2,846 results match your criteria Bulletin Of Mathematical Biology[Journal]


Multiscale Modelling of Fibres Dynamics and Cell Adhesion within Moving Boundary Cancer Invasion.

Bull Math Biol 2019 Apr 12. Epub 2019 Apr 12.

Division of Mathematics, University of Dundee, Dundee, Scotland, DD1 4HN, UK.

Recognised as one of the hallmarks of cancer, local cancer cell invasion is a complex multiscale process that combines the secretion of matrix-degrading enzymes with a series of altered key cell processes (such as abnormal cell proliferation and changes in cell-cell and cell-matrix adhesion leading to enhanced migration) to degrade important components of the surrounding extracellular matrix (ECM) and this way spread further in the human tissue. In order to gain a deeper understanding of the invasion process, we pay special attention to the interacting dynamics between the cancer cell population and various constituents of the surrounding tumour microenvironment. To that end, we consider the key role that ECM plays within the human body tissue, and in particular we focus on the special contribution of its fibrous proteins components, such as collagen and fibronectin, which play an important part in cell proliferation and migration. Read More

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http://dx.doi.org/10.1007/s11538-019-00598-wDOI Listing

The Quality of Genetic Code Models in Terms of Their Robustness Against Point Mutations.

Bull Math Biol 2019 Apr 5. Epub 2019 Apr 5.

Competence Center for Algorithmic and Mathematical Methods in Biology, Biotechnology and Medicine, Mannheim University of Applied Sciences, 68163, Mannheim, Germany.

In this paper, we investigate the quality of selected models of theoretical genetic codes in terms of their robustness against point mutations. To deal with this problem, we used a graph representation including all possible single nucleotide point mutations occurring in codons, which are building blocks of every protein-coding sequence. Following graph theory, the quality of a given code model is measured using the set conductance property which has a useful biological interpretation. Read More

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http://dx.doi.org/10.1007/s11538-019-00603-2DOI Listing
April 2019
1 Read

Towards the Construction of a Mathematically Rigorous Framework for the Modelling of Evolutionary Fitness.

Bull Math Biol 2019 Apr 4. Epub 2019 Apr 4.

Department of Mathematics, University of Leicester, Leicester, UK.

Modelling of natural selection in self-replicating systems has been heavily influenced by the concept of fitness which was inspired by Darwin's original idea of the survival of the fittest. However, so far the concept of fitness in evolutionary modelling is still somewhat vague, intuitive and often subjective. Unfortunately, as a result of this, using different definitions of fitness can lead to conflicting evolutionary outcomes. Read More

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http://dx.doi.org/10.1007/s11538-019-00602-3DOI Listing

Modeling Uniaxial Nonuniform Cell Proliferation.

Bull Math Biol 2019 Apr 3. Epub 2019 Apr 3.

School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia.

Growth in biological systems occurs as a consequence of cell proliferation fueled by a nutrient supply. In general, the nutrient gradient of the system will be nonconstant, resulting in biased cell proliferation. We develop a uniaxial discrete cellular automaton with biased cell proliferation using a probability distribution which reflects the nutrient gradient of the system. Read More

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http://dx.doi.org/10.1007/s11538-019-00601-4DOI Listing

Identifiability from a Few Species for a Class of Biochemical Reaction Networks.

Bull Math Biol 2019 Mar 22. Epub 2019 Mar 22.

Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, Ciudad Universitaria, Pab. I, C1428EGA, Buenos Aires, Argentina.

Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of a class of biochemical networks which are abundant, such as multisite phosphorylation systems and phosphorylation cascades (for example, MAPK cascades). For any system of this class, we explicitly exhibit a single species for each connected component of the associated digraph such that the successive total derivatives of its concentration allow us to identify all the parameters occurring in the component. Read More

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http://dx.doi.org/10.1007/s11538-019-00594-0DOI Listing

Backward Bifurcation as a Desirable Phenomenon: Increased Fecundity Through Infection.

Bull Math Biol 2019 Apr 2. Epub 2019 Apr 2.

Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, 69000, Huajuapan de León, Oaxaca, Mexico.

Backward or subcritical bifurcation is usually considered an undesirable phenomenon in epidemiology since control measures require a reduction in R not below one but below a much smaller value. However, there are contexts for which a backward or subcritical bifurcation is not a bad thing; it can even be desirable. Such is the case for any characteristic that can be passed to the next generation (genetically fixed or not) and that increases the effective reproductive rate of the host or the total number of individuals. Read More

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http://dx.doi.org/10.1007/s11538-019-00604-1DOI Listing
April 2019
6 Reads

Adapting a Plant Tissue Model to Animal Development: Introducing Cell Sliding into VirtualLeaf.

