Journal of Theoretical Biology

Published by Elsevier BV

Online ISSN: 1095-8541


Print ISSN: 0022-5193


  • Article

February 1975


25 Reads

John H. McClendon
The meaning of the word efficiency in ecology is compared with the basic English usage and with its technical usage in physics and economics. Three distinct kinds of technical efficiencies are identified on the basis of the aim or goal toward which the efficiency is addressed. Efficiency-I is the traditional thermodynamic efficiency, redefined with the goal of delayed production of entropy. Efficiency-II is commonplace in social, economic and ecological situations and is characterized by the goal of selfish use, or maximum power input. Efficiency-III governs systems of many parts, particularly ecosystems described in four dimensions, and is characterized by integration and survival. Efficiency-III also characterizes organisms, vis-à-vis their components. “Ecological efficiency” as commonly used to relate different trophic levels is found to be an unacceptable compound of efficiencies I and II.

On Blum's four-dimensional geometric explanation for the 0.75 exponent in metabolic allometry
  • Article
  • Full-text available

June 1990


120 Reads


Model-driven Approaches for in Vitro Combination Therapy using ONYX-015 Replicating Oncolytic Adenovirus

April 2007


50 Reads

Replicating genetically modified adenoviruses have shown promise as a new treatment approach against cancer. Recombinant adenoviruses replicate only in cancer cells which contain certain mutations, such as the loss of functional p53, as is the case in the virus ONYX-015. The successful entry of the viral particle into target cells is strongly dependent on the presence of the main receptor for adenovirus, the coxsackie- and adenovirus receptor (CAR). This receptor is frequently down-regulated in highly malignant cells, rendering this population less vulnerable to viral attack. It has been shown that the use of MEK inhibitors can up-regulate CAR expression, resulting in enhanced adenovirus entry into the cells. However, inhibition of MEK results in G1 cell cycle arrest, rendering infected cells temporarily unable to produce virus. This forces a tradeoff. While drug mediated up-regulation of CAR enhances virus entry into cancer cells, the consequent cell cycle arrest inhibits production of new virus particles and the replication of the virus. Optimal control-based schedules of MEK inhibitor application should increase the efficacy of this treatment, maximizing the overall tumor toxicity by exploiting the dynamics of CAR expression and viral production. We introduce a mathematical model of these dynamics and show simple optimal control based strategies which motivate this approach.

Knowledge-based virtual screening of HLA-A*0201-restricted CD8(+) T-cell epitope peptides from herpes simplex virus genome

July 2011


38 Reads

Jianjun Bi


Huilan Yang


Huacheng Yan




Jianyong Fan
A novel knowledge-based method is developed to virtually screen potential HLA-A*0201 binders from large-scale peptide candidates. This method utilizes the information from both the crystal structures and experimental affinities of various peptides bound with HLA-A*0201 to construct a single-position mutation free energy profile for accurately characterizing HLA-A*0201-peptide interaction and for effectively predicting the binding affinities of peptides to HLA-A*0201. We employ this method to analyze physicochemical properties and structural implication underlying the specific recognition and association between the HLA-A*0201 and a large panel of peptide segments generated from the herpes simplex virus type 1 (HSV-1) genome, and to evaluate the binding potencies of these peptide candidates to HLA-A*0201. As a result, 288 out of 38,020 candidates are predicted as the potential high-affinity binders of HLA-A*0201, from which three most promising peptides are picked out for further development of potent vaccines against HSV-1. In addition, we also demonstrate that this newly proposed method can successfully identify 8 known binders and 3 known nonbinders from the glycoproteins D and K of HSV-1.

