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The role of mitochondrial DNA (mtDNA) damage in ageing processes and in malignant transformation of a cell is discussed. A mathematical model of the mtDNA population in a cell and in tissue is constructed. The model describes the effects of mtDNA damages accumulated during ageing and some features of malignant transformation and regeneration.
A generalized nonlinear mathematical model which incorporates beta-cell kinetics, a glucose-insulin feedback system and a gastrointestinal absorption term for glucose, is presented. Numerical simulations using this model lead to time variations of plasma glucose and insulin levels that are consistent with clinical observations in normal groups. The results obtained after suitable reduction in some of the parameters are in agreement with the clinical profile and laboratory data in insulin-dependent diabetes mellitus (IDDM). Linear stability analysis of the equations shows that there is a change in the nature of the stability in the transition from the normal case to IDDM, and it is the decrease in the beta cell function which causes this change.
Copper is an essential micronutrient for life. It is required by a wide range of species, from bacteria to yeast, plants and mammals including humans. To prevent the consequences of the excess or deficit of copper, living organisms have developed molecular mechanisms that regulate the uptake, efflux, storage and use of the metal. However, the limits of homeostatic regulation are not known. Here, we take advantage of a simple biological mechanism involved in copper metabolism of Enterococcus hirae, to explore how the regulation is achieved by using a set of four proteins codified in the cop operon: two P-type ATP-ases copper transporters, one copper chaper-one and one Cu-response transcription factor. We propose a mathematical model, based on differential equations and the power-law formalism (see M.A. Savageau, Chaos 11(1) (2001) 142-159), for the behavior of the cop operon and we show that homeostasis is a result of transient dynamics. The results derived from the mathematical model allow to measure qualitatively the adaptability of the system to its environment. This detailed model has been possible thanks to the available experimental biological information provided in a sequence of recent works by Solioz and co-workers.
In a previous study the epidermal cell kinetics of hairless mice were investigated with bivariate DNA/anti-bromodeoxyuridine (BrdU) flow cytometry of isolated basal cells after BrdU pulse labelling. The results confirmed our previous observations of two kinetically distinct sub-populations in the G2 phase. However, the results also showed that almost all BrdU-positive cells had left S phase 6-12 h after pulse labelling, contradicting our previous assumption of a distinct, slowly cycling, major sub-population in S phase. The latter study was based on an experiment combining continuous tritiated thymidine [( 3H]TdR) labelling and cell sorting. The purpose of the present study was to use a mathematical model to analyse epidermal cell kinetics by simulating bivariate DNA/BrdU data in order to get more details about the kinetic organization and cell cycle parameter values. We also wanted to re-evaluate our assumption of slowly cycling cells in S phase. The mathematical model shows a good fit to the experimental BrdU data initiated either at 08.00 hours or 20.00 hours. Simultaneously, it was also possible to obtain a good fit to our previous continuous labelling data without including a sub-population of slowly cycling cells in S phase. This was achieved by improving the way in which the continuous [3H]TdR labelling was simulated. The presence of two distinct subpopulations in G2 phase was confirmed and a similar kinetic organization with rapidly and slowly cycling cells in G1 phase is suggested. The sizes of the slowly cycling fractions in G1 and G2 showed the same distinct circadian dependency. The model analysis indicates that a small fraction of BrdU labelled cells (3-5%) was arrested in G2 phase due to BrdU toxicity. This is insignificant compared with the total number of labelled cells and has a negligible effect on the average cell cycle data. However, it comprises 1/3 to 1/2 of the BrdU positive G2 cells after the pulse labelled cells have been distributed among the cell cycle compartments.
Several late complications jeopardize the clinical performance of recipients of the Fontan operation. The underlying causes have been referred to disturbed flow dynamics in the cavopulmonary connections. Presumably, the large pressure drops occurring in the inferior and superior connections play a pivotal role in the pressure level of the entire circulation, especially in the venous. To address this issue, we retrospectively reviewed catheterization data of six patients with failing Fontan circulation and compared them with those of six patients with functioning Fontan circulation. The impact on the systemic and pulmonary pressure of the increase in the cavopulmonary connection resistances was studied through a steady-state mathematical model of the univentricular closed-loop circulation. In the patients with failing Fontan, pressure in the venae cavae was found to be significantly higher, especially at the inferior cava (19.3 +/- 2.2 versus 12.5 +/- 2.3 mmHg) with the pressure drop at the inferior cavopulmonary connection significantly increased (4.7 +/- 3.1 versus 0.33 +/- 0.82 mmHg). The proposed mathematical model permits us to clearly relate the pressure increase in the venae cavae to an increased resistance in the cavopulmonary connections. Therefore, the present analysis confirms that, to avoid possible congestion of venous circulation, the definitive palliation of univentricular heart should not cause pressure drops at the cavopulmonary connections.
