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PubMedDate not supplied

Development of a transient segregated mathematical model of the semicontinuous microbial production process of dihydroxyacetone.

For the mathematical description of the semicontinuous two-stage repeated-fed-batch fermentation of dihydroxyacetone (DHA), a novel segregated model incorporating transient growth rates was developed. The fermentation process was carried out in two stages. A viable, not irreversibly product-inhibited culture was maintained in the first reactor stage until a predetermined DHA threshold value was reached. In the second reactor stage, high final product concentrations of up to 220 g L(-1) were reached while the culture was irreversibly product-inhibited. The experimentally observed changes of the physiological state of the culture due to product inhibition were taken into account by introducing a segregation into the mathematical model. It was shown that the state of the cells was dependent on the current environment and on the previous history. This phenomenon was considered in the model by utilizing delay time equations for the specific rates of growth on the primary and the secondary substrate. A comparison with reproducible measurements gave a good correlation between computation and experiment. The mathematical model was validated using independent own experimental data. A comparison with a stationary and nonsegregated model demonstrated the essential improvements of the novel model. It was deduced from the model calculations that high product formation rates of 3.3-3.5 g L(-1) h(-1) as well as high final DHA concentrations of 196-215 g L(-1) can be obtained with a residual broth volume in the first reactor stage of 2% and a DHA threshold value in the range of 100-110 g L(-1).

Bioreactors↗
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↗
PubMed1992

A mathematical model for the growth and classification of a solid tumor: a new approach via nonlinear elasticity theory using strain-energy functions.

Medically, tumors are classified into two important classes--benign and malignant. Generally speaking, the two classes display different behaviour with regard to their rate and manner of growth and subsequent possible spread. In this paper, we formulate a new approach to tumor growth using results and techniques from nonlinear elasticity theory. A mathematical model is given for the growth of a solid tumor using membrane and thick-shell theory. A central feature of the model is the characterization of the material composition of the tumor through the use of a strain energy function, thus permitting a mathematical description of the degree of differentiation of the tumor explicitly in the model. Conditions are given in terms of the strain energy function for the processes of invasion and metastasis occurring in a tumor, being interpreted as the bifurcation modes of the spherical shell, which the tumor is essentially modeled as. Our results are compared with actual medical experimental results and with the general behavior shown by benign and malignant tumors. Finally, we use these results in conjunction with aspects of surface morphogenesis of tumors (in particular, the Gaussian and mean curvatures of the surface of a solid tumor) in an attempt to produce a mathematical formulation and description of the important medical processes of staging and grading cancers. We hope that this approach may form the basis of a practical application.

Animals↗
PubMed1998

Mathematical modelling of effectiveness.

The effectiveness of a vaccine can be broadly defined as a practical measure of its costs and benefits when used in a community setting. What then is the relationship between a vaccine's efficacy and its effectiveness? Effectiveness certainly includes efficacy, but also encompasses secondary effects of vaccination, long-term efficacy of a vaccine (beyond that measured in conventional efficacy trials), the impact of vaccinating against one strain upon cross-reacting infections, costs of vaccination programmes and logistic considerations for vaccine delivery. This paper considers some of the biological determinants of effectiveness namely; secondary effects, long-term efficacy and competitive interactions amongst strains. Mathematical models of the transmission dynamics of infection and its disruption by vaccination are used as tools to help unravel some of the complexities that may arise when making interventions in non-linear biological systems.

Clinical Trials as Topic↗
PubMed1987

Sensitivity of RNA synthesis to actinomycin D inhibition is dependent on the frequency of transcription: a mathematical model.

