In: Bulletin of Mathematical Biology, 2009, vol. 71, no. 6, p. 1394-1431
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In: PLoS ONE, 2015, vol. 10, no. 7, p. e0127905
Plants are highly plastic in their potential to adapt to changing environmental conditions. For example, they can selectively promote the relative growth of the root and the shoot in response to limiting supply of mineral nutrients and light, respectively, a phenomenon that is referred to as balanced growth or functional equilibrium. To gain insight into the regulatory network that controls this...
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In: Journal of Mathematical Biology, 2014, vol. 68, no. 4, p. 879–909
The plant hormone auxin is fundamental for plant growth, and its spatial distribution in plant tissues is critical for plant morphogenesis. We consider a leading model of the polar auxin flux, and study in full detail the stability of the possible equilibrium configurations. We show that the critical states of the auxin transport process are composed of basic building blocks, which are...
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In: Bulletin of Mathematical Biology, 2009, vol. 71, no. 6, p. 1394-1431
Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856–860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by...
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In: SIAM Journal on Applied Mathematics, 2008, vol. 68, no. 3, p. 869-889
A skeletal muscle is composed of motor units, each consisting of a motoneuron and the muscle fibers it innervates. The input to the motor units is formed of electrical signals coming from higher motor centers and propagated to the motoneurons along a network of nerve fibers. Because of its complexity, this network still escapes actual direct observations. The present model describes the steady...
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In: Bioinformatics, 2007, vol. 23, no. 23, p. 3185-3192
Motivation: Regulatory gene networks contain generic modules such as feedback loops that are essential for the regulation of many biological functions. The study of the stochastic mechanisms of gene regulation is instrumental for the understanding of how cells maintain their expression at levels commensurate with their biological role, as well as to engineer gene expression switches of...
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In: Nature, 2004, vol. 427, p. 835-839
Food webs are descriptions of who eats whom in an ecosystem. Although extremely complex and variable, their structure possesses basic regularities. A fascinating question is to find a simple model capturing the underlying processes behind these repeatable patterns. Until now, two models have been devised for the description of trophic interactions within a natural community. Both are essentially...
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In: Mathematical Biosciences, 2004, vol. 191, p. 207
A model is presented of competition between sensory axons for trophic molecules (e.g. a neurotrophin such as NGF), produced in a region of skin small enough to permit their free diffusion throughout it; e.g., a touch dome, or a vibrissal follicle hair sinus. The variables specified are the number of high affinity trophic factor receptors per axon terminal and the concentration of trophic factor...
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In: Ecological Modelling
Levins and Ginzburg raised two paradoxes concerning the logistic equation of population growth. None of them received a satisfactory answer within the frame of the original equation. Here, we propose solutions to both paradoxes.
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