Effective rate models for the analysis of transport-dependent biosensor data.

Abstract:

:Optical biosensors, including the BIACORE, provide an increasingly popular method for determining reaction rates of biomolecules. In a flow chamber, with one reactant immobilized on a chip on the sensor surface, a solution containing the other reactant (the analyte) flows through the chamber. The time course of binding of the reactants is monitored. Scientists using the BIACORE to understand biomolecular reactions need to be able to separate intrinsic reaction rates from the effects of transport in the biosensor. For a model to provide a useful basis for such an analysis, it must reflect transport accurately, while remaining simple enough to couple with a routine for estimating reaction rates from BIACORE data. Models have been proposed previously for this purpose, consisting of an ordinary differential equation with 'effective rate coefficients' incorporating reaction and transport parameters. In this paper we investigate both the theoretical basis and numerical accuracy of these and related models.

journal_name

Math Biosci

journal_title

Mathematical biosciences

authors

Mason T,Pineda AR,Wofsy C,Goldstein B

doi

10.1016/s0025-5564(99)00023-1

subject

Has Abstract

pub_date

1999-07-01 00:00:00

pages

123-44

issue

2

eissn

0025-5564

issn

1879-3134

pii

S0025-5564(99)00023-1

journal_volume

159

pub_type

杂志文章
  • Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method.

    abstract::In this paper, two cancer therapies are investigated through their mathematical models. Namely, angiogenesis inhibition (P. Hahndfeldt, D. Panigrahy, J. Folkman, L. Hlatky, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Res. 59, 1...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2011.02.010

    authors: Kassara K,Moustafid A

    更新日期:2011-06-01 00:00:00

  • Estimation of vaccine efficacy from epidemics of acute infectious agents under vaccine-related heterogeneity.

    abstract::A stochastic epidemic model is formulated for the study of the protective effects of vaccination in a population that is stratified by vaccine-related factors. The epidemic model is transformed into a counting process, and then martingale-based methods are used to provide estimators of vaccine efficacy and their varia...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(93)90028-9

    authors: Longini IM Jr,Halloran ME,Haber M

    更新日期:1993-09-01 00:00:00

  • Optimal control of receptor reinsertion in the low density lipoprotein endocytic cycle.

    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

    authors: Echavarría-Heras H

    更新日期:1999-11-01 00:00:00

  • Comparing methods to quantify experimental transmission of infectious agents.

    abstract::Transmission of an infectious agent can be quantified from experimental data using the transient-state (TS) algorithm. The TS algorithm is based on the stochastic SIR model and provides a time-dependent probability distribution over the number of infected individuals during an epidemic, with no need for the experiment...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2007.04.009

    authors: Velthuis AG,De Jong MC,De Bree J

    更新日期:2007-11-01 00:00:00

  • Automatic learning of mortality in a CPN model of the systemic inflammatory response syndrome.

    abstract::The aim of this paper is to apply machine learning as a method to refine a manually constructed CPN for the assessment of the severity of the systemic inflammatory response syndrome (SIRS).The goal of tuning the CPN is to create a scoring system that uses only objective data, compares favourably with other severity-sc...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2016.11.004

    authors: Ward L,Paul M,Andreassen S

    更新日期:2017-02-01 00:00:00

  • Controlling the number of HIV infectives in a mobile population.

    abstract::The spread of the human immunodeficiency virus (HIV) depends prominently on the migration of people between different regions. An important consequence of this population mobility is that HIV control strategies that are optimal in a regional sense may not be optimal in a national sense. We formulate various mathematic...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2008.03.003

    authors: Sani A,Kroese DP

    更新日期:2008-06-01 00:00:00

  • Resistance of a food chain to invasion by a top predator.

    abstract::We study the invasion of a top predator into a food chain in a chemostat. For each trophic level, a bioenergetic model is used in which maintenance and energy reserves are taken into account. Bifurcation analysis is performed on the set of nonlinear ordinary differential equations which describe the dynamic behaviour ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(98)10083-4

    authors: Kooi BW,Boer MP,Kooijman SA

    更新日期:1999-03-15 00:00:00

  • An algebraic analysis of the two state Markov model on tripod trees.

    abstract::Methods of phylogenetic inference use more and more complex models to generate trees from data. However, even simple models and their implications are not fully understood. Here, we investigate the two-state Markov model on a tripod tree, inferring conditions under which a given set of observations gives rise to such ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2012.03.001

    authors: Klaere S,Liebscher V

    更新日期:2012-05-01 00:00:00

  • Some remarks on definition and validity of terms used in models for infectious disease spread.

