Good manners in good modeling: mathematical models and computer simulations of physiological systems.
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Computers↗
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Quantitative analysis of cytosolic free calcium oscillations in neutrophils by mathematical modelling.
Mathematical models are often used to elucidate mechanisms behind cytosolic Ca2+ oscillations. We have evaluated the use of mathematical modelling to analyse and quantify Ca2+ signal patterns, in single, adherent human neutrophils (PMN) after stimulation by the bacterial peptide N-formyl-methionyl-leucyl-phenylalanine (fMLP). The cells were loaded with Fura-2 and fluctuations in cytosolic Ca2+ recorded with a video based digital imaging system. A new indirect intracellular calibration method was introduced to avoid the uncertainty in obtaining an equilibrium between the extracellular and intracellular calcium concentrations. Two different approaches to mathematical modelling were used. First, we applied a sensitivity analysis with a two-pool model by assuming an optimal situation using reliable a priori estimates of all structural parameters (e.g. Hill coefficients and dissociation constants). We found that the a priori estimates of the other 5 more variable parameters must lie within the range of 25-400% of the postulated true parameter values to be reliable in a parameter estimation method. Small changes (less than 5%) in those variable parameter values induced very different types of signal patterns which may have some relevance in evaluating a possible functional significance to the oscillatory signals. Second, we employed a one-pool, non oscillatory model integrated with a power spectrum method as a tool to quantify the dose dependency between fMLP (1-1000 nM) and parameters describing the biphasic process of calcium signalling and parameters describing only the oscillatory components. We conclude that the frequency of the observed oscillations assembled around one characteristic frequency independent of fMLP concentration, and sinusoidal oscillations were observed most frequently in PMN stimulated to a moderate peak [Ca2+]i level.
Biological Assay↗
Description of cutaneous excision and suture using a mathematical model.
Mathematical models are being developed at a fast rate in industry thanks to computer technology; they are used to simulate motion and deformation over time to test materials and objects in a virtual manner. These modeling techniques are being developed in medicine, but they remain, at this time, in the domain of biomechanical research. We report a mathematical model for cutaneous excision and suture, which we have used to predict the deformations and tensions that result when using four different forms of excision. The results are expressed in numerical and graphic form. The results obtained corresponded with our experience in dermatologic surgery. Uses and limits of this model are discussed.
Biomechanical Phenomena↗
The impact of HIV epidemic phases on the effectiveness of core group interventions: insights from mathematical models.
Mathematical models have highlighted the disproportionate contribution of core group transmitters to the spread of sexually transmitted diseases. Because the effectiveness of interventions varies with time, it has been suggested that epidemic phases should be considered in the design of prevention strategies. This study aimed to examine the impact of HIV epidemic phases on the effectiveness of HIV interventions based on gonorrhoea screening and condom use, targeted to core groups. The results are based on a mathematical model of gonorrhoea and HIV transmission in a relatively slow spreading HIV epidemic using Cotonou (Benin) as an example. For epidemics with a low reproductive potential modest core group interventions can significantly reduce HIV incidence and prevalence. As the epidemic matures, effective interventions should also incorporate core and non-core populations. For epidemics with a high reproductive potential, core group interventions are necessary but not sufficient to have a rapid and large scale impact. A more general population approach is also needed early in the epidemic. Epidemic phases are also important in the evaluation of prevention strategies.
Benin↗
Viral kinetics and mathematical models.
Mathematical models can provide insights into the dynamics of viral diseases. Methods that were introduced to analyze human immunodeficiency virus dynamics in vivo can be modified to give insights into hepatitis C virus (HCV) dynamics, the mechanisms of action of interferon, and the consequences of giving different dosages of interferon. Patients received doses of 5, 10, or 15 mIU of interferon daily for 14 days followed by maintenance therapy of 5 mIU daily until day 90. HCV-RNA levels in serum dropped rapidly over the first 1 to 2 days of therapy. Comparing the kinetics of this response with mathematical models suggests that interferon acts by blocking the production or release of HCV virions from infected cells. The analysis further indicates that a daily dose of 5 mIU blocks approximately 80% of HCV production, and doses of 10 and 15 mIU block approximately 95% of HCV production. The serum level of HCV is approximately constant before treatment is initiated. Our model suggests that in order to maintain this constant level, on average, approximately 1 trillion virions are produced and cleared daily in an untreated HCV-infected person. The acute, rapid clearance of HCV, which occurs over the first 2 days of therapy, is followed by a slower phase of serum HCV decline. The rate of the second-phase decline may reflect the rate at which HCV-producing cells are killed, possibly by immune responses. Additional studies are needed to evaluate more fully the kinetics of the second-phase decline as well as its dose dependence and its predictive power with regard to eradication of HCV.