Bull Math Biol 2019 Mar 29. Epub 2019 Mar 29.

Centrum Wiskunde and Informatica, Science Park 123, 1098 XG, Amsterdam, The Netherlands.

Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles and predict the collective cell behavior that follows from a set of interaction rules. In particular, vertex-based models are a popular tool for studying the mechanics of confluent, epithelial cell layers. Read More

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http://dx.doi.org/10.1007/s11538-019-00599-9DOI Listing

Strain- or Stress-Sensing in Mechanochemical Patterning by the Phytohormone Auxin.

Bull Math Biol 2019 Mar 22. Epub 2019 Mar 22.

Reproduction et Développement des Plantes, ENS de Lyon, UCB Lyon 1, CNRS, INRA, Université de Lyon, Lyon Cedex 07, France.

Both chemical and mechanical fields are known to play a major role in morphogenesis. In plants, the phytohormone auxin and its directional transport are essential for the formation of robust patterns of organs, such as flowers or leaves, known as phyllotactic patterns. The transport of auxin was recently shown to be affected by mechanical signals, and conversely, auxin accumulation in incipient organs affects the mechanical properties of the cells. Read More

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http://dx.doi.org/10.1007/s11538-019-00600-5DOI Listing
March 2019
1 Read

A Mathematical Framework for Modelling the Metastatic Spread of Cancer.

Bull Math Biol 2019 Mar 22. Epub 2019 Mar 22.

School of Mathematics and Statistics, University of St Andrews, St Andrews, UK.

Cancer is a complex disease that starts with mutations of key genes in one cell or a small group of cells at a primary site in the body. If these cancer cells continue to grow successfully and, at some later stage, invade the surrounding tissue and acquire a vascular network, they can spread to distant secondary sites in the body. This process, known as metastatic spread, is responsible for around 90% of deaths from cancer and is one of the so-called hallmarks of cancer. Read More

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http://link.springer.com/10.1007/s11538-019-00597-x
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http://dx.doi.org/10.1007/s11538-019-00597-xDOI Listing
March 2019
7 Reads

Modeling Approach Influences Dynamics of a Vector-Borne Pathogen System.

Bull Math Biol 2019 Mar 21. Epub 2019 Mar 21.

Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, 79409, USA.

The choice of a modeling approach is a critical decision in the modeling process, as it determines the complexity of the model and the phenomena that the model captures. In this paper, we developed an individual-based model (IBM) and compared it to a previously published ordinary differential equation (ODE) model, both developed to describe the same biological system although with slightly different emphases given the underlying assumptions and processes of each modeling approach. We used both models to examine the effect of insect vector life history and behavior traits on the spread of a vector-borne plant virus, and determine how choice of approach affects the results and their biological interpretation. Read More

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http://dx.doi.org/10.1007/s11538-019-00595-zDOI Listing

Modeling the Chronification Tendency of Liver Infections as Evolutionary Advantage.

Bull Math Biol 2019 Mar 19. Epub 2019 Mar 19.

Institute of Computational Mathematics, AG PDE, TU Braunschweig, Universitätsplatz 2, 38106, Braunschweig, Germany.

Here, we discuss how the tendency of a liver infection to chronify can be seen as an evolutionary advantage for infected individuals. For this purpose, we present a set of reaction-diffusion equations as a mathematical model of viral liver infections, which allows chronic and acute courses of the liver infection. We introduce a cumulative wealth function, and finally, we show that an immune response favoring the chronification is evolutionary advantageous at the same time. Read More

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http://dx.doi.org/10.1007/s11538-019-00596-yDOI Listing

Number of Source Patches Required for Population Persistence in a Source-Sink Metapopulation with Explicit Movement.

Bull Math Biol 2019 Mar 7. Epub 2019 Mar 7.

Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada.

We consider a simple metapopulation model with explicit movement of individuals between patches, in which each patch is either a source or a sink. We prove that similarly to the case of patch occupancy metapopulations with implicit movement, there exists a threshold number of source patches such that the population potentially becomes extinct below the threshold and established above the threshold. In the case where the matrix describing the movement of populations between spatial locations is irreducible, the result is global; further, assuming a complete mobility graph with equal movement rates, we use the principle of equitable partitions to obtain an explicit expression for the threshold. Read More

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http://dx.doi.org/10.1007/s11538-019-00593-1DOI Listing

An Improved Version of the Classical Banister Model to Predict Changes in Physical Condition.