Low volume ventilation with permissive hypercapnia is becoming widely used in the treatment of acute respiratory distress syndrome. A mathematical model was developed to examine the effects of hypoventilation on pulmonary gas exchange in lungs with a range of shunt fractions. Hypoventilation did not worsen gas exchange, provided the inspired oxygen concentration was high enough to maintain PAO2 at an adequate level. In lungs with a high shunt fraction, some improvement in gas exchange may result, but these effects are small. A rightwards shift of the oxygen-haemoglobin dissociation curve induced by hypercapnia, is likely to be beneficial rather than detrimental in patients with acute respiratory distress syndrome. This analysis was limited to the direct effects of hypoventilation in lungs with constant shunt fractions, and did not encompass a number of possible secondary effects such as changes in cardiac output with PaCO2, changes in shunt fraction associated with a reduction in mean airway pressure and possible direct effects of hypercapnia on the pulmonary vasculature or airways.
The maternal age dependence of Down's syndrome rates was analyzed by two mathematical models, a discontinuous (DS) slope model which fits different exponential equations to different parts of the 20-49 age interval and a CPE model which fits a function that is the sum of a constant and exponential term over this whole 20-49 range. The CPE model had been considered but rejected by Penrose, who preferred models postulating changes with age assuming either a power function X10, where X is age or a Poisson model in which accumulation of 17 events was the assumed threshold for the occurrence of Down's syndrome. However, subsequent analyses indicated that the two models preferred by Penrose did not fit recent data sets as well as the DS or CPE model. Here we report analyses of broadened power and Poisson models in which n (the postulated number of independent events) can vary. Five data sets are analyzed. For the power models the range of the optimal n is 11 to 13; for the Poisson it is 17 to 25. The DS, Poisson, and power models each give the best fit to one data set; the CPE, to two sets. No particular model is clearly preferable. It appears unlikely that, with a data set from any single available source, a specific etiologic hypothesis for the maternal age dependence of Down's syndrome can be clearly inferred by the use of these or similar regression models.
Fluorescence recovery after photobleaching (FRAP) analyses of binding and unbinding of molecules that interact with insoluble scaffolds, such as the cytoskeleton and nuclear matrix, in living cells commonly assume that this process is at equilibrium over the time scale of fluorescence recovery. This assumption breaks down for relatively fast intracellular processes like focal adhesion assembly at the leading edge of a migrating cell, or changes of transcriptional activation in the nucleus, that can occur in a matter of a few minutes. In this paper, we formulate a mathematical model that permits FRAP to be used to determine kinetic rate constants of molecules that interact with insoluble cellular structures under non-steady state conditions. We show that unlike steady state FRAP, fluorescence recovery time scales under these unsteady conditions are determined not only by unbinding rates, but also by the overall assembly and disassembly dynamics of the structural scaffold which supports these binding interactions. Experimental data from FRAP analysis and quantification of scaffold assembly dynamics may be combined and used with our mathematical model to estimate kinetic rate constants, as well as the apparent rate constant of scaffold assembly and disassembly.
A mathematical model has been developed to describe the death rate dynamics in irradiated mammals. The model links statistical biometric functions with statistical and dynamic characteristics of the organism's "critical" system. There is an agreement between the results of modelling and experiments with respect to death rate dynamics of small laboratory animals subjected to acute and chronic irradiation with doses and dose-rates at which small intestine epithelium is "critical".
