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At least 1,657 records · Page 92Linked to original sources
PubMed2005

A mathematical model of N-linked glycosylation.

Metabolic engineering of N-linked oligosaccharide biosynthesis to produce novel glycoforms or glycoform distributions of a recombinant glycoprotein can potentially lead to an improved therapeutic performance of the glycoprotein product. A mathematical model for the initial stages of this process, up to the first galactosylation of an oligosaccharide, was previously developed by Umana and Bailey (1997) (UB1997). Building on this work, an extended model is developed to include further galactosylation, fucosylation, extension of antennae by N-acetyllactosamine repeats, and sialylation. This allows many more structural features to be predicted. A number of simplifying assumptions are also relaxed to incorporate more variables for the control of glycoforms. The full model generates 7565 oligosaccharide structures in a network of 22,871 reactions. Methods for solving the model for the complete product distribution and adjusting the parameters to match experimental data are also developed. A basal set of kinetic parameters for the enzyme-catalyzed reactions acting on free oligosaccharide substrates is obtained from the previous model and existing literature. Enzyme activities are adjusted to match experimental glycoform distributions for Chinese Hamster Ovary (CHO). The model is then used to predict the effect of increasing expression of a target glycoprotein on the product glycoform distribution and evaluate appropriate metabolic engineering strategies to return the glycoform profile to its original distribution pattern. This model may find significant utility in the future to predict glycosylation patterns and direct glycoengineering projects to optimize glycoform distributions.

Animals↗
PubMed2002

Kinetic heterogeneity of an experimental tumour revealed by BrdUrd incorporation and mathematical modelling.

In the present paper we propose a method of analysis of the cell kinetic characteristics of in vivo experimental tumours, that uses DNA-BrdUrd flow cytometry data at various times after the bromodeoxyuridine (BrdUrd) injection and mathematical modelling. The model of the cell population takes into account the cell-cell heterogeneity of the progression rate across cell cycle phases within the tumour, and assumes a strict correlation between the durations of S and G2M phases. The model also allows for a nonconstant DNA synthesis rate across S phase. In addition, the measurement process is modelled, considering the possibility of nonimpulsive labelling and providing a representation of the time course of the bivariate DNA-BrdUrd fluorescence distribution. Sequential DNA-BrdUrd distributions were obtained in vivo from a human ovarian carcinoma transplanted in mice and, for comparison, in vitro from a cell line of the same origin. From these data, that included the fractional density and the mean BrdUrd-fluorescence of BrdUrd-positive cells as a function of the DNA-fluorescence, kinetic parameters such as the potential doubling time (Tpot) and the mean and variance of the transit times in S and G2M phases, were estimated. This study revealed the presence of a substantial heterogeneity in S and G2M phases within the in vivo cell population and of a lower heterogeneity in the in vitro population. Moreover, our analysis suggests a nonnegligible effect of the BrdUrd pharmacokinetics in the in vivo cell labelling.

Animals↗
PubMed1989

Mathematical model for interpretation of Doppler velocity waveform indices.

Various empirical indices such as the pulsatility index (PI) are widely used for quantitative analysis of Doppler ultrasound velocity waveforms. The physical interpretation of these indices was studied using a mathematical model. Although the method has more general applicability, this particular study was concerned with the umbilical-placental circulation. A lumped element electrical circuit equivalent was used, with each arterial branch represented by a resistor and a capacitor. The placental villous bed was modelled by a two-step parallel branching structure. Placental vascular disease was modelled either as obliteration of a fraction of the terminal branches, or as a fractional decrease in the radius of the vessels. The main features of both normal and abnormal umbilical artery waveforms can be reproduced by this simple model. Theoretical relationships between the velocity waveform indices and the lumped resistances and capacitance of the system were obtained for different input pressure functions. Over a wide range of physically reasonable conditions, the umbilical artery PI is approximately proportional to the ratio of the placental resistance to the umbilical artery resistance. The PI also depends on the pulsatility of the input pressure waveform. The Fourier pulsatility index was evaluated for an arbitrary pressure function, and shown to behave like (PI)2 for the umbilical artery waveform.

