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Journal of Mathematical Biology

Renaud Dessalles, Vincent Fromion, Philippe Robert
This paper analyzes, in the context of a prokaryotic cell, the stochastic variability of the number of proteins when there is a control of gene expression by an autoregulation scheme. The goal of this work is to estimate the efficiency of the regulation to limit the fluctuations of the number of copies of a given protein. The autoregulation considered in this paper relies mainly on a negative feedback: the proteins are repressors of their own gene expression. The efficiency of a production process without feedback control is compared to a production process with an autoregulation of the gene expression assuming that both of them produce the same average number of proteins...
March 13, 2017: Journal of Mathematical Biology
Veronika Hajnová, Lenka Přibylová
The structured population LPA model is studied. The model describes flour beetle (Tribolium) population dynamics of four stage populations: eggs, larvae, pupae and adults with cannibalism between these stages. We concentrate on the case of non-zero cannibalistic rates of adults on eggs and adults on pupae and no cannibalism of larvae on eggs, but the results can be numerically continued to non-zero cannibalism of larvae on eggs. In this article two-parameter bifurcations in LPA model are analysed. Various stable and unstable invariant sets are found, different types of hysteresis are presented and abrupt changes in dynamics are simulated to explain the complicated way the system behaves near two-parameter bifurcation manifolds...
March 10, 2017: Journal of Mathematical Biology
Hirokazu Ninomiya, Yoshitaro Tanaka, Hiroko Yamamoto
Recent years have seen the introduction of non-local interactions in various fields. A typical example of a non-local interaction is where the convolution kernel incorporates short-range activation and long-range inhibition. This paper presents the relationship between non-local interactions and reaction-diffusion systems in the following sense: (a) the relationship between the instability induced by non-local interaction and diffusion-driven instability; (b) the realization of non-local interactions by reaction-diffusion systems...
March 9, 2017: Journal of Mathematical Biology
Horst R Thieme
Enclosure theorems are derived for homogeneous bounded order-preserving operators and illustrated for operators involving pair-formation functions introduced by Karl-Peter Hadeler in the late 1980s. They are applied to a basic discrete-time two-sex population model and to the relation between the basic turnover number and the basic reproduction number.
March 8, 2017: Journal of Mathematical Biology
Brooks Emerick, Gilberto Schleiniger, Bruce M Boman
The Wnt/[Formula: see text]-catenin pathway plays a crucial role in stem cell renewal and differentiation in the normal human colonic crypt. The balance between [Formula: see text]-catenin and APC along the crypt axis determines its normal functionality. The mechanism that deregulates this balance may give insight into the initiation of colorectal cancer. This is significant because the spatial dysregulation of [Formula: see text]-catenin by the mutated tumor suppressor gene/protein APC in human colonic crypts is responsible for the initiation and growth of colorectal cancer...
March 7, 2017: Journal of Mathematical Biology
F Meunier, V Couvreur, X Draye, J Vanderborght, M Javaux
Predicting root water uptake and plant transpiration is crucial for managing plant irrigation and developing drought-tolerant root system ideotypes (i.e. ideal root systems). Today, three-dimensional structural functional models exist, which allows solving the water flow equation in the soil and in the root systems under transient conditions and in heterogeneous soils. Yet, these models rely on the full representation of the three-dimensional distribution of the root hydraulic properties, which is not always easy to access...
March 2, 2017: Journal of Mathematical Biology
Seongwon Lee, Se-Woong Kim, Youngmin Oh, Hyung Ju Hwang
In this paper, we study how chemotaxis affects the immune system by proposing a minimal mathematical model, a reaction-diffusion-advection system, describing a cross-talk between antigens and immune cells via chemokines. We analyze the stability and instability arising in our chemotaxis model and find their conditions for different chemotactic strengths by using energy estimates, spectral analysis, and bootstrap argument. Numerical simulations are also performed to the model, by using the finite volume method in order to deal with the chemotaxis term, and the fractional step methods are used to solve the whole system...
February 27, 2017: Journal of Mathematical Biology
J M Nava-Sedeño, H Hatzikirou, F Peruani, A Deutsch
Cellular automata (CA) are discrete time, space, and state models which are extensively used for modeling biological phenomena. CA are "on-lattice" models with low computational demands. In particular, lattice-gas cellular automata (LGCA) have been introduced as models of single and collective cell migration. The interaction rule dictates the behavior of a cellular automaton model and is critical to the model's biological relevance. The LGCA model's interaction rule has been typically chosen phenomenologically...
February 27, 2017: Journal of Mathematical Biology
Arnd Scheel, Angela Stevens
We study mechanisms for wavenumber selection in a minimal model for run-and-tumble dynamics. We show that nonlinearity in tumbling rates induces the existence of a plethora of traveling- and standing-wave patterns, as well as a subtle selection mechanism for the wavenumbers of spatio-temporally periodic waves. We comment on possible implications for rippling patterns observed in colonies of myxobacteria.
February 21, 2017: Journal of Mathematical Biology
Cameron Browne
Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey-predator interactions. Of primary interests are the underlying structure and features which stabilize diverse ecological networks. Recently Korytowski and Smith (Theor Ecol 8(1):111-120, 2015) proved that a perfectly nested infection network, along with appropriate life history trade-offs, leads to coexistence and persistence of bacteria-phage communities in a chemostat model...
