A mathematical model of iron metabolism

A mathematical model of iron metabolism is presented. It comprises the following iron pools within the body: transferrin-bound iron in the plasma, iron in circulating red cells and their bone marrow precursors, iron in mucosal, parenchymal and reticuloendothelial cells. The control exerted by a hormone, called erythropoietin, on bone marrow utilization of iron for hemoglobin synthesis is taken into account. The model so obtained consists of a system of functional differential equations of retarded type. Most model parameters can be estimated from radiotracer experiments, others can be measured and numerical values can be assigned to the remaining ones making few reasonable assumptions according to the available physiological knowledge. Iron metabolism behavior under different therapeutical treatments was simulated. Model predictions were compared to experimental data collected in clinical routine.This work has been partially supported by C.N.R. (Italy) through grants N. 80.01227.07 and N. 81.00888.07     

A new mathematical model for combining growth and energy intake in animals: The case of the growing pig

A simultaneous model for analysis of net energy intake and growth curves is presented, viewing the animal's responses as a two dimensional outcome. The model is derived from four assumptions: (1) the intake is a quadratic function of metabolic weight; (2) the rate of body energy accretion represents the difference between intake and maintenance; (3) the relationship between body weight and body energy is allometric and (4) animal intrinsic variability affects the outcomes so the intake and growth trajectories are realizations of a stochastic process. Data on cumulated net energy intake and body weight measurements registered from weaning to maturity were available for 13 pigs. The model was fitted separately to 13 datasets. Furthermore, slaughter data obtained from 170 littermates was available for validation of the model. The parameters of the model were estimated by maximum likelihood within a stochastic state space model framework where a transform-both-sides approach was adopted to obtain constant variance. A suitable autocorrelation structure was generated by the stochastic process formulation. The pigs’ capacity for intake and growth were quantified by eight parameters: body weight at maximum rate of intake (149-281 kg); maximum rate of intake (25.7-35.7 MJ/day); metabolic body size exponent (fixed: 0.75); the daily maintenance requirement per kg metabolic body size (0.232-0.303 MJ/(day×kg^0.75)); reciprocal scaled energy density ; a dimensional exponent, θ₆ (0.730-0.867); coefficient for animal intrinsic variability in intake (0.120-0.248 MJ^0.5) and coefficient for animal intrinsic variability in growth (0.029-0.065 kg^0.5). Model parameter values for maintenance requirements and body energy gains were in good agreement with those obtained from slaughter data. In conclusion, the model provides biologically relevant parameter values, which cannot be derived by traditional analysis of growth and energy intake data.     

A new SWPAQ's scale predicts the effects of sleep deprivation on the segmental structure of alpha waves

The three-dimensional cube-in-globe model predicts the possibility to delineate six main adaptive abilities of the sleep - wake cycle (Putilov & Putilov, 2005). Such prediction led to the inclusion of a new sixth scale named “daytime wakeability” (Putilov & Putilov, 2006; Putilov, 2007) in the Sleep-Wake Pattern Assessment Questionnaire (SWPAQ; Putilov, 1990, 2000). This new scale permits self-assessment of the ability to keep waking at daytime in sleep provoking conditions. In the study reported here we applied the procedure of adaptive segmentation of the EEG record (SECTION 0.1®, Human Brain Research Group, Moscow State University) to determine whether sleep deprivation changes the temporal pattern of alpha activity and, if yes, whether this change is associated with state and trait self-measures of alertness/sleepiness including a score on “daytime wakeability” scale. In the course of sustained wakefulness, EEG was recorded nine times with three-hour intervals in frontal and occipital derivations in 39 healthy subjects. The procedure of adaptive segmentation allowed cutting EEG records on quasi-stationary segments and determining such characteristics of each segment as within-segmental amplitude, coefficient of its variation and segment length. These characteristics obtained in the morning hours on the first and second experimental days were compared. They were found to increase in the second morning, when eyes are open, but do not change when eyes are closed. It was also documented that “daytime wakeability” score along with other trait and state self-measures of alertness/sleepiness can serve as predictors of the response of alpha waves to sleep deprivation.     

