (say, greater than half the doubling time). This suggests that recovery phenomena cannot be neglected at long post-irradiation times.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476959
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 43
    Electronic Resource
    Electronic Resource
    Cell mass concentration variance resulting from fluctuations in the incoming nutrient concentration to a chemostat (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 337-342 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The cellular response in terms of steady-state variance of cell mass concentration to fluctuations in incoming nutrient concentration to a chemostat has been examined. A white noise process is assumed to describe incoming nutrient concentration fluctuations and the variance of cell mass concentration has been found to depend on cell yield (a lumped measure of nutrient concentration fluctuation magnitude and lifetime) and two system time constants.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459920
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 44
    Electronic Resource
    Electronic Resource
    Chaotic dynamics of information processing: The “magic number seven plus-minus two” revisited (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 343-365 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a well-known collection of his essays in cognitive psychology Miller (The Psychology of Communication. Penguin, 1974) describes in detail a number of experiments aiming at a determination of the limits (if any) of the human brain in processing information. He concludes that the ‘channel capacity’ of human subjects does not exceed a few bits or that the number of categories of (one-dimensional) stimuli from which unambiguous judgment can be made are of the order of ‘seven plus or minus two’. This ‘magic number’ holds also, Miller found, for the number of random digits a person can correctly recall on a row and also the number of sentences that can be inserted inside a sentence in a natural language and still be read through without confusion. In this paper we propose a dynamical model of information processing by a self-organizing system which is based on the possible use of strange attractors as cognitive devices. It comes as an amusing surprise to find that such a model can, among other things, reproduce the ‘magic number seven plus-minus two’ and also its variance in a number of cases and provide a theoretical justification for them. This justification is based on the optimum length of a code which maximizes the dynamic storing capacity for the strings of digits constituting the set of external stimuli. This provides a mechanism for the fact that the ‘human channel’, which is so narrow and so noisy (of the order of just a few bits per second or a few bits per category) possesses the ability of squeezing or ‘compressing’ practically an unlimited number of bits per symbol—thereby giving rise to a phenomenal memory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459921
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 45
    Electronic Resource
    Electronic Resource
    The extension of two-dimensional cable theory to arteries and arterioles (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 409-424 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Electrical polarization of an artery or an arteriole may be modeled by the use of equations developed for two-dimensional cable theory. Two special cases have previously been solved: those corresponding to the case in which the radius is either zero (one-dimensional cable theory) or infinite. This paper presents the general solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459923
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 46
    Electronic Resource
    Electronic Resource
    On the computation of the tertiary structure of globular proteins—IV. Use of secondary structure information (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 367-407 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The distance geometry approach for computing the tertiary structure of globular proteins emphasized in this series of papers (Goelet al., J. theor. Biol. 99, 705–757, 1982) is developed further. This development includes incorporation of some secondary structure information—the location of alpha helices in the primary sequence—in the algorithm to compute the tertiary structure of alpha helical globular proteins. An algorithm is developed which estimates the interresidue distances between chain-proximate helices. These distances, in conjunction with the global statistical average distances obtainable from a database of real proteins and determined by the primary sequence of the protein under study, are used to determine the tertiary structure. Five proteins, parvalbumin, hemerythrin, human hemoglobin, lamprey hemoglobin, and sperm whale myoglobin, are investigated. The root mean square (RMS) errors between the calculated structures and those determined by X-ray diffraction range from 4.78 to 7.56 Å. These RMSs are 0.21–2.76 Å lower than those estimated without the secondary structure information. Contact maps and three-dimensional backbone representations also show considerable improvements with the introduction of secondary structure information.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459922
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 47
    Electronic Resource
    Electronic Resource
    Editorial: Software survey section (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), 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/BF02459925
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 48
    Electronic Resource
    Electronic Resource
