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 action is close to the literal meaning of the term "non-interaction". Since this concept does not depend on the mechanisms of actions nor on the type of effect scale used, it is suitable as one of the basic criterion for the definition of synergism and antagonism. A general mathematical framework of independent action is presented in this paper based on the concept of "relative effect" as used in the literature. The different equations for independent action currently used in various areas are shown to be manifestations of a general formula under different sets of boundary conditions, which are the natural limiting values of the effects of the corresponding system observed at low and at high doses of the agents. The framework can be generalized to the combined action of n-agents as well as to the interaction of an agent with itself. In addition, the differential form of the formula for independent action is derived. This framework of systematic definitions and derived equations enable a more in-depth study of the implications of the concept of independent action and its relation to other concepts of non-interaction.

journal_name

Bull Math Biol

authors

Lam GK

doi

10.1007/BF02458276

subject

Has Abstract

pub_date

1994-09-01 00:00:00

pages

959-80

issue

5

eissn

0092-8240

issn

1522-9602

pii

S0092-8240(05)80299-X

journal_volume

56

pub_type

杂志文章
  • Surfing the Hyperbola Equations of the Steady-State Farquhar-von Caemmerer-Berry C3 Leaf Photosynthesis Model: What Can a Theoretical Analysis of Their Oblique Asymptotes and Transition Points Tell Us?

    abstract::The asymptotes and transition points of the net CO2 assimilation (A/Ci) rate curves of the steady-state Farquhar-von Caemmerer-Berry (FvCB) model for leaf photosynthesis of C3 plants are examined in a theoretical study, which begins from the exploration of the standard equations of hyperbolae after rotating the coordi...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00676-z

    authors: Miranda-Apodaca J,Marcos-Barbero EL,Morcuende R,Arellano JB

    更新日期:2019-12-23 00:00:00

  • Ligand Binding Dynamics for Pre-dimerised G Protein-Coupled Receptor Homodimers: Linear Models and Analytical Solutions.

    abstract::Evidence suggests that many G protein-coupled receptors (GPCRs) are bound together forming dimers. The implications of dimerisation for cellular signalling outcomes, and ultimately drug discovery and therapeutics, remain unclear. Consideration of ligand binding and signalling via receptor dimers is therefore required ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-017-0387-x

    authors: White C,Bridge LJ

    更新日期:2019-09-01 00:00:00

  • Schistosomiasis Transmission Model and its Control in Anhui Province.

    abstract::National Bureau of Statistics of China reports that the incidence of schistosomiasis has been increasing in recent years. To study dynamic behaviors of schistosomiasis transmission, based on practical experience of staff in Anhui Institute of Schistosomiasis, a mathematical schistosomiasis model with reinfection of re...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-018-0474-7

    authors: Qi L,Xue M,Cui JA,Wang Q,Wang T

    更新日期:2018-09-01 00:00:00

  • Mathematical models for the Aedes aegypti dispersal dynamics: travelling waves by wing and wind.

    abstract::Biological invasion is an important area of research in mathematical biology and more so if it concerns species which are vectors for diseases threatening the public health of large populations. That is certainly the case for Aedes aegypti and the dengue epidemics in South America. Without the prospect of an effective...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1016/j.bulm.2004.08.005

    authors: Takahashi LT,Maidana NA,Ferreira WC Jr,Pulino P,Yang HM

    更新日期:2005-05-01 00:00:00

  • Cell physician: reading cell motion: a mathematical diagnostic technique through analysis of single cell motion.

    abstract::Cell motility is an essential phenomenon in almost all living organisms. It is natural to think that behavioral or shape changes of a cell bear information about the underlying mechanisms that generate these changes. Reading cell motion, namely, understanding the underlying biophysical and mechanochemical processes, i...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-010-9580-x

    authors: Coskun H,Coskun H

    更新日期:2011-03-01 00:00:00

  • The effect of solution non-ideality on membrane transport in three-dimensional models of the renal concentrating mechanism.

