共查询到20条相似文献,搜索用时 31 毫秒
1.
We introduce inhomogeneous, substrate dependent cell division in a time discrete, nonlinear matrix model of size-structured
population growth in the chemostat, first introduced by Gage et al. [8] and later analysed by Smith [13]. We show that mass conservation is verified, and conclude that our system admits one
non zero globally stable equilibrium, which we express explicitly. Then we run numerical simulations of the system, and compare
the predictions of the model to data related to phytoplankton growth, whose obtention we discuss. We end with the identification
of several parameters of the system.
Received: 9 February 2000 / Revised version: 10 October 2001 / Published online: 23 August 2002
RID="*"
ID="*" Present address: Department of Mathematics and Statistics, University of Victoria, B.C., Canada. e-mail: jarino@math.uvic.ca
Key words or phrases: Chemostat – Structured population models – Discrete model – Inhomogeneous division size 相似文献
2.
The purpose of this paper is to present a mathematical model for the tumor vascularization theory of tumor growth proposed
by Judah Folkman in the early 1970s and subsequently established experimentally by him and his coworkers [Ausprunk, D. H.
and J. Folkman (1977) Migration and proliferation of endothelial cells in performed and newly formed blood vessels during
tumor angiogenesis, Microvasc Res., 14, 53–65; Brem, S., B. A. Preis, ScD. Langer, B. A. Brem and J. Folkman (1997) Inhibition of neovascularization by an extract
derived from vitreous Am. J. Opthalmol., 84, 323–328; Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64; Gimbrone, M. A. Jr, R. S. Cotran, S. B. Leapman and J. Folkman (1974) Tumor growth and neovascularization: an experimental
model using the rabbit cornea, J. Nat. Cancer Inst., 52, 413–419]. In the simplest version of this model, an avascular tumor secretes a tumor growth factor (TGF) which is transported
across an extracellular matrix (ECM) to a neighboring vasculature where it stimulates endothelial cells to produce a protease
that acts as a catalyst to degrade the fibronectin of the capillary wall and the ECM. The endothelial cells then move up the
TGF gradient back to the tumor, proliferating and forming a new capillary network. In the model presented here, we include
two mechanisms for the action of angiostatin. In the first mechanism, substantiated experimentally, the angiostatin acts as
a protease inhibitor. A second mechanism for the production of protease inhibitor from angiostatin by endothelial cells is
proposed to be of Michaelis-Menten type. Mathematically, this mechanism includes the former as a subcase.
Our model is different from other attempts to model the process of tumor angiogenesis in that it focuses (1) on the biochemistry
of the process at the level of the cell; (2) the movement of the cells is based on the theory of reinforced random walks;
(3) standard transport equations for the diffusion of molecular species in porous media.
One consequence of our numerical simulations is that we obtain very good computational agreement with the time of the onset
of vascularization and the rate of capillary tip growth observed in rabbit cornea experiments [Ausprunk, D. H. and J. Folkman
(1977) Migration and proliferation of endothelial cells in performed and newly formed blood vessels during tumor angiogenesis,
Microvasc Res., 14, 73–65; Brem, S., B. A. Preis, ScD. Langer, B. A. Brem and J. Folkman (1997) Inhibition of neovascularization by an extract
derived from vitreous Am. J. Opthalmol., 84, 323–328; Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64; Gimbrone, M. A. Jr, R. S. Cotran, S. B. Leapman and J. Folkman (1974) Tumor growth and neovascularization: An experimental
model using the rabbit cornea, J. Nat. Cancer Inst., 52, 413–419]. Furthermore, our numerical experiments agree with the observation that the tip of a growing capillary accelerates
as it approaches the tumor [Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64].
An erratum to this article is available at . 相似文献
3.
