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At least 1,477 records · Page 82Linked to original sources
PubMed1983

Mathematical model of L5178Y mouse lymphoma forward mutation assay.

A mathematical model of the biological protocol for the Mouse Lymphoma L5178Y Forward Mutation Bioassay is presented. The model relates the mutant progenitor frequency (MPF), the number of cells per million surviving cells with DNA damage after exposure to the chemical, to the mutant frequency (MF), the number of TFT-resistant cells per million survivors. For a given expression time, the deterministic relationship is linear and the proportionality constant depends on the relative suspension growth factor (rg) and relative cloning efficiencies (rc) of mutants to those of wild type cells: MF = (rg X rc) X MPF. Experimental noise leads to variations in the values of rg and rc and lack of reproducibility in the system. If mutant progenitors and their progeny grow as well as wild-type cells and if all of the parental mutant progenitors express the mutant phenotype, then rg = 1/2 and rc = 1. Biological mechanisms, such as differential growth characteristics of mutant and wild-type cells or DNA repair, can make the mutant frequency an inaccurate estimate of the MPF. For the assay to be useful as a screen for the mutagenic activity of chemicals, rg X rc has to be reasonably constant from chemical to chemical.

Animals↗
PubMed1986

A mathematical model of survival kinetics. II. Parameter estimation.

Procedures for the estimation of the four parameters of a new mathematical model of survival and mortality kinetics are given. A formulation of the model has been found which had the advantage of maintaining three of four parameters independent of the unit chosen for the age; in addition, two of these parameters have values falling in a narrow range, even when the model is applied to rather different curves. Since, in any problem of this type, the initial estimate of the parameters plays a major role in the achievement of good final estimates, some simple methods of estimation are indicated based upon the characteristics of the function. The initial estimates may enter three different types of procedures; the best one can be chosen according to the precision of the initial estimates. The method is capable of fitting both survivorship and dying functions directly to the empirical data. An interactive approach to the computer facilities has been used as at each step the operator has to decide whether or not to apply a corrective factor. Goodness of fit, usually high, is estimated by chi 2 test.

Aging↗
PubMed1994

Segregated mathematical model for the fed-batch cultivation of a high-producing strain of Penicillium chrysogenum.

A new segregated mathematical model for the penicillin fed-batch process is presented and applied to the growth of the pellet-forming, industrially used high-producing strain Penicillium chrysogenum S2. The model comprises two kinds of biomass (growing and producing, nongrowing and still producing), cell lysis, and complex medium as an important substrate for primary growth. In accordance with our experimental observation, product formation is not inhibited by glucose, but related to the growth rate. Maintenance metabolism is cell age-dependent. The model was verified with two sets of experimental data including exhaust gas measurements while keeping the estimated parameters almost constant. The presented model derived from that of Bajpai and Reuss (1980, 1981) does not describe our data properly. The particular influence of the pellet structure on the model is discussed. The necessity of new model assumptions (e.g., different kinds of biomass, non-constant maintenance coefficient) is explained by cell damage by lysis and shear forces, and the succeeding repair processes.

Biotechnology↗
PubMed1986

Mathematical description of the interaction between prostaglandins and calcium.

The interpretation of the biological action of prostaglandins is very difficult because the shape of the dose-response curves in different assays is often unusual. Horrobin has attempted to explain these unusual curves by supposing special interactions between Ca and the prostaglandin receptors. This paper gives a mathematical description of his theoretical models. The results of computer simulation based on these models were in good agreement with the reported experimental observations.

Binding, Competitive↗
PubMed1995

Detection and geometric modeling of molecular surfaces and cavities using digital mathematical morphological operations.

We developed a digital method based on mathematical morphological operations to obtain three types of surfaces: van der Waals surface, solvent-accessible surface, and molecular surface, to extract the cavities on the surface and interior part of the molecule and to extract the ligand portions in contact with the cavities. The molecular surface, the cavities and the portions, and the heme region are visualized using solid modeling. The method enables us to obtain the volumes of the cavities and inhibitor portions and the areas of the surfaces. Solid modeling enables us to obtain cross-sections at arbitrary positions. This will have considerable utility in docking studies.

Computer Graphics↗
PubMed1984

Determining "safe" levels of exposure: safety factors or mathematical models?

The object of regulatory toxicology is to determine "safe" levels of human exposure to toxicants present in the environment. The traditional safety factor approach is compared to more recent mathematical modeling techniques, outlining the underlying assumptions and statistical properties of each procedure. Several linear extrapolation procedures are examined in detail using computer simulation, along with the impact of nonlinear kinetics on the extrapolation process.

Biotransformation↗
PubMed1983

A mathematical model of biodegradability screening tests as an aid to interpretation of observed results.