    abstract::Previous models of the renal concentrating mechanism employ ideal approximations of solution thermodynamics for membrane transport calculation. In three-dimensional models of the renal medulla, predicted urine concentrations reach levels where these idealized approximations begin to break down. In this paper we derive...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02460469

    authors: Wang X,Wexler AS,Marsh DJ

    更新日期:1994-05-01 00:00:00

  • Resource consumption, sustainability, and cancer.

    abstract::Preserving a system's viability in the presence of diversity erosion is critical if the goal is to sustainably support biodiversity. Reduction in population heterogeneity, whether inter- or intraspecies, may increase population fragility, either decreasing its ability to adapt effectively to environmental changes or f...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章,评审

    doi:10.1007/s11538-014-9983-1

    authors: Kareva I,Morin B,Castillo-Chavez C

    更新日期:2015-02-01 00:00:00

  • Fitting a structured juvenile-adult model for green tree frogs to population estimates from capture-mark-recapture field data.

    abstract::We derive point and interval estimates for an urban population of green tree frogs (Hyla cinerea) from capture-mark-recapture field data obtained during the years 2006-2009. We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-011-9682-0

    authors: Ackleh AS,Carter J,Deng K,Huang Q,Pal N,Yang X

    更新日期:2012-03-01 00:00:00

  • Theoretical considerations of Fisher's theorem in small at-risk populations.

    abstract::Small populations at risk of extinction due to threshold or competitive exclusion have a vested interest in rapid growth. Taking chance of survival into account for diploid populations, Fisher's theorem predicts a sex ratio favoring females under certain circumstances. Theoretical consideration of competitive exclusio...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-009-9455-1

    authors: Johnson SD

    更新日期:2010-01-01 00:00:00

  • A mathematical model of Doxorubicin treatment efficacy for non-Hodgkin's lymphoma: investigation of the current protocol through theoretical modelling results.

    abstract::Doxorubicin treatment outcomes for non-Hodgkin's lymphomas (NHL) are mathematically modelled and computationally analyzed. The NHL model includes a tumor structure incorporating mature and immature vessels, vascular structural adaptation and NHL cell-cycle kinetics in addition to Doxorubicin pharmacokinetics (PK) and ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1016/j.bulm.2004.06.007

    authors: Ribba B,Marron K,Agur Z,Alarcón T,Maini PK

    更新日期:2005-01-01 00:00:00

  • Optimal reproduction strategies in two species of mound-building termites.

    abstract::We formulate a mathematical model for food collection and production of workers and nymphs in 2 species of mound building termites. We maximise the number of nymphs (reproductives) produced by each colony over its lifetime with respect to the proportion of eggs that hatch as nymphs as opposed to workers. The results p...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-007-9248-3

    authors: Cameron DA,Ivers DJ,Evans TA,Myerscough MR

    更新日期:2008-01-01 00:00:00

  • High Cooperativity in Negative Feedback can Amplify Noisy Gene Expression.

    abstract::Burst-like synthesis of protein is a significant source of cell-to-cell variability in protein levels. Negative feedback is a common example of a regulatory mechanism by which such stochasticity can be controlled. Here we consider a specific kind of negative feedback, which makes bursts smaller in the excess of protei...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-018-0438-y

    authors: Bokes P,Lin YT,Singh A

    更新日期:2018-07-01 00:00:00

  • Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China.

    abstract::Human rabies is one of the major public health problems in China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. In recent years, the number of wildlife-associated human rabies cases has increased, particularly in the southeast and northeast regions of...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-018-00537-1

    authors: Huang J,Ruan S,Shu Y,Wu X

    更新日期:2019-04-01 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

  • Evolution of defence portfolios in exploiter-victim systems.

    abstract::Some organisms maintain a battery of defensive strategies against their exploiters (predators, parasites or parasitoids), while others fail to employ a defence that seems obvious. In this paper, we shall investigate the circumstances under which defence strategies might be expected to evolve. Brood parasites and their...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-006-9178-5

    authors: Britton NF,Planqué R,Franks NR

    更新日期:2007-04-01 00:00:00

  • Modelling directional guidance and motility regulation in cell migration.

