Pub Date : 2018-04-19DOI: 10.11145/j.biomath.2018.07.217
R. Eftimie
The collective movement of animals occurs as a result of communicationbetween the members of the community. However, inter-individual commu-nication can be aected by the stochasticity of the environment, leading tochanges in the perception of neighbours and subsequent changes in individualbehaviour, which then in uence the overall behaviour of the animal aggre-gations. To investigate the eect of noise on the overall behaviour of animalaggregations, we consider a class of nonlocal stochastic and deterministic hy-perbolic models for the collective movement of animals. We show numericallythat strong noise does not seem to in uence the spatio-temporal pattern (i.e.,travelling aggregations) observed when all neighbours are perceived with thesame intensity (i.e., the environment is homogeneous). However, when neigh-bours ahead/behind are perceived dierently by a reference individual, noisecan lead to the destruction of the spatio-temporal pattern. Moreover, weshow that the increase in noise can lead to dierent transitions between dif-ferent spatio-temporal patterns, and these transitions are relatively similarto the transitions between patterns when we perturb deterministically someparameters.
{"title":"The impact of environmental noise on animal communication: pattern formation in a class of deterministic and stochastic hyperbolic models for self-organised biological aggregations","authors":"R. Eftimie","doi":"10.11145/j.biomath.2018.07.217","DOIUrl":"https://doi.org/10.11145/j.biomath.2018.07.217","url":null,"abstract":"The collective movement of animals occurs as a result of communicationbetween the members of the community. However, inter-individual commu-nication can be aected by the stochasticity of the environment, leading tochanges in the perception of neighbours and subsequent changes in individualbehaviour, which then in uence the overall behaviour of the animal aggre-gations. To investigate the eect of noise on the overall behaviour of animalaggregations, we consider a class of nonlocal stochastic and deterministic hy-perbolic models for the collective movement of animals. We show numericallythat strong noise does not seem to in uence the spatio-temporal pattern (i.e.,travelling aggregations) observed when all neighbours are perceived with thesame intensity (i.e., the environment is homogeneous). However, when neigh-bours ahead/behind are perceived dierently by a reference individual, noisecan lead to the destruction of the spatio-temporal pattern. Moreover, weshow that the increase in noise can lead to dierent transitions between dif-ferent spatio-temporal patterns, and these transitions are relatively similarto the transitions between patterns when we perturb deterministically someparameters.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43478298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-04-02DOI: 10.11145/J.BIOMATH.2018.12.047
Raluca Roxana Purnichescu Purtan, Irina Badralexi
We develop a stochastic model for an intracellular active transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (Mean First Passage Time). We study different biologically relevant scenarios, which include the possibility of multiple hidden targets (which breed competition) and the presence of obstacles. The purpose of including obstacles is to illustrate actual disruptions of the intracellular transport (which can result, for example, in several neurological disorders. From a mathematical point of view, the intracellular active transport is modelled by two independent continuous-time, discrete space Markov chains: one for the dynamics of the molecular motor in the space intervals and one for the domain of target. The process is time homogeneous and independent of the position of the molecular motor.
{"title":"A stochastic model for intracellular active transport","authors":"Raluca Roxana Purnichescu Purtan, Irina Badralexi","doi":"10.11145/J.BIOMATH.2018.12.047","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2018.12.047","url":null,"abstract":"We develop a stochastic model for an intracellular active transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (Mean First Passage Time). We study different biologically relevant scenarios, which include the possibility of multiple hidden targets (which breed competition) and the presence of obstacles. The purpose of including obstacles is to illustrate actual disruptions of the intracellular transport (which can result, for example, in several neurological disorders. From a mathematical point of view, the intracellular active transport is modelled by two independent continuous-time, discrete space Markov chains: one for the dynamics of the molecular motor in the space intervals and one for the domain of target. The process is time homogeneous and independent of the position of the molecular motor.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47049465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-03-03DOI: 10.11145/J.BIOMATH.2018.12.177
A. Diouf, B. I. Camara, D. Ngom, Héla Toumi, V. Felten, J. Masfaraud, J. Férard
The toxicokinetic and toxicodynamic models (TK-TD) are very well-known for their ability, at both the individual and the population level, to accurately describe life cycles such as the growth, reproduction and survival of sentinel organisms under the influence of an ecological biomarker. Being dynamics, the consistent inference of life history and environmental traits parameters that engender them is sometimes very complex numerically, especially as these parameters vary from one individual to another. In this paper, we estimate the parameters of a survival model TK-TD already applied and validated by the implementation of the R package GUTS (the General Unified Threshold Model of Survival) by another coding applied to another very recent implementation of Bayesian inference with the R package deBInfer in order to evaluate the survival effects of our ecotoxicological biomarker called Deltamethrin on our Daphnia sample. The study allowed us to evaluate from a population point of view especially the threshold concentration not to be exceeded to observe a survival effect commonly known NEC (No effect Concentration) and possibly determine the correlations between different variables of life history and the environment traits.