Bull Math Biol 2019 Mar 6. Epub 2019 Mar 6.

Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain.

In this paper, we formulate and provide the solutions to two new models to predict changes in physical condition by using the information of the training load of an individual. The first model is based on a functional differential equation, and the second one on an integral differential equation. Both models are an extension to the classical Banister model and allow to overcome its main drawback: the variations in physical condition are influenced by the training loads of the previous days and not only of the same day. Read More

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http://dx.doi.org/10.1007/s11538-019-00588-yDOI Listing

Modeling Pancreatic Cancer Dynamics with Immunotherapy.

Bull Math Biol 2019 Mar 6. Epub 2019 Mar 6.

Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, 79409-1042, USA.

We develop a mathematical model of pancreatic cancer that includes pancreatic cancer cells, pancreatic stellate cells, effector cells and tumor-promoting and tumor-suppressing cytokines to investigate the effects of immunotherapies on patient survival. The model is first validated using the survival data of two clinical trials. Local sensitivity analysis of the parameters indicates there exists a critical activation rate of pro-tumor cytokines beyond which the cancer can be eradicated if four adoptive transfers of immune cells are applied. Read More

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http://dx.doi.org/10.1007/s11538-019-00591-3DOI Listing
March 2019
1 Read

Emergence of Oscillations in a Mixed-Mechanism Phosphorylation System.

Bull Math Biol 2019 Mar 4. Epub 2019 Mar 4.

Texas A&M University, College Station, USA.

This work investigates the emergence of oscillations in one of the simplest cellular signaling networks exhibiting oscillations, namely the dual-site phosphorylation and dephosphorylation network (futile cycle), in which the mechanism for phosphorylation is processive, while the one for dephosphorylation is distributive (or vice versa). The fact that this network yields oscillations was shown recently by Suwanmajo and Krishnan. Our results, which significantly extend their analyses, are as follows. Read More

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http://dx.doi.org/10.1007/s11538-019-00580-6DOI Listing
March 2019
1 Read

Data-Driven Model Validation Across Dimensions.

Bull Math Biol 2019 Mar 4. Epub 2019 Mar 4.

Department of Microbiology and Immunology, University of Michigan, Ann Arbor, MI, USA.

Data-driven model validation across dimensions in mathematical and computational biology assumptions are often made (e.g., symmetry) to reduce the problem from three spatial dimensions (3D) to two (2D). Read More

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http://dx.doi.org/10.1007/s11538-019-00590-4DOI Listing
March 2019
1 Read

Global Sensitivity Analysis of High-Dimensional Neuroscience Models: An Example of Neurovascular Coupling.

Bull Math Biol 2019 Feb 28. Epub 2019 Feb 28.

Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand.

The complexity and size of state-of-the-art cell models have significantly increased in part due to the requirement that these models possess complex cellular functions which are thought-but not necessarily proven-to be important. Modern cell models often involve hundreds of parameters; the values of these parameters come, more often than not, from animal experiments whose relationship to the human physiology is weak with very little information on the errors in these measurements. The concomitant uncertainties in parameter values result in uncertainties in the model outputs or quantities of interest (QoIs). Read More

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http://dx.doi.org/10.1007/s11538-019-00578-0DOI Listing
February 2019

Using Experimental Data and Information Criteria to Guide Model Selection for Reaction-Diffusion Problems in Mathematical Biology.

Bull Math Biol 2019 Feb 27. Epub 2019 Feb 27.

School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.

Reaction-diffusion models describing the movement, reproduction and death of individuals within a population are key mathematical modelling tools with widespread applications in mathematical biology. A diverse range of such continuum models have been applied in various biological contexts by choosing different flux and source terms in the reaction-diffusion framework. For example, to describe the collective spreading of cell populations, the flux term may be chosen to reflect various movement mechanisms, such as random motion (diffusion), adhesion, haptotaxis, chemokinesis and chemotaxis. Read More

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http://dx.doi.org/10.1007/s11538-019-00589-xDOI Listing
February 2019

Resource Allocation for Epidemic Control Across Multiple Sub-populations.

Bull Math Biol 2019 Feb 26. Epub 2019 Feb 26.

Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EA, UK.

The number of pathogenic threats to plant, animal and human health is increasing. Controlling the spread of such threats is costly and often resources are limited. A key challenge facing decision makers is how to allocate resources to control the different threats in order to achieve the least amount of damage from the collective impact. Read More

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http://dx.doi.org/10.1007/s11538-019-00584-2DOI Listing
February 2019

A Mathematical Model for Amyloid-𝜷 Aggregation in the Presence of Metal Ions: A Timescale Analysis for the Progress of Alzheimer Disease.

