共查询到20条相似文献,搜索用时 31 毫秒
1.
研究了定义在格上并具有时滞的Lotka-Volterra合作系统的波前解.通过构造上下解得到了波前解的存在性,借助于比较原理和渐近传播理论得到了波前解的不存在性,进而在得到了波前解最小波速的充分条件. 相似文献
2.
利用上下解方法研究了一个具有年龄结构的单种群离散反应扩散模型波前解的存在性,并证明了存在具有临界波速的波前解. 相似文献
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We develop a systems based model for prostate cancer, as a sub-system of the organism. We accomplish this in two stages. We first start with a general ODE that includes organism response terms. Then, to account for normally observed spatial diffusion of cell populations, the ODE is extended to a PDE that includes spatial terms. Numerical solutions of the full PDE are provided, and are indicative of traveling wave fronts. This motivates the use of a well known transformation to derive a canonically related (non-linear) system of ODEs for traveling wave solutions. For biological feasibility, we show that the non-negative cone for the traveling wave system is time invariant. We also prove that the traveling waves have a unique global attractor. Biologically, the global attractor would be the limit for the avascular tumor growth. We conclude with comments on clinical implications of the model. 相似文献
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William I. Newman 《Journal of theoretical biology》1983,104(4):473-484
The Fisher (1937) or Kolmogoroff-Petrovsky-Piscounoff (1937) equation exemplifies wave-like phenomena occurring in population genetics and combustion. In an earlier paper, we proposed an extension of this equation and obtained closed form traveling wave, stationary, and “symmetric” solutions. Employing the transformation properties of the extended equation, two integral invariants for the problem are obtained and two Lyapunov functionals, which characterize the evolution of the profile to a uniformly propagating traveling wave, are constructed. A generalization of this modified Fisher equation is proposed and we obtain its integral invariants, traveling wave solutions and wave speeds, as well as the Lyapunov functionals which describe its asymptotic evolution. 相似文献
5.
《Biophysical journal》2022,121(9):1610-1618
Oscillations and waves are ubiquitous in living cellular systems. Generations of these spatiotemporal patterns are generally attributed to some mechanochemical feedbacks. Here, we treat cells as open systems, i.e., water and ions can pass through the cell membrane passively or actively, and reveal a new origin of wave generation. We show that osmotic shocks above a shock threshold will trigger self-sustained cell oscillations and result in long-range waves propagating without decrement, a phenomenon that is analogous to the excitable medium. The traveling wave propagates along the intercellular osmotic pressure gradient, and its wave speed scales with the magnitude of intercellular water flows. Furthermore, we also find that the traveling wave exhibits several hallmarks of solitary waves. Together, our findings predict a new mechanism of wave generation in living multicellular systems. The ubiquity of intercellular water exchanges implies that this mechanism may be relevant to a broad class of systems. 相似文献
6.
We develop and investigate a continuum model for invasion of a domain by cells that migrate, proliferate and differentiate.
The model is applicable to neural crest cell invasion in the developing enteric nervous system, but is presented in general
terms and is of broader applicability. Two cell populations are identified and modeled explicitly; a population of precursor
cells that migrate and proliferate, and a population of differentiated cells derived from the precursors which have impaired
migration and proliferation. The equation describing the precursor cells is based on Fisher’s equation with the addition of
a carrying-capacity limited differentiation term. Two variations of the proliferation term are considered and compared. For
most parameter values, the model admits a traveling wave solution for each population, both traveling at the same speed. The
traveling wave solutions are investigated using perturbation analysis, phase plane methods, and numerical techniques. Analytical
and numerical results suggest the existence of two wavespeed selection regimes. Regions of the parameter space are characterized
according to existence, shape, and speed of traveling wave solutions. Our observations may be used in conjunction with experimental
results to identify key parameters determining the invasion speed for a particular biological system. Furthermore, our results
may assist experimentalists in identifying the resource that is limiting proliferation of precursor cells. 相似文献
7.