The synthesis of ribosomal RNA is known to be up to 100-fold more sensitive to inhibition by actinomycin D than is messenger RNA. A model is presented here to explain the dose-response kinetics of this inhibition. The basic concept is that on very actively transcribed genes, such as ribosomal DNA, the first bound actinomycin D will sterically affect those densely packed polymerase molecules between it and the promoter, causing them to stack up into the promoter and interfere with the initiation of RNA synthesis. However, on less active genes, where the polymerases are widely spaced, the drug will inhibit individual polymerasas independently and only at the actinomycin blockade. Counteracting these inhibitory effects will be the tendency of genes bound with actinomycin to accumulate additional polymerases. A mathematical model is described which successfully explains previously reported dose-response kinetics of actinomycin inhibition in both frequently and infrequently transcribed genes. The analysis indicates that actinomycin inhibition is dependent on both polymerase packing and on gene size. The dose-response kinetics can be used to estimate both the size and transcriptional efficiency of individual genes. The model is also able to explain several other independent observations regarding the kinetics of inhibition of RNA synthesis by actinomycin.

Dactinomycin↗
PubMed1997

Mathematical model of the SOS response regulation of an excision repair deficient mutant of Escherichia coli after ultraviolet light irradiation.

A mathematical model for the development of the SOS signal in nucleotide-excision repair deficient Escherichia coli cells subjected to ultraviolet light irradiation is proposed, in which regions of single-stranded DNA (gaps) are created during replication of a damaged chromosome when the strand elongation stops at pyrimidine dimers. The concentration of single-stranded DNA of gaps as a function of time is obtained. The model for the interaction of the LexA and RecA proteins, a well-established key event in SOS regulation, is presented, resulting in a system of differential equations for the concentrations of LexA, RecA and activated RecA proteins. The simulated LexA protein kinetic curves agree with the experimental data for two excision repair deficient mutants: uvrA6 and dnaC28 uvrB(del), which is also a temperature-sensitive DNA replication initiation mutant. It is shown that the model can be used to quantitatively describe the kinetics of SOS response through the amount of the SOS signal (concentration of single-stranded DNA) in a cell as a function of time.

DNA Repair↗
PubMed2006

Mathematical modelling of aerosolised skin grafts incorporating keratinocyte clonal subtypes.

Severe burns can be very traumatic for the patient, and while burns caused by industrial or domestic accidents are common, there are also increasing numbers of burns associated with terrorism. A novel technique to assist in the healing process is to spray skin cells, keratinocytes, that are cultured from the patient's own tissue, directly onto the burn site. This process involves taking some undamaged skin from the patient, allowing the skin cells to proliferate rapidly in the laboratory over a period of 5-10 days, harvesting and separating the cells and then spraying them onto the burn. This paper deals with keratinocytes that have been cultured in vitro for a short period of time (early passage cultured cells). The spraying process has yet to be optimised with respect to the seeding density required for fastest re-epithelisation and thus there is a need for this process to be modelled. In this paper, we review some of the skin biology and develop a mathematical model of the growth patterns of cell colonies after they have been applied using a aerosolised technique. The model allows us to predict coverage over time and can be used as a decision support tool for clinicians.

Burns↗
PubMed2001

Estimation of early hepatitis C viral clearance in patients receiving daily interferon and ribavirin therapy using a mathematical model.

Patients with hepatitis C virus (HCV) genotype 1 infection are resistant to standard interferon (IFN) therapy. We used a mathematical model to estimate the duration of daily therapy necessary to maximize the number of patients achieving viral negativity before 12 weeks of therapy. Patients from a study to determine HCV RNA reduction over 4 weeks using 3 million units (MU), 5 MU, or 10 MU of IFN alfa daily plus Ribavirin were compared with a group receiving IFN alfa 3 MU three times a week. By extending the linear regression and prediction interval lines, the estimated time to negativity was greater than 12 weeks for the standard IFN group, 42 to greater than 84 days for the 3 MU IFN daily plus Ribavirin, 39 to 60 days for 5 MU IFN daily plus Ribavirin and 25 to 45 days for the 10 MU IFN daily and Ribavirin group, respectively. Thus, the use of a predictive model based on log transformation and linear regression of the early HCV RNA response suggests daily doses of 5 or 10 million units of IFN plus Ribavirin will be theoretically necessary for longer than 4 weeks to maximize the number of patients who clear virus by 12 weeks of therapy. This model may be useful in predicting response in groups of patients receiving other therapies.