Bull Math Biol 2019 Feb 26. Epub 2019 Feb 26.

School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box:19395-5746, Tehran, Iran.

The aggregation of amyloid-𝛽 (A𝛽) proteins through their self-assembly into oligomers, fibrils, or senile plaques is advocated as a key process of Alzheimer's disease. Recent studies have revealed that metal ions play an essential role in modulating the aggregation rate of amyloid-𝛽 (A𝛽) into senile plaques because of high binding affinity between A𝛽 proteins and metal ions. In this paper, we proposed a mathematical model as a set of coupled kinetic equations that models the self-assembly of amyloid-𝛽 (A𝛽) proteins in the presence of metal ions. Read More

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http://dx.doi.org/10.1007/s11538-019-00583-3DOI Listing
February 2019
1 Read

Asymptotic State of a Two-Patch System with Infinite Diffusion.

Authors:
Yuanshi Wang

Bull Math Biol 2019 Feb 25. Epub 2019 Feb 25.

School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People's Republic of China.

Mathematical theory has predicted that populations diffusing in heterogeneous environments can reach larger total size than when not diffusing. This prediction was tested in a recent experiment, which leads to extension of the previous theory to consumer-resource systems with external resource input. This paper studies a two-patch model with diffusion that characterizes the experiment. Read More

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http://dx.doi.org/10.1007/s11538-019-00582-4DOI Listing
February 2019

Modeling the Spatial Spread of Chagas Disease.

Bull Math Biol 2019 Feb 25. Epub 2019 Feb 25.

Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, Avenida dos Estados 5001, Santo André, SP, 09210-580, Brazil.

The aim of this work is to understand the spatial spread of Chagas disease, which is primarily transmitted by triatomines. We propose a mathematical model using a system of partial differential reaction-diffusion equations to study and describe the spread of this disease in the human population. We consider the respective subclasses of infected and uninfected individuals within the human and triatomine populations. Read More

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http://dx.doi.org/10.1007/s11538-019-00581-5DOI Listing
February 2019

Lesion Dynamics Under Varying Paracrine PDGF Signaling in Brain Tissue.

Bull Math Biol 2019 Feb 22. Epub 2019 Feb 22.

Precision Neurotherapeutics Innovation Program, Mayo Clinic, 5777 E Mayo Blvd, Phoenix, AZ, 85054, USA.

Paracrine PDGF signaling is involved in many processes in the body, both normal and pathological, including embryonic development, angiogenesis, and wound healing as well as liver fibrosis, atherosclerosis, and cancers. We explored this seemingly dual (normal and pathological) role of PDGF mathematically by modeling the release of PDGF in brain tissue and then varying the dynamics of this release. Resulting simulations show that by varying the dynamics of a PDGF source, our model predicts three possible outcomes for PDGF-driven cellular recruitment and lesion growth: (1) localized, short duration of growth, (2) localized, chronic growth, and (3) widespread chronic growth. Read More

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http://dx.doi.org/10.1007/s11538-019-00587-zDOI Listing
February 2019
2 Reads

Computing Weakly Reversible Deficiency Zero Network Translations Using Elementary Flux Modes.

Bull Math Biol 2019 May 21;81(5):1613-1644. Epub 2019 Feb 21.

Department of Mathematics, San José State University, One Washington Square, San Jose, CA, 95192, USA.

We present a computational method for performing structural translation, which has been studied recently in the context of analyzing the steady states and dynamical behavior of mass-action systems derived from biochemical reaction networks. Our procedure involves solving a binary linear programming problem where the decision variables correspond to interactions between the reactions of the original network. We call the resulting network a reaction-to-reaction graph and formalize how such a construction relates to the original reaction network and the structural translation. Read More

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http://dx.doi.org/10.1007/s11538-019-00579-zDOI Listing

Multistationarity in Structured Reaction Networks.

Bull Math Biol 2019 May 20;81(5):1527-1581. Epub 2019 Feb 20.

Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA.

Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an effective question in real algebraic geometry, it is in general difficult to determine whether a given network can give rise to a multistationary system, and if so, to identify witnesses to multistationarity, that is, specific parameter values for which the system exhibits multiple steady states. Here we investigate both problems. Read More

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http://dx.doi.org/10.1007/s11538-019-00572-6DOI Listing

Interplay Between the Persistent Random Walk and the Contact Inhibition of Locomotion Leads to Collective Cell Behaviors.

Bull Math Biol 2019 Feb 20. Epub 2019 Feb 20.