The evolution of a consumer exploiting two resources is investigated. The strategy x under selection represents the fraction of time or energy an individual invests into extracting the first resource. In the
model, a dimensionless parameter α quantifies how simultaneous consumption of both resources influences consumer growth; α<0
corresponds to hemi-essential resources, 0<α<1 corresponds to complementary resources, α=1 corresponds to perfectly substitutable
resources, and α>1 corresponds to antagonistic resources. An analysis of the ecological and evolutionary dynamics leads to
five conclusions. First, when α≤1, there is a unique singular strategy x
* for the adaptive dynamics and it is evolutionarily stable and globally convergent stable. Second, when α=1, the singular
strategy x
* corresponds to the populations exhibiting an ideal free distribution and a population playing this strategy can invade and
displace populations playing any other strategy. Third, when α>1, the strategies x=0 and x=1 are evolutionarily stable and convergent stable. Hence, if the populations initially specialize on one resource, evolution
amplifies this specialization. Fourth, when α is slightly larger than one (i.e. the resources are slightly antagonistic),
there is a convergent stable singular strategy whose basin of attraction is almost the entire strategy space (0,1). This singular
strategy is evolutionarily unstable and serves as an evolutionary branching point. Following evolutionary branching, our analysis
and numerical simulations suggest that evolutionary dynamics are driven toward an end state consisting of two populations
specializing on different resources. Fifth, when α>>1, there is only one singular strategy and it is convergent unstable and
evolutionarily unstable. Hence, if resources are overly antagonistic, evolutionary branching does not occur and ultimately
only one resource is exploited.
Received: 8 June 2002 / Revised version: 28 November 2002 /
Published online: 23 April 2003
This work was supported by NSF Grant DMS-0077986
Key words or phrases: Consumer-resource interactions – Adaptive dynamics – Evolutionary branching 相似文献
4.
Early development and quorum sensing in bacterial biofilms 总被引:3,自引:0,他引:3
Ward JP King JR Koerber AJ Croft JM Sockett RE Williams P 《Journal of mathematical biology》2003,47(1):23-55
We develop mathematical models to examine the formation, growth and quorum sensing activity of bacterial biofilms. The growth
aspects of the model are based on the assumption of a continuum of bacterial cells whose growth generates movement, within
the developing biofilm, described by a velocity field. A model proposed in Ward et al. (2001) to describe quorum sensing, a process by which bacteria monitor their own population density by the use of quorum
sensing molecules (QSMs), is coupled with the growth model. The resulting system of nonlinear partial differential equations
is solved numerically, revealing results which are qualitatively consistent with experimental ones. Analytical solutions derived
by assuming uniform initial conditions demonstrate that, for large time, a biofilm grows algebraically with time; criteria
for linear growth of the biofilm biomass, consistent with experimental data, are established. The analysis reveals, for a
biologically realistic limit, the existence of a bifurcation between non-active and active quorum sensing in the biofilm.
The model also predicts that travelling waves of quorum sensing behaviour can occur within a certain time frame; while the
travelling wave analysis reveals a range of possible travelling wave speeds, numerical solutions suggest that the minimum
wave speed, determined by linearisation, is realised for a wide class of initial conditions.
Received: 10 February 2002 / Revised version: 29 October 2002 /
Published online: 19 March 2003
Key words or phrases: Bacterial biofilm – Quorum sensing – Mathematical modelling – Numerical solution – Asymptotic analysis – Travelling wave
analysis 相似文献
5.
Senn W 《Biological cybernetics》2002,87(5-6):344-355
Spike-timing-dependent plasticity (STDP) strengthens synapses that are activated immediately before a postsynaptic spike,
and weakens those that are activated after a spike. To prevent an uncontrolled growth of the synaptic strengths, weakening
must dominate strengthening for uncorrelated spike times. However, this weight-normalization property would preclude Hebbian
potentiation when the pre- and postsynaptic neurons are strongly active without specific spike-time correlations. We show
that nonlinear STDP as inherent in the data of Markram et al. [(1997) Science 275:213–215] can preserve the benefits of both
weight normalization and Hebbian plasticity, and hence can account for learning based on spike-time correlations and on mean
firing rates. As examples we consider the moving-threshold property of the Bienenstock–Cooper–Munro rule, the development
of direction-selective simple cells by changing short-term synaptic depression, and the joint adaptation of axonal and dendritic
delays. Without threshold nonlinearity at low frequencies, the development of direction selectivity does not stabilize in
a natural stimulation environment. Without synaptic unreliability there is no causal development of axonal and dendritic delays.
