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At least 1,711 records · Page 95Linked to original sources
PubMed1976

[A mathematical model concerning the DNA-karyogram in connection with the cell cycle. I. Communication. The derivation of the DNA frequency distribution from the duration of the single phases of cell cycle (author's transl)].

Stimulated by our own experience on flow microfluorometry we establish a mathematical model concerning the connection between the duration of the single phases of cell cycle and frequency distribution of cell nuclei as a function of their DNA content. For the establishment of the equations we need some simplified suppositions. We interprete the distribution curve (DNA karyogram) as 3 superimposing portions: 1. A Gaussian distribution of G1-phase cells at the first or 2c-peak. 2. A Gaussian distribution of G2 + M phase cells at the second or 4c-peak (twofold DNA content). 3. Nuclei from the S-phase with DNA content between the mean values of the two Gaussian curves. Our model has the following pecularities: 1. The establishment of the equation for the curve and therefore the addition of the partial curves is done in a logarithmical (log-normal) system. Here we can assume the same standard deviation both for the first and the second peak. 2. The superimposing of the S-phase acts on the whole curve and not only between the mean values of the Gaussian curves. Here the integral of the Gaussian distribution is employed for the equation. The equations are elaborated for the whole curve with the periods of the single phases as parameter, for the positions of the maxima and the minimum and for the quotient of the arguments of the maxima ("rhythm of reduplication") as a function of the duration of the single phases. Some examples are given and drawn in diagrams. They demonstrate the shape of the DNA karyogram and the rhythm of reduplication as funtions of the duration of the single phases of the cell cycle. The transformation in the linear system distorts the shape of the curve up to the disappearance of the second peak. The results from the model are the base for the interpretation of DNA karyograms, originating for instance from cytophotometry, mainly from flow microfluorometry. With the model we can estimate a change in direction and quantity of the curves altered by different phases of the cell cycle.

Cell Division↗
PubMed2004

Mathematical modeling of RGS and G-protein regulation in yeast.

G-protein-activated signaling pathways are capable of adapting to a persistent external stimulus. Desensitization is thought to occur at the receptor level as well as through negative feedback by a family of proteins called regulators of G-protein signaling (RGS). The pheromone response pathway in yeast is a typical example of such a system, and the relative simplicity of this pathway makes it an attractive system in investigating the regulatory role of RGS proteins. Two studies have used computational modeling to gain insight into how this pathway is regulated (Hao et al., 2003; Yi et al., 2003). This article provides an introduction to computational analysis of signaling pathways by developing a mathematical model of the pheromone response pathway that synthesizes the results of these two investigations. Our model qualitatively captures many features of the pathway and suggests an additional mechanism for pathway inactivation. It also illustrates that a complete understanding of signaling pathways requires an investigation of their time-dependent behavior.

Computational Biology↗
PubMed2003

Nitric oxide delivery in stagnant systems via nitric oxide donors: a mathematical model.

As a small biological molecule, nitric oxide (NO), plays a key role in diverse functions including smooth muscle cell regulation, neurotransmission, inhibition of platelet aggregation, and cytotoxic actions. The assessment of NO effects in biological systems has extensively been studied using NO donor compounds that often have differing NO release mechanisms and kinetic rates. Due to the differing kinetic rates and release mechanisms, in addition to reactions involving NO (such as autoxidation of NO), the NO concentrations to which biological systems are exposed may vary significantly depending upon the NO donor compound. Thus, quantifying the effects of NO using different NO donors is difficult unless the NO concentration profile in the experimental system is predicted or measured. In this study, the spatial and temporal NO concentration in a stagnant system (such as a culture plate or micro-well) is modeled following the addition of an NO donor characterized with first-order NO release kinetics. Two NO donors were utilized: diethylamine NONOate (DEA/NO) and spermine NONOate (SPER/NO). The use of a mathematical model can eliminate the need of complex in situ NO measurements and be useful for predicting the physical loss of NO from the experimental system. In addition, properly scaling the NO concentration can be useful in estimating the maximum NO concentration that will exist in solution. The results show that under widely used in vitro experimental conditions, including varying NO donor concentrations, cellular oxygen consumption rates, and aqueous phase heights, the spatial and temporal NO concentration range can vary significantly. In addition, hypoxic conditions can occur in the vicinity of cells, and in some situations, the physical loss of NO from the experimental system may be significant.