Weldon School of Biomedical Engineering, Purdue University, 206 S. Martin Jischke Drive, West Lafayette, IN, 47907, USA.

Cell migration plays an important role in physiology and pathophysiology. It was observed in the experiments that cells, such as fibroblast, leukocytes, and cancer cells, exhibit a wide variety of migratory behaviors, such as persistent random walk, contact inhibition of locomotion, and ordered behaviors. To identify biophysical mechanisms for these cellular behaviors, we developed a rigorous computational model of cell migration on a two-dimensional non-deformable substrate. Read More

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http://dx.doi.org/10.1007/s11538-019-00585-1DOI Listing
February 2019

Analysis of an Epidemic System with Two Response Delays in Media Impact Function.

Bull Math Biol 2019 May 20;81(5):1582-1612. Epub 2019 Feb 20.

Department of Applied Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, People's Republic of China.

A functional differential model of SEIS-M type with two time delays, representing the response time for mass media to cover the current infection and for individuals' behavior changes to media coverage, was proposed to examine the delayed media impact on the transmission dynamics of emergent infectious diseases. The threshold dynamics were established in terms of the basic reproduction number [Formula: see text]. When there are no time delays, we showed that if the media impact is low, the endemic equilibrium is globally asymptotically stable for [Formula: see text], while the endemic equilibrium may become unstable and Hopf bifurcation occurs for some appropriate conditions by taking the level of media impact as bifurcation parameter. Read More

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http://dx.doi.org/10.1007/s11538-019-00586-0DOI Listing

A Diffuse Interface Framework for Modeling the Evolution of Multi-cell Aggregates as a Soft Packing Problem Driven by the Growth and Division of Cells.

Bull Math Biol 2019 Feb 18. Epub 2019 Feb 18.

Mechanical Engineering, University of Wisconsin-Madison, Madison, USA.

We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface methods, under which each cell is represented by a scalar phase field and the zero level set of the phase field represents the cell membrane. One crucial element in the treatment is the definition of a free energy density function that penalizes cell overlap, thus giving rise to a simple model of cell-cell contact. Read More

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http://dx.doi.org/10.1007/s11538-019-00577-1DOI Listing
February 2019
1 Read

Exact Variance-Reduced Simulation of Lattice Continuous-Time Markov Chains with Applications in Reaction Networks.

Bull Math Biol 2019 Feb 13. Epub 2019 Feb 13.

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St, Urbana, IL, 61801, USA.

We propose an algorithm to reduce the variance of Monte Carlo simulation for the class of countable-state, continuous-time Markov chains, or lattice CTMCs. This broad class of systems includes all processes that can be represented using a random-time-change representation, in particular reaction networks. Numerical studies demonstrate order-of-magnitude reduction in MSE for Monte Carlo mean estimates using our approach for both linear and nonlinear systems. Read More

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http://dx.doi.org/10.1007/s11538-019-00576-2DOI Listing
February 2019
1 Read

Quasi-Steady-State Approximations Derived from the Stochastic Model of Enzyme Kinetics.

Bull Math Biol 2019 May 12;81(5):1303-1336. Epub 2019 Feb 12.

Division of Biostatistics and Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA.

The paper outlines a general approach to deriving quasi-steady-state approximations (QSSAs) of the stochastic reaction networks describing the Michaelis-Menten enzyme kinetics. In particular, it explains how different sets of assumptions about chemical species abundance and reaction rates lead to the standard QSSA, the total QSSA, and the reverse QSSA. These three QSSAs have been widely studied in the literature in deterministic ordinary differential equation settings, and several sets of conditions for their validity have been proposed. Read More

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http://dx.doi.org/10.1007/s11538-019-00574-4DOI Listing

Comparison of Deterministic and Stochastic Regime in a Model for Cdc42 Oscillations in Fission Yeast.

Bull Math Biol 2019 May 12;81(5):1268-1302. Epub 2019 Feb 12.

Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA.

Oscillations occur in a wide variety of essential cellular processes, such as cell cycle progression, circadian clocks and calcium signaling in response to stimuli. It remains unclear how intrinsic stochasticity can influence these oscillatory systems. Here, we focus on oscillations of Cdc42 GTPase in fission yeast. Read More

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http://link.springer.com/10.1007/s11538-019-00573-5
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http://dx.doi.org/10.1007/s11538-019-00573-5DOI Listing
May 2019
4 Reads

Embracing Noise in Chemical Reaction Networks.

Bull Math Biol 2019 May;81(5):1261-1267

Mathematics Department, University of California, Irvine, Irvine, CA, USA.