A mathematical model, based on a modification of the Michaelis--Menten and Monod equations describing bacterial growth, has been used to predict the course of removal of the organic substrates in the modified OECD and other screening tests. A range of initial concentrations of bacteria in the inoculum has been selected, using published data on the total bacterial count in secondary sewage effluents and activated sludge, to simulate the wide range of volumes of these materials used in practice. The arbitrary definition of ready biodegradability adopted by the OECD, that is, 5 to the equivalent of 70% DOC removal in not more than 10 days in a total incubation period of 28 days, is expressed in terms of inoculum size and kinetic constants. Modifications are proposed to the screening test with the object of making it more useful and realistic in predicting whether or not a chemical will be removed in sewage treatment.

Bacteria↗
PubMed1987

A mathematical model of the development of drug resistance to cancer chemotherapy.

A mathematical model incorporating descriptions of tumour growth kinetics and the effects of cytotoxic chemotherapy on established tumours, is presented. It is shown how models of this kind may be used to investigate the potential of hypothetical chemotherapy strategies, and to identify general principles for successful treatment. The model is intended to be an aid to clinicians designing new chemotherapy programmes for diseases in which progress has been disappointing.

Antineoplastic Agents↗
PubMed1988

Mathematical models to predict behaviour of tumours?

Mathematical modeling is an important tool in science that allows the investigator to examine phenomena that are not easily studied by direct experiment. The growth of neoplasms and their response to treatment are processes that appear particularly well suited for study by this approach. The ready availability of inexpensive powerful microcomputers and sophisticated software makes this research avenue open to all experimental and clinical oncologists.

Drug Resistance↗
PubMed1984

Focal changes in cerebral blood flow produced by monetary incentive during a mental mathematics task in normal and depressed subjects.

The purpose of this experiment was to determine the effect of incentive-induced arousal on the diffuse and regional cerebral blood flow (rCBF) response during cognitive activation for normal and depressed groups. Two normal rest CBF measurements were followed by two mental mathematics activation CBF measurements. For the first activation measurement, half the subjects in each group were offered monetary incentive for correct performance and half the subjects received no monetary incentive. All subjects were offered monetary incentive on the final activation run. The effect of monetary incentive on the first activation run was to increase CBF activation at four detectors in the left hemisphere. Incentive did not affect the CBF activation response when introduced following practice on the activation task (on the final run). Depressed groups had lower resting blood flow than normals, but the distribution of flow and the CBF response to incentive were almost identical in the two groups.

Adult↗
PubMed1996

New methods of mathematical analysis for studies of intrauterine contraception.

The authors present two new procedures of mathematical analysis to evaluate the incidents which arise during the use of any contraceptive method. These two new approaches, which the authors call the Probability Index (PI) and the Weighted Average Index (WAI), are compared to those by Pearl and Tietze. Their conclusions are that the PI, although the best estimator of real probability, is not as functional as the WAI. The latter is not only much easier to calculate than PI, but also presents a greater correlation, prediction accuracy and discriminant power than the Pearl and Tietze indexes.

Contraception↗
PubMed1975

Nonlinear regression methods in design of experiments and mathematical modelling. Applications to the analysis of the steady-state kinetics of glutathione reductase.

A branching reaction pathway involving a ping pong and a sequential loop has been proposed for glutathione reductase (Biochem. Biophys. Res. Commun. 53 (1973) 1151). In the present investigation nonlinear regression methods have been applied in the fitting of rate equations to experimental data to test the validity of the model proposed and to discriminate between alternative mathematical models (cf. FEBS Lett. 26 (1972) 252). In the best rate law, some of the parameters were numerically redundant. Therefore, a feature-wise analysis of the rate equation was carried out by varying one substrate concentration at a time. The overall strategy used was a cyclic procedure involving: experimentation - analysis of data - modelling - design of experiments - new experimentation etc. Consideration was given to the experimental error structure and to the importance of weighting in the regression analysis. In the design of experiments for discrimination between rival models, a previously defined discrimination function was used. The results of the analysis support the branching reaction scheme proposed for glutathione reductase.

Glutathione↗
PubMed1975

Mathematical analysis of multienzyme systems. I. Modelling of the glycolysis of human erythrocytes.

A mathematical model for the glycolysis of human erythrocytes is presented which takes into account ATP-synthesis and -consumption. A set of three differential equations describes the steady states and the time-dependent changes of the metabolite concentrations under blood storage conditions. For a given parameter combination there are in general three stationary points of the system, one of which is unstable. At a low ATP-need the ATP-level is relatively constant for variations in the rate constant of the ATP-consuming processes. Above a critical level of the energy consumption the system breaks down. An important role of the 2.3P2G-bypass of the erythrocytes is its action as an "energy buffer", wasting ATP in case of ATP-overproduction and producing ATP in case of underproduction. A parameter combination consistent with the data on the isolated enzymes was found which gives a good agreement of theoretical predictions with the measured metabolite concentrations. Under blood preservation conditions the difference of the rates of ATP-production and -consumption is the most important factor for a high ATP-level over long periods.