{"title":"Bayesian inference of a dynamical model evaluating Deltamethrin effect on Daphnia survival","authors":"A. Diouf, B. I. Camara, D. Ngom, Héla Toumi, V. Felten, J. Masfaraud, J. Férard","doi":"10.11145/J.BIOMATH.2018.12.177","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2018.12.177","url":null,"abstract":"The toxicokinetic and toxicodynamic models (TK-TD) are very well-known for their ability, at both the individual and the population level, to accurately describe life cycles such as the growth, reproduction and survival of sentinel organisms under the influence of an ecological biomarker. Being dynamics, the consistent inference of life history and environmental traits parameters that engender them is sometimes very complex numerically, especially as these parameters vary from one individual to another. In this paper, we estimate the parameters of a survival model TK-TD already applied and validated by the implementation of the R package GUTS (the General Unified Threshold Model of Survival) by another coding applied to another very recent implementation of Bayesian inference with the R package deBInfer in order to evaluate the survival effects of our ecotoxicological biomarker called Deltamethrin on our Daphnia sample. The study allowed us to evaluate from a population point of view especially the threshold concentration not to be exceeded to observe a survival effect commonly known NEC (No effect Concentration) and possibly determine the correlations between different variables of life history and the environment traits.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42083951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-09-14DOI: 10.11145/j.biomath.2017.11.297
Nicholas A. Battista, L. Miller
We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a $2D$ fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials are coupled to muscular contraction and hence the overall pumping dynamics. In comparison to previous models, the electro-dynamical model does not use prescribed motion to initiate the pumping motion, but rather the pumping dynamics are fully coupled to an underlying electrophysiology model, governed by the FitzHugh-Nagumo equations. Perturbing the diffusion parameter in the FitzHugh-Nagumo model leads to a bifurcation in dynamics of action potential propagation. This bifurcation is able to capture a spectrum of different pumping regimes, with dynamic suction pumping and peristaltic-like pumping at the extremes. We find that more bulk flow is produced within the realm of peristaltic-like pumping.
{"title":"Bifurcations in valveless pumping techniques from a coupled fluid-structure-electrophysiology model in heart development","authors":"Nicholas A. Battista, L. Miller","doi":"10.11145/j.biomath.2017.11.297","DOIUrl":"https://doi.org/10.11145/j.biomath.2017.11.297","url":null,"abstract":"We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a $2D$ fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials are coupled to muscular contraction and hence the overall pumping dynamics. In comparison to previous models, the electro-dynamical model does not use prescribed motion to initiate the pumping motion, but rather the pumping dynamics are fully coupled to an underlying electrophysiology model, governed by the FitzHugh-Nagumo equations. Perturbing the diffusion parameter in the FitzHugh-Nagumo model leads to a bifurcation in dynamics of action potential propagation. This bifurcation is able to capture a spectrum of different pumping regimes, with dynamic suction pumping and peristaltic-like pumping at the extremes. We find that more bulk flow is produced within the realm of peristaltic-like pumping.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47420862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-03-09DOI: 10.11145/J.BIOMATH.2013.03.027
E. Flach, J. Norbury, S. Schnell
Convection-induced instability in reaction-diffusion systems produces complicated patterns of oscillations behind propagating wavefronts. We transform the system twice: into lambda-omega form, then into polar variables. We find analytical estimates for the wavefront speed which we confirm numerically. Our previous work examined a simpler system [E. H. Flach, S. Schnell, and J. Norbury, Phys. Rev. E 76, 036216 (2007)]; the onset of instability is qualitatively different in numerical solutions of this system. We modify our estimates and connect the two different behaviours. Our estimate explains how the Turing instability fits with pattern found in reaction-diffusion-convection systems. Our results can have important applications to the pattern formation analysis of biological systems.
在反应扩散系统中，对流诱导的不稳定性在传播波前后产生复杂的振荡模式。我们把这个系统变换两次:首先是形式，然后是极坐标变量。我们找到了波前速度的分析估计，并进行了数值验证。我们之前的工作研究了一个更简单的系统[E]。H. Flach, S. Schnell和J. Norbury, Phys。[j];在该系统的数值解中，不稳定性的开始在性质上是不同的。我们修改我们的估计并将两种不同的行为联系起来。我们的估计解释了图灵不稳定性如何与反应-扩散-对流系统中的模式相匹配。我们的研究结果对生物系统的模式形成分析具有重要的应用价值。
{"title":"More than Skew: Asymmetric Wave Propagation in a Reaction-Diffusion-Convection System.","authors":"E. Flach, J. Norbury, S. Schnell","doi":"10.11145/J.BIOMATH.2013.03.027","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2013.03.027","url":null,"abstract":"Convection-induced instability in reaction-diffusion systems produces complicated patterns of oscillations behind propagating wavefronts. We transform the system twice: into lambda-omega form, then into polar variables. We find analytical estimates for the wavefront speed which we confirm numerically. Our previous work examined a simpler system [E. H. Flach, S. Schnell, and J. Norbury, Phys. Rev. E 76, 036216 (2007)]; the onset of instability is qualitatively different in numerical solutions of this system. We modify our estimates and connect the two different behaviours. Our estimate explains how the Turing instability fits with pattern found in reaction-diffusion-convection systems. Our results can have important applications to the pattern formation analysis of biological systems.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63527345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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