    abstract::Although cell migration is an essential process in development, how cells reach their final destination is not well understood. Secreted molecules are known to have a migratory effect, but it remains unclear whether such molecules act as directional guidance cues or as motility regulators. There is potential to use si...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-005-9028-x

    authors: Cai AQ,Landman KA,Hughes BD

    更新日期:2006-01-01 00:00:00

  • A stochastic version of the Eigen model.

    abstract::We exhibit a stochastic discrete time model that produces the Eigen model (Naturwissenschaften 58:465-523, 1971) in the deterministic and continuous time limits. The model is based on the competition among individuals differing in terms of fecundity but with the same viability. We explicitly write down the Markov matr...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-010-9525-4

    authors: Musso F

    更新日期:2011-01-01 00:00:00

  • An Alternative to Moment Closure.

    abstract::Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several weaknesses: Conditions for validity of the approximations are not known, magnit...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-017-0321-2

    authors: Nåsell I

    更新日期:2017-09-01 00:00:00

  • A Mathematical Framework for Understanding Four-Dimensional Heterogeneous Differentiation of CD4+ T Cells.

    abstract::At least four distinct lineages of CD4+ T cells play diverse roles in the immune system. Both in vivo and in vitro, naïve CD4+ T cells often differentiate into a variety of cellular phenotypes. Previously, we developed a mathematical framework to study heterogeneous differentiation of two lineages governed by a mutual...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-015-0076-6

    authors: Hong T,Oguz C,Tyson JJ

    更新日期:2015-06-01 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

  • Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces.

    abstract::In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and e...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-017-0255-8

    authors: Dhillon DS,Milinkovitch MC,Zwicker M

    更新日期:2017-04-01 00:00:00

  • A geometric buildup algorithm for the solution of the distance geometry problem using least-squares approximation.

    abstract::We propose a new geometric buildup algorithm for the solution of the distance geometry problem in protein modeling, which can prevent the accumulation of the rounding errors in the buildup calculations successfully and also tolerate small errors in given distances. In this algorithm, we use all instead of a subset of ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-009-9431-9

    authors: Sit A,Wu Z,Yuan Y

    更新日期:2009-11-01 00:00:00

  • Biomechanical modelling of colorectal crypt budding and fission.

    abstract::This paper presents a biomechanical model for the small pits, called crypts, that line the colon. A continuum approach is adopted, with the crypt epithelium modelled as a growing beam attached to the underlying lamina by cell bonds, which generate tension within the layer. These cell attachments are assumed to be visc...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-007-9199-8

    authors: Edwards CM,Chapman SJ

    更新日期:2007-08-01 00:00:00

  • Predicting Pattern Formation in Multilayer Networks.

    abstract::We investigate how the structure of interactions between coupled oscillators influences the formation of asynchronous patterns in a multilayer network by formulating a simple, general multilayer oscillator model. We demonstrate the analysis of this model in three-oscillator systems, illustrating the role of interactio...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00682-1

    authors: Hayes SM,Anderson KE

    更新日期:2019-12-20 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

  • Modelling Dictyostelium discoideum morphogenesis: the culmination.

    abstract::The culmination of the morphogenesis of the cellular slime mould Dictyostelium discoideum involves complex cell movements which transform a mound of cells into a globule of spores on a slender stalk. We show that cyclic AMP signalling and differential adhesion, combined with cell differentiation and slime production, ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1006/bulm.2001.0277

    authors: Marée AF,Hogeweg P

    更新日期:2002-03-01 00:00:00

  • Analysis and characterization of asynchronous state transition graphs using extremal states.

    abstract::Logical modeling of biological regulatory networks gives rise to a representation of the system's dynamics as a so-called state transition graph. Analysis of such a graph in its entirety allows for a comprehensive understanding of the functionalities and behavior of the modeled system. However, the size of the vertex ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-012-9782-5

    authors: Lorenz T,Siebert H,Bockmayr A

    更新日期:2013-06-01 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

  • 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

  • A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run-Tumble Motion.

    abstract::We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been ap...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-016-0155-3

    authors: Thygesen UH

    更新日期:2016-03-01 00:00:00