Multistationarity and Bistability for Fewnomial Chemical Reaction Networks.

Abstract:

:Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open mathematical problem. One successful strategy consists of analyzing small networks and deducing that some of the properties are preserved upon passage to the full network. Motivated by this, we study chemical reaction networks with few chemical complexes. Under mass action kinetics, the steady states of these networks are described by fewnomial systems, that is polynomial systems having few distinct monomials. Such systems of polynomials are often studied in real algebraic geometry by the use of Gale dual systems. Using this Gale duality, we give precise conditions in terms of the reaction rate constants for the number and stability of the steady states of families of reaction networks with one non-flow reaction.

journal_name

Bull Math Biol

authors

Feliu E,Helmer M

doi

10.1007/s11538-018-00555-z

subject

Has Abstract

pub_date

2019-04-01 00:00:00

pages

1089-1121

issue

4

eissn

0092-8240

issn

1522-9602

pii

10.1007/s11538-018-00555-z

journal_volume

81

pub_type

杂志文章
  • Analyzing the fitch method for reconstructing ancestral states on ultrametric phylogenetic trees.

    abstract::The accuracy of the Fitch method for reconstructing ancestral states on ultrametric phylogenetic trees is studied. Two recurrence relations for computing the accuracy are given here. Using these relations, we analyze the convergence of the accuracy of the Fitch method for reconstructing the root state on a complete bi...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-010-9505-8

    authors: Zhang L,Shen J,Yang J,Li G

    更新日期:2010-10-01 00:00:00

  • A Computational Approach to Steady State Correspondence of Regular and Generalized Mass Action Systems.

    abstract::It has been recently observed that the dynamical properties of mass action systems arising from many models of biochemical reaction networks can be characterized by considering the corresponding properties of a related generalized mass action system. The correspondence process known as network translation in particula...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-015-0077-5

    authors: Johnston MD

    更新日期:2015-06-01 00:00:00

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

    abstract::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 ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00585-1

    authors: Hassan AR,Biel T,Umulis DM,Kim T

    更新日期:2019-08-01 00:00:00

  • Mechanical Cell Competition in Heterogeneous Epithelial Tissues.

    abstract::Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimension...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-020-00807-x

    authors: Murphy RJ,Buenzli PR,Baker RE,Simpson MJ

    更新日期:2020-09-26 00:00:00

  • Mathematical insights in evaluating state dependent effectiveness of HIV prevention interventions.

    abstract::Mathematical models have been used to simulate HIV transmission and to study the use of preexposure prophylaxis (PrEP) for HIV prevention. Often a single intervention outcome over 10 years has been used to evaluate the effectiveness of PrEP interventions. However, different metrics express a wide variation over time a...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-013-9824-7

    authors: Zhao Y,Dimitrov DT,Liu H,Kuang Y

    更新日期:2013-04-01 00:00:00

  • Consequences of dispersal heterogeneity for population spread and persistence.

    abstract::Dispersal heterogeneity is increasingly being observed in ecological populations and has long been suspected as an explanation for observations of non-Gaussian dispersal. Recent empirical and theoretical studies have begun to confirm this. Using an integro-difference model, we allow an individual's diffusivity to be d...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-014-0014-z

    authors: Stover JP,Kendall BE,Nisbet RM

    更新日期:2014-11-01 00:00:00

  • Uni-directional interaction and plant-pollinator-robber coexistence.

    abstract::A mathematical model for the plant-pollinator-robber interaction is studied to understand the factors leading to the widespread occurrence and stability of such interactions. In the interaction, a flowering plant provides resource for its pollinator and the pollinator has both positive and negative effects on the plan...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-012-9750-0

    authors: Wang Y,DeAngelis DL,Holland JN

    更新日期:2012-09-01 00:00:00

  • A general formulation of the concept of independent action for the combined effects of agents.

    abstract::Analysis schemes for the classification of synergism and antagonism for mixed agents operate on the discrepancies between observed and calculated results. As such they cannot be confirmed by experiments and therefore have to be tested in terms of mathematical and logical self-consistency. The concept of independent ac...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02458276

    authors: Lam GK

    更新日期:1994-09-01 00:00:00

  • On Stable Parameter Estimation and Forecasting in Epidemiology by the Levenberg-Marquardt Algorithm with Broyden's Rank-one Updates for the Jacobian Operator.

    abstract::Rigorously calibrating dynamic models with time-series data can pose roadblocks. Oftentimes, the problem is ill-posed and one has to rely on appropriate regularization techniques to ensure stable parameter estimation from which forward projections with quantified uncertainty could be generated. If the inversion proced...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00650-9

    authors: Smirnova A,Sirb B,Chowell G

    更新日期:2019-10-01 00:00:00

  • Meeting the Needs of A Changing Landscape: Advances and Challenges in Undergraduate Biology Education.

