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PubMed2002

Kinetic model for designing a cancer therapy.

A kinetic model has been developed to study cancer growth. Cancer growth has been considered as interaction between various independent but interacting compartments. The model considers cell growth and metastasis resulting in the formation of new tumor masses. Using certain representative parameter values, cell growth has been modeled in the absence and the presence of various cancer therapies. Based on this analysis, the critical parameters involved in cancer development have been identified. This model may thus be useful in studying and designing a cancer therapy using the data obtained from specific in vitro experiments.

Journal Article↗
PubMed2002

Kinetic model of DNA replication in eukaryotic organisms.

We formulate a kinetic model of DNA replication that quantitatively describes recent results on DNA replication in the in vitro system of Xenopus laevis prior to the mid-blastula transition. The model describes well a large amount of different data within a simple theoretical framework. This allows one, for the first time, to determine the parameters governing the DNA replication program in a eukaryote on a genome-wide basis. In particular, we have determined the frequency of origin activation in time and space during the cell cycle. Although we focus on a specific stage of development, this model can easily be adapted to describe replication in many other organisms, including budding yeast.

Animals↗
PubMed2006

Tools for kinetic modeling of biochemical networks.

The number of software packages for kinetic modeling of biochemical networks continues to grow. Although most packages share a common core of functionality, the specific capabilities and user interfaces of different packages mean that choosing the best package for a given task is not trivial. We compare 12 software packages with respect to their functionality, reliability, efficiency, user-friendliness and compatibility. Although most programs performed reliably in all numerical tasks tested, SBML compatibility and the set-up of multicompartmentalization are problematic in many packages. For simple models, GEPASI seems the best choice for non-expert users. For large-scale models, environments such as Jarnac/JDesigner are preferable, because they allow modular implementation of models. Virtual Cell is the most versatile program and provides the simplest and clearest functionality for setting up multicompartmentalization.

Biochemistry↗
PubMed2002

Helical nature of sperm swimming affects the fit of fertilization-kinetics models to empirical data.

Models of fertilization kinetics rely upon estimates of the swimming velocity of sperm to predict collision rates between egg and sperm. Most investigators measure sperm swimming velocity without accounting for the helical motion of sperm, thereby obtaining an inflated estimate of the velocity with which sperm approach eggs. In turn, models of fertilization predict inflated rates of sperm/egg collision. I observed sea urchin sperm colliding with eggs, quantified the rate of sperm/egg collision, and measured sperm velocity as a component of the helix through which they swim. I also adjusted the "target size" of eggs to reflect the diameter of the helix. My estimate of sperm swimming velocity is an order of magnitude lower than other estimates for the same species. By using helical parameters in fertilization kinetics models and accounting for dead sperm in laboratory trials, I was able to accurately predict lower rates of sperm/egg collision. Moreover, making these adjustments in the model increased the estimated proportion of sperm that initiate fertilization by 6- to 7-fold, suggesting that a better understanding of sperm swimming might lead to a more complete understanding of fertilization biology and natural selection on gamete traits.

Animals↗
PubMed2004

Kinetic models for volatile chlorinated hydrocarbons removal by zero-valent iron.

Kinetic models for removal of trichloroethylene, trichloromethane and tetrachloroethylene from water by zero-valent iron were tested. The dehalogenation reactions were modelled by first-order and power law models, pseudo-stationary models with a controlling surface reaction rate and non-stationary models without the assumption of rate controlling step. Regression analysis proved, that the first-order kinetic is not suitable for the modelling of chlorinated hydrocarbons dechlorination. On the other hand, power law models, Langmuir-Hinshelwood analogy models and general models of heterogeneous reactions are reliable for the kinetic description of dechlorination. In spite of an empirical or semi-empirical character, the power law models and models of controlling surface reaction rate can be recommended for the regression analysis owing to the their simple regression parameters interpretation.

Hydrocarbons, Chlorinated↗
PubMed2001

COMKAT: compartment model kinetic analysis tool.