研究一类含时滞的Logistic滞反应扩散方程的波前解.通过构造合适的上下解,证明了当时滞充分小时,方程存在波前解.用线性化方法,给出了存在波前解的时滞τ取值范围的一个估计. 相似文献
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《Biophysical journal》2022,121(15):2940-2951
Sounds entering the mammalian ear produce waves that travel from the base to the apex of the cochlea. An electromechanical active process amplifies traveling wave motions and enables sound processing over a broad range of frequencies and intensities. The cochlear amplifier requires combining the global traveling wave with the local cellular processes that change along the length of the cochlea given the gradual changes in hair cell and supporting cell anatomy and physiology. Thus, we measured basilar membrane (BM) traveling waves in vivo along the apical turn of the mouse cochlea using volumetric optical coherence tomography and vibrometry. We found that there was a gradual reduction in key features of the active process toward the apex. For example, the gain decreased from 23 to 19 dB and tuning sharpness decreased from 2.5 to 1.4. Furthermore, we measured the frequency and intensity dependence of traveling wave properties. The phase velocity was larger than the group velocity, and both quantities gradually decrease from the base to the apex denoting a strong dispersion characteristic near the helicotrema. Moreover, we found that the spatial wavelength along the BM was highly level dependent in vivo, such that increasing the sound intensity from 30 to 90 dB sound pressure level increased the wavelength from 504 to 874 μm, a factor of 1.73. We hypothesize that this wavelength variation with sound intensity gives rise to an increase of the fluid-loaded mass on the BM and tunes its local resonance frequency. Together, these data demonstrate a strong interplay between the traveling wave propagation and amplification along the length of the cochlea. 相似文献
10.
A continuum model and a discrete model are developed to capture the population-scale and cell-scale behavior in a wound-healing cell migration assay created from a scrape wound in a confluent cell monolayer. During wound closure, the cell population forms a sustained traveling wave, with close contact between cells behind the wavefront. Cells exhibit contact inhibition of migration and contact-limited proliferation. The continuum model includes the two dominant mechanisms and characteristics of cell migration and proliferation, using a cell diffusivity function that decreases with cell density and a logistic proliferative growth term. The discrete model arises naturally from the continuum model. Individual cells are simulated as continuous-time random walkers with nearest-neighbor transitions, together with a birth/death process. The migration and proliferation parameters are determined by analysing individual mice 3T3 fibroblast cell trajectories obtained during the development of a confluent cell monolayer and in a wound healing assay. The population-scale model successfully predicts the shape and speed of the traveling wave, while the discrete model is also successful in capturing the contact inhibition of migration effects. 相似文献
11.
This paper is concerned with the spreading speeds and traveling wave solutions of discrete time recursion systems, which describe
the spatial propagation mode of two competitive invaders. We first establish the existence of traveling wave solutions when
the wave speed is larger than a given threshold. Furthermore, we prove that the threshold is the spreading speed of one species
while the spreading speed of the other species is distinctly slower compared to the case when the interspecific competition
disappears. Our results also show that the interspecific competition does affect the spread of both species so that the eventual
population densities at the coexistence domain are lower than the case when the competition vanishes. 相似文献
12.
Rapid changes in cellular morphology require a cell body that is highly flexible yet retains sufficient strength to maintain structural integrity. We present a mechanism that meets both of these requirements. We demonstrate that compression (folding) and subsequent dilation (unfolding) of the coupled plasma membrane–cortex layer generates rapid shape transformations in rounded cells. Two- and three-dimensional live-cell images showed that the cyclic process of membrane-cortex compression and dilation resulted in a traveling wave of cortical actin density. We also demonstrate that the membrane-cortex traveling wave led to amoeboid-like cell migration. The compression–dilation hypothesis offers a mechanism for large-scale cell shape transformations that is complementary to blebbing, where the plasma membrane detaches from the actin cortex and is initially unsupported when the bleb extends as a result of cytosolic pressure. Our findings provide insight into the mechanisms that drive the rapid morphological changes that occur in many physiological contexts, such as amoeboid migration and cytokinesis. 相似文献
13.