We provide a short review of stochastic modeling in chemical reaction networks for mathematical and quantitative biologists. We use as case studies two publications appearing in this issue of the Bulletin, on the modeling of quasi-steady-state approximations and cell polarity. Reasons for the relevance of stochastic modeling are described along with some common differences between stochastic and deterministic models. Read More

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http://dx.doi.org/10.1007/s11538-019-00575-3DOI Listing
May 2019
5 Reads

A New Model System for Exploring Assembly Mechanisms of the HIV-1 Immature Capsid In Vivo.

Bull Math Biol 2019 May 31;81(5):1506-1526. Epub 2019 Jan 31.

School of Mathematics and Statistics, Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, 430072, China.

The assembly of the HIV-1 immature capsid (HIC) is an essential step in the virus life cycle. In vivo, the HIC is composed of [Formula: see text] hexameric building blocks, and it takes 5-6 min to complete the assembly process. The involvement of numerous building blocks and the rapid timecourse makes it difficult to understand the HIC assembly process. Read More

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http://dx.doi.org/10.1007/s11538-019-00571-7DOI Listing
May 2019
1 Read

Perspectives on the Role of Mathematics in Drug Discovery and Development.

Bull Math Biol 2019 Jan 28. Epub 2019 Jan 28.

Oncology R&D, AstraZeneca, Waltham, MA, 02451, USA.

The goals of this article and special issue are to highlight the value of mathematical biology approaches in industry, help foster future interactions, and suggest ways for mathematics Ph.D. students and postdocs to move into industry careers. Read More

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http://dx.doi.org/10.1007/s11538-018-00556-yDOI Listing
January 2019
1 Read

Modeling the Role of Feedback in the Adaptive Response of Bacterial Quorum Sensing.

Bull Math Biol 2019 May 28;81(5):1479-1505. Epub 2019 Jan 28.

Department of Mathematics, University of Utah, Salt Lake City, UT, 84112, USA.

Bacterial quorum sensing (QS) is a form of intercellular communication that relies on the production and detection of diffusive signaling molecules called autoinducers. Such a mechanism allows the bacteria to track their cell density in order to regulate group behavior, such as biofilm formation and bioluminescence. In a number of bacterial QS systems, including V. Read More

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http://link.springer.com/10.1007/s11538-019-00570-8
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http://dx.doi.org/10.1007/s11538-019-00570-8DOI Listing
May 2019
9 Reads

Extending the Mathematical Palette for Developmental Pattern Formation: Piebaldism.

Bull Math Biol 2019 May 28;81(5):1461-1478. Epub 2019 Jan 28.

Anatomy, Section of Medicine, University of Fribourg, Route Albert-Gockel 1, 1700, Fribourg, Switzerland.

Here, we present a theoretical investigation with potential insights on developmental mechanisms. Three biological factors, consisting of two diffusing factors and a cell-autonomous immobile transcription factor are combined with different feedback mechanisms. This results in four different situations or fur patterns. Read More

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http://dx.doi.org/10.1007/s11538-019-00569-1DOI Listing
May 2019
1 Read

Genotypic Selection in Spatially Heterogeneous Producer-Grazer Systems Subject to Stoichiometric Constraints.

Bull Math Biol 2019 Jan 18. Epub 2019 Jan 18.

Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA.

Various environmental conditions may exert selection pressures leading to adaptation of stoichiometrically important traits, such as organismal nutritional content or growth rate. We use theoretical approaches to explore the connections between genotypic selection and ecological stoichiometry in spatially heterogeneous environments. We present models of a producer and two grazing genotypes with different stoichiometric phosphorus/carbon ratios under spatially homogenous and heterogeneous conditions. Read More

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http://dx.doi.org/10.1007/s11538-018-00559-9DOI Listing
January 2019

Attractor Stability in Finite Asynchronous Biological System Models.

Bull Math Biol 2019 May 17;81(5):1442-1460. Epub 2019 Jan 17.

Department of Physics, University of California, Irvine, CA, USA.

We present mathematical techniques for exhaustive studies of long-term dynamics of asynchronous biological system models. Specifically, we extend the notion of [Formula: see text]-equivalence developed for graph dynamical systems to support systematic analysis of all possible attractor configurations that can be generated when varying the asynchronous update order (Macauley and Mortveit in Nonlinearity 22(2):421, 2009). We extend earlier work by Veliz-Cuba and Stigler (J Comput Biol 18(6):783-794, 2011), Goles et al. Read More

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http://dx.doi.org/10.1007/s11538-018-00565-xDOI Listing

Mathematical Analysis of a Transformed ODE from a PDE Multiscale Model of Hepatitis C Virus Infection.