A mathematical model to distinguish sociological and biological susceptibility factors in disease transmission in the context of H1N1/09 influenza

July 2011


39 Reads

The pandemic H1N1/09 influenza virus differs from seasonal influenza in its greater prevalence among younger individuals. It is well known that younger individuals interact with one another and society as a whole more than older individuals, suggesting that this could account for the skewed prevalence. However, the observed skewed disease prevalence could also be due to a lesser biological vulnerability (cross-immunity or partial immunity) in the older generation. We develop an age-structured, compartmental mathematical model to quantify the degree to which the skewed disease prevalence among younger individuals is due to a lesser biological vulnerability in the older generation. The model incorporates synthetic data regarding sociological interaction between different age groups generated from the simulation software EpiSims, which allows a clear distinction of the sociological and biological susceptibility effects on the transmission rate of the disease. After fitting the model to available data, we quantify the degree of biological susceptibility of five age groups in the population of the United States. Our model indicates that individuals over the age of 60 are 1/15 as susceptible to H1N1/09 influenza as those under 30 years of age. The key feature in the model is separating social contact factors of disease transmission from biological ones.

Mathematical modelling of 3-(3 ',4 '-dichlorophenyl)-1,1-dimethylurea action in plant leaves

April 1998


70 Reads

A mathematical model of the action of a photosystem II herbicide 3-(3',4'-dichlorophenyl)-1, 1-dimenthylurea, DCMU, in plant leaves upon an external application is presented. The diffusion of DCMU in a plant tissue is described with the help of Fick's laws and the following reaction of the herbicide with the QB-binding site of photosystem II by the mass action theory. The model is used for a description of the effect of the herbicide on chlorophyll fluorescence induction (the O-J-I-P curve) measured with spring barley primary leaves submerged in the herbicide solution. The increase of the J step during the herbicide action is ascribed to an increase of the number of photosystem II centres with bound herbicide molecules and malfunctioning in the electron transport to the plastoquinone pool. The experimental data were fitted with the help of the mathematical model. Values of the diffusion coefficient and the second order rate constant of the reaction of the herbicide with photosystem II, obtained by the fitting procedure, are discussed.Copyright 1998 Academic Press Limited

Conformation of N-formyl-1,3-dihydroxy-Δ31-pentene, a model compound of sphingomyelin

December 1976


17 Reads

The conformations of 2S,3R-2-(N-formyl)amino-l,3-dihydroxy-Δ31-pentene, a model compound of sphingomyelin, have been studied both by the classical potential function and by the INDO molecular orbital method. The results suggest that the preferred conformation of sphingomyelin in the membrane is such that the olefinic double bond of the γ-hydrocarbon chain and the planar amide group of the β-chain are parallel and stack in an antiparallel manner with dihedral angles β1′(C3-C2-N21-C21) = −100 ° and γ1(C2-C3-C31-C32) = −100 °.

Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors

August 2008


53 Reads

Considerable insight into intracellular responses has been obtained through the development of whole cell models that are based on molecular mechanisms, e.g., single channel kinetics of the inositol 1,4,5-trisphosphate ( ) receptor channel. However, a limitation of most whole cell models to date is the assumption that receptor channels ( s) are globally coupled by a “continuously stirred” bulk cytosolic [ ], when in fact open s experience elevated “domain” concentrations. Here we present a -compartment whole cell model of local and global responses mediated by diffusely distributed s, each represented by a four-state Markov chain. Two of these compartments correspond to bulk cytosolic and luminal concentrations, and the remaining compartments represent time-dependent cytosolic and luminal domains associated with each . Using this Monte Carlo model as a starting point, we present an alternative formulation that solves a system of advection–reaction equations for the probability density of cytosolic and luminal domain [ ] jointly distributed with state. When these equations are coupled to ordinary differential equations for the bulk cytosolic and luminal [ ], a realistic but minimal model of whole cell dynamics is produced that accounts for the influence of local signaling on channel gating and global responses. The probability density approach is benchmarked and validated by comparison to Monte Carlo simulations, and the two methods are shown to agree when the number of channels is large (i.e., physiologically realistic). Using the probability density approach, we show that the time scale of domain formation and collapse (both cytosolic and luminal) may influence global oscillations, and we derive two reduced models of global dynamics that account for the influence of local signaling on global dynamics when there is a separation of time scales between the stochastic gating of s and the dynamics of domain .