Biomedical Engineering↗
PubMed2004

Principles of rapid polymerase chain reactions: mathematical modeling and experimental verification.

Polymerase chain reaction (PCR) is an important diagnostic tool for the amplification of DNA. The PCR process can be treated as a problem in biochemical engineering. This study focuses on the development of a mathematical model of the polymerase chain reaction. The PCR process consists of three steps: denaturation of target DNA, annealing of sequence-specific oligonucleotide primers and the enzyme-catalyzed elongation of the annealed complex (primer:DNA:polymerase). The denaturation step separates the double strands of DNA; this model assumes denaturation is complete. The annealing step describes the formation of a primer-fragment complex followed by the attachment of the polymerase to form a ternary complex. This step is complicated by competitive annealing between primers and incomplete fragments including primer-primer reactions. The elongation step is modeled by a stochastic method. Species that compete during the elongation step are deoxynucleotide triphosphates dCTP, dATP, dTTP, dGTP, dUTP, and pyrophosphate. Thermal deamination of dCTP to form dUTP is included in the model. The probability for a species to arrive at the active site is based on its molar fraction. The number of random insertion events depends on the average processing speed of the polymerase and the elongation time of the simulation. The numerical stochastic experiment is repeated a sufficient number of times to construct a probability density distribution (PDF). The moment of the PDF and the annealing step products provide the product distribution at the end of the elongation step. The overall yield is compared to six experimental values of the yield. In all cases the comparisons are very good.

Algorithms↗
PubMed2005

Mathematical modeling of nucleotide excision repair reveals efficiency of sequential assembly strategies.

Nucleotide excision repair (NER) requires the concerted action of many different proteins that assemble at sites of damaged DNA in a sequential fashion. We have constructed a mathematical model delineating hallmarks and general characteristics for NER. We measured the assembly kinetics of the putative damage-recognition factor XPC-HR23B at sites of DNA damage in the nuclei of living cells. These and other in vivo kinetic data allowed us to scrutinize the dynamic behavior of the nucleotide excision repair process in detail. A sequential assembly mechanism appears remarkably advantageous in terms of repair efficiency. Alternative mechanisms for repairosome formation, including random assembly and preassembly, can readily become kinetically unfavorable. Based on the model, new experiments can be defined to gain further insight into this complex process and to critically test model predictions. Our work provides a kinetic framework for NER and rationalizes why many multiprotein processes within the cell nucleus show sequential assembly strategy.

Animals↗
PubMed2004

Effects of diffusion and topological factors on the efficiency of energy coupling in chloroplasts with heterogeneous partitioning of protein complexes in thylakoids of grana and stroma. A mathematical model.

In this work, we studied theoretically the effects of diffusion restrictions and topological factors that could influence the efficiency of energy coupling in the heterogeneous lamellar system of higher plant chloroplasts. Our computations are based on a mathematical model for electron and proton transport in chloroplasts coupled to ATP synthesis in chloroplasts that takes into account the nonuniform distribution of electron transport and ATP synthase complexes in the thylakoids of grana and stroma. Numerical experiments allowed the lateral profiles of pH in the thylakoid lumen and in the narrow gap between grana thylakoids to be simulated under different metabolic conditions (in the state of photosynthetic control and under conditions of photophosphorylation). This model also provided an opportunity to simulate the effects of steric constraints (the extent of appression of thylakoids in grana) on the rates of non-cyclic electron transport and ATP synthesis. This model demonstrated that there might be two mechanisms of regulation of electron and proton transport in chloroplasts: 1) slowing down of non-cyclic electron transport due to a decrease in the intra-thylakoid pH, and 2) retardation of plastoquinone reduction due to slow diffusion of protons inside the narrow gap between the thylakoids of grana. Numerical experiments for model systems that differ with respect to the arrangement of thylakoids in grana allowed the effects of osmolarity on the photophosphorylation rate in chloroplasts to be explained.