    The unidirectional flux transient as a tool for quantifying parallel diffusional pathways through membranes. Exact solution for two pathways (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 425-434 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract If a plane membrane consists of patches, each with a given area and a given diffusion coefficient, then the transient of the total unidirectional flux of a diffusing substance (as defined experimentally by Ussing) is predictable. Here the inverse problem is studied: given only the observed transient of the total unidirectional diffusion flux, the unknown membrane heterogeneity transverse to the flux is to be quantified. The ratio of the arithmetic and of the harmonic means (both area-weighted) of the diffusion coefficients, evaluated over the membrane, is expressed in terms of the observed transient alone and is used to characterize the heterogeneity. A unique exact solution of the inverse problem for two kinds of patches is obtained in closed form. A singular limit of this solution pertains to currently postulated models of endothelial membranes, for which a characteristically shaped transient is predicted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459924
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 49
    Electronic Resource
    Electronic Resource
    Editor's comments (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 435-435 
    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/BF02460005
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 50
    Electronic Resource
    Electronic Resource
    Sequence similarity (‘Homology’) searching for molecular biologists (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 437-474 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Major types of sequence similarity searching (often, and incorrectly, called ‘homology’ searching) are reviewed and examples of each are presented. The features and limitations of each type of program, and individual implementations of each type are discussed. Two pairs of sequences are used as examples to show how implementations of each type differ in their results and their presentation. Both local and global alignment programs are examined, and the programs reviewed run on many different types of computer architectures, from laboratory computers such as the IBM PC, minicomputers such as the VAX, to large mainframe computers such as DEC-10/20 series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460006
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 51
    Electronic Resource
    Electronic Resource
    The existence of stable equilibria in Volterra predator-prey systems represented by loop graphs (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 489-494 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Criteria for the existence of globally stable equilibria in classical Volterra predator-prey systems represented by loop graphs are provided by comparing the community matrix with a matrix belonging to matrix classS W .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460008
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 52
    Electronic Resource
    Electronic Resource
    Pattern regulation in reaction-diffusion systems-the problem of size invariance (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 475-487 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Ordinary reaction-diffusion mechanisms do not account for size invariance properties of morphogenetic fields. We show that such a failure results from ignoring cell individuality. By considering purely topological factors, such as the number of intercellular contacts or the extent of the cell surface in contact with neighbouring cells, size invariance exists in reaction-diffusion systems. Our results are general, model independent and may be applied to any multi-unit ensemble exhibiting coherent behaviour.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460007
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 53
    Electronic Resource
    Electronic Resource
    Effects of twist on pulse waves in arteries (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 495-502 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The artery is treated as a thick-walled cylindrical shell. Using the large deformation theory, an analytical expression for the pulse wave speed is obtained and the effect of twist on the wave speed is discussed. Numerical results indicate that although phase velocity increases with pressure, it decreases with increasing twist angle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460009
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 54
    Electronic Resource
    Electronic Resource
    Effects of the shape of stenosis on the resistance to blood flow through an artery (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 545-550 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The effect of the shape of stenosis on the resistance to blood flow through an artery with mild local narrowing has been studied. It is shown that the resistance to flow decreases as the shape of stenosis changes and the maximum resistance is attained in the case of symmetric stenosis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460013
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 55
    Electronic Resource
    Electronic Resource
    A method for numbering binary rooted and unrooted phylogenies and their hypothetical taxonomic units (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 535-543 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A set of 2n−2 relations (edges) and a set ofn−1 hypothetical taxonomic units (HTUs) derive from the estimation of a binary phylogeny of a set ofn operational taxonomic units (OTUs). We propose an easy way for numbering thesen−1 hypothetical taxonomic units, as well as for then−2 interior points of an unrooted binary phylogeny. We also present an alternative method to the one proposed by Rohlf (Bull. math. Biol. 45, 33–40, 1983) for numbering the π i=1 n (2i−3) possible rooted binary phylogenies and the π i=1 n−1 (2i−3) possible unrooted binary phylogenies conerning a set ofn operational taxonomic units. An illustrative example of the method is presented. It is hoped that some studies in phylogenetics will become more accessible, from the viewpoint of computational economy, by the use of this method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460012
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 56
    Electronic Resource
    Electronic Resource