Benzene, a ubiquitous environmental pollutant, is known to cause leukemia and aplastic anemia in humans and hematotoxicity and myelotoxicity in rodents. Toxicity is thought to be exerted through oxidative metabolites formed in the liver, primarily via pathways mediated by cytochrome P450 2E1 (CYP2E1). Phenol, hydroquinone and trans-trans-muconaldehyde have all been hypothesized to be involved in benzene-induced toxicity. Recent reports indicate that benzene oxide is produced in vitro and in vivo and may be sufficiently stable to reach the bone marrow. Our goal was to improve existing mathematical models of microsomal benzene metabolism by including time course data for benzene oxide, by obtaining better parameter estimates and by determining if enzymes other than CYP2E1 are involved. Microsomes from male B6C3F1 mice and F344 rats were incubated with [(14)C]benzene (14 microM), [(14)C]phenol (303 microM) and [(14)C]hydroquinone (8 microM). Benzene and phenol were also incubated with mouse microsomes in the presence of trans-dichloroethylene, a CYP2E1 inhibitor, and benzene was incubated with trichloropropene oxide, an epoxide hydrolase inhibitor. These experiments did not indicate significant contributions of enzymes other than CYP2E1. Mathematical model parameters were fitted to rodent data and the model was validated by predicting human data. Model simulations predicted the qualitative behavior of three human time course data sets and explained up to 81% of the total variation in data from incubations of benzene for 16 min with microsomes from nine human individuals. While model predictions did deviate systematically from the data for benzene oxide and trihydroxybenzene, overall model performance in predicting the human data was good. The model should be useful in quantifying human risk due to benzene exposure and explicitly accounts for interindividual variation in CYP2E1 activity.
In the present paper an original mathematical model of the chemical oxygen-dependent cerebral blood flow (CBF) regulation in the rat is proposed. Taking into account recent experimental works, the model assumes that oxygen acts on cerebral vessels through an indirect mechanism, mediated by the release of two metabolic substances (adenosine and H+) from tissue, and that any change in perivascular concentration of these substances affects the diameter of both the medium and small pial arteries as well as of intracerebral arterioles. The model is composed of several submodels, each closely related to a different physiological event. mathematical equations, which describe the reaction of the vasoactive portion of the cerebral vascular bed, are reported in detail and justified. The model permits the simulation of the role played by chemical factors in the control of CBF under many different physiological and pathological conditions in an attempt to clarify their relevance. Several events associated with an alteration in oxygen supply to tissue (auto-regulation to changes in arterial and venous pressure, reactive hyperemia following on cerebral ischemia, arterial hypoxia) have been simulated with the model. The results suggest that chemical factors, adenosine and H+, play a significant but not exclusive role in the regulation of the cerebral vascular bed. The action of other mechanisms (which are probably neurogenic) must be hypothesized to explain completely the CBF changes occurring in vivo.
The mathematical relations developed by various researchers for the oxygen dissociation curve are reviewed. Using well-known mechanisms of chemical kinetics of various species in the blood, we have developed a mathematical formula to compute the oxygen dissociation curve in the blood showing its dependence on the pH and PCO2. The functional form, proposed here, is much simpler in comparison to those available in the literature for use in the mathematical modelling of O2 transport in the pulmonary and systemic circulations. In the process, the well-known Hill's equation has been generalized showing an explicit dependence on PCO2 and pH. It is shown that the oxygen dissociation curve computed from our comparatively simpler equation, fits in fairly well with the documented data and shows realistic shift with PCO2 and pH.
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.
The integrase class site specific recombinases FLP from Saccharomyces cerevisiae, and Cre from bacteriophage P1, have been extensively used to direct DNA rearrangements in heterologous organisms. Although their reaction mechanisms have been relatively well characterised, little comparative analysis of the two enzymes has been published. We present a comparative kinetic analysis of FLP and Cre, which identifies important differences. Gel mobility shift assays show that Cre has a higher affinity for its target, loxP (7. 4x10(10) M-1), than FLP for its target, FRT (8.92x10(8) M-1). We show that both recombinases bind the two halves of their target sites cooperatively, and that Cre shows approximately threefold higher cooperativity than FLP. Using a mathematical model describing the sequential binding of recombinase monomers to DNA, we have determined values for the association and dissociation rate constants for FLP and Cre.FLP and Cre also showed different characteristics in in vitro recombination assays. In particular, approximately tenfold more active FLP was required than Cre to optimally recombine a given quantity of excision substrate. FLP was able to reach maximum excision levels approaching 100%, whilst Cre-mediated excision did not exceed 75%. To investigate possible reasons for these differences a mathematical model describing the excision recombination reaction was established. Using measured DNA binding parameters for FLP and Cre in the model, and comparing simulated and experimental recombination data, the values of the remaining unknown parameters were determined. This analysis indicates that the synaptic complex is more stable for Cre than for FLP.