    abstract::The epidemiology of infectious diseases makes use of a number of terms, such as exposure, infected, carrier, attack rate, and immunity. Researchers who intend to model the spread of epidemics should be aware of the problems with some of these terms. The role played by inapparent, or subclinical, infections is receivin...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(91)90001-y

    authors: Giesecke J

    更新日期:1991-12-01 00:00:00

  • Spreading speeds as slowest wave speeds for cooperative systems.

    abstract::It is well known that in many scalar models for the spread of a fitter phenotype or species into the territory of a less fit one, the asymptotic spreading speed can be characterized as the lowest speed of a suitable family of traveling waves of the model. Despite a general belief that multi-species (vector) models hav...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2005.03.008

    authors: Li B,Weinberger HF,Lewis MA

    更新日期:2005-07-01 00:00:00

  • Visibility in a pure model of golden spiral phyllotaxis.

    abstract::This paper considers the geometry of plants with golden spiral phyllotaxis, i.e. growing leaf by leaf on a spiral with golden divergence angle, via the simplest mathematical model, a cylinder with regular arrangement of points on its surface. As is well-known, Fibonacci numbers appear by means of the order of parastic...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2018.05.003

    authors: Herrmann B

    更新日期:2018-07-01 00:00:00

  • Patient-specific modeling of the neuroendocrine HPA-axis and its relation to depression: Ultradian and circadian oscillations.

    abstract::In the Western world approximately 10% of the population experience severe depression at least once in their lifetime and many more experience a mild form of depression. Depression has been associated with malfunctions in the hypothalamus-pituitary-adrenal (HPA) axis. We suggest a novel mechanistic non-linear model ca...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2014.07.013

    authors: Gudmand-Hoeyer J,Timmermann S,Ottesen JT

    更新日期:2014-11-01 00:00:00

  • Infection dynamics in HIV-specific CD4 T cells: does a CD4 T cell boost benefit the host or the virus?

    abstract::Recent experimental data have shown that HIV-specific CD4 T cells provide a very important target for HIV replication. We use mathematical models to explore the effect of specific CD4 T cell infection on the dynamics of virus spread and immune responses. Infected CD4 T cells can provide antigen for their own stimulati...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2007.01.007

    authors: Wodarz D,Hamer DH

    更新日期:2007-09-01 00:00:00

  • Intracellular delay limits cyclic changes in gene expression.

    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 intro...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2006.08.010

    authors: Rateitschak K,Wolkenhauer O

    更新日期:2007-02-01 00:00:00

  • Recent advances in mathematical modeling and statistical analysis of exocytosis in endocrine cells.

    abstract::Most endocrine cells secrete hormones as a result of Ca2+-regulated exocytosis, i.e., fusion of the membranes of hormone-containing secretory granules with the cell membrane, which allows the hormone molecules to escape to the extracellular space. As in neurons, electrical activity and cell depolarization open voltage...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章,评审

    doi:10.1016/j.mbs.2016.11.010

    authors: Pedersen MG,Tagliavini A,Cortese G,Riz M,Montefusco F

    更新日期:2017-01-01 00:00:00

  • On using Lehmann alternatives with nonresponders.

    abstract::The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the known number of respon...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(92)90052-x

    authors: Razzaghi M,Nanthakumar A

    更新日期:1992-04-01 00:00:00

  • Practical identifiability and uncertainty quantification of a pulsatile cardiovascular model.

    abstract::Mathematical models are essential tools to study how the cardiovascular system maintains homeostasis. The utility of such models is limited by the accuracy of their predictions, which can be determined by uncertainty quantification (UQ). A challenge associated with the use of UQ is that many published methods assume t...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2018.07.001

    authors: Marquis AD,Arnold A,Dean-Bernhoft C,Carlson BE,Olufsen MS

    更新日期:2018-10-01 00:00:00

  • Global dynamics of an SEIR epidemic model with saturating contact rate.

    abstract::Heesterbeek and Metz [J. Math. Biol. 31 (1993) 529] derived an expression for the saturating contact rate of individual contacts in an epidemiological model. In this paper, the SEIR model with this saturating contact rate is studied. The basic reproduction number R0 is proved to be a sharp threshold which completely d...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(03)00087-7

    authors: Zhang J,Ma Z

    更新日期:2003-09-01 00:00:00

  • Evaluating spread of invaders from gravity scores--a way of using gravity models in ecology.

    abstract::This study is a theoretical excursion into gravity models and their usability in evaluating importance of spatial structure and population development for the spread of colonizing organisms. A so called "gravity score" for sites is deduced, and such a score could be used for predicting risk of colonization once one si...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2009.08.008

    authors: Järemo J

    更新日期:2009-11-01 00:00:00

  • Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays.