Animals↗
PubMed2006

Insight into the basis of root growth in Arabidopsis thaliana provided by a simple mathematical model.

Plant organ growth changes under genetic and environmental influences can be observed as altered cell proliferation and volume growth. The two aspects are mutually dependent and intricately related. For comprehensive growth analysis, it is necessary to specify the relationship quantitatively. Here, we develop a simple mathematical model for this purpose. Our model assumes that the biological activity of a given organ is proportional to the cell number of the organ and is allocated into three aspects: cell proliferation, volume growth, and organ maintenance. We analyzed the growth of primary roots of Arabidopsis thaliana (L.) Heynh. in one tetraploid and four diploid strains using this model. The analysis determined various growth parameters, such as specific cost coefficients of cell proliferation and volume growth for each strain. The results provide insight into the basis of interstrain variations and ploidy effects in root growth.

Arabidopsis↗
PubMed1986

A new mathematical model of proliferation control during immune response.

A considerable proliferation of participating cells is a characteristic feature of the immune response. This proliferation may be controlled by Interleukin 2. Assumptions on the course of the immune response under such a control are formulated, and a new mathematical model of the immune response involving regulation of the proliferation of appropriate cells is constructed.

Antibody Formation↗
PubMed1996

A mathematical model for predicting trends in carbon monoxide emissions and exposures on urban arterial highways.

The roadway is one of the most important microenvironments for human exposure to carbon monoxide (CO). To evaluate long-term changes in pollutant exposure due to in-transit activities, a mathematical model has been developed to predict average daily vehicular emissions on highways. By utilizing measurements that are specific for a given location and year (e.g., traffic counts, fleet composition), this model can predict emissions for a specific roadway during various time periods of interest, allowing examination of long-term trends in human exposure to CO. For an arterial highway in northern California, this model predicts that CO emissions should have declined by 58% between 1980 and 1991, which agrees fairly well with field measurements of human exposure taken along that roadway during those two years. An additional reduction of up to 60% in CO emissions is predicted to occur between 1991 and 2002, due solely to the continued replacement of older cars with newer, cleaner vehicles.

Carbon Monoxide↗
PubMed2001

Relative significance of different pathways of immune reconstitution in HIV type 1 infection as estimated by mathematical modeling.

A major goal of antiretroviral HIV-1 therapy is the reversal of HIV-1-associated immunological dysfunction. However, the pathogenetic mechanisms involved and their significance are largely unknown. On the basis of the life cycle of naive, activated, and memory CD4(+) T cell subsets, a mathematical model of immune reconstitution was developed and applied to data for T cell subsets in individuals with acute or chronic HIV-1 infection receiving antiretroviral therapy. The final model that most accurately fitted the data, and resulted in realistic estimates for CD4(+) T cell turnover, considered three pathways of immune reconstitution for naive cells, including thymic production, peripheral expansion, and redistribution of naive cells from lymphoid tissue. The reconstitution of the memory compartment was fitted through differentiation and expansion of naive cells and peripheral expansion of memory cells as well as redistribution of memory cells trapped in the lymphoid tissue. Estimated median half-lives for naive and memory CD4(+) T cells were 114 and 21 days, while total production rates were 9.1 x 10(7) and 2.4 x 10(9) cells/day, respectively. Peripheral expansion and thymic production contributed equally to the regeneration of naive cells, but peripheral expansion of memory cells was larger than production of these cells by differentiation of naive cells. A comparison of immune reconstitution in acute and chronic HIV-1 infection revealed that, after adjustment for age, the main difference was the more rapid release of a larger number of naive cells in treated acute HIV-1 infection. Thymic function and peripheral expansion rates, however, were similar in both cohorts.