UNLABELLED: Compartment models are the basis for most physiologically based quantification of nuclear medicine data. Although some software packages are available for this purpose, many are expensive, run on relatively few types of computers or are of limited capability, and cannot be extended because of the unavailability of source code. Consequently, institutions with modeling expertise often develop software for themselves, which has the disadvantages of lack of standardization and possible replication of effort. Therefore, general-purpose compartment-modeling software distributed with source code would be a welcome resource for the nuclear medicine community. METHODS: We formulated a mathematic framework within which compartment models containing unimolecular and bimolecular (receptor saturation) kinetics can be described. We implemented this framework within MATLAB and call the resultant software COMKAT (Compartment Model Kinetic Analysis Tool). RESULTS: COMKAT simplifies the process of defining and solving standard blood flow, 18F-FDG, and receptor models as well as models of a user's own design. In particular, COMKAT automatically defines and implements state, analytic sensitivity, and Jacobian equations. Given these, COMKAT can perform simulations in which model outputs are solved for specified parameter values, thereby allowing the user to predict how sensitive data are to these parameters. In addition, COMKAT can be used to estimate values for the parameters by fitting model output to experimental data. COMKAT is equipped with command-line and graphic user interfaces from which the user can access these features. Examples of these applications are presented along with validation and performance summaries. CONCLUSION: COMKAT is a useful software tool and is available without cost to researchers, at www.nuclear.uhrad.com/comkat.

Computer Simulation↗
PubMed2001

An analytically solved kinetic model for pesticide degradation in single compartment systems.

An analytical kinetic model was developed to simulate the degradation of pesticides in systems such as soil or water. Based on a single compartment system, a set of simultaneous first-order differential equations was analytically solved by the eigenvalue and eigenvector method. The developed model is capable of simulating the concentrations of parent compound and any net of degradation products connected by irreversible reactions.

Biodegradation, Environmental↗
PubMed1998

Temporal sampling requirements for the tracer kinetics modeling of breast disease.

The physiological parameters measured in the tracer kinetics modeling of data from a dynamic contrast-enhanced magnetic resonance (MR) breast exam (blood flow-extraction fraction product [FE], volume of the extracellular extravascular space [Ve], and blood volume [Vb]) may enable non-invasive diagnosis of breast cancer. One of the factors that compromises the accuracy and precision of the parameter estimates, and therefore their diagnostic potential, is the temporal resolution of the MR scans used to measure contrast agent (gadolinium-diethylenetriamine pentaacetic acid [Gd-DTPA]) concentration in an artery (arterial input function [AIF]) and in the tissue (tissue residue function [TRF]). Using computer simulations, we have examined, for several AIF widths, the errors introduced into estimates of tracer kinetic parameters in breast tissue due to insufficient temporal sampling. Temporal sampling errors can be viewed as uncertainties and biases in the parameter estimates introduced by the uncertainty in the relative alignments of the AIF, TRF, and sampling grid. These effects arise from the model's inherent sensitivity to error in either the AIF or TRF, which is dependent on the values of the tracer kinetic parameters and increases with AIF width. Based on the results of the simulations, to ensure that the error in FE and Ve will be under 10% of their true values, we recommend a rapid bolus injection of contrast agent (approximately 10 s), that the AIF be sampled every second, and that the TRF be sampled every 16 s or less. An accurate measurement of Vb requires that the TRF be sampled at least every 4 s. The results of these investigations can be used to set minimum dynamic imaging rates for tracer kinetics modeling of the breast.

Breast↗
PubMed1986

Kinetic models of induction: I. Persistence of the inducing substance.

A kinetic model for induction is presented which includes the pharmacokinetics of the inducing agent. When simulations based on this model are carried out, they demonstrate situations where the observed rate constant governing the change from the basal to the induced state, or from the induced to the basal state, differs substantially from the true turnover rate constant. This arises from the confounding influences of the accumulation or persistence of either the inducing agent itself or some intermediary metabolic process. Depending on the relationships between the kinetic constants, there are four experimental subsets which require various interpretative schemes to obtain a correct estimate of the turnover rate constant. These interpretive schemes point out the necessity of measuring the pharmacokinetics of the inducer in all experiments.

Enzyme Induction↗
PubMed1996

First-order kinetic model of Alzheimer's beta-amyloid fibril extension in vitro.