A potential role of modulating inositol 1,4,5-trisphosphate receptor desensitization and recovery rates in regulating ovulation

February 2005


49 Reads

Regulation of the human menstrual cycle is a frequency dependent process controlled in part by the pulsatile release of gonadotropin releasing hormone (GnRH) from the hypothalamus. The binding of GnRH to gonadotroph cells in the pituitary stimulates inositol 1,4,5-trisphosphate (IP3) mediated release of calcium from the endoplasmic reticulum, resulting in calcium oscillations and the secretion of luteinizing hormone (LH). A sudden increase in serum LH concentrations known as the LH surge triggers ovulation. Here we model the intracellular calcium dynamics of gonadotroph cells by adapting the model of Li and Rinzel (J. Theor. Biol. 166 (1994) 461) to include the desensitization of IP3 receptors to IP3. Allowing the resensitization rate of these receptors to vary over the course of the cycle suffices to explain the LH surge in both the normal menstrual cycle, and in the treatment of Kallmann's syndrome (a condition where endogenous production of GnRH is absent).

Metabotropic receptor activation, desensitization and sequestration - I: Modelling calcium and inositol 1,4,5-trisphosphate dynamics following receptor activation

August 2003


50 Reads

A mathematical account is given of the processes governing the time courses of calcium ions (Ca2+), inositol 1,4,5-trisphosphate (IP(3)) and phosphatidylinositol 4,5-bisphosphate (PIP(2)) in single cells following the application of external agonist to metabotropic receptors. A model is constructed that incorporates the regulation of metabotropic receptor activity, the G-protein cascade and the Ca2+ dynamics in the cytosol. It is subsequently used to reproduce observations on the extent of desensitization and sequestration of the P(2)Y(2) receptor following its activation by uridine triphosphate (UTP). The theory predicts the dependence on agonist concentration of the change in the number of receptors in the membrane as well as the time course of disappearance of receptors from the plasmalemma, upon exposure to agonist. In addition, the extent of activation and desensitization of the receptor, using the calcium transients in cells initiated by exposure to agonist, is also predicted. Model predictions show the significance of membrane PIP(2) depletion and resupply on the time course of IP(3) and Ca2+ levels. Results of the modelling also reveal the importance of receptor recycling and PIP(2) resupply for maintaining Ca2+ and IP(3) levels during sustained application of agonist.

Signal-induced Ca2+Oscillations through the Regulation of the Inositol 1,4,5-trisphosphate-gated Ca2+Channel: an Allosteric Model

July 1997


22 Reads

We propose a molecular model for InsP3-sensitive Ca2+ oscillations based on the allosteric properties of the InsP3 receptor/Ca2+ channel. Our model interprets the cooperatively towards InsP3 saturation, of calcium efflux from intravesicular stores as well as the absence of cooperativity in the binding process of InsP3 on the receptor. It takes into account quantitatively the two antagonist, concentration-dependent effects (fast activator and slow inhibitor) that cytosolic Ca2+ exerts on the InsP3 receptor/Ca2+ channel. Assuming that a single pool of releasable Ca2+ exists in the endoplasmic reticulum, the model leads to cytosolic and intravesicular oscillations in Ca2+ at fixed InsP3 concentration. Activation of the receptor by cytosolic calcium is essential for the triggering of oscillations whereas the slow Ca2+ inhibition effect is irrelevant in this respect, although this regulation loop might prevent the system from entering the unstable domain in absence of a true agonist stimulation. Activating cytosolic Ca2+ and InsP3 have quite distinct functions for the induction of Ca2+ release: cytosolic Ca2+ triggers oscillations whereas InsP3 only brings the receptor into a potentially oscillatory regime. Hence, the increasing slope of Ca2+ spiking is constitutively independent from the intensity of the hormonal stimuli in our model, in accord with experimental observations. Comparisons with other existing models are given and additional possible coupling mechanisms are discussed in order to explain particular facts (such as possible oscillations of InsP3) which do not depend on the intrinsic properties of the oscillator.