    Mathematical modeling of opiate binding to mouse brain membrane (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 503-512 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The heterogeneity of rat brain opiate receptors was examined by analyzing competition data. The binding of three prototypical tritiated opioid agonists, [3H]-dihydromorphine ([3H]-DHM), [3H]-D-ala2-D-leu5-enkephalin ([3H]-DADLE), and [3H]-ethylketocyclazocine ([3H]-EKC) was determined in the presence of varying concentrations of each of these unlabeled ligands, generating nine displacement curves. A computer program was then used to find the best fit of a model system to these data, assuming two, three or four independent binding sites. The best fit was a four-site model. One of these sites is specific for DHM; two are relatively selective for DHM and DADLE respectively, but also bind EKC. The remaining site binds only EKC with high affinity. These results, together with displacement data using naloxone, FK33824, and D-ala2-met5-enkephalinamide, are discussed in terms of current opiate receptor models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460010
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 57
    Electronic Resource
    Electronic Resource
    A note on the mathematical biology of automobile driving (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 187-188 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is pointed out that the three different stimuli for a corrective turn, namely the distance from the edge of the lane, the rate of approach to the edge, and the angle between the direction of the car and the direction of the lane (Bull. Math. Biophysics,28, 645–654, 1966,29, 181–186, 1967) may act all three simultaneously. It is found that in that case the tracking curve of the car is stable below a critical speed and becomes unstable above it.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476971
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 58
    Electronic Resource
    Electronic Resource
    Mathematical biology of automobile driving (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 181-186 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Continuing a previous study (Bull. Math. Biophysics, 28, 645–654, 1966), the biophysical mechanism of a corrective turn is investigated for the case where the stimulus for the corrective turn is produced not only by the perception of the nearness of an edge of the lane, but also by the rate of approach of the car towards the edge. In that case it is found that the tracking curve of the car may consist of a series of damped sinusoids and safe driving would be possible at any speed if it were not for the endogenous fluctuation in the driver's central nervous system. If the effect of the rate of approach increases sufficiently rapidly as the distance to the edge of the lane decreases, then a stable undamped oscillating tracking curve is possible. The case is also studied where the driver makes a corrective turn in response to a direct perception of the angle between the direction of the lane and the longitudinal axis of the car.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476970
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 59
    Electronic Resource
    Electronic Resource
    Angles of branching and diameters of branches in the human bronchial tree (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 245-259 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The principle of minimal work requires that the conducting airways of the human lung should have a maximum radius for minimal resistance to gas flow. At the same time there is a requirement that the airways should have a minimal volume for economy of space. These two opposing requirements have been investigated mathematically, and a method for calculating the angle of branching which produces minimal volume has been derived. The relationship of the radii of the parent and daughter branches to produce minimal resistance has been similarly defined. By measurement of a bronchial cast from a human lung the extent to which the predicted optimum structure is realized in practice has been shown. The change in structure associated with change of function at the transition from conducting airway to diffusion zone has been demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476898
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 60
    Electronic Resource
    Electronic Resource
    Finite linnaean structures (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 191-206 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper considers a class of set-theoretical entities, calledn-rank Linnaean structures, which are intended as abstract models of the taxonomic classificatory systems of biology. In the first part, devoted to formalism, finite Linnaean structures are discussed in complete generality; but, in addition, eight distinct subclasses are noted and some of the properties of their elements are explored. In the second part, concerned with applications, it is shown that taxonomic systems may be recast in the form of finite Linnaean structures, and an effort is made to show that some undesirable features of earlier models are avoided without artificiality and without abandoning extensional mathematics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476893
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 61
    Electronic Resource
    Electronic Resource
    Abstract power structures (APS) and related bumping orders (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 207-216 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Generalizing an idea of M. Richardson (Fundamentals of Mathematics, New York: Macmillan Co., 1958), an APS on a given populationP is a non-empty collection of non-empty subsets ofP such that ifA is in the collection andA⊆B, thenB is in the collection. From a structure of this kind a partial ordering ofP, called therelated bumping order, is derived. The question is raised as to what kinds of partial orderings can be so obtained. For structures determined by voting weights of the members of the population, a complete characterization of all possible bumping orders is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476894