Bull Math Biol 2019 May 14;81(5):1427-1441. Epub 2019 Jan 14.

Mathematical Biology Laboratory, Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka, 819-0395, Japan.

Mathematical modeling has revealed the quantitative dynamics during the process of viral infection and evolved into an important tool in modern virology. Coupled with analyses of clinical and experimental data, the widely used basic model of viral dynamics described by ordinary differential equations (ODEs) has been well parameterized. In recent years, age-structured models, called "multiscale model," formulated by partial differential equations (PDEs) have also been developed and become useful tools for more detailed data analysis. Read More

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http://dx.doi.org/10.1007/s11538-018-00564-yDOI Listing

The Effects of Stochasticity on Pattern Formation in a Space- and Time-Discrete Predator-Prey System with Strong Allee Effect in the Prey.

Bull Math Biol 2019 May 14;81(5):1369-1393. Epub 2019 Jan 14.

Department of Mathematics, Federal University of Santa Maria, Santa Maria, Brazil.

The effects of demographic and environmental noise on the vital dynamics and spatial pattern formation are studied for a predator-prey system with strong Allee effect in the prey species. Time and space are taken discrete. It is shown that noise can promote extinction depending on the growth and interaction parameters as well as the noise type and amplitude. Read More

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http://dx.doi.org/10.1007/s11538-018-00539-zDOI Listing

A Model of [Formula: see text] Dynamics in an Accurate Reconstruction of Parotid Acinar Cells.

Bull Math Biol 2019 May 14;81(5):1394-1426. Epub 2019 Jan 14.

Department of Mathematics, The University of Auckland, 38 Princes Street, Auckland, 1010, New Zealand.

We have constructed a spatiotemporal model of [Formula: see text] dynamics in parotid acinar cells, based on new data about the distribution of inositol trisphophate receptors (IPR). The model is solved numerically on a mesh reconstructed from images of a cluster of parotid acinar cells. In contrast to our earlier model (Sneyd et al. Read More

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http://dx.doi.org/10.1007/s11538-018-00563-zDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6449190PMC

From Fixation Probabilities to d-player Games: An Inverse Problem in Evolutionary Dynamics.

Bull Math Biol 2019 Jan 11. Epub 2019 Jan 11.

Instituto de Matemática e Estatística, Universidade Federal Fluminense, R. Prof. Marcos Waldemar de Freitas Reis, s/n, Niterói, RJ, 24210-201, Brasil.

The probability that the frequency of a particular trait will eventually become unity, the so-called fixation probability, is a central issue in the study of population evolution. Its computation, once we are given a stochastic finite population model without mutations and a (possibly frequency dependent) fitness function, is straightforward and it can be done in several ways. Nevertheless, despite the fact that the fixation probability is an important macroscopic property of the population, its precise knowledge does not give any clear information about the interaction patterns among individuals in the population. Read More

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http://dx.doi.org/10.1007/s11538-018-00566-wDOI Listing
January 2019
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Dynamics of a Producer-Grazer Model Incorporating the Effects of Phosphorus Loading on Grazer's Growth.

Bull Math Biol 2019 May 11;81(5):1352-1368. Epub 2019 Jan 11.

Department of Mathematics and Statistics, Texas Tech University, Lubbock, USA.

Phosphorus is an essential element for all life forms, and it is also a limiting nutrient in many aquatic ecosystems. To keep track of the mismatch between the grazer's phosphorus requirement and producer phosphorus content, stoichiometric models have been developed to explicitly incorporate food quality and food quantity. Most stoichiometric models have suggested that the grazer dynamics heavily depends on the producer phosphorus content when the producer has insufficient nutrient content [low phosphorus (P):carbon (C) ratio]. Read More

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http://dx.doi.org/10.1007/s11538-018-00567-9DOI Listing

Impacts of the Dispersal Delay on the Stability of the Coexistence Equilibrium of a Two-Patch Predator-Prey Model with Random Predator Dispersal.

Bull Math Biol 2019 May 9;81(5):1337-1351. Epub 2019 Jan 9.

Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada.

In this paper, we study a predator-prey system with random predator dispersal over two habitat patches. We show that in most cases the dispersal delay does not affect the stability and instability of the coexistence equilibrium. However, if the mean time that the predator spent in one patch is much shorter than the timescale of reproduction of the prey and is larger than the double mean time of capture of prey, the dispersal delay can induce stability switches such that an otherwise unstable coexistence equilibrium can be stabilized over a finite number of stability intervals. Read More

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http://dx.doi.org/10.1007/s11538-018-00568-8DOI Listing

Can VEGFC Form Turing Patterns in the Zebrafish Embryo?