Received: 22 April 2002 / Accepted: 23 May 2002
Acknowledgements. This study was supported by the Swiss National Science Foundation (grant 3152-065234.01) and the Silva-Casa foundation. The
author thanks Stefano Fusi, Henry Markram, and Misha Tsodyks for helpful discussions, Nissim Buchs and Martin Schneider for
their simulations, and Jan Reutimann for proof reading.
Correspondence to: e-mail: wsenn@cns.unibe.ch, Tel.: +41-31-6318721, Fax: 41-31-6314611 相似文献
6.
Exact formulas for the mean and variance of the proportion of different types in a fixed generation of a multi-type Galton-Watson
process are derived. The formulas are given in terms of iterates of the probability generating function of the offspring distribution.
It is also shown that the sequence of types backwards from a randomly sampled particle in a fixed generation is a non-homogeneous
Markov chain where the transition probabilities can be given explicitly, again in terms of probability generating functions.
Two biological applications are considered: mutations in mitochondrial DNA and the polymerase chain reaction.
Received: 10 June 2001 / Revised version: 21 November 2001 / Published online: 23 August 2002
Mathematics Subject Classification (2000): Primary 60J80, Secondary 92D10, 92D25
Key words or phrases: Multi-type Galton-Watson process – sampling formula – PCR – mitochondrial DNA 相似文献
7.
We consider a partially coupled diffusive population model in which the state variables represent the densities of the immature
and mature population of a single species. The equation for the mature population can be considered on its own, and is a delay
differential equation with a delay-dependent coefficient. For the case when the immatures are immobile, we prove that travelling
wavefront solutions exist connecting the zero solution of the equation for the matures with the delay-dependent positive equilibrium
state. As a perturbation of this case we then consider the case of low immature diffusivity showing that the travelling front
solutions continue to persist. Our findings are contrasted with recent studies of the delayed Fisher equation. Travelling
fronts of the latter are known to lose monotonicity for sufficiently large delays. In contrast, travelling fronts of our equation
appear to remain monotone for all values of the delay.
Received: 1 November 2001 / Revised version: 10 May 2002 / Published online: 23 August 2002
Mathematics Subject Classification (2000): 35K57, 92D25
Key words or phrases: Age-structure – Time-delay – Travelling Fronts – Reaction-diffusion 相似文献
8.
We consider a discrete time model of semelparous biennial population dynamics. Interactions between individuals are modelled
with the aid of an ``environmental' variable I. The impact on and the sensitivity to the environmental condition is age specific. The main result is that competitive exclusion
between the year classes is possible as is their coexistence. For moderate values of the basic reproduction ratio R
0
there is a strict dichotomy: depending on the other parameters we either find competitive exclusion or coexistence. We characterize
rather precisely the patterns of age specific impact and sensitivity that lead to either of these outcomes.
Received: 13 July 2001 / Revised version: 26 June 2002 / Published online: 19 November 2002
Key words or phrases: Competitive exclusion – Semelparous species – Periodical insects 相似文献
9.
The urine concentrating mechanism of mammals and birds depends on a counterflow configuration of thousands of nearly parallel
tubules in the medulla of the kidney. Along the course of a renal tubule, cell type may change abruptly, resulting in abrupt
changes in the physical characteristics and transmural transport properties of the tubule. A mathematical model that faithfully
represents these abrupt changes will have jump discontinuities in model parameters. Without proper treatment, such discontinuities
may cause unrealistic transmural fluxes and introduce suboptimal spatial convergence in the numerical solution to the model
equations. In this study, we show how to treat discontinuous parameters in the context of a previously developed numerical
method that is based on the semi-Lagrangian semi-implicit method and Newton's method. The numerical solutions have physically
plausible fluxes at the discontinuities and the solutions converge at second order, as is appropriate for the method.
Received: 13 November 2001 / Revised version: 28 June 2002 / Published online: 26 September 2002
This work was supported in part by the National Institutes of Health (National Institute of Diabetes and Digestive and Kidney
Diseases, grant DK-42091.)
Mathematics Subject Classification (2000): 65-04, 65M12, 65M25, 92-04, 92C35, 35-04, 35L45
Keywords or phrases: Mathematical models – Differential equations – Mathematical biology – Kidney – Renal medulla – Semi-Lagrangian semi-implicit 相似文献
10.