    abstract::To understand how a gene regulatory network functioning as an oscillator is built, a genetic regulatory network with two transcriptional delays is investigated. We show by mathematical analysis and simulation that autorepression of mRNA and protein can provide a mechanism for the intracellular oscillator. Based on the...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2008.05.004

    authors: Xiao M,Cao J

    更新日期:2008-09-01 00:00:00

  • Analysis of logistic growth models.

    abstract::A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(02)00096-2

    authors: Tsoularis A,Wallace J

    更新日期:2002-07-01 00:00:00

  • What can trigger the onset of Parkinson's disease - A modeling study based on a compartmental model of α-synuclein transport and aggregation in neurons.

    abstract::The aim of this paper is to develop a minimal model describing events leading to the onset of Parkinson's disease (PD). The model accounts for α-synuclein (α-syn) production in the soma, transport toward the synapse, misfolding, and aggregation. The production and aggregation of polymeric α-syn is simulated using a mi...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2016.05.002

    authors: Kuznetsov IA,Kuznetsov AV

    更新日期:2016-08-01 00:00:00

  • Multi-gene-loci inheritance in resistance modeling.

    abstract::The ability of an organism to degrade harmful substances to less toxic compounds is referred to as metabolic resistance. The biochemical processes result in a shift of dose-response curves associated with the toxic substances. Hence, the development of metabolic resistance may cause great problems of managing pests an...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2012.11.010

    authors: Langemann D,Richter O,Vollrath A

    更新日期:2013-03-01 00:00:00

  • Sharpening spots: correcting for bleedover in cDNA array images.

    abstract::For cDNA array methods that depend on imaging of a radiolabel, we show that bleedover of one spot onto another, due to the gap between the array and the imaging media, can be a major problem. The images can be sharpened, however, using a blind convolution method based on the EM algorithm. The sharpened images look lik...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(01)00101-8

    authors: Therneau T,Tschumper RC,Jelinek D

    更新日期:2002-03-01 00:00:00

  • Global dynamics of a discrete age-structured SIR epidemic model with applications to measles vaccination strategies.

    abstract::We investigate an SIR epidemic model with discrete age groups to understand the transmission dynamics of an infectious disease in a host population with an age structure. We derive the basic reproduction number R0 and show that it is a sharp threshold parameter. If R0≤1, the disease-free equilibrium E0 is globally sta...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2018.12.003

    authors: Zhou L,Wang Y,Xiao Y,Li MY

    更新日期:2019-02-01 00:00:00

  • Density functions of residence times for deterministic and stochastic compartmental systems.

    abstract::A significant consideration in modeling systems with stages is to obtain models for the individual stages that have probability density functions (pdfs) of residence times that are close to those of the real system. Consequently, the theory of residence time distributions is important for modeling. Here I show first t...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(02)00110-4

    authors: Jacquez JA

    更新日期:2002-11-01 00:00:00

  • Mean and quasideterministic equivalence for linear stochastic dynamics.

    abstract::In linear, stochastic dynamics it is shown that the quasideterministic population size is equivalent to the mean population size. The quasideterministic dynamics are defined by the conditional infinitesimal mean of the process. The stochastic component of the dynamics includes both Gaussian and Poisson white noise, wi...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(89)90010-2

    authors: Hanson FB,Ryan D

    更新日期:1989-03-01 00:00:00

  • Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus.

    abstract::A pandemic of a novel Coronavirus emerged in December of 2019 (COVID-19), causing devastating public health impact across the world. In the absence of a safe and effective vaccine or antivirals, strategies for controlling and mitigating the burden of the pandemic are focused on non-pharmaceutical interventions, such a...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2020.108364

    authors: Ngonghala CN,Iboi E,Eikenberry S,Scotch M,MacIntyre CR,Bonds MH,Gumel AB

    更新日期:2020-07-01 00:00:00

  • An alternative approach to Michaelis-Menten kinetics that is based on the renormalization group.

    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

    authors: Coluzzi B,Bersani AM,Bersani E

    更新日期:2018-05-01 00:00:00

  • Phylogenetic diversity and biodiversity indices on phylogenetic networks.

    abstract::In biodiversity conservation it is often necessary to prioritize the species to conserve. Existing approaches to prioritization, e.g. the Fair Proportion Index and the Shapley Value, are based on phylogenetic trees and rank species according to their contribution to overall phylogenetic diversity. However, in many cas...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2018.02.005

    authors: Wicke K,Fischer M

    更新日期:2018-04-01 00:00:00