Adenosine Triphosphatases↗
PubMed1990

Mathematical modelling of the purine metabolism of the rat liver.

The regulation of the purine metabolism of the rat liver is studied on the basis of a mathematical model which comprises rate laws and kinetic constants of all physiologically relevant reactions. The computed stationary and time-dependent concentrations are in good accordance with experimental data obtained in the ischaemic rat liver and in isolated hepatocytes. In particular, model-based simulations of the adenine nucleotide metabolism have been performed for situations where ATP-deficient states of the cell (hypoxia, anoxia or ischaemia) of various length are followed by onset of ATP production (reoxygenation). These simulations confirm the experimentally observed incomplete recovery of ATP and of the total pool of adenine nucleotides within a few hours of reoxygenation after long-term ATP depletion. Therefore, it can be concluded that this phenomenon is an intrinsic regulatory property of the purine metabolism and not necessarily due to some irreversible changes in the activity of the enzymes involved.

Animals↗
PubMed1991

Stimulation of alanine metabolism by ammonia in the perfused rat liver. Quantitative analysis by means of a mathematical model.

The effect of ammonia on the catabolism of alanine was studied in the perfused rat liver. Addition of 0.5 mM NH4Cl to the perfusion medium containing 5 mM alanine plus 0.1 mM octanoate produced drastic changes in the metabolite concentrations in the efflux medium. Not only the rate of ureogenesis was activated, but also the formation of glucose, lactate and pyruvate. Additionally, respiration was stimulated, the output of ketone bodies decreased, and the redox ratios lactate/pyruvate as well as 3-hydroxybutyrate/acetoacetate became more oxidized. To interpret the causes of these metabolic changes, a mathematical model was developed. It contains kinetic equations by which fluxes through essential pathways of alanine catabolism, gluconeogenesis and energy metabolism were related to the intracellular concentrations of pyruvate, oxaloacetate and ammonia, as well as to the redox ratios lactate/pyruvate and 3-hydroxybutyrate/acetoacetate. Using a nonlinear regression procedure, the model was suitable to be fitted to the data found in the experiments. The consistency of the model and experiment allowed the changes caused by ammonia to be explained. Primarily, ammonia stimulated ureogenesis hence accelerating the deamination of alanine which led to the increased formation of pyruvate, lactate and glucose. The enhanced energetic load resulting from ureogenesis and gluconeogenesis shifted the mitochondrial and cytosolic NAD systems towards more oxidized states which additionally modified the flux rates. The results demonstrate that there is a high degree of cooperativity between the metabolic pathways.

3-Hydroxybutyric Acid↗
PubMed1993

The epidemiology of neural tube defects. A mathematical model.

The incidence of neural tube defects (NTDs) shows a seasonal variation; and incidence as well as female/male ratio show a relation with latitude. The interrelation of these phenomena is presented as a mathematical model, which has a 'predictive' value, and is an instrument in estimating the local gene frequency. The model offers a simple explanation of the conundrum why the double X-chromosome has a variable influence on the sex ratio. UV light and the herpes virus fit in this model as related causative factors of NTDs.

Epidemiologic Factors↗
PubMed1995

Mathematical formulae for the prediction of the residual beta cell function during the first two years of disease in children and adolescents with insulin-dependent diabetes mellitus.

On the basis of a retrospective study of 71 children followed for 24 months after diagnosis of type I insulin dependent diabetes a fitted mathematical model was constructed for the prediction of the course of beta cell function from the time of diagnosis. Two equations were derived, one for the maximal basal (B-max) and the other for the maximal i.v. glucagon stimulated peak C-peptide (P-max) levels reached during the remission period. The prognostic variables selected for analysis were: peak C-peptide levels at diagnosis (Po), age sex, degree of obesity, pubertal rating, the presence of islet cell antibodies (ICA) and levels of GHb. Multivariate analysis of the data showed that Po (p = 0.0006), puberty (p = 0.041). obesity (p = 0.0021), sex (p = 0.031), ICA (p = 0.0045) and GHb(p = 0.0066) significantly contributed to the prediction formula obtained for B-max whereas the contribution of the above variables for P-max were: Po (p = 0.0019), puberty (p = 0.0187), obesity (p = 0.0058), sex (p = 0.0598), ICA (p = 0.0187) and GHb (p = 0.0027). The residuals of the observed values from the values fitted by the predicted equations served to define two separate groups demonstrating distinct differences in the natural course of beta cell function in type I diabetes. This fitted model may thus be useful in distinguishing between newly diagnosed young patients who will undergo remission, requiring lower insulin doses, and those who have little chance for remission. It might also be helpful in the selection of patients most likely to benefit from immunosuppression or modulation, to maximize the benefit to risk ratio for such patients.

Adolescent↗