Adenosine Triphosphate↗
PubMed1994

A mathematical model describing catch-up growth in celiac disease.

Celiac disease may lead to various degrees of growth retardation. In general, catch-up growth is completed in the first 2 years after the start of therapy. A mathematical model for catch-up growth in celiac disease can be useful as a reference to which the growth pattern observed during treatment of other conditions can be compared. In this study we performed a non-linear regression analysis on individual growth data of 16 celiac disease patients using a monomolecular growth function. The goodness of fit was significant in all cases (p < 0.05), which illustrates that this function adequately describes catch-up growth in individuals with celiac disease. From the individual models we have composed a cross-sectional curve and a longitudinal description of the pattern of catch-up growth for the entire population.

Celiac Disease↗
PubMed2005

The epidemiological impact of antiretroviral use predicted by mathematical models: a review.

This review summarises theoretical studies attempting to assess the population impact of antiretroviral therapy (ART) use on mortality and HIV incidence. We describe the key parameters that determine the impact of therapy, and argue that mathematical models of disease transmission are the natural framework within which to explore the interaction between antiviral use and the dynamics of an HIV epidemic. Our review focuses on the potential effects of ART in resource-poor settings. We discuss choice of model type and structure, the potential for risk behaviour change following widespread introduction of ART, the importance of the stage of HIV infection at which treatment is initiated, and the potential for spread of drug resistance. These issues are illustrated with results from models of HIV transmission. We demonstrate that HIV transmission models predicting the impact of ART use should incorporate a realistic progression through stages of HIV infection in order to capture the effect of the timing of treatment initiation on disease spread. The realism of existing models falls short of properly reproducing patterns of diagnosis timing, incorporating heterogeneity in sexual behaviour, and describing the evolution and transmission of drug resistance. The uncertainty surrounding certain effects of ART, such as changes in sexual behaviour and transmission of ART-resistant HIV strains, demands exploration of best and worst case scenarios in modelling, but this must be complemented by surveillance and behavioural surveys to quantify such effects in settings where ART is implemented.

Journal Article↗
PubMed1987

[Mathematical model of removal of impurities from antibiotic pastes].

The process of antibiotic paste washing by repulpation in a solvent, as well as the process of replacing washing of antibiotic filter cakes was studied. This enabled to develop a mathematical model of the process of admixture removing from antibiotic pastes by successive repulpation and replacing washing. The model connects the initial admixture levels in pastes, the filter cake characteristics, the specification requirements to the drug quality and the technological parameters of the process. The results of the studies confirmed the model adequacy.

Anti-Bacterial Agents↗
PubMed2004

The effect of prosthetic mass properties on the gait of transtibial amputees--a mathematical model.

PURPOSE: Present models in the literature, predicting that prostheses should not be too lightweight, are not supported by empirical evidence. Recent studies suggest that these models are incorrectly based on the assumption that the swing phase is uninfluenced by muscle activity. The purpose of the present study was to introduce a new mathematical model to predict the effect of mass properties on the gait of transtibial amputees, based on experimental findings that subjects adapt to mass perturbations by maintaining the same joint kinematics. METHOD: Effect of mass perturbations on the lower leg was evaluated in terms of muscular cost and forces between stump and socket, using a linked-segment model of the swing phase. Gait analysis and anthropometric data from 10 transtibial amputees were used as model input. RESULTS: Location of perturbation strongly influenced the muscular cost. Cost generally increased after distally adding mass but decreased after proximally adding mass to the lower leg. Stump-socket interface forces always increased after mass addition. CONCLUSIONS: A new model was introduced, predicting that the weight of distally located components (e.g. foot, ankle, shoe) strongly influence the estimated muscular cost, in contrast to proximal components. A comparison with experimental literature suggests this new model better describes the experimental data than existing models.