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 62
    Electronic Resource
    Electronic Resource
    Stability analysis of a mathematical neuron model (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 217-226 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The “second method” of Liapunov is used to perform a stability analysis of a mathematical model of the neuron. This analysis is based on the hypothesis that the firing of the neuron coincides with a temporary state of instability of the system, and that the initiation of all-or-none process depends on the magnitude of membrane depolarization and its first time derivative. It is found that the stability (and hence the possibility of a second firing) is restored approximately when the rate of membrane repolarization is at a maximum. This result predicts that the duration of the period of absolute refractoriness in neurons would be about 75 per cent of the spike duration, and thus shorter than the value usually obtained from experimental measurements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476895
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 63
    Electronic Resource
    Electronic Resource
    A neural net model for masking phenomena (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 227-232 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some aspects of masking phenomena are considered in terms of the simplest possible model of two-factor neural elements. The effect of a number of variables can be accounted for, but the introduction of an internuncial element results in a masking function which need not be symmetric about zero delay interval. As an illustration, the results for a special case are compared with available data. In general, such a model results in a masking function which depends on the intensity, area, and duration of the stimuli, as well as on the temporal and spatial separation between them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476896
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 64
    Electronic Resource
    Electronic Resource
    Capillary operators—II (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 651-668 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This work continues with an examination of capillary exchange models as operators, namely the operatorsO k andK αk relating extravascular and intravascular concentration to input for the Krogh cylinder model of a single capillary, a model basic to many organ models. Fundamental algebraic and analytic properties are presented: the operators belong to a commutative Banach algebra; an addition theorem holdsK αk +K βk =K α+β,k ; the operatorK αk has an inverse;K αk -1 , (as an operator on LebesgueL p space or on the locally integrable functions); partial derivatives are given forK αk [f](t) andO k [f](t) (sensitivity functions); and inequalities are established for the derivatives. Dominance relations between model curves are inferred. Error bound formulas are presented forK andO as bounds on ‖K αk f-K βl f‖ p and ‖O k f-O l f‖ p for allL p . Consequent limitations on relative errors are shown. The implications for operators on a finite time interval are deduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460131
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 65
    Electronic Resource
    Electronic Resource
    A theoretical analysis for determining the nonlinear hydraulic permeability of a soft tissue from a permeation experiment (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 669-683 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The nonlinear nature of the hydraulic permeability, as well as the corresponding pressure and displacement fields, in a soft tissue are studied for steady-state permeation. From a two-phase continuum model analytical expressions are derived that can be used with the results from a permeation experiment to determine the dependence of the permeability on the strain. In the process it is found that, because of the compaction of the tissue arising from fluid flow, it is necessary to distinguish between the apparent and intrinsic permeability. The former, which is an averaged quantity, is the permeability usually obtained in permeation studies. However, as shown from the analysis, it can differ substantially from the latter, which is the local permeability in the tissue.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460132
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 66
    Electronic Resource
    Electronic Resource
    Editorial: Software survey section (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), 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/BF02460134
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 67
    Electronic Resource
    Electronic Resource
    Editor's comments (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 695-695 
    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/BF02469298
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 68
    Electronic Resource
    Electronic Resource
    Chaotic phenomena (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 697-738 
    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/BF02469299
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 69
    Electronic Resource
    Electronic Resource
    Effects of the torso boundary and internal conductivity interfaces in electrocardiography: An evaluation of the ‘Infinite medium’ approximation (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 685-694 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The analytic, eccentric spheres model of the torso was used to examine the validity of approximating the ‘infinite medium’ potential by integrating ‘finite medium potentials’ over the torso surface. Although idealized, the analytic model is sophisticated enough for all important torso conductivity and geometry parameters to be preserved in the formulation. The model generates both ‘finite medium’ potentials (for which the torso is surrounded by air) and also ‘infinite medium’ potentials (for which the outermost layer of the torso extends outward to infinity). The finite medium torso potentials were integrated over the torso surface in accordance with the approximation used by many investigators in an effort to make the surface distribution more representative of the primary cardiac sources. The resulting potential distribution was compared with the true infinite medium potential, in which the effects of internal inhomogeneities (secondary sources) were taken into account. The difference between the two representations was found to be significant, and caution should be used when interpreting such data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460133