Anti-inflammatory effects of purine nucleosides, adenosine and inosine, in a mouse model of pleurisy: evidence for the role of adenosine A2 receptors

Adenosine and its metabolite, inosine, have been described as molecules that participate in regulation of inflammatory response. The aim of this study was to investigate the effect of adenosine and inosine in a mouse model of carrageenan-induced pleurisy as well as the participation of adenosine receptors in this response. Injection of carrageenan into the pleural cavity induced an acute inflammatory response characterized by leukocyte migration, pleural exudation, and increased release of interleukin-1β and tumor necrosis factor-α in pleural exudates. The treatment with adenosine (0.3–100 mg/kg, i.p.) and inosine (0.1–300 mg/kg, i.p.) 30 min before carrageenan injection reduced significantly all these parameters analyzed. Our results also demonstrated that A_2A and A_2B receptors seem to mediate the adenosine and inosine effects observed, since pretreatment with selective antagonists of adenosine A_2A (ZM241385) and A_2B (alloxazine) receptors, reverted the inhibitory effects of adenosine and inosine in pleural inflammation. The involvement of A₂ receptors was reinforced with adenosine receptor agonist {"type":"entrez-protein","attrs":{"text":"CGS21680","term_id":"878113053","term_text":"CGS21680"}}CGS21680 treatment, since its anti-inflammatory effects were reversed completely and partially with ZM241385 and alloxazine injection, respectively. Moreover, the combined treatment with subeffective dose of adenosine (0.3 mg/kg) and inosine (1.0 mg/kg) induced a synergistic anti-inflammatory effect. Thus, based on these findings, we propose that inosine contributes with adenosine to exert anti-inflammatory effects in pleural inflammation, reinforcing the notion that endogenous nucleosides play an important role in controlling inflammatory diseases. This effect is likely mediated by the activation of adenosine A₂ subtype receptors and inhibition of production or release of pro-inflammatory cytokines.     

A model for the spread of an epidemic

A temporally continuous and spatially discrete stochastic model for the spread of an epidemic within some set of holdings is constructed. A recursion formula is given for the probability that a certain set of holdings is infected at a certain moment. Moreover, under an additional condition (which will always be satisfied in practice) a formula for the expected value and the variance of the moment when a certain holding is infected the first time is given.     

A mathematical model to study the effects of drugs administration on tumor growth dynamics

A mathematical model for describing the cancer growth dynamics in response to anticancer agents administration in xenograft models is discussed. The model consists of a system of ordinary differential equations involving five parameters (three for describing the untreated growth and two for describing the drug action). Tumor growth in untreated animals is modelled by an exponential growth followed by a linear growth. In treated animals, tumor growth rate is decreased by an additional factor proportional to both drug concentration and proliferating cells. The mathematical analysis conducted in this paper highlights several interesting properties of this tumor growth model. It suggests also effective strategies to design in vivo experiments in animals with potential saving of time and resources. For example, the drug concentration threshold for the tumor eradication, the delay between drug administration and tumor regression, and a time index that measures the efficacy of a treatment are derived and discussed. The model has already been employed in several drug discovery projects. Its application on a data set coming from one of these projects is discussed in this paper.     

A mathematical model for drug administration by using the phagocytosis of red blood cells

 A mathematical model for the delivery of drug directly to the macrophages by using the phagocytosis of senescent red blood cells is proposed. The model is based on the following assumption: At time t=0 a preassigned red blood cell population n(0, a)=φ(a), a>0, loaded by the drug, is injected in the blood circulation. Among the cells of that population only those with an age a≧ā (ā=120 days) will be phagocytosed by macrophages. Of course, the lifetime of the drug must be higher than ā. Within the red blood cells it cannot be metabolized, neither can it diffuse through their membranes. The emphasis of the paper is on the mathematical properties and on the formulation of the control problem. Received 15 December 1994; received in revised form 20 July 1995     

A mathematical model for the dynamics of malaria in mosquitoes feeding on a heterogeneous host population

We describe and develop a difference equation model for the dynamics of malaria in a mosquito population feeding on, infecting and getting infected from a heterogeneous population of hosts. Using the force of infection from different classes of humans to mosquitoes as parameters, we evaluate a number of entomological parameters, indicating malaria transmission levels, which can be compared to field data. By assigning different types of vector control interventions to different classes of humans and by evaluating the corresponding levels of malaria transmission, we can compare the effectiveness of these interventions. We show a numerical example of the effects of increasing coverage of insecticide-treated bed nets in a human population where the predominant malaria vector is Anopheles gambiae.     