Adult↗
PubMed1997

Effect of haemoglobin concentration on brain oxygenation in focal stroke: a mathematical modelling study.

Acute perioperative anaemia may affect neurological injury from permanent focal ischaemic insults. We modelled the opposing effects of haemodilution (increasing cerebral blood flow, decreasing arterial oxygen content) on oxygen availability and uptake in the ischaemic penumbra. First, we validated a mathematical model of regional cerebral oxygen uptake by using published arterial oxygen content and cerebral blood flow values from normal rabbits with progressive anaemia. Then we applied the model to the problem of interest (i.e. the ischaemic penumbra of a focal embolic stroke). We re-analysed published experimental data giving the cerebral blood flow response to anaemia in the ischaemic penumbra. Penumbral extraction reserves were nearly exhausted at a haemoglobin concentration of approximately 10g 100ml-1. Oxygen uptake in the ischaemic penumbra decreased progressively when haemoglobin concentrations decreased to less than 10g 100ml-1. We conclude that, given the available clinical and experimental literature, and until a suitable randomized clinical study has been performed, a haemoglobin concentration of 10 g 100 ml-1 is the rational transfusion "trigger" for the acutely anaemic stroke patient.

Anemia↗
PubMed2004

Mathematical modeling of cardiovascular system dynamics using a lumped parameter method.

This work reviews the main aspects of cardiovascular system dynamics with an emphasis on modeling hemodynamic characteristics by the use of a lumped parameter approach. The methodological and physiological aspects of the circulation dynamics are summarized with the help of existing mathematical models. The main characteristics of the hemodynamic elements, such as the heart and arterial and venous systems, are first described. Distributed models of an arterial network are introduced, and their characteristics are compared with those of lumped parameter models. We also discuss the nonlinear characteristics of the pressure-volume relationship in veins. Then the control pathways that participate in feedback mechanisms (baroreceptors and cardiopulmonary receptors) are described to explain the interaction between hemodynamics and autonomic nerve control in the circulation. Based on a set-point model, the computational aspects of reflex control are explained.

Animals↗
PubMed2006

A mathematical model gives insights into nutritional and genetic aspects of folate-mediated one-carbon metabolism.

Impaired folate-mediated 1-carbon metabolism has been linked to multiple disease outcomes. A better understanding of the nutritional and genetic influences on this complex biochemical pathway is needed to comprehend their impact on human health. To this end, we created a mathematical model of folate-mediated 1-carbon metabolism. The model uses published data on folate enzyme kinetics and regulatory mechanisms to simulate the impact of genetic and nutritional variation on critical aspects of the pathway. We found that the model predictions match experimental data, while providing novel insights into pathway kinetics. Our primary observations were as follows: 1) the inverse association between folate and homocysteine is strongest at very low folate concentrations, but there is no association at high folate concentrations; 2) the DNA methylation reaction rate is relatively insensitive to changes in folate pool size; and 3) as folate concentrations become very high, enzyme velocities decrease. With regard to polymorphisms in 5,10-methylenetetrahydrofolate reductase (MTHFR), the modeling predicts that decrease MTHFR activity reduces concentrations of S-adenosylmethionine and 5-methyltetrahydrofolate, as well as DNA methylation, while modestly increasing S-adenosylhomocysteine and homocysteine concentrations and thymidine or purine synthesis. Decreased folate together with a simulated vitamin B-12 deficiency results in decreases in DNA methylation and purine and thymidine synthesis. Decreased MTHFR activity superimposed on the B-12 deficiency appears to reverse the declines in purine and thymidine synthesis. These mathematical simulations of folate-mediated 1-carbon metabolism provide a cost-efficient approach to in silico experimentation that can complement and help guide laboratory studies.

Betaine↗
PubMed1992

A mathematical model of axillary lymph node involvement based on 1446 complete axillary dissections in patients with breast carcinoma.