Adult↗
PubMed2000

Mathematic modeling to predict abruptio placentae.

OBJECTIVE: This study was undertaken to identify correlates of abruptio placentae and to develop a mathematic model for the prediction of abruptio placentae. STUDY DESIGN: A total of 170,258 singleton birth records from 1991 to 1996 contained in the Schleswig-Holstein perinatal database were analyzed. Fifty-two recognized obstetric risk factors were subjected to univariate analysis. Correlates of abruptio placentae then underwent stepwise forward binary logistic regression. A constant value B(0), coefficients B(1) through B(p), an odds ratio, and a 95% confidence interval were calculated for individual correlates. RESULTS: Abruptio placentae occurred in 874 of 170,258 singleton gestations (0.5%). Of the 52 risk factors 31 proved to be correlates of abruptio placentae, with 16 among primiparous women and 25 among multiparous women. Ten correlates for primiparous, women and 13 for multiparous women emerged from the linear regression, with 7 correlates being shared by both primiparous and multiparous women. CONCLUSION: The probability that abruptio placentae will occur (p) can be calculated according to the following expression: p = e (z)/(1 + e (z)), where z = B(0) + B(1), em leaderB(p). For example, for a primiparous woman who smokes with bleeding at >28 weeks' gestation and a male fetus in the breech position, the following calculation would yield the chance of abruptio placentae:z = -2.25 + 2.51 + 0.41 + 0.24 + 0.60 = 1.51; p = e (1.51)/ (1 + e (1.51)) = 4. 53/5.53 = 0.82, or 82%.

Abruptio Placentae↗
PubMed1985

Mathematical models of central pattern generators in locomotion: III. Interlimb model for the cat.

Possible neural connective patterns and functions with respect to interlimb coordination are studied theoretically with a mathematical model of the central pattern generating system for cat locomotion. Activities in populations of neurons controlling limb joint flexors and extensors in all four limbs are represented by a system of nonlinear differential equations. Solutions of the system for various parameter values simulate various gaits of the cat. The model is shown to be capable of generating all gaits of the cat and accounting for corresponding phase changes in interlimb coordination. The model also exhibits smooth changes of gait, and smooth initiation and termination of stepping. Further, within each limb, muscle sequencing, step cycle phases, and flexor-extensor interactions can be studied. The model suggests that one of the simplest mechanisms for a central command system to change the gait is via inhibition of specific interlimb propriospinal pathways. In a final section, properties of both proposed single limb and interlimb models are reviewed with specific reference to planning future experimental and theoretical studies.

Journal Article↗
PubMed2004

Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour.

In this paper a mathematical model describing the growth of a solid tumour in the presence of an immune system response is presented. In particular, attention is focused upon the attack of tumour cells by so-called tumour-infiltrating cytotoxic lymphocytes (TICLs), in a small, multicellular tumour, without necrosis and at some stage prior to (tumour-induced) angiogenesis. At this stage the immune cells and the tumour cells are considered to be in a state of dynamic equilibrium--cancer dormancy--a phenomenon which has been observed in primary tumours, micrometastases and residual disease after ablation of the primary tumour. Nonetheless, the precise biochemical and cellular mechanisms by which TICLs control cancer dormancy are still poorly understood from a biological and immunological point of view. Therefore we focus on the analysis of the spatio-temporal dynamics of tumour cells, immune cells and chemokines in an immunogenic tumour. The lymphocytes are assumed to migrate into the growing solid tumour and interact with the tumour cells in such a way that lymphocyte-tumour cell complexes are formed. These complexes result in either the death of the tumour cells (the normal situation) or the inactivation (sometimes even the death) of the lymphocytes. The migration of the TICLs is determined by a combination of random motility and chemotaxis in response to the presence of chemokines. The resulting system of four nonlinear partial differential equations (TICLs, tumour cells, complexes and chemokines) is analysed and numerical simulations are presented. We consider two different tumour geometries--multi-layered cell growth and multi-cellular spheroid growth. The numerical simulations demonstrate the existence of cell distributions that are quasi-stationary in time and heterogeneous in space. A linear stability analysis of the underlying (spatially homogeneous) ordinary differential equation (ODE) kinetics coupled with a numerical investigation of the ODE system reveals the existence of a stable limit cycle. This is verified further when a subsequent bifurcation analysis is undertaken using a numerical continuation package. These results then explain the complex heterogeneous spatio-temporal dynamics observed in the partial differential equation (PDE) system. Our approach may lead to a deeper understanding of the phenomenon of cancer dormancy and may be helpful in the future development of more effective anti-cancer vaccines.