A mathematical model for the growth of mycelial pellet populations

In liquid culture, filamentous organisms often grow in the form of pellets. Growth result in an increase in radius, whereas shear forces result in release of hyphal fragments which act as centers for further pellet growth and development. A previously published model for pellet growth of filamentous microorganisms has been examined and is found to be unstable for certain parameter values. This instability has been identified as being due to inaccuracies in estimating the numbers of fragments which seed the pellet population. A revised model has been formulated, based on similar premises, but adopting a finite element approach. This considers the population of pellets to be distributed in a range of size classes. Growth results in movement to classes of increasing pellet size, while fragments enter the smallest size class, from which they grow to form further pellets. The revised model is stable and predicts changes in the distribution of pellet sizes within a population growing in liquid batch culture. It considers pellet growth and death, with fragmentation providing new centers of growth within the pellet population, and predicts the effects of shear forces on pellet growth and size distribution. Predictions of pellet size distributions are tested using previously published data on the growth of fungal pellets and further predictions are generated which are suitable for experimental testing using cultures of filamentous fungi or actinomycetes. (c) 1995 John Wiley & Sons, Inc.     

A comparison of the effects of agonist and antagonist muscle fatigue on performance of rapid movements

The aim of this study was to investigate the effects of agonist and antagonist muscle fatigue on the performance of rapid, self-terminating movements. Six subjects performed rapid, consecutive elbow flexion and extension movements between two targets prior to and after fatiguing either the elbow flexor or elbow extensor muscles. The experiments demonstrated consistent results. Agonist muscle fatigue was associated with a decrease in peak velocity and peak deceleration, while a decrease in peak acceleration was particularly prominent. Antagonist muscle fatigue, however, was associated with a decrease in peak deceleration, while a decrease in both the peak velocity and peak acceleration was modest and, in some tests, non-significant. The relative acceleration time (i.e. acceleration time as a proportion of the total movement time) increased when agonists were fatigued, but decreased when antagonists were fatigued. Taken together, these results emphasize the mechanical roles of the agonist and antagonist muscles; namely, the fatigue of each muscle group particularly affected the movement phase in which that group accelerated a limb, while changes of the movement kinematics pattern provided more time for action of the fatigued muscles. In addition, the results presented suggest that agonist muscle fatigue affects movement velocity more than antagonist muscle fatigue, even in movements that demonstrate prominently both mechanical and myoelectric activity of the antagonist muscles, such as rapid, self-terminating movements. Accepted: 11 February 1997     

A numerical model for blood oxygenation in the pulmonary capillaries — Effect of pulmonary membrane resistance

A study of the blood oxygenation in pulmonary capillaries is made by considering the transport mechanisms of molecular diffusion, convection and the facilitated diffusion due to the presence of haemoglobin. The resistance offered by the pulmonary membrane on the transport of gases has been incorporated. The resulting system of coupled, non-linear partial differential equations is solved numerically.

It is found that, in the immediate neighbourhood of the entry, the amount of dissolved O₂ decreases. This decreases further as the resistance offered by the pulmonary membrane increases. The rate of oxygenation of blood increases as the permeability coefficient for O₂(P_o) increases. It is shown that the ideally permeable case for both O₂ and CO₂ can be approximated by taking P_o ˜ 10 cm/s. Further, it is shown that the oxygen takes longest and CO₂ is the fastest to attain equilibration. The equilibration length increases as the resistance offered by the membrane increases. Finally, some of the pulmonary diseases such as pulmonary oedema and fibrosis have been analyzed.     

Investigation of the performance of fermentation processes using a mathematical model including effects of metabolic bottleneck and toxic product on cells

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 death of cells. The present work therefore studies the effect of bottleneck on product concentrations under different product toxicity conditions. A generalized bottleneck model in a fed-batch fermentation is constructed including both the bottleneck and the product influences on cell growth and death. The simulation result reveals that when the toxic product strongly influences the cell growth and death, the final product concentration is hardly changed even if the bottleneck is removed, whereas it is markedly changed by the degree of product toxicity. The performance of an ethanol fermentation process is also discussed as a case example to validate this result. In conclusion, when the product is highly toxic, one cannot expect a significant increase in the final product concentration even if removing the bottleneck; rather, it may be more effective to somehow protect the cells so that they can continuously produce the product.     

Strategies for dealing with incomplete information in the modeling of molecular interaction networks

Modelers of molecular interaction networks encounter the paradoxical situation that while large amounts of data are available, these are often insufficient for the formulation and analysis of mathematical models describing the network dynamics. In particular, information on the reaction mechanisms and numerical values of kinetic parameters are usually not available for all but a few well-studied model systems. In this article we review two strategies that have been proposed for dealing with incomplete information in the study of molecular interaction networks: parameter sensitivity analysis and model simplification. These strategies are based on the biologically justified intuition that essential properties of the system dynamics are robust against moderate changes in the value of kinetic parameters or even in the rate laws describing the interactions. Although advanced measurement techniques can be expected to relieve the problem of incomplete information to some extent, the strategies discussed in this article will retain their interest as tools providing an initial characterization of essential properties of the network dynamics.     