Recently, several studies have proposed models describing the mechanisms of Alzheimer's beta-amyloid fibril formation in vitro. However, these models are somewhat controversial and no exact kinetic analyses measuring the polymerization velocity as an indicator of the reaction, have thus far been available. We first formed beta-amyloid fibrils from a synthetic peptide, beta-amyloid(1-40), and determined the optimum conditions for quantitative fluorometry of these beta-amyloid fibrils with thioflavine T. Optimum fluorescence measurements of beta-amyloid fibrils were obtained at the excitation and emission wavelengths of 446 and 490 nm, respectively, with the reaction mixture containing 5 microM thioflavine T and 50 mM of glycine-NaOH buffer, pH 8.5. We then focused our study on the extension phase of beta-amyloid fibril formation in vitro. When beta-amyloid fibrils were incubated with monomeric beta-amyloid(1-40) in conditions where de novo seed formation does not occur, the extension of beta-amyloid fibrils was observed with electron microscopy. Quantitative fluorometry revealed that: (a) extension of amyloid fibrils proceeded by a pseudo-first-order exponential increase as measured by the fluorescence of thioflavine T; (b) the rate of extension was maximum around pH 7.5, and was dependent on the incubation temperature. Between 20 and 37 degrees C, good linearity was observed between the common logarithm of the initial rate and the reciprocal of the absolute temperature; (c) the rate of polymerization was found to be proportional to the product of beta-amyloid fibrils number concentration and the beta-amyloid(1-40) concentration; (d) the net rate of extension was the sum of the rates of polymerization and depolymerization. These results show that beta-amyloid fibril formation can be explained by a first-order kinetic model: i.e., the extension of beta-amyloid fibrils proceeds via the consecutive association of beta-amyloid(1-40) onto the ends of existing fibrils.

Alzheimer Disease↗
PubMed2006

Chemical kinetic modeling study of the effects of oxygenated hydrocarbons on soot emissions from diesel engines.

A detailed chemical kinetic modeling approach is used to examine the phenomenon of suppression of sooting in diesel engines by the addition of oxygenated hydrocarbon species to the fuel. This suppression, which has been observed experimentally for a few years, is explained kinetically as a reduction in concentrations of soot precursors present in the hot products of a fuel-rich diesel ignition zone when oxygenates are included. The kinetic model is also used to show how different oxygenates, ester structures in particular, can have different soot-suppression efficiencies due to differences in the molecular structure of the oxygenated species.

Journal Article↗
PubMed1970

Kinetic model of conduction changes across excitable membranes.

A kinetic model describing conduction changes across excitable membranes is proposed. It assumes that a population of discrete membrane sites is distributed among several distinct functional states determined by the voltage across the membrane. Interconversion of these states is postulated to occur by first-order reactions. It provides a satisfactory description of the central aspects of excitable membrane behavior, including current-time and current-voltage relationships, action potential, and effects of inhibitors.

Acridines↗
PubMed2006

Data analysis of kinetic modelling used in drug stability studies: isothermal versus nonisothermal assays.

PURPOSE: Kinetic modelling was applied to predict the stability of cholecystokinin fragment CCK-4 in aqueous solution, which was analyzed by isothermal and nonisothermal methods using a validated stability indicating HPLC method. METHODS: The isothermal studies were performed in the temperature range 40 to 80 degrees C at pH 12 and ionic strength 0.01 M as constants, whereas nonisothermal stability studies were performed using a linear increasing temperature program, heating rate 0.25 degrees C/h and a temperature interval 40-82 degrees C. The isothermal studies require two-step linear regression to estimate the parameters, resulting in a well-defined confidence interval. Nonisothermal kinetic studies require nonlinear or linear regression by previous transformation of data to estimate the parameters. In this case, the two most popular approaches, derivative and integral, were used and compared. RESULTS: Under isothermal conditions, an apparent first-order degradation process was observed at all temperatures. The linear Arrhenius plot suggested that the CCK-4 degradation mechanism was the same within the studied temperature range, with quite large uncertainties due to the small number of degrees of freedom based only on the scatter in the plot, and giving an estimated shelf life at 25 degrees C of 35.2 days. The derivative approach yields high variability in the Arrhenius parameters, since they are dependent on the number of polynomial terms chosen, so several statistical criteria were applied to select the best model. The integral approach allows activation parameters to be calculated directly from experimental data, and provides results in good agreement with those of the traditional method, but have the advantage that the uncertainty in the final result directly reflects the goodness of fit of the experimental data to the chosen kinetic model. The application of the bootstrap technique to estimating confidence limits for the Arrhenius parameters and shelf life is also illustrated, and shows there is no difference between the asymptotic and bootstrap confidence intervals. CONCLUSIONS: Nonisothermal studies give us fast and valuable information about drug stability, although their potential for predicting isothermal behaviour is conditioned by the data analysis method applied.

