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Bulletin of Mathematical Biology

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https://www.readbyqxmd.com/read/29052101/effects-of-hydraulic-soil-properties-on-vegetation-pattern-formation-in-sloping-landscapes
#1
Gerardo Severino, Francesco Giannino, Fabrizio Cartení, Stefano Mazzoleni, Daniel M Tartakovsky
Current models of vegetation pattern formation rely on a system of weakly nonlinear reaction-diffusion equations that are coupled by their source terms. While these equations, which are used to describe a spatiotemporal planar evolution of biomass and soil water, qualitatively capture the emergence of various types of vegetation patterns in arid environments, they are phenomenological and have a limited predictive power. We ameliorate these limitations by deriving the vertically averaged Richards' equation to describe flow (as opposed to "diffusion") of water in partially saturated soils...
October 19, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/29047051/time-inhomogeneous-mutation-models-with-birth-date-dependence
#2
Adrien Mazoyer
The classic Luria-Delbrück model for fluctuation analysis is extended to the case where the split instant distributions of cells are not i.i.d.: the lifetime of each cell is assumed to depend on its birth date. This model takes also into account cell deaths and non-exponentially distributed lifetimes. In particular, it is possible to consider subprobability distributions and to model non-exponential growth. The extended model leads to a family of probability distributions which depend on the expected number of mutations, the death probability of mutant cells, and the split instant distributions of normal and mutant cells...
October 18, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/29030805/an-explicit-structural-model-of-root-hair-and-soil-interactions-parameterised-by-synchrotron-x-ray-computed-tomography
#3
Samuel David Keyes, Konstantinos C Zygalakis, Tiina Roose
The rhizosphere is a zone of fundamental importance for understanding the dynamics of nutrient acquisition by plant roots. The canonical difficulty of experimentally investigating the rhizosphere led long ago to the adoption of mathematical models, the most sophisticated of which now incorporate explicit representations of root hairs and rhizosphere soil. Mathematical upscaling regimes, such as homogenisation, offer the possibility of incorporating into larger-scale models the important mechanistic processes occurring at the rhizosphere scale...
October 13, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/29030804/a-multi-stage-representation-of-cell-proliferation-as-a-markov-process
#4
Christian A Yates, Matthew J Ford, Richard L Mort
The stochastic simulation algorithm commonly known as Gillespie's algorithm (originally derived for modelling well-mixed systems of chemical reactions) is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular level it is often reasonable to assume that times between successive reaction/interaction events are exponentially distributed and can be appropriately modelled as a Markov process and hence simulated by the Gillespie algorithm...
October 13, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/29022203/modeling-the-dynamics-of-heterogeneity-of-solid-tumors-in-response-to-chemotherapy
#5
Heyrim Cho, Doron Levy
In this paper, we extend the model of the dynamics of drug resistance in a solid tumor that was introduced by Lorz et al. (Bull Math Biol 77:1-22, 2015). Similarly to the original, radially symmetric model, the quantities we follow depend on a phenotype variable that corresponds to the level of drug resistance. The original model is modified in three ways: (i) We consider a more general growth term that takes into account the sensitivity of resistance level to high drug dosage. (ii) We add a diffusion term in space for the cancer cells and adjust all diffusion terms (for the nutrients and for the drugs) so that the permeability of the resource and drug is limited by the cell concentration...
October 11, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28993971/ancestral-sequence-reconstruction-with-maximum-parsimony
#6
Lina Herbst, Mareike Fischer
One of the main aims in phylogenetics is the estimation of ancestral sequences based on present-day data like, for instance, DNA alignments. One way to estimate the data of the last common ancestor of a given set of species is to first reconstruct a phylogenetic tree with some tree inference method and then to use some method of ancestral state inference based on that tree. One of the best-known methods both for tree inference and for ancestral sequence inference is Maximum Parsimony (MP). In this manuscript, we focus on this method and on ancestral state inference for fully bifurcating trees...