Traveling waves of calcium are widely observed under the condition that the free cytosolic calcium is buffered. Thus it is
of physiological interest to determine how buffers affect the properties of calcium waves. Here we summarise and extend previous
results on the existence, uniqueness and stability of traveling wave solutions of the buffered bistable equation, which is
the simplest possible model of the upstroke of a calcium wave. Taken together, the results show that immobile buffers do not
change the existence, uniqueness or stability of the traveling wave, while mobile buffers can eliminate a traveling wave.
However, if a wave exists in the latter case, it remains unique and stable.
相似文献
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本文讨论了一类造血生物模型在Dirichlet边值条件下稳态解的全局吸引性,并利用上、下解技术和单调迭代方法讨论了行波解的存在性. 相似文献
16.
Mechanical stimulation of Nitella often produces responses resembling propagated negative variations but traveling faster and going past a killed spot. They appear to result from a mechanical disturbance traveling along the cell and stimulating each spot it touches (i.e. the stimulus itself travels). They are called mechanical variations to distinguish them from propagated negative variations. A mechanical disturbance may cause an irreversible change (death wave), but in traveling along the cell it may lose intensity and then produce only a reversible response (mechanical variation) which may eventually change to a propagated negative variation. The all or none law does not apply to incomplete mechanical variations, for the response varies with the strength of the stimulus. 相似文献
17.
Using high sensitivity fluorescence imaging with shutter speeds approximately 600,000 times faster than those of video frames, we have characterized Ca2+ waves within cells in exquisite detail to reveal Ca2+ signaling routes. Polarized neutrophils exhibited a counterclockwise rotating ryanodine-sensitive juxtamembrane Ca2+ wave during temporal calcium spikes. During stimulation with fMLP, a chemotactic factor, two Ca2+ waves traveling in opposite directions around the perimeter of the cell emanated from sites of stimulation (the clockwise wave is verapamil sensitive). Phagocytosed targets exhibit counterclockwise Ca2+ waves traveling about their periphery originating from the plasma membrane. This study: 1) outlines the technology to observe Ca2+ signaling circuitry within small living cells; 2) shows that extracellular spatial information in the form of a chemotactic factor gradient is transduced into intracellular chemical patterns, which provides fresh insights in signaling; 3) suggests that a line of communication exits between the cell surface and phagosomes; and 4) suggests that spatiotemporal Ca2+ patterns contribute to drug actions. 相似文献
18.
Outer hair cell (OHC) somatic motility plays a key role in mammalian cochlear frequency selectivity and hearing sensitivity, but the mechanism of cochlear amplification is not well understood and remains a matter of controversy. We have visualized and quantified the effects of electrically evoked OHC somatic motility within the gerbil organ of Corti using an excised cochlear preparation. We found that OHC motility induces oscillatory motion of the medial olivocochlear fibers where they cross the tunnel of Corti (ToC) in their course to innervate the OHCs. We show that this motion is present at physiologically relevant frequencies and remains at locations distal to the OHC excitation point. We interpret this fiber motion to be the result of oscillatory fluid flow in the ToC. We show, using a simple one-dimensional hydromechanical model of the ToC, that a fluid wave within the tunnel can travel without significant attenuation for distances larger than the wavelength of the cochlear traveling wave at its peak. This ToC fluid wave could interact with the cochlear traveling wave to amplify the motion of the basilar membrane. The ToC wave could also provide longitudinal coupling between adjacent sections of the basilar membrane, and such coupling may be critical for cochlear amplification. 相似文献
19.
We establish the existence of traveling wave solutions for a nonlinear partial differential equation that models a logistically
growing population whose movement is governed by an advective process. Conditions are presented for which traveling wave solutions
exist and for which they are stable to small semi-finite domain perturbations. The wave is of mathematical interest because
its behavior is determined by a singular differential equation and those with small speed of propagation steepen into a shock-like
solutions. Finally, we indicate that the smoothing presence of diffusion allows wave persistence when an advective slow moving
wave may collapse.
Received: 24 November 1997 / Revised version: 13 July 1998 相似文献
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