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 70
    Electronic Resource
    Electronic Resource
    An environ analysis for nonlinear compartment models (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 739-748 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Environ analysis, an input-output analysis for models of ecological systems, has been previously formulated for linear systems. This note has a twofold purpose: first, we indicate that a variation of parameters technique can be applied, at least in principle, to computeboth input and output environs; and second, we show that this technique may be used for computation of environs in nonautonomous, nonlinear compartment models. This nonlinear theory, obtained as a direct extension of dynamical system developments, allows the traditional environ partitioning of compartmental storages and flows. An example of a nonlinear nutrient-producer-consumer system whose output environs can be computed asymptotically is presented to illustrate these concepts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02469300
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 71
    Electronic Resource
    Electronic Resource
    Dependence of tetanic hyperpolarization on pump conductance in the cyanide-treatedXenopus node (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 749-755 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Prolonged exposure to cyanide leads to a delayed but reversible disappearance of tetanic hyperpolarization in theXenopus node (G. M. Schoepfle,Am. J. Physiol. 231, 1033–1038, 1976). This effect is attributed to a pronounced decline in the absolute values of the ATP and ADP concentrations, such that the ATP-driven ion translocation is no longer possible, regardless of the existing values for (Na)i, (K)i and the (ATP)/(ADP) ratio. Mathematically, this would imply a vanishing of a constant pump conductance gp in the exression for electrogenic pump current densitityJ p, whereJ p=g p (V m −E p) in whichV m is membrane potential andE p is an ATP-and sodium-dependent e.m.f.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02469301
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 72
    Electronic Resource
    Electronic Resource
    Stress-strain behavior for curved exponential strips (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 757-764 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract For the two-parameter (A, α) exponentially-stiffening constituitive relation, typical of many biological materials, it is shown that the uniaxial stress-strain behavior of an initially curved strip is significantly changed by the residual bending stresses. Closedform theoretical results depend on the thickness to radius ratio (h/R) and the relative strain level ε(h/R). The bending stresses tend to obscure accurate measurement ofA and α unless care is taken. However, it is shown that by changing co-ordinates to (dℝ/d∈, ℝ)-space, bothA and α can be recovered from the high stress data, and α alone can be recovered from the low stress data. This has practical application to the mechanics of cornea, sclera, and heart muscle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02469302
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 73
    Electronic Resource
    Electronic Resource
    A mathematical note on the fahraeuslindqvist effect in power law fluid (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 765-769 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An axisymmetric flow of a power law fluid through circular tubes under constant pressure gradient with the flow parameters varying radially is analyzed theoretically. The main finding is that for the Fahraeus-Lindqvist (F-L) effect to occur, it is necessary to have at least one of the parametersK (consistency) andn (index) as a discontinuous function ofr in the absence of wall slip; and with slip condition the parameters could be continuous functions ofr under specific conditions. In both the cases the existence of more than one discontinuity cannot be ruled out. The results obtained are consistent with experimental findings of blood flow through narrow tubes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02469303
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 74
    Electronic Resource
    Electronic Resource
    Zygotic algebra for two linked loci with sexually different recombination rates (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 771-782 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This is a study of the properties of a zygotic algebra of two linked autosomal loci with different recombination rates in males and females, without selection or mutation and with random mating. The above-mentioned zygotic algebra contains a genetic subalgebra. A canonical basis of this subalgebra is constructed and the train roots are calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02469304
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 75
    Electronic Resource
    Electronic Resource
    Third International Summer School on Mathematical Modelling in Physiology and Clinical Medicine (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 799-799 
    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/BF02469307
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 76
    Electronic Resource
    Electronic Resource