October 5, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28983864/modeling-sexual-selection-in-t%C3%A3%C2%BAngara-frog-and-rationality-of-mate-choice
#7
Esteban Vargas Bernal, Camilo Sanabria Malagon
The males of the species of frogs Engystomops pustulosus produce simple and complex calls to lure females, as a way of intersexual selection. Complex calls lead males to a greater reproductive success than what simple calls do. However, the complex calls are also more attractive to their main predator, the bat Trachops cirrhosus. Therefore, as M. Ryan suggests in (The túngara frog: a study in sexual selection and communication. University of Chicago Press, Chicago, 1985), the complexity of the calls lets the frogs keep a trade-off between reproductive success and predation...
October 5, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28983765/meandering-rivers-how-important-is-lateral-variability-for-species-persistence
#8
Yu Jin, Frithjof Lutscher, Yuan Pei
Models for population dynamics in rivers and streams have highlighted the importance of spatial and temporal variations for population persistence. We present a novel model that considers the longitudinal variation as introduced by the sinuosity of a meandering river where a main channel is laterally extended to point bars in bends. These regions offer different habitat conditions for aquatic populations and therefore may enhance population persistence. Our model is a nonstandard reaction-advection-diffusion model where the domain of definition consists of the real line (representing the main channel) with periodically added intervals (representing the point bars)...
October 5, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28975563/on-the-reproduction-number-of-a-gut-microbiota-model
#9
Carles Barril, Àngel Calsina, Jordi Ripoll
A spatially structured linear model of the growth of intestinal bacteria is analysed from two generational viewpoints. Firstly, the basic reproduction number associated with the bacterial population, i.e. the expected number of daughter cells per bacterium, is given explicitly in terms of biological parameters. Secondly, an alternative quantity is introduced based on the number of bacteria produced within the intestine by one bacterium originally in the external media. The latter depends on the parameters in a simpler way and provides more biological insight than the standard reproduction number, allowing the design of experimental procedures...
October 3, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28940123/short-term-antiretroviral-treatment-recommendations-based-on-sensitivity-analysis-of-a-mathematical-model-for-hiv-infection-of-formula-see-text-cells
#10
Ana-Maria Croicu, Angela M Jarrett, N G Cogan, M Yousuff Hussaini
HIV infection is one of the most difficult infections to control and manage. The most recent recommendations to control this infection vary according to the guidelines used (US, European, WHO) and are not patient-specific. Unfortunately, no two individuals respond to infection and treatment quite the same way. The purpose of this paper is to make use of the uncertainty and sensitivity analysis to investigate possible short-term treatment options that are patient-specific. We are able to identify the most significant parameters that are responsible for ART outcome and to formulate some insights into the ART success...
September 22, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28940114/fractional-poisson-nernst-planck-model-for-ion-channels-i-basic-formulations-and-algorithms
#11
Duan Chen
In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation...
September 22, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28940113/scaling-for-dynamical-systems-in-biology
#12
Glenn Ledder
Asymptotic methods can greatly simplify the analysis of all but the simplest mathematical models and should therefore be commonplace in such biological areas as ecology and epidemiology. One essential difficulty that limits their use is that they can only be applied to a suitably scaled dimensionless version of the original dimensional model. Many books discuss nondimensionalization, but with little attention given to the problem of choosing the right scales and dimensionless parameters. In this paper, we illustrate the value of using asymptotics on a properly scaled dimensionless model, develop a set of guidelines that can be used to make good scaling choices, and offer advice for teaching these topics in differential equations or mathematical biology courses...
September 22, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28924915/multiscale-modeling-of-diffusion-in-a-crowded-environment
#13
Lina Meinecke
We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid...
September 18, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28916986/continuous-structured-population-models-for-daphnia-magna
#14
Erica M Rutter, H T Banks, Gerald A LeBlanc, Kevin B Flores
We continue our efforts in modeling Daphnia magna, a species of water flea, by proposing a continuously structured population model incorporating density-dependent and density-independent fecundity and mortality rates. We collected new individual-level data to parameterize the individual demographics relating food availability and individual daphnid growth. Our model is fit to experimental data using the generalized least-squares framework, and we use cross-validation and Akaike Information Criteria to select hyper-parameters...