Drug Stability↗
PubMed1996

Tracer kinetic modelling of receptor data with mathematical metabolite correction.

Quantitation of metabolic processes with dynamic positron emission tomography (PET) and tracer kinetic modelling relies on the time course of authentic ligand in plasma, i.e. the input curve. The determination of the latter often requires the measurement of labelled metabolites, a laborious procedure. In this study we examined the possibility of mathematical metabolite correction, which might obviate the need for actual metabolite measurements. Mathematical metabolite correction was implemented by estimating the input curve together with kinetic tissue parameters. The general feasibility of the approach was evaluated in a Monte Carlo simulation using a two tissue compartment model. The method was then applied to a series of five human carbon-11 iomazenil PET studies. The measured cerebral tissue time-activity curves were fitted with a single tissue compartment model. For mathematical metabolite correction the input curve following the peak was approximated by a sum of three decaying exponentials, the amplitudes and characteristic half-times of which were then estimated by the fitting routine. In the simulation study the parameters used to generate synthetic tissue time-activity curves (K1-k4) were refitted with reasonable identifiability when using mathematical metabolite correction. Absolute quantitation of distribution volumes was found to be possible provided that the metabolite and the kinetic models are adequate. If the kinetic model is oversimplified, the linearity of the correlation between true and estimated distribution volumes is still maintained, although the linear regression becomes dependent on the input curve. These simulation results were confirmed when applying mathematical metabolite correction to the [11C]iomazenil study. Estimates of the distribution volume calculated with a measured input curve were linearly related to the estimates calculated using mathematical metabolite correction with correlation coefficients >0.990. However, the slope of the regression line displayed considerable variability among the subjects (0.33-0.95), demonstrating that absolute quantitation of the distribution volume was impaired. Mathematical metabolite correction is a feasible method and may prove useful in cases where actual metabolite data cannot be obtained. The potential for absolute quantitation seems limited, but the method allows the quantitative assessment of regional ratios of receptor measures.

Adult↗
PubMed2000

In vitro skin penetration and degradation of peptides and their analysis using a kinetic model.

The main purpose of this study was to estimate the net percutaneous absorption of physiologically active peptides in vitro. The degradation of two peptides, Leu-enkephalin (Enk) and Tyr-Pro-Leu-Gly amide (TPLG), during skin penetration and on the dermal side following penetration, and the prevention of degradation by some protease inhibitors, were investigated using rat skin in vitro. In addition, these permeation and degradation data were analyzed using a kinetic model. These peptides were rapidly degraded in the receptor fluid of a Franz diffusion cell (rate constant: 0.977 h(-1) for Enk and 0.250 h(-1) for TPLG). The addition of phenylmethylsulfonyl fluoride (PMSF) and phenanthroline and the pretreatment of skin with these inhibitors prevented almost completely any degradation in the receptor fluid and skin, respectively. The pretreatment of skin with PMSF and phenanthroline had no effect on the penetration of dextran (1000 Da). The degradation rate constant during skin penetration, calculated from the difference in the penetration rate constants via pretreated and untreated skins, was also high (0.037 h(-1) for Enk and 0.050 h(-1) for TPLG). A kinetic model including an input rate (zero-order), the permeation rate across the viable skin (first-order) and the degradation rate in skin (first-order) was sufficient to describe the apparent steady-state flux of the peptides through skin. We have, thus, established a method for measuring the true flux of peptides across skin in vitro and a kinetic model which simply describes the skin penetration of peptides.