We start from a stochastic SIS model for the spread of epidemics among a population partitioned into M sites, each containing
N individuals; epidemic spread occurs through within-site (`local') contacts and global contacts. We analyse the limit behaviour
of the system as M and N increase to ∞. Two limit procedures are considered, according to the order in which M and N go to ∞; independently of the order, the limiting distribution of infected individuals across sites is a probability measure,
whose evolution in time is governed by the weak form of a PDE. Existence and uniqueness of the solutions to this problem is
shown. Finally, it is shown that the infected distribution converges, as time goes to infinity, to a Dirac measure at the
value x
*
, the equilibrium of a single-patch SIS model with contact rate equal to the sum of local and global contacts.
Received: 18 July 2001 / Revised version: 16 March 2002 / Published online: 26 September 2002
Mathematics Subject Classification (2000): 92D30, 60F99
Key words or phrases: SIS epidemic – Metapopulation – Markov population processes – Weak convergence of measures 相似文献
11.
The development of synchronous bursting in neuronal ensembles represents an important change in network behavior. To determine
the influences on development of such synchronous bursting behavior we study the dynamics of small networks of sparsely connected
excitatory and inhibitory neurons using numerical simulations. The synchronized bursting activities in networks evoked by
background spikes are investigated. Specifically, patterns of bursting activity are examined when the balance between excitation
and inhibition on neuronal inputs is varied and the fraction of inhibitory neurons in the network is changed. For quantitative
comparison of bursting activities in networks, measures of the degree of synchrony are used. We demonstrate how changes in
the strength of excitation on inputs of neurons can be compensated by changes in the strength of inhibition without changing
the degree of synchrony in the network. The effects of changing several network parameters on the network activity are analyzed
and discussed. These changes may underlie the transition of network activity from normal to potentially pathologic (e.g.,
epileptic) states.
Received: 21 May 2002 / Accepted in revised form: 3 December 2002 / Published online: 7 March 2003
Correspondence to: P. Kudela (e-mail: pkudela@jhmi.edu)
Acknowledgements. This research was supported by NIH grant NS 38958. 相似文献
12.
Waxman D 《Journal of mathematical biology》2003,46(3):225-240
Two results are presented for problems involving alleles with a continuous range of effects. The first result is a simple
yet highly accurate numerical method that determines the equilibrium distribution of allelic effects, moments of this distribution,
and the mutational load. The numerical method is explicitly applied to the mutation-selection balance problem of stabilising
selection. The second result is an exact solution for the distribution of allelic effects under weak stabilising selection
for a particular distribution of mutant effects. The exact solution is shown to yield a distribution of allelic effects that,
depending on the mutation rate, interpolates between the ``House of Cards' approximation and the Gaussian approximation.
The exact solution is also used to test the accuracy of the numerical method.
Received: 7 November 2001 / Revised version: 5 September 2002 / Published online: 18 December 2002
Key words or phrases: Continuum of alleles – Numerical solution – Exact solution – Mutation selection balance – Stabilising selection 相似文献
13.
We describe a neural network that enhances and completes salient closed contours in images. Our work is different from all
previous work in three important ways. First, like the input provided to primary visual cortex (V1) by the lateral geniculate
nucleus (LGN), the input to our computation is isotropic. That is, it is composed of spots, not edges. Second, our network
computes a well-defined function of the input based on a distribution of closed contours characterized by a random process.
Third, even though our computation is implemented in a discrete network, its output is invariant to continuous rotations and
translations of the input image.
Received: 11 July 2002 / Accepted in revised form: 25 October 2002
Acknowledgements. L.R.W. was supported in part by Los Alamos National Laboratory. J.W.Z. was supported in part by the Albuquerque High Performance
Computing Center. We wish to thank Jonas August and Steve Zucker for their insightful comments.
Correspondence to: L.R. Williams (e-mail: Williams@cs.unm.edu) 相似文献
14.
Weinberger HF 《Journal of mathematical biology》2002,45(6):511-548
It is shown that the methods previously used by the author [Wei82] and by R. Lui [Lui89] to obtain asymptotic spreading results
and sometimes the existence of traveling waves for a discrete-time recursion with a translation invariant order preserving
operator can be extended to a recursion with a periodic order preserving operator. The operator can be taken to be the time-one
map of a continuous time reaction-diffusion model, or it can be a more general model of time evolution in population genetics
or population ecology in a periodic habitat. Methods of estimating the speeds of spreading in various directions will also
be presented.