Cell Division↗
PubMed1992

Evaluation of four mathematical models of glucose and insulin dynamics with analysis of effects of age and obesity.

Despite there being a number of mathematical models of glucose and insulin dynamics, there have been no evaluations of their operation in large groups of subjects. We have carried out intravenous glucose tolerance tests on a group of 182 healthy males, with determination of plasma glucose, insulin, and C-peptide concentrations. Parameters of glucose and insulin dynamics were determined using the minimal model of glucose disappearance, a minimal model of peripheral insulin delivery, and two different models of pancreatic insulin secretion (models I and II). Successful identifications were obtained in 96, 95, 76, and 100% of cases, respectively. The models were evaluated in terms of their ability to recover effects of obesity and aging on carbohydrate metabolism. The glucose disappearance model successfully detected the insulin resistance of both obesity and aging, whereas the peripheral insulin delivery model indicated an increased responsiveness of insulin delivery to glucose in obesity but detected no significant change associated with age. No parameter of pancreatic secretion model I exhibited a significant association with either age or obesity. Insulin secretion model II indicated that the hyperinsulinemia accompanying obesity resulted from both increased pancreatic secretion and decreased hepatic insulin uptake.

Adult↗
PubMed2005

Dynamical mechanisms of pacemaker generation in IK1-downregulated human ventricular myocytes: insights from bifurcation analyses of a mathematical model.

Dynamical mechanisms of the biological pacemaker (BP) generation in human ventricular myocytes were investigated by bifurcation analyses of a mathematical model. Equilibrium points (EPs), periodic orbits, stability of EPs, and bifurcation points were determined as functions of bifurcation parameters, such as the maximum conductance of inward-rectifier K+ current (I(K1)), for constructing bifurcation diagrams. Stable limit cycles (BP activity) abruptly appeared around an unstable EP via a saddle-node bifurcation when I(K1) was suppressed by 84.6%. After the bifurcation at which a stable EP disappears, the I(K1)-reduced system has an unstable EP only, which is essentially important for stable pacemaking. To elucidate how individual sarcolemmal currents contribute to EP instability and BP generation, we further explored the bifurcation structures of the system during changes in L-type Ca2+ channel current (I(Ca,L)), delayed-rectifier K+ currents (I(K)), or Na(+)/Ca2+ exchanger current (I(NaCa)). Our results suggest that 1), I(Ca,L) is, but I(K) or I(NaCa) is not, responsible for EP instability as a requisite to stable BP generation; 2), I(K) is indispensable for robust pacemaking with large amplitude, high upstroke velocity, and stable frequency; and 3), I(NaCa) is the dominant pacemaker current but is not necessarily required for the generation of spontaneous oscillations.

Biological Clocks↗
PubMed2000

Mathematical modeling of the effect of the sarcoplasmic reticulum calcium pump function on load dependent myocardial relaxation.

