A mean-field theory of cellular growth

Mombach, José C. M.; Lemke, Ney; Bodmann, B. E. J.; Idiart, Marco

doi:10.1209/epl/i2002-00244-6

Cited by 57 publications

(70 citation statements)

References 16 publications

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“…It means that all spatially separated sublements (cells) of the whole system (tumor) are interrelated via long-range (slowly decaying) interactions, which seem to be an essential ingredient of the self-organized Gompertzian growth (Mombach et al, 2002). Such interactions can be mediated, e.g.…”

Section: Resultsmentioning

confidence: 99%

“…Such interactions can be mediated, e.g. through diffusive substances (growth factors), which interact with specific receptors on the surface of the cells, affecting proliferation (Mombach et al, 2002). The long-range interactions are indispensable in coherent formation of the specific growth patterns, cooperative phenomena, self-organization, positive and negative feedbacks on (between) all hierarchical structures of life.…”

Section: Resultsmentioning

confidence: 99%

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On the Gompertzian growth in the fractal space–time

Molski

Konarski

2008

Biosystems

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

On the Gompertzian growth in the fractal space–time

Molski

Konarski

2008

Biosystems

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“…[38] and reworked in [10,16,39]. The result of this model is the fact that some observed macroscopic properties are consequences of the inhibitory interactions between the microcomponents of the system.…”

Section: Microscopic Modelmentioning

confidence: 99%

An attempt to unify some population growth models from first principles

Ribeiro

2016

Rev. Bras. Ensino Fís.

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In this work, some phenomenological growth models based only on the population information (macroscopic level) are deduced in an intuitive way. These models, for instance Verhulst, Gompertz and Bertalanffy-Richards models, are introduced in such a way that all the parameters involved have a physical interpretation. A model based on the interaction (distance dependent) between the individuals (microscopic level) is also presented. This microscopic model have some phenomenological models as particular cases. In this approach, the Verhulst model represents the situation in which all the individuals interact in the same way, regardless of the distance between them (mean field approach). Other phenomenological models are retrieved from the microscopic model according to two quantities: i) the way that the interaction decays as a function the distance between two individuals and ii) the dimension of the spatial structure formed by the individuals of the population. This microscopic model allows understanding population growth by first principles, because it predicts that some phenomenological models can be seen as a consequence of interaction at individual level. The microscopic model discussed here paves the way to finding universal patterns that are common to all types of growth, even in systems of very different nature. Keywords: Population growth, Complex Systems, Mathematical Modelling Neste trabalho, alguns modelos fenomenológicos de crescimento populacional são deduzidos de uma forma intuitiva. Estes modelos, por exemplo os modelos de Verhulst, Gompertz e Bertalanffy-Richards, são introduzidos de maneira que todos os parâmetros envolvidos tenham uma interpretação física. Um modelo baseado na interação (dependente da distância) entre os indivíduos (nível microscópico) tambéḿ e apresentado.É mostrado que alguns modelos fenomenológicos são casos particulares deste modelo microscópico, de acordo com: i) a forma com que a interação competitiva entre indivíduos decai com a distância que os separam; e ii) a dimensão euclidiana da estrutura espacial formada pelos indivíduos da população. Nestas circunstâncias, o modelo de Verhulst, por exemplo, decorre quando todos os indivíduos interagem de forma independente da distância que os separam: uma situação tipo campo-médio. Este modelo microscópico permite compreender o crescimento populacional por primeiros princípios, uma vez que mostra que alguns modelos fenomenológicos são explicados a partir de interações no nível do indivíduo. Dessa forma, o modelo microscópico discutido aqui abre caminho para encontrar padrões universais que sejam comuns a todos os tipos de crescimento. Palavras-chave: Crescimento Populacional, Sistemas Complexos, Modelagem Matemática

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“…[4,18,21]. This parameter is related to the range of interaction between the individuals that compose the population and the fractal pattern of the population structure.…”

Section: Generalized One-species Modelmentioning

confidence: 99%

Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

Cabella

Ribeiro

Martinêz

2012

Physica A: Statistical Mechanics and its Applications

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We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics.

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A mean-field theory of cellular growth

Cited by 57 publications

References 16 publications

On the Gompertzian growth in the fractal space–time

On the Gompertzian growth in the fractal space–time

An attempt to unify some population growth models from first principles

Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

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