    abstract::Over the last 25 years, reforms in undergraduate biology education have transformed the way biology is taught at many institutions of higher education. This has been fueled in part by a burgeoning discipline-based education research community, which has advocated for evidence-based instructional practices based on fin...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-020-00739-6

    authors: Aikens ML

    更新日期:2020-05-13 00:00:00

  • From plateau to pseudo-plateau bursting: making the transition.

    abstract::Bursting electrical activity is ubiquitous in excitable cells such as neurons and many endocrine cells. The technique of fast/slow analysis, which takes advantage of time scale differences, is typically used to analyze the dynamics of bursting in mathematical models. Two classes of bursting oscillations that have been...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-010-9559-7

    authors: Teka W,Tsaneva-Atanasova K,Bertram R,Tabak J

    更新日期:2011-06-01 00:00:00

  • Close Encounters of the Cell Kind: The Impact of Contact Inhibition on Tumour Growth and Cancer Models.

    abstract::Cancer is a complex phenomenon, and the sheer variation in behaviour across different types renders it difficult to ascertain underlying biological mechanisms. Experimental approaches frequently yield conflicting results for myriad reasons, and mathematical modelling of cancer is a vital tool to explore what we cannot...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00677-y

    authors: Grimes DR,Fletcher AG

    更新日期:2020-01-22 00:00:00

  • Inferring the dynamics of a spatial epidemic from time-series data.

    abstract::Spatial interactions are key determinants in the dynamics of many epidemiological and ecological systems; therefore it is important to use spatio-temporal models to estimate essential parameters. However, spatially-explicit data sets are rarely available; moreover, fitting spatially-explicit models to such data can be...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1016/j.bulm.2003.09.002

    authors: Filipe JA,Otten W,Gibson GJ,Gilligan CA

    更新日期:2004-03-01 00:00:00

  • A periodically-forced mathematical model for the seasonal dynamics of malaria in mosquitoes.

    abstract::We describe and analyze a periodically-forced difference equation model for malaria in mosquitoes that captures the effects of seasonality and allows the mosquitoes to feed on a heterogeneous population of hosts. We numerically show the existence of a unique globally asymptotically stable periodic orbit and calculate ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-011-9710-0

    authors: Chitnis N,Hardy D,Smith T

    更新日期:2012-05-01 00:00:00

  • Oscillations and Multiple Equilibria in Microvascular Blood Flow.

    abstract::We investigate the existence of oscillatory dynamics and multiple steady-state flow rates in a network with a simple topology and in vivo microvascular blood flow constitutive laws. Unlike many previous analytic studies, we employ the most biologically relevant models of the physical properties of whole blood. Through...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-015-0089-1

    authors: Karst NJ,Storey BD,Geddes JB

    更新日期:2015-07-01 00:00:00

  • Modeling transcriptional control in gene networks--methods, recent results, and future directions.

    abstract::Mathematical models are useful for providing a framework for integrating data and gaining insights into the static and dynamic behavior of complex biological systems such as networks of interacting genes. We review the dynamic behaviors expected from model gene networks incorporating common biochemical motifs, and we ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章,评审

    doi:10.1006/bulm.1999.0155

    authors: Smolen P,Baxter DA,Byrne JH

    更新日期:2000-03-01 00:00:00

  • Statistical evaluation of dendritic growth models.

    abstract::A mathematical model (Kliemann, W. 1987. Bull. math. Biol. 49, 135-152.) that predicts the quantitative branching pattern of dendritic tree was evaluated using the apical and basal dendrites of rat hippocampal neurons. The Wald statistic for chi 2-test was developed for the branching pattern of dendritic trees and for...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02458630

    authors: Carriquiry AL,Ireland WP,Kliemann W,Uemura E

    更新日期:1991-01-01 00:00:00

  • Identifiability and Reconstructibility of Species Phylogenies Under a Modified Coalescent.

    abstract::Coalescent models of evolution account for incomplete lineage sorting by specifying a species tree parameter which determines a distribution on gene trees, and consequently, a site pattern probability distribution. It has been shown that the unrooted topology of the species tree parameter of the multispecies coalescen...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-018-0456-9

    authors: Long C,Kubatko L

    更新日期:2019-02-01 00:00:00

  • Chemotherapeutic treatments: a study of the interplay among drug resistance, toxicity and recuperation from side effects.

    abstract::A system of differential equations for the control of tumor growth cells in a cycle nonspecific chemotherapy is analyzed. Spontaneously acquired drug resistance is taken into account, and a criterion for the selection of chemotherapeutic treatment is used. This criterion purports to describe the possibility of improve...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02462001

    authors: Costa MI,Boldrini JL

    更新日期:1997-03-01 00:00:00

  • Bistability and Asynchrony in a Boolean Model of the L-arabinose Operon in Escherichia coli.