Acute Disease↗
PubMed2006

Mathematical model for the androgenic regulation of the prostate in intact and castrated adult male rats.

The testicular-hypothalamic-pituitary axis regulates male reproductive system functions. Understanding these regulatory mechanisms is important for assessing the reproductive effects of environmental and pharmaceutical androgenic and antiandrogenic compounds. A mathematical model for the dynamics of androgenic synthesis, transport, metabolism, and regulation of the adult rodent ventral prostate was developed on the basis of a model by Barton and Anderson (1997). The model describes the systemic and local kinetics of testosterone (T), 5alpha-dihydrotestosterone (DHT), and luteinizing hormone (LH), with metabolism of T to DHT by 5alpha-reductase in liver and prostate. Also included are feedback loops for the positive regulation of T synthesis by LH and negative regulation of LH by T and DHT. The model simulates maintenance of the prostate as a function of hormone concentrations and androgen receptor (AR)-mediated signal transduction. The regulatory processes involved in prostate size and function include cell proliferation, apoptosis, fluid production, and 5alpha-reductase activity. Each process is controlled through the occupancy of a representative gene by androgen-AR dimers. The model simulates prostate dynamics for intact, castrated, and intravenous T-injected rats. After calibration, the model accurately captures the castration-induced regression of the prostate compared with experimental data that show that the prostate regresses to approximately 17 and 5% of its intact weight at 14 and 30 days postcastration, respectively. The model also accurately predicts serum T and AR levels following castration compared with data. This model provides a framework for quantifying the kinetics and effects of environmental and pharmaceutical endocrine active compounds on the prostate.

Androgens↗
PubMed1994

Efficacy of the Frame and Hu mathematical model for the quantitative analysis of agents influencing growth of chick embryo fibroblasts.

The experiments on the effect of various sera and substratum surface area upon growth of chick embryo fibroblast-like cells in secondary cultures are described and discussed on the grounds of a mathematical model for growth of anchorage-dependent cells proposed by Frame and Hu [14]. The model and presented results demonstrate the mutual independence of the effects of agents influencing the rate of cell proliferation (i.e. accelerating or retarding growth) and the agents that modify the limitation of cell proliferation (i.e. maximum cell density at confluence). The model proposed by Frame and Hu due to its relative simplicity offers an easy mode of description and quantitative evaluation of experiments concerning cell growth regulation. It is shown that various sera added at constant concentration significantly modify the rate of cell proliferation with little effect upon the maximum cell density attainable. The cells grew much more slowly in the presence of calf serum than in the presence of chick serum and the addition of iron and zinc complexes to calf serum significantly accelerated cell growth. An increase in the substratum surface area by the addition of glass wool to culture vessels significantly increased cell density per constant volume of medium even when retardation of growth was observed. The results presented point to the need of direct cell counting for estimation of cell growth curves and discussion of effects of agents influencing parameters characterizing cell proliferation.

Aneuploidy↗
PubMed1998

Mathematical model of the fission yeast cell cycle with checkpoint controls at the G1/S, G2/M and metaphase/anaphase transitions.

All events of the fission yeast cell cycle can be orchestrated by fluctuations of a single cyclin-dependent protein kinase, the Cdc13/Cdc2 heterodimer. The G1/S transition is controlled by interactions of Cdc13/Cdc2 and its stoichiometric inhibitor, Rum1. The G2/M transition is regulated by a kinase-phosphatase pair, Wee1 and Cdc25, which determine the phosphorylation state of the Tyr-15 residue of Cdc2. The meta/anaphase transition is controlled by interactions between Cdc13/Cdc2 and the anaphase promoting complex, which labels Cdc13 subunits for proteolysis. We construct a mathematical model of fission yeast growth and division that encompasses all three crucial checkpoint controls. By numerical simulations we show that the model is consistent with a broad selection of cell cycle mutants, and we predict the phenotypes of several multiple-mutant strains that have not yet been constructed.