    The possible role of solitonic processes during A to B conformational changes in DNA (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 783-789 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Among the conformations which the DNA molecule can adopt, the transition beween the A and B families, controlled by water content (relative humidity), seems to be implicated in the transcription process. Focusing on the main structural difference involved (tilting of base normals with respect to the helix axis), a model is constructed, solitary wave solutions of the resulting equation of motion are demonstrated and possible experimental implications indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02469305
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 77
    Electronic Resource
    Electronic Resource
    On the distribution of the time required to remove white balls from an URN (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 791-797 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Balls are removed one-at-a-time at equal time intervals from an urn initially containingw 0 white balls and a large number b of black balls and each black or white ball is immediately replaced by a black ball. The distribution of the number of white balls remaining aftert iterations (under certain limiting operations) is taken from the literature. The problem is to use this result to find the time required to remove a fixed number of white ballsw 1 from the urn. We then find the mean and variance of this distribution and also look at the special case whenw 1 =w 0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02469306
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 78
    Electronic Resource
    Electronic Resource
    Editorial: Software survey section (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), 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/BF02469308
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 79
    Electronic Resource
    Electronic Resource
    The struggle for life: I. Two species (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 377-388 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The general equations are discussed describing two species in competition or in symbiosis or feeding one on the other.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476909
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 80
    Electronic Resource
    Electronic Resource
    A note on Rashevsky’s postulate of relational forces (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 403-404 
    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/BF02476912
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 81
    Electronic Resource
    Electronic Resource
    Organismic sets and biological epimorphism (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 389-393 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that the principle of biological epimorphism (Rashevsky,Mathematical Principles in Biology and Their Applications, Springfield, Ill.: Charles Thomas, 1960) is contained in the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967) if an additional postulate not directly connected to mappings is made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476910
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 82
    Electronic Resource
    Electronic Resource
    An equation for flow in the renal proximal tubule (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 29-57 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460061
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 83
    Electronic Resource
    Electronic Resource
    Out-of-print volumes and back issues of the Bulletin of Mathematical Biophysics (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 407-407 
    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/BF02476914
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 84
    Electronic Resource
    Electronic Resource
    Model of urethra under uniform circumferential tension (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 409-409 
    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/BF02476915
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 85
    Electronic Resource
    Electronic Resource
    Seventeenth Annual Meeting of the Classification Society of North America (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 105-105 
    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/BF02460066
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 86
    Electronic Resource
    Electronic Resource
    Editorial: Software Survey Section (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), 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/BF02460067
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 87
    Electronic Resource
    Electronic Resource
    Dominance of geometric overelastic factors in pulse transmission through arterial branching (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 97-103 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460065
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 88
    Electronic Resource
    Electronic Resource
    Galerkin's finite element-Laplace transform technique to transient heat migration in human skin and subcutaneous tissues (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 125-136 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Galerkin's finite element-Laplace transform technique (GAFELTTE) has been used to study transient temperature distribution in human skin and subcutaneous tissues. This study incorporates heat conduction, heat carried by perfusion of blood in the capillary beds and metabolic heat generation in the tissues. Different values of various quantities have been considered in all three parts, namely epidermis, dermis and subcutaneous tissues, depending on physiological considerations. The GAFELTTE provides interface temperatures for a wide range of the values of skin surface temperatures. These values have been used to obtain temperature profiles in the region considered. Steady-state temperature distribution has been deduced from the solution obtained by GAFELTTE and has been compared with the results obtained by using different methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460018
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 89
    Electronic Resource
    Electronic Resource