The pKa value of His 57-Asp 102 couple in the active site of bovine pancreatic β-trypsin: A molecular orbital study

January 1983


45 Reads

The charge relay hypothesis generated a large number of theoretical and experimental studies that tested the ideas involved. Opinion based upon theoretical and experimental studies is divided on the prediction, although there are many experimental data which do not support the hypothesis. The essential feature is the proton transfer from the histidine imidazole to the aspartate. Thus, we have performed the detailed calculations of the proton transfer from His 57 to Asp 102 including the environment of the couple in protonated bovine pancreatic β-trypsin. The charge state of the His 57-Asp 102 couple is greatly influenced by the environment of the enzyme around it. In this paper, it is shown that the proton between His 57 and Asp 102 is covalently bonded to the His 57 imidazole in the protonated β-trypsin. Our MO calculations, which support the neutral-pK-histidine theory as the results, do not support the charge relay mechanism.

Stochastic fluctuations in a one product enyzme system: are they ever relevant? J Theor Biol 30: 395-104

March 1971


8 Reads

The stochastic fluctuations in the initial phase of a one substrate one product enzyme system have been calculated for an actual enzyme reaction, using the model of Heyde & Heyde (1969). The experimental data are for the reaction catalysed by triose phosphate isomerase. It is shown that for this system the stochastic fluctuations in free enzyme, enzyme-substrate or enzyme-product complex, substrate and product are negligible. Using a more general stochastic model it is shown that stochastic fluctuations will in general be negligible for such systems except at the beginning of the transient phase.

Symbolic logic analysis of cause of dealth in humans: Application to 108 patients after coronary artery bypass graft surgery

November 1981


9 Reads

Over the past two decades there has been increasing interest in the development of an objective, or formalized “medical logic”, and many authors have employed classical symbolic logic as a part of their approach. On the other hand, it has become clear that certain patterns of reasoning which are commonplace in evaluating patients clinicopathologically are awkward to handle in classical symbolic logic. The present paper proposes an extension of classical symbolic logic which addresses three problems in medical reasoning: (i) the problem of provisional diagnosis, (ii) the problem of inaccessible data, and (iii) the problem of the adequate discharge summary. It is proved mathematically that with a suitably constructed logic, the system “complains” until all questions involving threats to the patient's health are either answered or shown to be unanswerable because of inaccessibility of data. To illustrate this method, the cause of death was studied in 108 patients who had been autopsied at The Johns Hopkins Hospital after coronary artery bypass surgery. The analysis disclosed that 46% of patients suffered a fatal complication which could be attributed to events in the perioperative period; in 15% of patients the cause of death was unexplained by the analysis. Computerized symbolic logic analysis is a useful supplement to intuitive reasoning in assigning cause of death to patients with complex medical histories.

Münkemüller T, Bugmann H, Johst K. Hutchinson revisited: patterns of density regulation and the coexistence of strong competitors. J Theor Biol 259: 109-117

April 2009


71 Reads

Ecologists have long been searching for mechanisms of species coexistence, particularly since G.E. Hutchinson raised the 'paradox of the plankton'. A promising approach to solve this paradox and to explain the coexistence of many species with strong niche overlap is to consider over-compensatory density regulation with its ability to generate endogenous population fluctuations. Previous work has analysed the role of over-compensation in coexistence based on analytical approaches. Using a spatially explicit time-discrete simulation model, we systematically explore the dynamics and conditions for coexistence of two species. We go beyond the analytically accessible range of models by studying the whole range of density regulation from under- to very strong over-compensation and consider the impact of spatial structure and temporal disturbances. In particular, we investigate how coexistence can emerge in different types of population growth models. We show that two strong competitors are able to coexist if at least one species exhibits over-compensation. Analysing the time series of population dynamics reveals how the differential responses to density fluctuations of the two competitors lead to coexistence: The over-compensator generates density fluctuations but is the inferior competitor at strong amplitudes of those fluctuations; the competitor, therefore, becomes frequent and dampens the over-compensator's amplitudes, but it becomes inferior under dampened fluctuations. These species interactions cause a dynamic alternation of community states with long-term persistence of both species. We show that a variety of population growth models is able to reproduce this coexistence although the particular parameter ranges differ among the models. Spatial structure influences the probability of coexistence but coexistence is maintained for a broad range of dispersal parameters. The flexibility and robustness of coexistence through over-compensation emphasize the importance of nonlinear density dependence for species interactions, and they also highlight the potential of applying more flexible models than the classical Lotka-Volterra equations in community ecology.