Computation of spiking activity for a stochastic spatial neuron model: effects of spatial distribution of input on bimodality and CV of the ISI distribution

We obtain computational results for a new extended spatial neuron model in which the neuronal electrical depolarization from resting level satisfies a cable partial differential equation and the synaptic input current is also a function of space and time, obeying a first order linear partial differential equation driven by a two-parameter random process. The model is first described explicitly with the inclusion of all biophysical parameters. Simplified equations are obtained with dimensionless space and time variables. A standard parameter set is described, based mainly on values appropriate for cortical pyramidal cells. When the noise is small and the mean voltage crosses threshold, a formula is derived for the expected time to spike. A simulation algorithm, involving one-dimensional random processes is given and used to obtain moments and distributions of the interspike interval (ISI). The parameters used are those for a near balanced state and there is great sensitivity of the firing rate around the balance point. This sensitivity may be related to genetically induced pathological brain properties (Rett's syndrome). The simulation procedure is employed to find the ISI distribution for some simple patterns of synaptic input with various relative strengths for excitation and inhibition. With excitation only, the ISI distribution is unimodal of exponential type and with a large coefficient of variation. As inhibition near the soma grows, two striking effects emerge. The ISI distribution shifts first to bimodal and then to unimodal with an approximately Gaussian shape with a concentration at large intervals. At the same time the coefficient of variation of the ISI drops dramatically to less than 1/5 of its value without inhibition.     

A model for the impact of herbicide tolerance on the performance of oilseed rape as a volunteer weed

The introduction of genetically modified, herbicide-tolerant, oilseed rape into the agricultural environment will have ramifications beyond weed control of the crop. Herbicide-tolerant rape will undoubtedly become part of established volunteer weed populations that occur in many cereal rotations, but its longevity in these populations and its impact as a weed and contaminant of future oilseed rape crops is uncertain. A life cycle model of volunteer oilseed rape was therefore constructed, incorporating existing information on physiological processes such as emergence pattern, longevity of buried seed, death rates of various structures and flowering and seeding as functions of density. The model was designed to allow interaction with control factors such as harvesting efficiency, herbicide treatment, ploughing and the sequence of crops in the rotation. Many of the physiological parameters (including seed decay rates, fecundity at high density) are uncertain, simply through lack of information in the appropriate context. Other parameters such as harvesting efficiency and herbicide kill rates, are inherently variable in farming. Accordingly, a Monte-Carlo approach, in which the model was run many times with different random realisations of parameter sets, was used to expose factors to which the seedbank was sensitive. Sets of 1250 realisations were compared for each of two extreme conditions: where herbicide could be used according to current intensive farming practice and where it was not an option (representing total herbicide tolerance). Modelled seedbank numbers after 5 yr ranged from 10^-3to 10⁴m^-2, realistic values found in arable soils. The use of herbicide, together with efficient harvesting of seed, clearly has an important suppressive effect on the oilseed rape seedbank, keeping it lower than 10²m^-2(a typical sowing rate) after 5 yr in more than 80% of realisations. In the absence of herbicide, seedbanks were invariably greater, but their absolute value depended strongly on harvesting efficiency and the extent to which high density of plants suppressed fecundity. Analysis of the time series from the simulations showed that the seedbank levels fluctuated by orders in magnitude from year to year in the absence of herbicide use. The sensitivity analysis of the life-cycle model led to the development of a simplified model for the seedbank dynamics. The model shows that the essential features of the dynamics result from an interaction between density-dependent fecundity and the perturbations due to management. Therefore predictions of the effect of herbicide tolerance on seedbank dynamics are highly uncertain without knowledge of the density dependence of fecundity. Furthermore, the sensitivity to management practices suggests that seedbank levels will be substantially more difficult to control if the efficacy of herbicide is compromised. It is concluded that the model and Monte-Carlo approach have many potential uses in exploring the effects of management, cultivar physiology and the nature of the transgenes.     