    Multiple stable equilibria in a predator-prey system (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 137-148 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Necessary and sufficient conditions are given for three equilibria to occur in a predatorprey model and conditions are given for two of these to be stable. The existence of two stable equilibria requires predator intraspecific competition for either space or food, and the lower the prey growth rate the stronger this predator self-regulation must be. A prey growth rate that is skewed to the right, the ability of a few predators to survive at low prey densities, and predators with high searching effectiveness, long handling times, and large maximum per capita rate of increase all make two stable equilibria more likely.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460019
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 90
    Electronic Resource
    Electronic Resource
    Servocontrol of the heart rate in homeothermic animals: On recognizing butterfly catastrophy models in biology (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 107-124 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Drawing evidence from a variety of cardiovascular studies on the heart rate in homeothermic animals, the author establishes the following thesis. The servocontrol (i.e. the autonomic and reflex control) by the medulla oblongata of the heart (rate) is a negative feedback dynamic which is isomorphic (i.e. ‘diffeomorphic’) to the dyamic underlying the heat rate control in those animals (cf. Kuyk,Bull. math. Biol. 46, 81–102, 1984). In fact, unlike in the heat rate case, the qualitative evidence supporting this thesis can not be fully complemented by quantitative data stemming from experiments, because of a lack of pertinent experiments—which, indeed, should measuresimultaneously the heart rate state parameter and thefour control parameters at the input side of the medulla. The results of some of the existing experiments on animal preparations can nevertheless be adduced to recognize that this dynamic can be graphed by the five-dimensional butterfly catastrophe type. The theory leads to new ways of looking at experiments in the field and/or setting up such experiments in the future.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460017
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 91
    Electronic Resource
    Electronic Resource
    Simulation of cellular compaction and internalization in mammalian embryo development as driven by minimization of surface energy (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 167-187 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model based upon minimization of surface energy is proposed as an explanation for compaction and internalization of cells during mammalian embryo development. The model is used to simulate and graphically display these phenomena on a computer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460021
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 92
    Electronic Resource
    Electronic Resource
    Topological properties of binary trees grown with order-dependent branching probabilities (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 197-211 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper describes a growth model for binary topological trees. The model defines the branching probability of all segments in the tree. The branching probability of a segment is formulated as a function of two variables, one indicating its type (intermediate or terminal), the other representing its order, i.e. the topological distance to the root segment. The function is determined by two parameters, namely the ratio of branching probabilities of intermediate and terminal segments and the strength of the order dependency, implemented in an exponential form. Expressions are derived for the calculation of symmetry properties of the partitions and it is indicated which part of the parameter domain results in predominantly symmetrical trees.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460023
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 93
    Electronic Resource
    Electronic Resource
    Pattern formation and morphogenesis: A reaction-diffusion model (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 213-228 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of cellular differentiation and consequent pattern generation during embryonic development has been mathematically investigated with the help of a reaction-diffusion model. It is by now a well-recognized fact that diffusion of micromolecules (through intercellular gap junctions), which is dependent on the spatial parameter (r), serve the purpose of ‘positional information’ for differentiation. Based on this principle the present model has been constructed by coupling the Goodwin-type equations for RNA and protein synthesis with the diffusion process. The homogeneous Goodwin system can exhibit stable periodic solution if the value of the cooperativity as measured by the Hill coefficient (ρ) is greater than 8, which is not biologically realistic. In the present work it has been observed that inclusion of a negative cross-diffusion can drive the system into local instability for any value of ρ and thus a time-periodic spatial solution is possible around the unstable local equilibrium, eventually leading to a definite pattern formation. Inclusion of a negative cross-diffusion thus makes the system biologically realistic. The cross-diffusion can also give rise to a stationary wave-like dissipative structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460024
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 94
    Electronic Resource
    Electronic Resource
    Editorial: Software survey section (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), 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/BF02460027
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 95
    Electronic Resource
    Electronic Resource