Erratum to “Zero-order ultrasensitivity: A study of criticality and fluctuations under the total quasi-steady state approximation in the linear noise regime” [J. Theor. Biol. 344 (2014) 1–11]

December 2013


94 Reads

Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenon in enzyme networks. Here, a substrate is reversibly modified by two antagonistic enzymes (a 'push-pull' system) and the fraction in modified state undergoes a sharp switching from near-zero to near-unity at a critical value of the ratio of the enzyme concentrations, under saturation conditions. ZOU and its extensions have been studied for several decades now, ever since the seminal paper of Goldbeter and Koshland (1981); however, a complete probabilistic treatment, important for the study of fluctuations in finite populations, is still lacking. In this paper, we study ZOU using a modular approach, akin to the total quasi-steady state approximation (tQSSA). This approach leads to a set of Fokker-Planck (drift-diffusion) equations for the probability distributions of the intermediate enzyme-bound complexes, as well as the modified/unmodified fractions of substrate molecules. We obtain explicit expressions for various average fractions and their fluctuations in the linear noise approximation (LNA). The emergence of a 'critical point' for the switching transition is rigorously established. New analytical results are derived for the average and variance of the fractional substrate concentration in various chemical states in the near-critical regime. For the total fraction in the modified state, the variance is shown to be a maximum near the critical point and decays algebraically away from it, similar to a second-order phase transition. The new analytical results are compared with existing ones as well as detailed numerical simulations using a Gillespie algorithm.

Molecular modeling, simulation and virtual screening of ribosomal phosphoprotein P1 from Plasmodium falciparum (Vol 343, pg 113, 2014)

November 2013


357 Reads

Ribosomal phosphoprotein P1 (RPP1) is acidic phosphoprotein which in association with neutral phosphoprotein P0 and acidic phosphoprotein P2 forms ribosomal P protein complex as (P1)2-P0-(P2)2. P protein is known to be immunogenic and has important role in protein translation. 3D structure of P1 is not known. We have built an ab-initio model of RPP1 of Plasmodium falciparum using I-TASSER. Stereochemical stability of structure was checked using PROCHECK and the normality of the local environment of amino acids was checked using WHATIF. Comparison between known protein structures in PDB database and model protein was done using Dali server. Molecular dynamic simulation study and virtual screening of RPP1 was carried out. Three dimensional model structure of RPP1 was generated and model validation studies proved the model to be steriochemically significant. RPP1 structure was found to be stable at room temperature in water environment demonstrated by 30ns molecular dynamic simulation study. Dali superimposition showed 69% superimposition to known 3D structures in PDB. Further virtual screening and docking studies promoted good interaction of ligands Ecgonine, Prazepam and Ethyl loflazepate with RPP1. The work provides insight for molecular understanding of RPP1 of Plasmodium falciparum and can be used for development of antimalarial drugs.