A mixed model for the effects of single gene,polygenes and their interaction on quantitative traits

Summary A model for the effects of single gene (SG), polygenes (PG) and their interaction on quantitative traits was developed. It is a mixed model where the SG is a fixed effect and the PG is a random effect. A two-way factorial experiment, in which the SG and the PG are the main effects, is proposed. The experimental material is comprised of F₃ families derived from F₂ plants heterozygous for the SG. For this experiment an ANOVA table with expected mean square is proposed, which facilitates estimation of the components of the model and testing of their significance. A detailed method for the interpretation of results from such an experiment is proposed, with emphasis on the analysis of the SG × PG interaction. Theoretical and applied aspects of SG × PG interaction is discussed.This paper is part of a Ph.D. Thesis of the senior author to be submitted to the Hebrew University of Jerusalem     

A neural circuit model for changing the amount of information maintained in short-term memory depending on stimuli relationships

We propose a neural circuit model of changes in amount of information maintained in short-term memory depending on stimuli relationships. The relationships between stimuli are represented by the synchronous firings of overlapping neuronal groups for semantically related stimuli and the excitatory mutual connections for semantically unrelated but simultaneously presented stimuli. We conduct computer simulations to confirm our proposed neural circuit model. The resultant numbers of stored informational input patterns are almost consistent with the maximum numbers in the psychological experiments for both semantically related and unrelated stimuli. This agreement with the psychological experiments suggests that the structure and informational representation of the proposed model are appropriate.     

A new analytical method for wildlife habitat conservation planning on a city scale using the classification of physiologically homogeneous areas

Kyoto has a tradition of positively protecting scenic landscapes. However, a question has arisen about the effectiveness of the present legislative system on biodiversity conservation because most laws aim to essentially preserve the aesthetic value of the landscape. It is necessary to identify gaps in the present conservation system to develop an effective conservation policy for the city. The authors propose a practical method of analysis for wildlife habitat conservation planning without wildlife distribution information, which is the usual situation in many cities, and discuss the usefulness and limitations of the method by applying it to Kyoto. The proposed method relies on both of the following two assumptions: (1) the physical properties of the environment are closely related to the potential vegetation communities and (2) the conservation or restoration of rare or extinct vegetation communities ensures diverse wildlife habitats, contributing to biodiversity enhancement in a region. Thus it should be deemed a supplementary analysis to other types of analyses employing endangered, umbrella and/or flagship species in the planning process. A unique aspect of the method is to evaluate land potential, which is important for long-term conservation planning and the determination of target vegetation communities in restoration projects. In Kyoto, this revealed that the candidates for vegetation communities, prioritized for conservation and restoration, were appropriate. Moreover, identifying physiotopes corresponding with none of the existing vegetation communities was another advantage providing useful information for restoration planning. However, it was considered that a filtering process, with auxiliary information about the trend of vegetation communities over time, was necessary after applying the proposed method.     

A calorimetric and spectroscopic comparison of the effects of ergosterol and cholesterol on the thermotropic phase behavior and organization of dipalmitoylphosphatidylcholine bilayer membranes

We performed comparative DSC and FTIR spectroscopic measurements of the effects of cholesterol (Chol) and ergosterol (Erg) on the thermotropic phase behavior and organization of DPPC bilayers. Ergosterol is the major sterol in the biological membranes of yeasts, fungi and many protozoa. It differs from Chol in having two additional double bonds, one in the steroid nucleus at C7-8 and another in the alkyl chain at C22-23. Erg also has an additional methyl group in the alkyl chain at C24. Our DSC studies indicate that the incorporation of Erg is more effective than Chol is in reducing the enthalpy of the pretransition. At lower concentrations Erg is also more effective than Chol in reducing the enthalpies of both the sharp and broad components of main phase transition. However, at sterol concentrations from 30 to 50 mol%, Erg is generally less effective at reducing the enthalpy of the broad components and does not completely abolish the cooperative hydrocarbon chain-melting phase transition at 50 mol%, as does Chol. Nevertheless, in this higher ergosterol concentration range, there is no evidence of the formation of ergosterol crystallites. Our FTIR spectroscopic studies demonstrate that Erg incorporation produces a similar ordering of liquid-crystalline DPPC bilayers as does Chol, but an increased degree of hydrogen bonding of the fatty acyl carbonyl groups in the glycerol backbone region of the DPPC bilayer. These and other results indicate that Erg is less miscible in DPPC bilayers at higher concentrations than is Chol. Finally, we provide a tentative molecular explanation for the comparative experimental and computation results obtained for Erg and Chol in phospholipid bilayers, emphasizing the dynamic conformational differences between these two sterols.