Antiviral Agents↗
[The hematopoietic system during chronic irradiation with high dose rates (mathematical modeling)].
Mathematical models have been developed to describe dynamics of some haemopoietic compartments in mammals subjected to long-term irradiation. Within the framework of the models developed an equation has been obtained for a critical dose-rate (Ncr) of chronic irradiation, leading to complete depletion of certain haemopoietic compartments, that helps to prognose the dangerous Ncr values without preliminary experiments.
Animals↗
[A study of the effect of radiation on megakaryocytopoiesis using a mathematical model].
Mathematical modelling used in analysing the postirradiation changes in megakaryocytopoiesis permitted to determine the level of radiation-induced injury in each experiment conducted and to show that megakaryocytopoiesis regulation followed the same mechanism after irradiation as it does normally and after the effect of hydroxyurea and anti-thrombocyte serum. The analysis has demonstrated that after the stem cell death induced by ionizing radiation, the regeneration can be provided by the committed cells, and the level of regeneration is determined by the maturity of precursors.
Animals↗
The transport of oxygen, glucose, carbon dioxide and lactic acid in the human brain: mathematical models.
Mathematical models of the transport of oxygen, glucose, carbon dioxide and lactic acid in the human brain have been developed and solved for both steady-state and dynamic cases which include normal conditions, arterial and venous hypoxia, reduced flow and hematocrit, hypocapnia, reduced glucose and transient arterial upsets. Results indicate that local concentration deficits of oxygen and/or glucose and excesses of lactic acid can exist within the system described by the models and therefore possibly could exist in the tissues of the human brain under similar conditions.
Biological Transport, Active↗
Dynamics of calcium fluxes in nonexcitable cells: mathematical modeling.
Mathematical models simulating the dynamics of calcium redistribution (elicited by experimental interference with the pathways of calcium fluxes) in cellular compartments have been developed, based on a minimal scheme of the pathways of calcium fluxes in nonexcitable cells suspended in calcium-free medium. The models are consistent with available experimental data. All parameters are quantitatively related to the intrinsic properties of calcium adenosine triphosphatases (ATPases) and cellular membranes; there is no interdependence between the parameters. The models can be used as the basis for quantitative analysis and interpretation of experimental data. The activities of plasma membrane and sarcoendoplasmic reticulum calcium ATPases (PMCA and SERCAs) are governed by different mechanisms. PMCA is likely to undergo transitions from inactive to active to "dormant" (not identical to the initial) and back to inactive states, the mean duration of the cycle lasting for minutes or longer. The sequence of the transitions is initiated, presumably, by an increase in cytosolic calcium concentration. The transition of PMCA from inactive to active (at least at low rates of increase in cytosolic calcium concentration) is likely to be slower than that from active to dormant. SERCA, presumably, transits from inactive to active state in response to increases in calcium leakage from calcium stores. Whereas PMCA extrudes excess calcium (a definite quantity of it) in a short pulse, SERCA retakes calcium back into the stores permanently at a high rate. The models presented here may be the best means for the moment to quantitatively relate the dynamics of calcium fluxes in nonexcitable cells with known or putative properties of the mechanisms underlying activation of calcium ATPases.
Algorithms↗
Adenylate gradients and Ar:O(2) effects on legume nodules: I. Mathematical models.
Mathematical models were developed to test the likelihood that large cytosolic adenylate concentration gradients exist across the bacteria-infected cells of legume nodules. Previous studies hypothesized that this may be the case to account for the unusually low adenylate energy charge (AEC; 0.65) measured in the plant fraction of metabolically active nodules (M.M. Kuzma, H. Winter, P. Storer, I. Oresnik, C.A. Atkins, D.B. Layzell [1999] Plant Physiol 119: 399-407). Simulations coupled leghemoglobin-facilitated O(2) diffusion into the infected cell, through bacteroid nitrogenase activity, with the ATP demand for transport and ammonia assimilation in the plant fraction of ureide- and amide-producing nodules. Although large cytosolic adenylate gradients were predicted to exist in both nodule types, amide nodules were predicted to have steeper AEC gradients (0.82-0.52) than ureide nodules (0.82-0.61). The differences were attributed to an additional ATP demand for Asn synthesis in the amide nodule. Simulations for nodules transferred to an Ar:O(2) atmosphere predicted a major reduction in the magnitude of adenylate gradients and an increase in the AEC of the plant fraction. Results were consistent with a number of experimental studies and were used to propose an experimental test of the models.