The game of the pentose phosphate cycle. J Theor Biol 117: 251-263

December 1985


62 Reads

Sugar rearrangement in the pentose phosphate cycle for transformation of six pentoses into five hexoses is analysed by abstraction to a mathematical model consisting of the resolution of a logical mathematical game of optimization. In the model, the problem is to arrive at five boxes containing six balls each, having started with six boxes containing five balls each, where boxes simulate the sugars and balls simulate the carbons in each. This is achieved by means of transferring two or three balls from any box to any other in each step, according to transketolase and transaldolase (or aldolase) mechanisms which account for sugar interconversions in the living cell. A hypothesis of simplicity is imposed in order to arrive at the objective with the least number of steps and with the least number of balls in the intermediary boxes. A symmetrical solution is obtained, demonstrating that this is the simplest solution, which is the procedure carried out by biological systems. The same treatment is applied for sugar rearrangement in the non-oxidative phase of the Calvin cycle in photosynthesis and the analysis of the "L-type" of pentose phosphate cycle is also treated, obtaining similar solutions in both cases, which allow us to make some physiological reflections.

Molecular dynamics study of the fibril elongation of the prion protein fragment PrP106-126

April 2007


16 Reads

The present paper aims at exploring the elongation of the PrP106-126 fibril under acid environments through molecular dynamics simulation. It shows that influenced by the edge strands of the fibril, single PrP106-126 peptide forms beta-sheet and becomes a new element of the fibril. Under acidic condition, single PrP106-126 fragment presents a much larger variety of conformations than it does under neural condition. However, acidic condition does not largely affect the stability of the PrP106-126 fibril. Consequently, the speed of the fibril elongation can be dramatically increased by lowering the pH value of the solution. The pH values are adjusted by either altering the protonation state of the residues or adding hydronium ions or hydroxyl ions.

Cosmides LM, Tooby J.. Cytoplasmic inheritance and intragenomic conflict. J Theor Biol 89: 83-129

April 1981


88 Reads

The differing inheritance patterns of cytoplasmic genes and the sex chromosomes from the Mendelian autosomal patterns can be used to divide the genome into fractions whose defining rule is that the fitness of all genes in a set is maximized in the same way. Each set will be selected to modify the phenotype of the organism in a way which maximally propagates the genes comprising the set, and hence in ways inconsistent with the other sets which comprise the total genome. The coexistence of such multiple sets in the same genome creates intragenomic conflict. Evidence is presented in which the fitness of cytoplasmic and other non-autosomal genetic sets are increased at the expense of the autosomal genetic set. The relationship of such intragenomic conflict to the evolution of anisogamy, dioecy, skewed sex ratios, differential male mortality, systems of sex determination, and altruism is discussed.

Charlesworth B.. The evolution of mate choice in a fluctuating environment. J Theor Biol 130: 191-204

February 1988


9 Reads

This paper analyzes the evolutionary dynamics of a locus controlling the degree of female mating preference in a temporally fluctuating environment. Preference for mating with males with respect to their genotypes at a locus that is subject to temporally varying natural selection pressure is considered first. With weak selection and free recombination between the choice locus and the selected locus, preference for mating with heterozygotes appears to be favored. With strong selection, preference for homozygous mates may be favored. In each case, choice alleles may increase from very low initial frequencies to near fixation, in contrast to previous models of mate choice in varying environments. Linkages between the two loci has complex effects on the strength and direction of selection for mate choice. Preference for mating with males with the currently fitter genotypes at the locus under natural selection is also modelled. Provided that the environmental period is not too short, a rare allele conferring such preference may be favored and spread to fixation. Strong natural selection, tight linkage and a short environmental period may produce polymorphism for the level of mate choice.

Sokolove PG, Bushell WN. The chi square periodogram: its utility for analysis of circadian rhythms. J Theor Biol 72: 131-160

June 1978


473 Reads

It is proposed that chi-square statistic be employed in constructing periodograms for the analysis of hourly time series data obtained in studies of circadian rhythmicity. We show that even for relatively short (10 day) time series, the integral-valued chi-square periodogram can distinguish circadian-periodic from random series at a level of significance of about 0·01. In addition, we describe the effects of serial correlation and examine the resolving power of the method for two periodic components in the circadian range. We suggest how the method can be most profitably employed in the analysis of event-recorder data for detection of rhythmicity in the range 14 to 34 h., and for the estimation of period to ±0·2 h.

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