Administration, Cutaneous↗
PubMed2000

A Sorption-Kinetic Model for Surfactant-Driven Spreading of Aqueous Drops on Insoluble Liquid Substrates.

Spreading of aqueous drops on hydrocarbon liquids occurs only when particular surfactants are added to the droplets above a critical concentration. For surfactant solutions of didodecyl ammonium bromide (DDAB) in water spreading over mineral oil, rates of droplet expansion are much slower than those corresponding to pure liquids spreading over immiscible liquid substrates with the same initial spreading coefficients. We present a sorption-kinetic model to explain quantitatively the spreading histories for aqueous DDAB droplets on mineral oil. Due to surfactant transport limitations, spreading occurs only when enough surfactant arrives at the dilating lens surfaces to establish a slightly positive, but near-zero spreading coefficient. We solve the convective diffusion equation for a cylindrical disk-like lens under the integral constraint of a constant surfactant adsorption density corresponding to a near-zero spreading coefficient. All observed spreading behavior is correctly portrayed by the proposed sorption-kinetic model including final equilibrium lens formation and spreading rates that are sensibly independent of drop volume, but are strongly dependent on drop surfactant concentration. Quantitative agreement is found with the experimental spreading data for a surfactant diffusion coefficient of 6x10(-12) m(2)/s and an effective adsorption rate constant of 6.5x10(-7) m/s. Both values prove physically reasonable. The sorption-kinetic model provides a new mechanism for understanding slow surfactant-driven spreading. Copyright 2000 Academic Press.

Journal Article↗
PubMed1995

Kinetic models for nucleocytoplasmic transport of messenger RNA.

Much is known about the mechanism by which mRNAs cross the nuclear envelope (the translocation stage of nucleocytoplasmic transport), but far less is known about the preceding (intranuclear migration/release) and succeeding (cytoplasmic binding) stages. Therefore, existing information suffices for articulating detailed kinetic models of translocation, but not models for the overall mRNA transport process. In this paper, we show that simple kinetic models of translocation can (i) accommodate data about nucleocytoplasmic distributions of endogenous transcripts; (ii) predict the overall effects on these distributions of effectors such as insulin and epidermal growth factor; (iii) throw some light on the mechanism(s) of action of the HIV-1 protein Rev and produce experimentally testable predictions about this mechanism; and (iv) account for the action of influenza virus NS1 protein. However, the simplest forms of translocation models apparently fail to account for some properties of viral regulators such as HIV Rev and adenovirus E1B-E4 complex. To elucidate these topics, less narrowly focused models of mRNA transport are required, describing intranuclear binding/release as well as translocation. On the basis of our examination of translocation models, we suggest some criteria that the requisite broadly based models must satisfy.

Animals↗
PubMed1996

Evaluating lead bioavailability data by means of a physiologically based lead kinetic model.

A method of bioavailability estimation is presented in which a physiologically based kinetic model of lead kinetics is fit simultaneously to blood and bone lead concentrations after a period of exposure to dietary lead. Optimization of the simultaneous fit, varying only fractional absorption, gives the best estimate of fractional bioavailability for each treatment group. The analysis was applied to data from three separate studies in which rats were fed for 30 consecutive days purified diets containing lead added as lead acetate, mine waste-contaminated test soils, or mine waste itself. Fractional absorption decreased as lead intake increased, regardless of the source of the lead; but the magnitude of this dose dependence was lead source-dependent. There were no differences in lead absorption by male and female rats when lead intake was expressed per unit body weight. Fractional absorption varied from 4 to 5%, at low exposure rates (1-2 mg lead/kg/day) when lead acetate was added to the diet, to 0.24% at a high exposure rate (24 mg/kg/day) when a mine waste-contaminated test soil was added to the diet. Comparison of the results of this analysis with the results of a more conventional analysis, in which the bone and blood lead concentrations were separately compared with bone and blood lead concentrations in rats given daily injections of lead acetate intravenously for 29 consecutive days, demonstrated that the standard analysis failed to reveal the dose dependence of fractional absorption.

Animal Feed↗