Earlier, we developed a mathematical model of myocardial contraction-relaxation cycle regulation. A great number of mechanical experiments was simulated in the model, the phenomenon of load dependent relaxation (LDR) included. In the present work we used the same model to analyze experimental data revealing that high temperature leads to reduction of LDR. We simulated three main factors arising due to high temperature, which a priori may cause LDR reduction: increasing the cross-bridges cycling rate, decreasing the duration of the Ca transient ascending limb, and increasing Ca pumping rate. Indeed, these factors together result in LDR reduction; i.e., the model correctly simulates the effect of high temperature on LDR in general. At the same time, the sensitivity of LDR to the third factor is much higher than to the first and the second ones; i.e., increasing the rate of Ca pumping is sufficient to induce the observed effect in the framework of the model. This seems to contrast with the result of our previous study dealing with the simulation of LDR disappearance due to increasing Ca pumping rate as it happens during relatively severe cardiac hypertrophy. However, the model analysis shows that the specific mechanism underlying the change in Ca pumping rate in either case is extremely important for the effect on LDR. Particularly, the model predicts that LDR will reduce if this rate increases due to enhanced ATP hydrolysis rate by the Ca pump; and vice versa, if this rate increases due to decreasing retroinhibition of the pump ATPase, it may result in LDR increase. Probably, but the first mechanism is operational due to high temperature and makes LDR to reduce, whereas slowing down Ca pumping due to increasing retroinhibition results in LDR disappearance during severe cardiac hypertrophy.

Adenosine Triphosphate↗
PubMedDate not supplied

[A mathematical model of the role of Ca2+/calmodulin-dependent protein kinase in the long term increase in effectiveness of synaptic plasticity].

A mathematical model describing initiation and restoring of the long-term potentiation (LTP) is proposed. This model is based on an assumption that Ca2+/Calmodulin-dependent protein kinase from some of second messengers exists in a number of states. The protein kinase ability for securing LTP restoring is connected with autophosphorylation.

Calcium-Calmodulin-Dependent Protein Kinases↗
PubMed1994

Mathematical modelling of immunotherapy in HIV infection.

The effect of active or passive immunotherapy on HIV infection was simulated using a mathematical model of CD4+ lymphocyte depletion. Permanently effective active immunotherapy increased CD4+ lymphocyte counts to a steady-state level depending on the intensity of the therapy. Active HIV immunization effective for one or more years increased CD4+ lymphocyte counts during the treatment period and prolonged survival substantially; this prolongation exceeded the time interval of therapy duration. Intensive passive immunotherapy by anti-HIV antibodies led to a temporary increase of CD4+ lymphocyte numbers and an apparent prolongation of survival.

CD4 Lymphocyte Count↗
PubMed2005

Two mathematical models for the correction of carbohydrate and protein interference in the determination of uronic acids by the m-hydroxydiphenyl method.

The most common method in the routine determination of uronic acids, the m-hydroxydiphenyl reaction, recently adapted to rapid microplate analysis, has as a main inconvenience, in any one of their modalities, interferences due to the frequent presence of proteins and neutral carbohydrates in the samples. Corresponding corrections in the literature are unsatisfactory when applied to complex matrices, and further adaptation to the microplate analysis is not free from additional problems. With particular reference to hyaluronic acid, the interactions between the principal reactants and the interfering materials are studied kinetically under realistic conditions, and simple mathematical models are proposed which satisfactorily describe the experimental results and allow adequate corrections to be made.

Animals↗
PubMed2003

League tables and school effectiveness: a mathematical model.

'School performance tables', an alphabetical list of secondary schools along with aggregates of their pupils' performances in national tests, have been published in the UK since 1992. Inevitably, the media have responded by publishing ranked 'league tables'. Despite concern over the potentially divisive effect of such tables, the current government has continued to publish this information in the same form. The effect of this information on standards and on the social make-up of the community has been keenly debated. Since there is no control group available that would allow us to investigate this issue directly, we present here a simple mathematical model. Our results indicate that, while random fluctuations from year to year can cause large distortions in the league-table positions, some schools still establish themselves as 'desirable'. To our surprise, we found that 'value-added' tables were no more accurate than tables based on raw exam scores, while a different method of drawing up the tables, in which exam results are averaged over a period of time, appears to give a much more reliable measure of school performance.

Adolescent↗