Received: 12 July 2001 / Revised version: 19 July 2002 / Published online: 17 October 2002
Mathematics Subject Classification (2000): 92D40, 92D25, 35K55, 35K57, 35B40
Keywords or phrases: Periodic – Spreading speed – Traveling wave 相似文献
15.
Walter R. Stahl 《Bulletin of mathematical biology》1962,24(1):81-108
The application of dimensional analysis in biology is further illustrated by functional equations composed of dimensionless
numbers and dealing with renal physiology, lung physiology and plant leaf shape. Dimensional variables and dimensionless numbers
are examined from the viewpoint of numerical invariant properties of a certain physical system. Utilization of the method
for problems such as design of an artificial kidney is considered briefly. A tabulation of variables useful in biology is
given, with suggestions for a number of new dimensional entities. A continuation of the list of dimensionless invariants from
Part I (Bull. Math. Biophysics,23, 355–376, 1961) is provided and includes terms pertaining to general physiology, geometric growth, metabolism, ecological
interactions, muscle kinetics and other areas. It is pointed out that use of dimensionless ratios (similarity criteria) makes
possible a direct comparison of form or shape factors and relative growth ratios with a variety of physical ratios, through
the use of functional equations containing only dimensionless entities. Organismal similarity during growth and development,
and between genetically related species, may be analyzed in terms of “automodel” or “self-similar” systems governed by certain
dimensionless invariants. Tables of biological variables and dimensionless groupings are included. 相似文献
16.
The coloration of cells of the cyanobacterium Synechococcus sp. PCC 7002 changed from normal blue-green to yellow-green when cells were grown at 15° C in a medium containing nitrate
as the sole nitrogen source. This change of coloration was similar to a general response to nutrient deprivation (chlorosis).
For the chlorotic cells at 15° C, the total amounts of phycobiliproteins and chlorophyll a decreased, high levels of glycogen accumulated, and growth was arithmetic rather than exponential. These changes in composition
and growth occurred in cells grown at low (50 μE m–2 s–1) as well as high (250 μE m–2 s–1) light intensity. After a temperature shift-up to 38° C, chlorotic cells rapidly regained their normal blue-green coloration
and normal exponential growth rate within 7 h. When cells were grown at 15° C in a medium containing urea as the reduced nitrogen
source, cells grew exponentially and the symptoms of chlorosis were not observed. The decrease in photosynthetic oxygen evolution
activity at low temperature was much smaller than the decrease in growth rate for cells grown on nitrate as the nitrogen source.
These studies demonstrate that low-temperature-induced chlorosis of Synechococcus sp. PCC 7002 is caused by nitrogen limitation and is not the result of limited photosynthetic activity or photodamage to
the photosynthetic apparatus, and that nitrogen assimilation is an important aspect of the low-temperature physiology of cyanobacteria.
Received: 24 April 1997 / Accepted: 5 August 1997 相似文献
17.
The nature of the association between two species may vary depending on population abundances, age or size of individuals,
or environmental conditions. Interactions may switch between beneficial and detrimental depending on the net balance of costs
and benefits involved for each species. We study the repercussion of the ecological setting on the outcomes of conditional
or variable interactions by means of a model that incorporates density-dependent interaction coefficients; that is, interaction α-functions. These characterize the responsiveness and sensitivity of the association to changes in partner's abundance, and can take
positive and negative values. Variable outcomes – and transitions between them – are categorized as homeo- or allo-environmental, that is, occurring under the same ecological setting, or not, respectively. Bifurcation analyses show that these dynamics
are moulded by ecological factors that are: intrinsic to the nature of the association (concerning the sensitivity of the interaction), and extrinsic to the association itself (the quality of the environment referred to each species alone). The influence of these factors
may be conflicting; consequently, the dynamics involve catastrophic events. In a facultative variable association, stable coexistence is expected when environmental conditions are adverse; otherwise, the exclusion of one species is the likely outcome. Remarkable situations as the switching of victim-exploiter roles illustrate the theoretical perspective.