    abstract::The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean model that captures the bistabili...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-017-0306-1

    authors: Jenkins A,Macauley M

    更新日期:2017-08-01 00:00:00

  • Susceptibilities of an irreversible Michaelis-Menten enzyme.

    abstract::The nonlinear response of the simplest irreversible Michaelis-Menten enzyme is considered. In the context of metabolic networks, i.e. in vivo, the enzyme is subject to sustained, frequently time-dependent, input fluxes that keep the system out of equilibrium. The connection between the fluxes and the response is inves...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-006-9111-y

    authors: Torralba AS,Rodríguez Y

    更新日期:2006-08-01 00:00:00

  • Dynamical behaviour of biological regulatory networks--I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state.

    abstract::In the field of biological regulation, models dictated by experimental work are usually complex networks comprising intertwined feedback loops. In this paper the biological roles of individual positive loops (multistationarity, differentiation) and negative loops (homeostasis, with or without oscillations, buffering o...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02460618

    authors: Thomas R,Thieffry D,Kaufman M

    更新日期:1995-03-01 00:00:00

  • Alternative Models to Hodgkin-Huxley Equations.

    abstract::The Hodgkin and Huxley equations have served as the benchmark model in electrophysiology since 1950s. But it suffers from four major drawbacks. Firstly, it is only phenomenological not mechanistic. Secondly, it fails to exhibit the all-or-nothing firing mechanism for action potential generation. Thirdly, it lacks a th...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-017-0289-y

    authors: Deng B

    更新日期:2017-06-01 00:00:00

  • Computational fluid dynamics of fish gill rakers during crossflow filtration.

    abstract::We study crossflow filtration mechanisms in suspension-feeding fishes using computational fluid dynamics to model fluid flow and food particle movement in the vicinity of the gill rakers. During industrial and biological crossflow filtration, particles are retained when they remain suspended in the mainstream flow tra...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-011-9709-6

    authors: Cheer A,Cheung S,Hung TC,Piedrahita RH,Sanderson SL

    更新日期:2012-04-01 00:00:00

  • Evolutionary entropy: a predictor of body size, metabolic rate and maximal life span.

    abstract::Body size of organisms spans 24 orders of magnitude, and metabolic rate and life span present comparable differences across species. This article shows that this variation can be explained in terms of evolutionary entropy, a statistical parameter which characterizes the robustness of a population, and describes the un...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-008-9382-6

    authors: Demetrius L,Legendre S,Harremöes P

    更新日期:2009-05-01 00:00:00

  • A community model of ciliate Tetrahymena and bacteria E coli: Part II. interactions in a batch system.

    abstract::Premised on relatively simple assumptions, mathematical models like those of Monod, Pirt or Droop inadequately explain the complex transient behavior of microbial populations. In particular, these models fail to explain many aspects of the dynamics of a Tetrahymena pyriformis-Escherichia coli community. In this study ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02458309

    authors: Jaworska JS,Hallam TG,Schultz TW

    更新日期:1996-03-01 00:00:00

  • An Edge-Based Model of SEIR Epidemics on Static Random Networks.

    abstract::Studies have been done using networks to represent the spread of infectious diseases in populations. For diseases with exposed individuals corresponding to a latent period, an SEIR model is formulated using an edge-based approach described by a probability generating function. The basic reproduction number is computed...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-020-00769-0

    authors: Alota CP,Pilar-Arceo CPC,de Los Reyes V AA

    更新日期:2020-07-16 00:00:00

  • Simple stochastic fingerprints towards mathematical modeling in biology and medicine 2. Unifying Markov model for drugs side effects.

    abstract::Most of present mathematical models for biological activity consider just the molecular structure. In the present article we pretend extending the use of Markov chain models to define novel molecular descriptors, which consider in addition other parameters like target site or biological effect. Specifically, this math...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-005-9013-4

    authors: Cruz-Monteagudo M,González-Díaz H,Uriarte E

    更新日期:2006-10-01 00:00:00

  • Identifying environmental determinants of diurnal distribution in marine birds and mammals.

    abstract::Marine birds and mammals move between various habitats during the day as they engage in behaviors related to resting, sleeping, preening, feeding, and breeding. The per capita rates of movement between these habitats, and hence the habitat occupancy dynamics, often are functions of environmental variables such as tide...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-005-9009-0

    authors: Henson SM,Hayward JL,Damania SP

    更新日期:2006-02-01 00:00:00

  • The Effects of Insulin Resistance on Individual Tissues: An Application of a Mathematical Model of Metabolism in Humans.

    abstract::Whilst the human body expends energy constantly, the human diet consists of a mix of carbohydrates and fats delivered in a discontinuous manner. To deal with this sporadic supply of energy, there are transport, storage and utilisation mechanisms, for both carbohydrates and fats, around all tissues of the body. Insulin...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-016-0181-1

    authors: Pearson T,Wattis JA,King JR,MacDonald IA,Mazzatti DJ

    更新日期:2016-06-01 00:00:00