The major prognostic indicator in patients with breast cancer is the presence of metastases in axillary lymph nodes. The authors developed a mathematical model, based on 1446 complete axillary dissections performed in Milan between 1983 and 1986, and determined the following: (1) the sample size from Level I necessary for a 90% certainty degree of N0 axillary status; (2) the probability of residual tumor in the axilla after axillary sampling from Level I; and (3) the maximum number of involved axillary nodes in Levels I, II, and III to be expected (90% certainty) after sampling from Level I. Thus, this model permitted the determination of the cutoff level for a true N0 axillary status when only a few nodes are sampled from Level I. The cutoff level for a T1 primary tumor is ten axillary nodes removed and found uninvolved. Also, this model provides guidance in managing possible residual tumor after an incomplete axillary dissection. This information is important in indicating adjuvant axillary radiation therapy and chemotherapy or hormone therapy.

Adult↗
PubMed1997

A mathematical model to determine the optimal number of fragments for comparison of bacterial chromosomic macrorestriction patterns.

To our knowledge, although comparison of chromosomic macrorestriction patterns has become one of the most feasible molecular tools of the current microbial taxonomy, a mathematical approach to optimize the choice of a restriction enzyme among the endonucleases tested for such comparison has not been previously described. The coincidence of restriction patterns for two tested bacterial strains with this chosen endonuclease will ensure a high genetic relatedness between them. We report a mathematical model to determine the probability of hazardously obtaining a particular chromosomic macrorestriction pattern by PFGE and to calculate the optimal number of fragments for its comparison. The model presented allows us to determine the optimal number of fragments in order to compare chromosomic restriction patterns. The model calculates this values as a function of the chromosome size and the restriction site length. The model is not useful for choosing a restriction enzyme previous to experimental steps, but as a tool for the choice of the restriction enzyme that yields the lowest probability of hazardously obtaining coincidences of chromosomic patterns. The applicability of this model has been exemplified by determining the optimal number of fragments for some well-characterized bacteria and by comparing these values with those that have been experimentally used.

Bacteria↗
PubMed2005

A whole-plant mathematical model for the phytoextraction of lead (Pb) by maize.

Phytoextraction is a technology that uses plants to remove heavy metals from contaminated soils. Although it is economically attractive compared to other methods, little attention has been paid to the mathematical modeling of the mechanisms involved. In this work, we simulate the phytoextraction of Pb using a mechanistic system dynamics modelling approach and the physiology model of maize (Zea mays) as a model system as it is a good Pb accumulator and translocator. Simulation results showed that precipitation is the most important mechanism related to the uptake of Pb from the ground. The most important model parameters have been identified through sensitivity analysis.

Biodegradation, Environmental↗
PubMed1993

An improved mathematical model of hydrodynamical self-cleansing of pulmonary alveoli.

In the present paper we postulate a hydrodynamical mechanism of pulmonary alveoli cleansing and explain the role of the lung surfactant system in this phenomenon. Then a new, significantly refined mathematical model of the dynamics of the layer lining alveoli is derived and tested numerically in order to check theoretically whether the mechanism postulated can explain the phenomenon observed and to establish the influence of various physicochemical and physiological parameters on the rate of alveolar cleansing. The results obtained confirmed our hypothesis and two examples of the model verification were also shown.

Humans↗
PubMed1990

Correlation of umbilical cord whole blood viscosity and the presence of fetal distress at birth: a mathematical modelling study.

This study was designed to investigate the relationship between umbilical cord blood viscosity and clinical parameters such as maternal parity, maternal smoking, mode of delivery, sex of infant and the incidence of fetal distress at birth using mathematical modelling. The results demonstrated vaginal delivery, male infants, infants of primigravidas and low cord whole blood viscosity at a high shear rate were covariables and were associated with an increased incidence of fetal distress and low Apgar scores.

Adult↗