Abstract：
:Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-kappaB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding and mRNA production. This description of natural variability for delays introduces a transition from a stable steady state to limit cycle oscillations and then a second transition back to a stable steady state which has not been observed in previously published models. We demonstrate our approach for two models. The first model describes Hes1 autorepression with equations for Hes1 mRNA production and Hes1 protein translation. The second model describes Hes1 repression by the protein complex Gro/TLE1/Hes1, where Gro/TLE1 is activated by Hes1 phosphorylation. Finally, we discuss our analytical and numerical results in relation to experimental data.
journal_name
Math Bioscijournal_title
Mathematical biosciencesauthors
Rateitschak K,Wolkenhauer Odoi
10.1016/j.mbs.2006.08.010subject
Has Abstractpub_date
2007-02-01 00:00:00pages
163-79issue
2eissn
0025-5564issn
1879-3134pii
S0025-5564(06)00143-Xjournal_volume
205pub_type
杂志文章abstract：:Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.12.011
更新日期：2014-02-01 00:00:00
abstract：:We consider a host-parasitoid system with individuals moving on a square grid of patches. We study the effects of increasing movement frequency of hosts and parasitoids on the spatial dynamics of the system. We show that there exists a threshold value of movement frequency above which spatial synchrony occurs and the ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2006.03.019
更新日期：2006-10-01 00:00:00
abstract：:Microorganisms exhibit varied regulatory strategies such as direct regulation, symmetric anticipatory regulation, asymmetric anticipatory regulation, etc. Current mathematical modeling frameworks for the growth of microorganisms either do not incorporate regulation or assume that the microorganisms utilize the direct ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.11.005
更新日期：2014-02-01 00:00:00
abstract：:The assumptions of well-mixed and zero bulk flow in compartmental analysis are reexamined. Using Poiseuille flow inside and radial flow outside a pore, the mass-transfer equations are solved by perturbations on simple diffusion. Formulas are obtained for solute distribution, total mass transfer, and apparent permeabil...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(89)90054-0
更新日期：1989-07-01 00:00:00
abstract：:It has been shown in the literature that myocytes isolated from the ventricular walls at various intramural depths have different action potential durations (APDs). When these myocytes are embedded in the ventricular wall, their inhomogeneous properties affect the sequence of repolarization and the actual distribution...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2006.06.002
更新日期：2006-11-01 00:00:00
abstract：:In this work, we derive and analyze a 2n+1-dimensional deterministic differential equation modeling the transmission and treatment of HIV (Human Immunodeficiency Virus) disease. The model is extended to a stochastic differential equation by introducing noise in the transmission rate of the disease. A theoretical treat...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2018.03.013
更新日期：2018-05-01 00:00:00
abstract：:In this paper, we consider a deterministic malaria transmission model with standard incidence rate and treatment. Human population is divided into susceptible, infectious and recovered subclasses, and mosquito population is split into susceptible and infectious classes. It is assumed that, among individuals with malar...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2015.05.005
更新日期：2015-08-01 00:00:00
abstract：:This article examines the functional and clinical impact of time delays that arise in human physiological systems, especially control systems. An overview of the mathematical and physiological contexts for considering time delays will be illustrated, from the system level to cell level, by examining models that incorp...
journal_title：Mathematical biosciences
pub_type： 杂志文章,评审
doi：10.1016/j.mbs.2011.08.006
更新日期：2011-12-01 00:00:00
abstract：:In the present paper, we propose and analyze an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit-lynx model are performed. Results show that in the...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2016.08.014
更新日期：2016-11-01 00:00:00
abstract：:In a standard procedure of food safety testing, the presence of the pathogenic bacterium Listeria monocytogenes can be masked by non-pathogenic Listeria. This phenomenon of Listeria overgrowth is not well understood. We present a mathematical model for the growth of a mixed population of L. innocua and L. monocytogene...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.10.008
更新日期：2014-01-01 00:00:00
abstract：:In this paper we study the dynamics of two competing species when one of them is subject to a disease. In order to keep the model simple, we present it under the strong assumption that the disease cannot cross the species barrier. We answer several important questions about the long term behavior of the environment. I...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(01)00081-5
更新日期：2001-12-01 00:00:00
abstract：:On the basis of this study, it is concluded that within physiological limits the minimum value for the mean capture time of LDL receptors by coated pits must be induced fundamentally by an optimal characterization of their insertion rate function. The corresponding steady-state surface aggregation patterns for the unb...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(99)00043-7
更新日期：1999-11-01 00:00:00
abstract：:The transmission dynamics of a communicable disease in a subdivided population where the spread among groups follows the proportionate mixing model while the within-group transmission can correspond to preferred mixing, proportionate mixing among subgroups, or mixing between social and nonsocial subgroups, is analyzed...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(89)90061-8
更新日期：1989-10-01 00:00:00
abstract：:The problem of biological invasion in a model single-species community is considered, the spatiotemporal dynamics of the system being described by a modified Fisher equation. For a special case, we obtain an exact solution describing self-similar growth of the initially inhabited domain. By comparison with numerical s...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(01)00068-2