Adenosine Monophosphate↗
Crypt dynamics and colorectal cancer: advances in mathematical modelling.
Mathematical modelling forms a key component of systems biology, offering insights that complement and stimulate experimental studies. In this review, we illustrate the role of theoretical models in elucidating the mechanisms involved in normal intestinal crypt dynamics and colorectal cancer. We discuss a range of modelling approaches, including models that describe cell proliferation, migration, differentiation, crypt fission, genetic instability, APC inactivation and tumour heterogeneity. We focus on the model assumptions, limitations and applications, rather than on the technical details. We also present a new stochastic model for stem-cell dynamics, which predicts that, on average, APC inactivation occurs more quickly in the stem-cell pool in the absence of symmetric cell division. This suggests that natural niche succession may protect stem cells against malignant transformation in the gut. Finally, we explain how we aim to gain further understanding of the crypt system and of colorectal carcinogenesis with the aid of multiscale models that cover all levels of organization from the molecular to the whole organ.
Cell Differentiation↗
Selection of a moxifloxacin dose that suppresses drug resistance in Mycobacterium tuberculosis, by use of an in vitro pharmacodynamic infection model and mathematical modeling.
BACKGROUND: Moxifloxacin is a quinolone antimicrobial that has potent activity against Mycobacterium tuberculosis. To optimize moxifloxacin dose and dose regimen, pharmacodynamic antibiotic-exposure targets associated with maximal microbial kill and complete suppression of drug resistance in M. tuberculosis must be identified. METHODS: We used a novel in vitro pharmacodynamic infection model of tuberculosis in which we exposed M. tuberculosis to moxifloxacin with a pharmacokinetic half-life of decline similar to that encountered in humans. Data obtained from this model were mathematically modeled, and the drug-exposure breakpoint associated with the suppression of drug resistance was determined. Monte-Carlo simulations were performed to determine the probability that 10,000 clinical patients taking different doses of moxifloxacin would achieve or exceed the drug-exposure breakpoint needed to suppress resistance to moxifloxacin in M. tuberculosis. RESULTS: The ratio of the moxifloxacin-free (non-protein-bound) area under the concentration-time curve from 0 to 24 h to the minimum inhibitory concentration associated with complete suppression of the drug-resistant mutant population was 53. For patients taking moxifloxacin doses of 400, 600, or 800 mg/day, the calculated target-attainment rates to suppress drug resistance were 59%, 86%, and 93%, respectively. CONCLUSION: A moxifloxacin dose of 800 mg/day is likely to achieve excellent M. tuberculosis microbial kill and to suppress drug resistance. However, tolerability of this higher dose is still unknown.
Antitubercular Agents↗
Advances and challenges in predicting the impact of lymphatic filariasis elimination programmes by mathematical modelling.
Mathematical simulation models for transmission and control of lymphatic filariasis are useful tools for studying the prospects of lymphatic filariasis elimination. Two simulation models are currently being used. The first, EPIFIL, is a population-based, deterministic model that simulates average trends in infection intensity over time. The second, LYMFASIM, is an individual-based, stochastic model that simulates acquisition and loss of infection for each individual in the simulated population, taking account of individual characteristics. For settings like Pondicherry (India), where Wuchereria bancrofti infection is transmitted by Culex quinquefasciatus, the models give similar predictions of the coverage and number of treatment rounds required to bring microfilaraemia prevalence below a level of 0.5%. Nevertheless, published estimates of the duration of mass treatment required for elimination differed, due to the use of different indicators for elimination (EPIFIL: microfilaraemia prevalence < 0.5% after the last treatment; LYMFASIM: reduction of microfilaraemia prevalence to zero, within 40 years after the start of mass treatment). The two main challenges for future modelling work are: 1) quantification and validation of the models for other regions, for investigation of elimination prospects in situations with other vector-parasite combinations and endemicity levels than in Pondicherry; 2) application of the models to address a range of programmatic issues related to the monitoring and evaluation of ongoing control programmes. The models' usefulness could be enhanced by several extensions; inclusion of different diagnostic tests and natural history of disease in the models is of particular relevance.
Journal Article↗
[Adaptive mutagenesis accelerates microorganism evolution only while competing for resources: mathematic modeling].
Mathematical simulation of adaptive mutagenesis was carried out. The results obtained indicate that adaptive mutagenesis can play an essential role in the survival of microbial populations. We show that the competition for natural resources is a necessary factor of adaptive mutagenesis.
Adaptation, Physiological↗
Mathematical modeling of polyamine metabolism in mammals.