Anaphase↗
PubMed1977

[A mathematical model for the description of oxygen-diffusion in the intervillous space of the human placenta (author's transl)].

The oxygen consumption has a central place in the complicated interaction between diminished oxygen supply and degenerative trophoblastic tissue change. In the present investigation, that serves as a mathematical model, the problem of the diffusion equation for the constant state is discussed and solved. It is shown that the diminishing of length of the radius of the maternal blood compartment has the same meaning as the decrease in the flow velocity. The influence of the mass transfer coefficient h on the oxygen partial pressure and on the oxygen transfer is investigated. The influence of parameter variations on the placental alterations during toxemia is discussed and their clinical importance is obvious. Our theoretical model elusidates the value of an early therapeutical approach in the case of toxemia.

Blood Flow Velocity↗
PubMed2004

Static pressure-volume curve characteristics are moderate estimators of optimal airway pressures in a mathematical model of (primary/pulmonary) acute respiratory distress syndrome.

OBJECTIVE: To study the value of objective pressure-volume characteristics for predicting optimal airway pressures and the development of atelectasis and overstretching during a structured lung volume recruitment procedure with subsequent reduction in airway pressures. METHODS: We used a mathematical model of a lung with adjustable characteristics of acute respiratory distress syndrome (ARDS) characteristics. Simulations were performed in five grades of ARDS in the presence of pure alveolar or combined alveolar-small airway closure as well complete or incomplete lung volume recruitability. For each simulation optimal end-expiratory pressure was determined. A static pressure-volume curve was constructed and objective characteristics of this curve calculated. The predictive value of these characteristics for end-expiratory atelectasis, overstretching, and optimal end-expiratory pressure was assessed. RESULTS: Simultaneous alveolar recruitment and overstretching during inflation were more pronounced than alveolar derecruitment and overstretching during deflation. End-expiratory pressure needed to prevent significant alveolar collapse in severe ARDS resulted in maximal safe tidal volumes that may be insufficient for adequate ventilation using conventional mechanical ventilatory modes. Plateau pressures well below the "upper corner point" (airway pressure where compliance decreases) resulted in significant alveolar overstretching. CONCLUSIONS: A recruitment maneuver followed by subsequent reduction in airway pressure limits end-expiratory atelectasis, overstretching, and pressure. None of the objective characteristics of the pressure-volume curve was predictive for end-expiratory atelectasis, overstretching, or optimal airway pressure.

Humans↗
PubMed1999

Mathematical modeling of retinal birefringence scanning.

Retinal birefringence scanning (RBS) is a new technique that is used to detect the fixation of the eye remotely and noninvasively. The method is based on analysis of polarization changes induced by the retina. In this study, the principles of RBS were mathematically modeled to facilitate a better understanding of the origins of the signals obtained. Stokes vector analysis and Mueller matrix multiplication were augmented with Poincaré sphere representation. The cornea was modeled as a linear retarder. The foveal area was modeled as a radially symmetric birefringent medium. The model accurately predicted the frequency and phase of RBS signals obtained during central and paracentral fixation. The signal that indicates central fixation during RBS likely results from a combination of the radial birefringence of the Henle fibers and the overlying corneal birefringence.

Birefringence↗
PubMed2000

Estimation of the sporozoite rate of malaria vectors using the polymerase chain reaction and a mathematical model.

We developed a sensitive polymerase chain reaction (PCR) method for the detection of Plasmodium falciparum DNA from mosquitoes collected in the field. Plasmodium falciparum was detected from 15.2% of 1-parous mosquitoes, Anopheles farauti, in the Solomon Islands through use of the PCR method. A novel mathematical model was developed to estimate the sporozoite rate based on the malaria-positive rate of 1-parous mosquitoes. Using this model, the sporozoite rate of Anopheles farauti in the Solomon Islands was calculated to be 0.09%. This method enables estimation of the sporozoite rate based on a relatively small number (100-200) of mosquitoes compared with the number needed for the ELISA method.