The mass transport mechanisms involved in the controlled delivery of drugs to living brain tissue are complex and yet not fully understood. Often the drug is embedded within a polymeric or lipidic matrix, which is directly administered into the brain tissue, that is, intracranially. Different types of systems, including microparticles and disc- or rod-shaped implants are used to control the release rate and, thus, to optimize the drug concentrations at the site of action in the brain over prolonged periods of time. Most of these dosage forms are biodegradable to avoid the need for the removal of empty remnants after drug exhaustion. Various physical and chemical processes are involved in the control of drug release from these systems, including water penetration, drug dissolution, degradation of the matrix and drug diffusion. Once the drug has been released from the delivery system, it has to be transported through the living brain tissue to the target site(s). Again, a variety of phenomena, including diffusion, drug metabolism and degradation, passive or active uptake into CNS tissue and convection can be of importance for the fate of the drug. An overview is given of the current knowledge of the nature of barriers to free access of drug to tumour sites within the brain and the state of the art of: (i) mathematical modeling approaches describing the physical transport processes and chemical reactions which can occur in different types of intracranially administered drug delivery systems, and of (ii) theories quantifying the mass transport phenomena occurring after drug release in the living tissue. Both, simplified as well as complex mathematical models are presented and their major advantages and shortcomings discussed. Interestingly, there is a significant lack of mechanistically realistic, comprehensive theories describing both parts in detail, namely, drug transport in the dosage form and in the living brain tissue. High quality experimental data on drug concentrations in the brain tissue are difficult to obtain, hence this is itself an issue in testing mathematical approaches. As a future perspective, the potential benefits and limitations of these mathematical theories aiming to facilitate the design of advanced intracranial drug delivery systems and to improve the efficiency of the respective pharmacotherapies are discussed.
We devised a model suitable for mathematical analysis of beat-to-beat differences (BBDs) in fetal heart rates (FHRs). Factor analysis was applied, using a computer system, on a specially devised model of an FHR matrix. This matrix was arranged with FHRs and BBDs at 1-beat/min intervals by rows and columns, respectively. After obtaining the BBD by subtracting the antecedent FHR from the following FHR in a given pair of two consecutive FHRs, both variables of the antecedent FHR and BBD were crossed and the number of one was recorded at the corresponding element of the matrix. This procedure was done for all pairs of FHR and BBD yielding a matrix containing the cumulative incidences. Investigated was a total of 225,282 FHRs obtained from 20 fetuses between 37 and 41 weeks of gestation, by means of a scalp-lead electrocardiograph taken during labor. As shown by clusters of BBDs in units of beats/min, three different factors become evident: fluctuation around zero bpm, plus deviations and minus deviations. The first is considered to play a role in maintaining so-called baseline FHRs, and the second and the third indicate accelerating and decelerating actions on FHRs, respectively. This analytical model is discussed with reference to the findings obtained.
A new mathematical model is proposed to analyze the mass transfer behavior in lactic acid fermentation using immobilized cells entrapped in calcium alginate. The model is comprised of material balance equations for glucose, free lactic acid, and several ions. The dissociation rate of lactic acid (rdiss) is involved in the proposed equations. To solve the equations numerically, a modified calculating method is proposed. Through model analysis, the possible mass transfer behavior in the gel bead was discussed. The model is validated by comparisons with the experimental results obtained from batch and continuous fermentation. The simulations using the model were made to investigate the mass transfer limitation in the gel beads. The results showed that the cell density gradient was formed in the gel beads and it was caused by the accumulation of the inhibitory product (free lactic acid), not by substrate starvation. Moreover, unusual mass transfer behavior of lactate ion in the immobilization support was pointed out.
The structure of a computerized mathematical model for resource allocation in population programs (REALPOP) and its application to the Dominican Republic's national family planning program are described. The model integrates demographic and management science approaches in the analysis of resource allocation, program planning, goal evaluation, and growth strategies of a family planning program. It is designed primarily to aid administrative decision-makers. The Dominican National Population and Family Council (NPFC) established a goal of reducing the crude birth rate from its 1968 level of 48 per thousand population to 28 per thousand in 15 years. Further, the program has established a clear set of program plans and alternatives. This study investigates the implication of these plans for the program's stated goals.