Received: 15 December 2001 / Revised version: 18 November 2002 /
Published online: 28 February 2003
Key words or phrases: Variable population interactions – Conditional interactions – Costs and benefits – Density dependent interaction coefficient
– Hysteresis – Symbiosis – Mutualism – Parasitism 相似文献
18.
Progression age enhanced backward bifurcation in an epidemic model with super-infection 总被引:10,自引:0,他引:10
We consider a model for a disease with a progressing and a quiescent exposed class and variable susceptibility to super-infection.
The model exhibits backward bifurcations under certain conditions, which allow for both stable and unstable endemic states
when the basic reproduction number is smaller than one.
Received: 11 October 2001 / Revised version: 17 September 2002 /
Published online: 17 January 2003
Present address: Department of Biological Statistics and Computational Biology, 434 Warren Hall, Cornell University, Ithaca, NY 14853-7801
This author was visiting Arizona State University when most of the research was done.
Research partially supported by NSF grant DMS-0137687.
This author's research was partially supported by NSF grant DMS-9706787.
Key words or phrases: Backward bifurcation – Multiple endemic equilibria – Alternating stability – Break-point density – Super-infection – Dose-dependent
latent period – Progressive and quiescent latent stages – Progression age structure – Threshold type disease activation –
Operator semigroups – Hille-Yosida operators – Dynamical systems – Persistence – Global compact attractor 相似文献
19.
To identify a basidiomycetous fungus isolated from butt rot of Chamaecyparis obtusa, Japanese cypress, its cultural features were examined, and sequences of its nuclear ribosomal 18S and ITS1–5.8S–ITS2 regions
were analyzed. In culture, this fungus is characterized by the occurrence of chlamydospores, blastoconidium-like cells, and
clavate-to-spathulate hyphal ends at the tips of aerial hyphae, and production of a small basidioma on the mycelial mat after
3 months of incubation. The morphological features of the basidioma are identical to those of Phlebia brevispora. Furthermore, molecular data of the sequences of these strains and P. brevispora showed a high level of similarity. These results appear to justify determining the present fungus as P. brevispora. This is the first report of this species for Japan and outside of southeastern USA.
Received: March 11, 2002 / Accepted: September 20, 2002
Acknowledgments We thank Dr. Karen K. Nakasone, Center for Forest Mycology Research, Forest Products Laboratory, USDA Forest Service, for
providing the fungal strains used in this study.
Correspondence to:R. Kondo 相似文献
20.
Nikodem J. Popławski Ubirajara Agero J. Scott Gens Maciej Swat James A. Glazier Alexander R. A. Anderson 《Bulletin of mathematical biology》2009,71(5):1189-1227
We study the interface morphology of a 2D simulation of an avascular tumor composed of identical cells growing in an homogeneous
healthy tissue matrix (TM), in order to understand the origin of the morphological changes often observed during real tumor growth. We use the Glazier–Graner–Hogeweg
model, which treats tumor cells as extended, deformable objects, to study the effects of two parameters: a dimensionless diffusion-limitation
parameter defined as the ratio of the tumor consumption rate to the substrate transport rate, and the tumor-TM surface tension.
We model TM as a nondiffusing field, neglecting the TM pressure and haptotactic repulsion acting on a real growing tumor;
thus, our model is appropriate for studying tumors with highly motile cells, e.g., gliomas. We show that the diffusion-limitation
parameter determines whether the growing tumor develops a smooth (noninvasive) or fingered (invasive) interface, and that
the sensitivity of tumor morphology to tumor-TM surface tension increases with the size of the dimensionless diffusion-limitation
parameter. For large diffusion-limitation parameters, we find a transition (missed in previous work) between dendritic structures,
produced when tumor-TM surface tension is high, and seaweed-like structures, produced when tumor-TM surface tension is low.
This observation leads to a direct analogy between the mathematics and dynamics of tumors and those observed in nonbiological
directional solidification. Our results are also consistent with the biological observation that hypoxia promotes invasive
growth of tumor cells by inducing higher levels of receptors for scatter factors that weaken cell-cell adhesion and increase
cell motility. These findings suggest that tumor morphology may have value in predicting the efficiency of antiangiogenic
therapy in individual patients. 相似文献