February 20, 2017: Journal of Mathematical Biology
Michelle Baker, Bindi S Brook, Markus R Owen
Osteoarthritis (OA) is a degenerative disease which causes pain and stiffness in joints. OA progresses through excessive degradation of joint cartilage, eventually leading to significant joint degeneration and loss of function. Cytokines, a group of cell signalling proteins, present in raised concentrations in OA joints, can be classified into pro-inflammatory and anti-inflammatory groups. They mediate cartilage degradation through several mechanisms, primarily the up-regulation of matrix metalloproteinases (MMPs), a group of collagen-degrading enzymes...
February 17, 2017: Journal of Mathematical Biology
Hao Ji, Hans-Georg Müller, Nikos T Papadopoulos, James R Carey
Residual demography is a recent concept that has proved to be a useful tool to gain insights about the age distributions of wild populations, especially insects. We develop an operator equation that permits the derivation of functionals of the age distribution in wild populations, such as mean age, within the framework of residual demography. Our method combines information from an observed captive cohort, which consists of subjects that are sampled from the wild with unknown ages and then raised in the laboratory until death, and from a reference cohort that consists of subjects raised in the laboratory since birth of the same population...
February 17, 2017: Journal of Mathematical Biology
Pavel Drábek, Peter Takáč
We consider a one-dimensional population genetics model for the advance of an advantageous gene. The model is described by the semilinear Fisher equation with unbalanced bistable non-Lipschitzian nonlinearity f(u). The "nonsmoothness" of f allows for the appearance of travelling waves with a new, more realistic profile. We study existence, uniqueness, and long-time asymptotic behavior of the solutions u(x, t), [Formula: see text]. We prove also the existence and uniqueness (up to a spatial shift) of a travelling wave U...
February 14, 2017: Journal of Mathematical Biology
Daniele Avitable, Kyle C A Wedgwood
We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory...
February 1, 2017: Journal of Mathematical Biology
Jacob Østergaard, Anders Rahbek, Susanne Ditlevsen
We present cointegration analysis as a method to infer the network structure of a linearly phase coupled oscillating system. By defining a class of oscillating systems with interacting phases, we derive a data generating process where we can specify the coupling structure of a network that resembles biological processes. In particular we study a network of Winfree oscillators, for which we present a statistical analysis of various simulated networks, where we conclude on the coupling structure: the direction of feedback in the phase processes and proportional coupling strength between individual components of the system...
January 30, 2017: Journal of Mathematical Biology
Bertrand Cloez, Coralie Fritsch
In a chemostat, bacteria live in a growth container of constant volume in which liquid is injected continuously. Recently, Campillo and Fritsch introduced a mass-structured individual-based model to represent this dynamics and proved its convergence to a more classic partial differential equation. In this work, we are interested in the convergence of the fluctuation process. We consider this process in some Sobolev spaces and use central limit theorems on Hilbert space to prove its convergence in law to an infinite-dimensional Gaussian process...
January 27, 2017: Journal of Mathematical Biology
E Lanzarone, S Pasquali, G Gilioli, E Marchesini
Control interventions in sustainable pest management schemes are set according to the phenology and the population abundance of the pests. This information can be obtained using suitable mathematical models that describe the population dynamics based on individual life history responses to environmental conditions and resource availability. These responses are described by development, fecundity and survival rate functions, which can be estimated from laboratory experiments. If experimental data are not available, data on field population dynamics can be used for their estimation...
January 27, 2017: Journal of Mathematical Biology
Apollos Besse, Thomas Lepoutre, Samuel Bernard
We propose and analyze a simplified version of a partial differential equation (PDE) model for chronic myeloid leukemia (CML) derived from an agent-based model proposed by Roeder et al. This model describes the proliferation and differentiation of leukemic stem cells in the bone marrow and the effect of the drug Imatinib on these cells. We first simplify the PDE model by noting that most of the dynamics occurs in a subspace of the original 2D state space. Then we determine the dominant eigenvalue of the corresponding linearized system that controls the long-term behavior of solutions...
January 25, 2017: Journal of Mathematical Biology
D Iron, J Rumsey
In this paper we construct and analyze a model of cell receptor aggregation. Experiments have shown that receptors in an aggregated state have greatly reduced mobility. We model the effects of this reduced mobility with a density dependent diffusion and study the impact of density dependent diffusion on aggregate formation in a one-dimensional domain. Critical values of receptor diffusivity and receptor activation are found and compared with numerical simulations. We find that the role of density dependant diffusion is quite limited in the formation of aggregate structures...
January 25, 2017: Journal of Mathematical Biology
Ying Zhou, William F Fagan
In this paper, we use periodic and stochastic integrodifference models to study the persistence of a single-species population in a habitat with temporally varying sizes. We extend a persistence metric for integral operators on bounded domains to that of integral operators on unbounded domains. Using this metric in the periodic model, we present new perspectives of the critical habitat size problem in the case of dynamically changing habitat sizes. Specifically, we extend the concept of critical habitat size to that of lower minimal limit size in a period-2 scenario, and prove the existence of the lower minimal limit size...
January 18, 2017: Journal of Mathematical Biology
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