September 15, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28913585/on-the-number-of-non-equivalent-ancestral-configurations-for-matching-gene-trees-and-species-trees
#15
Filippo Disanto, Noah A Rosenberg
An ancestral configuration is one of the combinatorially distinct sets of gene lineages that, for a given gene tree, can reach a given node of a specified species tree. Ancestral configurations have appeared in recursive algebraic computations of the conditional probability that a gene tree topology is produced under the multispecies coalescent model for a given species tree. For matching gene trees and species trees, we study the number of ancestral configurations, considered up to an equivalence relation introduced by Wu (Evolution 66:763-775, 2012) to reduce the complexity of the recursive probability computation...
September 14, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28900833/cell-volume-regulation-in-the-proximal-tubule-of-rat-kidney-proximal-tubule-cell-volume-regulation
#16
Aurélie Edwards, Anita T Layton
We developed a dynamic model of a rat proximal convoluted tubule cell in order to investigate cell volume regulation mechanisms in this nephron segment. We examined whether regulatory volume decrease (RVD), which follows exposure to a hyposmotic peritubular solution, can be achieved solely via stimulation of basolateral K[Formula: see text] and [Formula: see text] channels and [Formula: see text]-[Formula: see text] cotransporters. We also determined whether regulatory volume increase (RVI), which follows exposure to a hyperosmotic peritubular solution under certain conditions, may be accomplished by activating basolateral [Formula: see text]/H[Formula: see text] exchangers...
September 12, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28887768/population-model-of-quorum-sensing-with-multiple-parallel-pathways
#17
Gaoyang Fan, Paul C Bressloff
Quorum sensing (QS) is a bacterial communication mechanism that uses signal-receptor binding to regulate gene expression based on cell density, resulting in group behaviors such as biofilm formation, bioluminescence and stress response. In certain bacterial species such as Vibrio harveyi, several parallel QS signaling pathways drive a single phosphorylation-dephosphorylation cycle, which in turn regulates QS target genes. In this paper, we investigate the possible role of parallel signaling pathways by developing a mathematical model of QS in V...
September 8, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28887745/modeling-human-mortality-from-all-diseases-in-the-five-most-populated-countries-of-the-european-union
#18
Josef Dolejs
Age affects mortality from diseases differently than it affects mortality from external causes, such as accidents. Exclusion of the latter leads to the "all-diseases" category. The age trajectories of mortality from all diseases are studied in the five most populated countries of the EU, and the shape of these 156 age trajectories is investigated in detail. The arithmetic mean of ages where mortality reaches a minimal value is 8.47 years with a 95% confidence interval of [8.08, 8.85] years. Two simple deterministic models fit the age trajectories on the two sides of the mortality minimum...
September 8, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28884446/analysis-of-homeostatic-mechanisms-in-biochemical-networks
#19
Michael Reed, Janet Best, Martin Golubitsky, Ian Stewart, H Frederik Nijhout
Cell metabolism is an extremely complicated dynamical system that maintains important cellular functions despite large changes in inputs. This "homeostasis" does not mean that the dynamical system is rigid and fixed. Typically, large changes in external variables cause large changes in some internal variables so that, through various regulatory mechanisms, certain other internal variables (concentrations or velocities) remain approximately constant over a finite range of inputs. Outside that range, the mechanisms cease to function and concentrations change rapidly with changes in inputs...
September 7, 2017: Bulletin of Mathematical Biology
https://www.readbyqxmd.com/read/28875359/volatile-chemical-emission-as-a-weapon-of-rearguard-action-a-game-theoretic-model-of-contest-behavior
#20
Mike Mesterton-Gibbons, Yao Dai, Marlène Goubault, Ian C W Hardy
We use a game-theoretic model to explore whether volatile chemical (spiroacetal) emissions can serve as a weapon of rearguard action. Our basic model explores whether such emissions serve as a means of temporary withdrawal, preventing the winner of the current round of a contest from translating its victory into permanent possession of a contested resource. A variant of this model explores an alternative possibility, namely, that such emissions serve as a means of permanent retreat, attempting to prevent a winner from inflicting costs on a fleeing loser...
September 5, 2017: Bulletin of Mathematical Biology
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