更新日期：2001-08-01 00:00:00
abstract：:A mathematical model is presented for the growth of a multicellular spheroid that comprises a central core of necrotic cells surrounded by an outer annulus of proliferating cells. The model distinguishes two mechanisms for cell loss: apoptosis and necrosis. Cell loss due to apoptosis is defined to be programmed cell d...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(96)00023-5
更新日期：1996-07-15 00:00:00
abstract：:The existence of cooperation in this world is a mysterious phenomenon. One of the mechanisms that explain the evolution of cooperation is repeated interaction. If interactions between the same individuals repeat and individuals cooperate conditionally, cooperation can evolve. A previous study pointed out that if indiv...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2017.04.002
更新日期：2017-07-01 00:00:00
abstract：:Rooted phylogenetic networks provide an explicit representation of the evolutionary history of a set X of sampled species. In contrast to phylogenetic trees which show only speciation events, networks can also accommodate reticulate processes (for example, hybrid evolution, endosymbiosis, and lateral gene transfer). A...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2019.04.009
更新日期：2019-07-01 00:00:00
abstract：:A mathematical model of oxygen (O2) transport within a capillary utilizes axisymmetric red blood cell (RBC) shapes that were predicted theoretically by Zarda et al. in 1977. Chemical kinetics and both free and facilitated diffusion of O2 are accounted for in this time-dependent model. The finite-element method is used...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(93)90062-f
更新日期：1993-07-01 00:00:00
abstract：:In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2016.02.006
更新日期：2016-05-01 00:00:00
abstract：:The vaccination program for pertussis (whooping cough) in the United States consists of giving multiple doses of pertussis vaccine to young children. A demographic model with a steady-state age distribution is used as a basis for building an epidemiologic model for the transmission of pertussis. This age-structured mo...
journal_title：Mathematical biosciences
pub_type： 历史文章,杂志文章
doi：10.1016/s0025-5564(97)00014-x
更新日期：1997-10-15 00:00:00
abstract：:An important factor in the dynamic transmission of HIV is the mobility of the population. We formulate various stochastic models for the spread of HIV in a heterosexual mobile population, under the assumptions of constant and varying population sizes. We also derive deterministic and diffusion analogues for these mode...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2006.09.024
更新日期：2007-07-01 00:00:00
abstract：:Pharmacokinetic models are particularly useful to study the underlying and complex physiological mechanisms contributing to clinical differences across patient subgroups or special populations. Unfortunately, the inherent variability of biological systems and knowledge gaps in physiological data limit confidence in mo...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2018.12.011
更新日期：2019-02-01 00:00:00
abstract：:For a wide range of airborne infectious diseases, transmission within the family or household is a key mechanism for the spread and persistence of infection. In general, household-based transmission is relatively strong but only involves a limited number of individuals in contact with each infectious person. In contra...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2008.01.011
更新日期：2008-05-01 00:00:00
abstract：:We apply to Michaelis-Menten kinetics an alternative approach to the study of Singularly Perturbed Differential Equations, that is based on the Renormalization Group (SPDERG). To this aim, we first rebuild the perturbation expansion for Michaelis-Menten kinetics, beyond the standard Quasi-Steady-State Approximation (s...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2017.11.012
更新日期：2018-05-01 00:00:00
abstract：:We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation tim...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.02.007
更新日期：2013-09-01 00:00:00
abstract：:A number of recent research studies have focused on theoretical and experimental investigation of a bottleneck in a metabolic reaction network. However, there is no study on how the bottleneck affects the performance of a fermentation process when a product is highly toxic and remarkably influences the growth and deat...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2010.08.001
更新日期：2010-11-01 00:00:00
abstract：:This paper deals with a two-microbial species model in competition for a single-resource in the chemostat including general intra- and interspecific density-dependent growth rates with distinct removal rates for each species. In order to understand the effects of intra- and interspecific interference, this general mod...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2017.02.007
更新日期：2017-04-01 00:00:00
abstract：:The goal of this article is to formulate and analyze the simplest logistic pair-formation model and to contrast its dynamics to that of the corresponding Malthusian pair-formation model, that is, a generalization of the Kendall-Keyfitz model. The Malthusian pair-formation model supports a unique nontrivial stable expo...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(94)00077-d
更新日期：1995-07-01 00:00:00
abstract：:Under the influence of randomly occurring disasters, the eventual extinction probability, q, of a birth and death process, Z, is a random variable. In this paper, we obtain an integral expression for the probability density function g(x) of q under the assumption that the population process Z is a time homogeneous lin...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(99)00059-0
更新日期：2000-03-01 00:00:00
abstract：:The authors determine the time-dependent ligand current into a spherical cell that is covered with a large number of age-dependent receptors. These receptors can be in either of two states: active (i.e., available for ligand binding) or inactive. An active receptor turns inactive upon binding a ligand, and it can reap...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(90)90122-f
更新日期：1990-03-01 00:00:00