Bull Math Biol 2019 Apr 3;81(4):1201-1237. Epub 2019 Jan 3.

Faculty of Engineering and the Environment, University of Southampton, Highfield Campus, Southampton, SO17 1BJ, UK.

This paper is concerned with a late stage of lymphangiogenesis in the trunk of the zebrafish embryo. At 48 hours post-fertilisation (HPF), a pool of parachordal lymphangioblasts (PLs) lies in the horizontal myoseptum. Between 48 and 168 HPF, the PLs spread from the horizontal myoseptum to form the thoracic duct, dorsal longitudinal lymphatic vessel, and parachordal lymphatic vessel. Read More

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http://dx.doi.org/10.1007/s11538-018-00560-2DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6397306PMC

Statistical Inconsistency of Maximum Parsimony for k-Tuple-Site Data.

Bull Math Biol 2019 Apr 3;81(4):1173-1200. Epub 2019 Jan 3.

Institute of Mathematics and Computer Science, University of Greifswald, Greifswald, Germany.

One of the main aims of phylogenetics is to reconstruct the "Tree of Life." In this respect, different methods and criteria are used to analyze DNA sequences of different species and to compare them in order to derive the evolutionary relationships of these species. Maximum parsimony is one such criterion for tree reconstruction, and it is the one which we will use in this paper. Read More

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http://dx.doi.org/10.1007/s11538-018-00552-2DOI Listing

Two-dimensional Finite Element Model of Breast Cancer Cell Motion Through a Microfluidic Channel.

Bull Math Biol 2019 Apr 3;81(4):1238-1259. Epub 2019 Jan 3.

Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN, USA.

A two-dimensional model for red blood cell motion is adapted to consider the dynamics of breast cancer cells in a microfluidic channel. Adjusting parameters to make the membrane stiffer, as is the case with breast cancer cells compared with red blood cells, allows the model to produce reasonable estimates of breast cancer cell trajectories through the channel. In addition, the model produces estimates of quantities not as easily obtained from experiment such as velocity and stress field information throughout the fluid and on the cell membrane. Read More

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http://dx.doi.org/10.1007/s11538-018-00557-xDOI Listing

A Deficiency-Based Approach to Parametrizing Positive Equilibria of Biochemical Reaction Systems.

Bull Math Biol 2019 Apr 31;81(4):1143-1172. Epub 2018 Dec 31.

Department of Mathematics, West Virginia University, Morgantown, WV, 26506, USA.

We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (1) if the underlying generalized chemical reaction network has an effective deficiency of zero, then the set of positive equilibria coincides with the parametrized set of complex-balanced equilibria and (2) if the network is weakly reversible and has a kinetic deficiency of zero, then the equilibrium set is nonempty and has a positive, typically rational, parametrization. Via the method of network translation, we apply our results to classical mass-action systems studied in the biochemical literature, including the EnvZ-OmpR and shuttled WNT signaling pathways. Read More

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http://dx.doi.org/10.1007/s11538-018-00562-0DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6397143PMC

Vector Preference Annihilates Backward Bifurcation and Reduces Endemicity.

Bull Math Biol 2018 Dec 19. Epub 2018 Dec 19.

Centro de Investigación en Matemáticas, A.C. (CIMAT), Jalisco S/N, Col. Valenciana, CP: 36023, Guanajuato, Gto, Mexico.

We propose and analyze a mathematical model of a vector-borne disease that includes vector feeding preference for carrier hosts and intrinsic incubation in hosts. Analysis of the model reveals the following novel results. We show theoretically and numerically that vector feeding preference for carrier hosts plays an important role for the existence of both the endemic equilibria and backward bifurcation when the basic reproduction number [Formula: see text] is less than one. Read More

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http://dx.doi.org/10.1007/s11538-018-00561-1DOI Listing
December 2018

A Hybrid Model for the Population Dynamics of Periodical Cicadas.

Bull Math Biol 2019 Apr 19;81(4):1122-1142. Epub 2018 Dec 19.

Department of Environmental Science and Policy, University of California, Davis, CA, 95616, USA.

In addition to their unusually long life cycle, periodical cicadas, Magicicada spp., provide an exceptional example of spatially synchronized life stage phenology in nature. Within regions ("broods") spanning 50,000-500,000 km[Formula: see text], adults emerge synchronously every 13 or 17 years. Read More

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http://dx.doi.org/10.1007/s11538-018-00554-0DOI Listing