Bulletin of Mathematical Biology

Xiao, Sa; Zhao, Liang; Zhang, Jia-Lin; Wang, Xiang-Tai; Chen, Shu-Yan

doi: 10.1007/s11538-012-9800-7pmid: 23307234

Among numerous mechanisms shaping the unimodal relationship between diversity and community biomass, the trade-off model of “CRS” theory is the most famous one. However, recent researches indicate that this relationship may also emerge under the neutral model where all species are identical with each other. By using an individual-based spatially-explicit model, we evaluated the underlying mechanisms shaping this curve for both models under different disturbance levels. We found unimodal relationships emerged for both models at low and medium disturbance levels; the richness for the trade-off community was lower than the neutral community for most of the environment severity levels, especially at the benign environment due to the strong competitive exclusions among species. Whereas under high disturbance level, the positive relationships emerged for both models; both communities had similar richness with their curves nearly overlapped with each other, that is, because the high disturbance intensity strongly decreased the competitive exclusions within the trade-off community. Our results indicate that although the underlying mechanisms are totally different, both models will produce the similar relationship between diversity and community biomass under different disturbance levels.

Weir, Brad; Miller, Robert; Spitz, Yvette

doi: 10.1007/s11538-012-9801-6pmid: 23292361

We introduce an implicit method for state and parameter estimation and apply it to a stochastic ecological model. The method uses an ensemble of particles to approximate the distribution of model solutions and parameters conditioned on noisy observations of the state. For each particle, it first determines likely values based on the observations, then samples around those values. This approach has a strong theoretical foundation, applies to nonlinear models and non-Gaussian distributions, and can estimate any number of model parameters, initial conditions, and model error covariances. The method is called implicit because it updates the particles without forming a predictive distribution of forward model integrations. As a point of comparison for different assimilation techniques, we consider examples in which one or more bifurcations separate the true parameter from its initial approximation. The implicit estimator is asymptotically unbiased, has a root-mean-squared error comparable to or less than the other methods, and is accurate even with small ensemble sizes.

Berec, Luděk; Maxin, Daniel

doi: 10.1007/s11538-012-9802-5pmid: 23292362

Models of sexually transmitted infections have become a fixture of mathematical epidemiology. A common attribute of all these models is treating reproduction and mating, and hence pathogen transmission, as uncoupled events. This is fine for humans, for example, where only a tiny fraction of sexual intercourses ends up with having a baby. But it can be a deficiency for animals in which mating and giving birth are tightly coupled, and mating thus mediates both reproduction and pathogen transmission. Here, we model dynamics of sterilizing, sexually transmitted infections in such animals, assuming structural consistency between the processes of reproduction and pathogen transmission. We show that highly sterilizing, sexually transmitted pathogens trigger bistability in the host population. In particular, the host population can end up in two extreme alternative states, disease-free persistence and pathogen-driven extinction, depending on its initial state. Given that sterilizing, sexually transmitted infections that affect animals are abundant, our results might implicate an effective pest control tactic that consists of releasing the corresponding pathogens, possibly after genetically enhancing their sterilization power.

Zhao, Gaiping; Yan, Wentao; Chen, Eryun; Yu, Xiaoli; Cai, Wenjie

doi: 10.1007/s11538-012-9805-2pmid: 23292363

The present work formulates and analyzes the inhibitory effect of anti-angiogenic factor angiostatin excreted by the primary tumor on metastatic tumor angiogenesis, blood perfusion, and interstitial fluid flow in the tumor microenvironment by means of a numerical experiment. The simulation results demonstrate that angiostatin has an obvious impact on the morphology, growth rate, and the number of branches of microvascular network inside and outside the metastatic tumor, and angiostatin has the capacity to regulate and inhibit the formation of new blood vessels. Heterogeneous blood perfusion, widespread interstitial hypertension, and low convection within the metastatic tumor have obviously improved under the inhibitory effect of angiostatin, which are consistent with physiological observed facts. The simulation results may provide beneficial information and theoretical models for clinical research of anti-angiogenic therapy strategies.

Allena, Rachele

doi: 10.1007/s11538-012-9806-1pmid: 23319383

Cell migration triggered by pseudopodia (or “false feet”) is the most used method of locomotion. A 3D finite element model of a cell migrating over a 2D substrate is proposed, with a particular focus on the mechanical aspects of the biological phenomenon. The decomposition of the deformation gradient is used to reproduce the cyclic phases of protrusion and contraction of the cell, which are tightly synchronized with the adhesion forces at the back and at the front of the cell, respectively. First, a steady active deformation is considered to show the ability of the cell to simultaneously initiate multiple pseudopodia. Here, randomness is considered as a key aspect, which controls both the direction and the amplitude of the false feet. Second, the migration process is described through two different strategies: the temporal and the spatial sensing models. In the temporal model, the cell “sniffs” the surroundings by extending several pseudopodia and only the one that receives a positive input will become the new leading edge, while the others retract. In the spatial model instead, the cell senses the external sources at different spots of the membrane and only protrudes one pseudopod in the direction of the most attractive one.

Miȩkisz, Jacek; Szymańska, Paulina

doi: 10.1007/s11538-013-9808-7pmid: 23354928

We analyze a simple model of a self-repressing system with multiple gene copies. Protein molecules may bound to DNA promoters and block their own transcription. We derive analytical expressions for the variance of the number of protein molecules in the stationary state in the self-consistent mean-field approximation. We show that the Fano factor (the variance divided by the mean value) is bigger for the one-gene case than for two gene copies and the difference decreases to zero as frequencies of binding and unbinding increase to infinity.

Saini, Ashish; Hou, Jingyu

doi: 10.1007/s11538-013-9809-6pmid: 23321799

In recent years, significant effort has been given to predicting protein functions from protein interaction data generated from high throughput techniques. However, predicting protein functions correctly and reliably still remains a challenge. Recently, many computational methods have been proposed for predicting protein functions. Among these methods, clustering based methods are the most promising. The existing methods, however, mainly focus on protein relationship modeling and the prediction algorithms that statically predict functions from the clusters that are related to the unannotated proteins. In fact, the clustering itself is a dynamic process and the function prediction should take this dynamic feature of clustering into consideration. Unfortunately, this dynamic feature of clustering is ignored in the existing prediction methods. In this paper, we propose an innovative progressive clustering based prediction method to trace the functions of relevant annotated proteins across all clusters that are generated through the progressive clustering of proteins. A set of prediction criteria is proposed to predict functions of unannotated proteins from all relevant clusters and traced functions. The method was evaluated on real protein interaction datasets and the results demonstrated the effectiveness of the proposed method compared with representative existing methods.

Bokes, Pavol; King, John; Wood, Andrew; Loose, Matthew

doi: 10.1007/s11538-013-9811-zpmid: 23354929

Hybrid models for gene expression combine stochastic and deterministic representations of the underlying biophysical mechanisms. According to one of the simplest hybrid formalisms, protein molecules are produced in randomly occurring bursts of a randomly distributed size while they are degraded deterministically. Here, we use this particular formalism to study two key regulatory motifs—the autoregulation loop and the toggle switch. The distribution of burst times is determined and used as a basis for the development of exact simulation algorithms for gene expression dynamics. For the autoregulation loop, the simulations are compared to an analytic solution of a master equation. Simulations of the toggle switch reveal a number of qualitatively distinct scenarios with implications for the modelling of cell-fate selection.