Polyamines are considered as essential compounds in living cells, since they are involved in cell proliferation, transcription, and translation processes. Furthermore, polyamine homeostasis is necessary to cell survival, and its deregulation is involved in relevant processes, such as cancer and neurodegenerative disorders. Great efforts have been made to elucidate the nature of polyamine homeostasis, giving rise to relevant information concerning the behavior of the different components of polyamine metabolism, and a great amount of information has been generated. However, a complex regulation at transcriptional, translational, and metabolic levels as well as the strong relationship between polyamines and essential cell processes make it difficult to discriminate the role of polyamine regulation itself from the whole cell response when an experimental approach is given in vivo. To overcome this limitation, a bottom-up approach to model mathematically metabolic pathways could allow us to elucidate the systemic behavior from individual kinetic and molecular properties. In this paper, we propose a mathematical model of polyamine metabolism from kinetic constants and both metabolite and enzyme levels extracted from bibliographic sources. This model captures the tendencies observed in transgenic mice for the so-called key enzymes of polyamine metabolism, ornithine decarboxylase, S-adenosylmethionine decarboxylase and spermine spermidine N-acetyl transferase. Furthermore, the model shows a relevant role of S-adenosylmethionine and acetyl-CoA availability in polyamine homeostasis, which are not usually considered in systemic experimental studies.
Acetyl Coenzyme A↗
[Interactive determination of the parameters of mathematical models for planning radiotherapy of malignant tumors. I. Mathematical models for calculating dose tolerance, adequate doses and the likelihood of development of radiation complications in normal organs and tissues].
Mathematical models for calculating tolerance doses, adequate doses and the likelihood of radiation complications in the body's normal tissues are considered. To determine the parameters of these models that describe the outcomes of radiation exposure of complicated biological systems, a method of local adjustment of the parameters of the models has been developed, which will be described in parts 2 and 3 of the proposed paper. In part 1 (the present paper), particular emphasis is laid on the inclusion of an important parameter, such as a volume, into Ellis and LQ models. A mathematical model is presented for calculating the likelihood of a radiation complication in the tissue, which is the basis for deriving a formula to calculate an adequate uniform tissue radiation dose that is equivalent to the nonuniform tissue distribution of a dose in terms of the likelihood of radiation complications.
Humans↗
The diffusive transport of gibberellins and abscisic acid through the aleurone layer of germinating barley grain: a mathematical model.
A mathematical model of the diffusive transport of abscisic acid (ABA) and gibberellins (GAs) through the aleurone layer of barley (Hordeum vulgare L.) grain is presented. The model consists of two partial differential equations describing the accumulation of phytohormone in the apoplastic and symplasmic compartments of the aleurone layer, both spatially and temporally. The mathematical model contains the morphology of the barley grain and the physicochemical properties of the two phytohormones. A mathematical derivation of the accumulation ratios for the two phytohormones between the symplast and apoplast under equilibrium conditions resulted in different distribution mechanisms for GAs and ABA. A sensitivity analysis of the accumulation ratio for GAs indicated high sensitivity to the apoplastic pH and the membrane potential, whereas the accumulation ratio for ABA proved to be most sensitive to the pH difference between the apoplast and symplast. The diffusive transport time for GAs to the basal site of the aleurone layer as calculated with the mathematical model is within a physiologically plausible timescale according to experimental data from the literature. Abscisic acid cannot be transported by diffusion to the end of the aleurone layer as quickly as GAs, according to model simulations. Therefore, the functional role of ABA in germination is likely to be in the vicinity of the embryo.
Abscisic Acid↗
[Study of the combined action of an antibiotic and an immunostimulator using mathematical modeling].
A mathematical model of antibiotic and immunostimulator (IMS) combined effect on various elements of the immune system and general state of patients with infectious diseases is described. The model was constructed as a system including 6 usual differential equations of the 1st order. With the use of this model and a computer many diverse variants of infection development under conditions of treatment with IMS at the background of antibiotic therapy were modeled. Ii was shown that IMS-antibiotic complexes markedly improved the indices of antibiotic therapy as compared to the use of the antibiotics alone. In combined use of IMS and antibiotics it was possible to lower the antibiotic doses without lowering the antimicrobial effect. The use of IMS at the optimal period led to balanced activation of the host specific and nonspecific resistance factors at the background of antibacterial therapy. The results of the mathematical modeling corresponded to the data on protective effect of salmozan (IMS) and doxycycline (antibiotic) combination in animals (albino mice). It was concluded that the described mathematical model was adequate for validation and optimization of schemes for combined use of IMS and antibacterial agents.
Adjuvants, Immunologic↗