Animals↗
PubMed1998

Numerical techniques and mathematical modelling for CI857-controlled gene expression and cell growth in recombinant E. coli.

Recombinant gene expression, monitored by beta-galactosidase activity, is studied in a pL, pR-CI857 plasmid expression system in temperature-induced E. coli batch cultures. The experimental procedure has been mathematically modelled, and the corresponding parameters are estimated from specific statistical and numerical methods, basically by using a global least-squares procedure under some constraints induced by the model. The numerical techniques proposed in this work act by accumulation of data coming from several runs of the modelled experiment, so that more accuracy is obtained in the parameter estimation. In particular, for the production process, an extra-model parameter depending on an indicator vector is introduced for each run of the experiment in order to globalize the data. The analysis of the data obtained leads to an integrated model for both cell growth and gene expression, which describes an asymmetric dynamics between culture growth and recombinant protein yield, and can serve to predict the maximal value of accumulated gene expression and the time required for it to be achieved at any age of the preinducing cell growth.

Algorithms↗
PubMed1991

A mathematical model of the relationship between cerebral blood volume and intracranial pressure changes: the generation of plateau waves.

The relationship between intracranial pressure (ICP), cerebral blood volume (CBV), cerebrospinal fluid dynamics, and the action of cerebral blood-flow (CBF) regulatory mechanisms is examined in this work with the help of an original mathematical model. In building the model, particular emphasis is placed on reproducing the mechanical properties of proximal cerebral arteries and small pial arterioles, and their active regulatory response to perfusion pressure and cerebral blood flow changes. The model allows experimental results on cerebral vessel dilatation and cerebral blood-flow regulation, following cerebral perfusion pressure decrease, to be satisfactorily reproduced. Moreover, the effect of cerebral blood volume changes--induced by autoregulatory adjustments--on the intracranial pressure time pattern can be examined at different levels of arterial hypotension. The results obtained with normal parameter values demonstrate that, at the lower limits of autoregulation, when dilatation of small arterioles becomes maximal, the increase in cerebral blood volume can cause a significant, transient increase in intracranial pressure. This antagonism between intracranial pressure and autoregulatory adjustments can lead to instability of the intracranial system in pathological conditions. In particular, analysis of the linearized system "in the small" demonstrates that an impairment in cerebrospinal fluid (CSF) reabsorption, a decrease in intracranial compliance and a high-regulatory capacity of the cerebrovascular bed are all conditions which can lead the system equilibrium to become unstable (i.e., the real part of at least one eigenvalue to turn out positive). Accordingly, mathematical simulation "in the large," in the above-mentioned conditions, exhibits intracranial pressure periodic fluctuations which closely resemble, in amplitude, duration, frequency and shape, the well-known Lundberg A-waves (or plateau waves).

Biomechanical Phenomena↗
PubMed2006

Systemic cancer progression and tumor dormancy: mathematical models meet single cell genomics.

Metastatic progression is thought to result from genetically advanced "fully-malignant" tumor cells. Within the concept the prevailing view holds that such cells disseminate mostly from large tumors and are capable of growing into metastases once they arrive at a distant site. Support for this scenario comes from numerous mouse models in which transplanted tumor cells grow into metastases within days or weeks. However, the assumption of such fully-malignant disseminating cells in human cancer is misleading and is neither supported by mathematical modeling of survival data from cancer patients nor by ex-vivo genomic data from disseminated cancer cells. For example, in breast cancer the growth of metastases is highly homogeneous and takes on average six years, the number of disseminated tumor cells before diagnosis of metastasis is similar for different tumor stages, and the genomic aberrations of disseminated cancer cells do rarely correspond to those in the primary tumor. Since these facts question conventional concepts of metastatic progression we provide a model of cancer progression in which time considerations and direct ex-vivo data form a starting point. In the proposed model tumor dormancy is a characteristic of almost all migrated tumor cells and metastatic growth is a rare, stochastic, evolutionary process of selection and mutation of cells that often disseminate shortly after transformation at the primary site.

Animals↗