    Bimolecular systems: II. Nonlinear systems of complexes (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 605-613 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper deals with bimolecular systems in which also complex-complex interactions occur. Because of the complexity of the problem, an approximation in a form of coupled linear systems of complexes (Bull. Math. Biophysics,29, 1–16, 1967) is considered. Two types of couplings, serial and parallel, are studied. In the serial coupling the nonlinear system of complexes has the same behavior as its subsystems. An entity, initial sensitivity, has interesting properties: in serial coupling it is at most equal to the product and in parallel coupling, at most equal to the sum of partial initial sensitivities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476597
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 96
    Electronic Resource
    Electronic Resource
    Bimolecular systems: III. Catalytic systems (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 615-623 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Amplification effect in the catalytic bimolecular systems is a consequence of the kinetic characteristic of the catalyst. Two types of the coefficient of amplification are defined. The applicability of these definitions is given by the type of the bimolecular system. In a simple example it is shown that the concept of amplification is meaningful in these systems. Furthermore, two rules, analogous to those for a coupling of amplifiers, are derived for the two basic modes of coupling of catalytic systems. Thus, in biological systems the catalytic reactions may be regarded as biologically effective amplifiers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476598
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 97
    Electronic Resource
    Electronic Resource
    A theory of cell hydration governed by adsorption of water on cell proteins rather than by osmotic pressure (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 583-596 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is postulated that cell hydration is governed by adsorption of water on cell proteins in accord with the Bradley adsorption isotherm, and that the action of a solute in the surrounding solution is to lower the vapor pressure of the solution so that cell water adsorption is decreased by moving down the Bradley isotherm. From these concepts, it is derived that cell volume (V) should be related to solute concentration (x) by the equationV=−E log10 x+F whereE andF are constants which are independent of type of solute. For a non-adsorbed solute this agrees well with experimental data. For solutes which are adsorbed by cell proteins, a correction in the above equation may be necessary at higher solute concentrations, which is shown to be compatible with various experimental data. The types of experiments which are generally used to support the osmotic pressure theory of cell hydration agree equally well with the adsorption theory. The virtue of the adsorption theory is that, unlike the osmotic pressure theory of cell swelling, it is compatible with permeability of the cell membrane to solutes, which has been experimentally observed for various solutes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476595
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 98
    Electronic Resource
    Electronic Resource
    Considerations of quasi-stationarity in electrophysiological systems (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 657-664 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Conditions under which a time varying electromagnetic field problem (such as arises in electrophysiology, electrocardiography, etc.) can be reduced to the conventional quasistatic problem are summarized. These conditions are discussed for typical physiological parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476917
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 99
    Electronic Resource
    Electronic Resource
    The dead space in a compartmental lung model (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 711-718 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A compartmental lung model with any number of synchronously filling and emptying functional chambers and a common dead space or conducting region is considered. It is shown that the model gives rise to an output, in an open circuit washout determination, which is a weighted sum of exponentials. From estimates of these weights and exponential components, estimates of the model parameters can be recovered. Relations giving the unique correspondence between the output parameters and the model parameters are derived and the existence and uniqueness of solutions established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476922
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 100
    Electronic Resource
    Electronic Resource
    A charge transfer process in the visual pigments (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 677-690 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A physical model that incorporates all the experimental information on the formation of the visual pigment rhodopsin is presented. The visual pigments consist of a chromophore bound to an appropriate protein. Thus rhodopsin (λm 505 mμ) is formed by a Schiff’s base linkage C19H27CH=NH+-opsin (λm 440 mμ) between 11-cis retinal (λm 380 mμ) and the protein opsin (λm 280 mμ). It is found that there exists a red shift in the spectrum of rhodopsin from the Schiff’s base. The model brings an explanation for this red shift. It is shown that such a shift may be due to a charge transfer process (R. S. Mulliken,J. Am. Chem. Soc.,74, 811–824, 1952) between an electron at the double bond of carbons C11−C12 and an atomic orbital of the sulphur present in cysteine. This provides an explanation of the presence of SH-groups in the protein after the absorption of light. A one-electron approximation is used and the dipole momentμ NV ; hence, the oscillator strengthf of the transitionNV is estimated and compared with the experimentally determined extinction coefficient ∈m by mixing 3.5×10−3 M of 11-cis retinal with 8.3×10−5 M of cysteine at pH ranges 6 through 8. Reasonable agreement is found. Solvent, concentration and temperature dependence are shown also.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476919
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...