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Computerized kinetic modeling: a new tool in the quest for adequacy in peritoneal dialysis.

Until recently, kinetic modeling of peritoneal dialysis (PD) was performed by engineers, scientists, or nephrologists at major teaching institutions. Now there are several "user-friendly" computer programs which permit the practicing nephrologist and dialysis staff to monitor adequacy of the individual PD patient and to optimize the dialysis prescription. In this brief article, the capabilities, methods, and data requirements of three programs are reviewed, and specific recommendations for the selection of a particular program are discussed.

Computer Simulation↗

Maternal, fetal, and amniotic fluid transport of thyroxine, triiodothyronine, and iodide in sheep: a kinetic model.

A mathematical model of iodine kinetics in maternal and fetal sheep has been developed by combining separate iodide, T3, and T4 subsystems. The individual subsystem models were developed from literature studies of maternal-fetal exchange under thyroid-blocked and unblocked conditions. Rates of exchange, concentrations, and spaces of distribution were calculated by the SAAM computer program. The models for each of the subsystems required exchange compartments within the mother and fetus, exchanges between maternal and fetal circulations, and between the fetus and amniotic fluid. The fetal-amniotic fluid exchange was observed directly for iodide and indirectly for T3 and T4. No exchange between mother and amniotic fluid was required. It is possible that the amniotic fluid acts as a reservoir for these and other substances. Maternal-fetal kinetics suggest that low fetal T3 levels are maintained by an active transport of T3 from fetus to mother, a decreased transport from mother to fetus, and a low fetal T3 production. The model also requires that all fetal T3 loss occur via transport to the maternal system rather than via fetal utilization. In contrast, the fetal T4 system is largely autonomous, the small maternal exchange not significantly contributing to the fetal T4 economy. Fetal iodide seems to be supplied by a facilitated bidirectional exchange with the mother.

Amniotic Fluid↗

Pharmacodynamic effects of sub-MICs of benzylpenicillin against Streptococcus pyogenes in a newly developed in vitro kinetic model.

The pharmacodynamic effects of benzylpenicillin against Streptococcus pyogenes were studied in a new in vitro kinetic model in which bacterial outflow was prevented by a filter membrane. Following the administration of an initial dose of antibiotic, decreasing concentrations were produced by dilution of the medium. A magnetic stirrer was placed above the filter to avoid blockage of the membrane and to ensure homogeneous mixing of the culture. Repeated samplings were easily provided through a silicon diaphragm. Streptococci were exposed to a single dose corresponding to 1.5, 10, 100, or 500 x the MIC of benzylpenicillin and also to an initial concentration of 10 x the MIC of benzylpenicillin, followed by exposure to a repeated dose after 8 h yielding 10 or 1.5 x the MIC. Experiments were also performed with 10 x the MIC of benzylpenicillin with a half-life of 3 h or an initial half-life of 1.1 h that was altered to 3 h at the time point at which the antibiotic concentrations and MIC intersected. Bacterial killing and regrowth were followed by determining viable counts. The post-MIC effect (PME) was defined as the difference in time for the numbers of CFU in the culture vessel to increase 1 log10 CFU/ml, calculated from the numbers obtained at the time when the antibiotic concentration had declined to the MIC, and the corresponding time for a control culture, grown in a glass tube without antibiotic, to increase 1 log10 CFU/ml. To determine how much of the PME was attributable to subinhibitory concentrations, penicillinase was added to a part of the culture drawn from the flask at the time when the antibiotic concentration had fallen to the MIC. The longest PME was found in the experiments in which the half-life was extended from 1.1 to 3 h at the MIC. This illustrated that sub-MICs are sufficient to prevent regrowth. However, when the half-life was 3 h during the whole experiment, the PME was shorter, indicating that when concentrations decline slowly penicillin-binding proteins will already be present in amounts sufficient for regrowth at the time when the MIC is reached. The PME may prove to be a more reliable factor than the in vitro postantibiotic effect or postantibiotic sub-MIC effect for the design of optimal dosing schedules, since the PME, like the in vivo postantibiotic effect, includes the effects of subinhibitory concentrations and therefore better reflects the clinical situation with fluctuating antibiotic concentrations.

Colony Count, Microbial↗

Use of anatomical and kinetic models in the evaluation of human food additive safety.

Toxicological testing in animals is relied upon as a surrogate for clinical testing of most food additives. Both animal and human clinical test results are generally available for direct additives when high levels of exposure are expected. Limited animal studies or in vitro test results may be the only sources of toxicological data available when low levels of exposure (microg/person/day) are expected and where no effects of the additive on the food itself are desired. Safety assessment of such materials for humans requires mathematical extrapolation from any effects observed in test animals to arrive at acceptable daily intakes (ADIs) for humans. Models of anatomy may be used to estimate tissue and organ weights where that information is missing and necessary for evaluation of a data set. The effect of growth on target tissue exposure during critical phases of organ development can be more accurately assessed when models of growth and known physiological changes are combined with pharmacokinetic results for test species. Kinetic models, when combined with limited chemical property, kinetic, and distribution data, can often be used to predict steady-state plasma and tissue levels of a test material over the range of doses employed in chronic studies to aid in interpretation of effects that are often nonlinear with respect to delivered dose. A better understanding of the reasons for nonlinearity of effects in animals improves our confidence in extrapolation to humans.

Animals↗

Kinetic modeling of ouabain tissue distribution based on slow and saturable binding to Na,K-ATPase.

The significance of the binding to Na,K-ATPase in the tissue distribution of ouabain was previously documented (Harashima et al., Pharm. Res. 9:474-479, 1992). The purpose of this study was to obtain a kinetic model of ouabain tissue distribution. In most tissues, the ouabain concentration continued to rise after the termination of infusion (5 min), with the peak tissue concentration at approximately 20 min. This delay could not be explained by the rapid equilibrium model (RE model), nor could the kinetics of ouabain be explained by an RE model modified for saturable binding. Since ouabain binding to Na,K-ATPase is slow, the association and dissociation processes were incorporated into a model that can accurately fit the observed time courses of ouabain. The obtained binding parameters corresponded well with the observed values in the in vitro binding experiments, except for muscle. These results quantitatively support the role of the slow and saturable binding of ouabain to Na,K-ATPase in its tissue distribution.

Animals↗

A kinetic model of bone marrow neutrophil production that characterizes late phenotypic maturation.

Acute inflammatory stimuli rapidly mobilize neutrophils from the bone marrow by shortening postmitotic maturation time and releasing younger neutrophils; however, the kinetics of this change in maturation time remains unknown. We propose a kinetic model that examines the rate of change in neutrophil average age at exit from the bone marrow during active mobilization to quantify this response and use this model to examine the temporal profile of late neutrophil phenotypic maturation. Total and CD10(-)/CD16(low) circulating neutrophils were quantified in cardiac surgery patients during extracorporeal circulation (ECC). Net growth in the circulating neutrophil pool occurred during the procedural (0.04 +/- 0.02 x 10(9) x l(-1) x min(-1)), warming (0.14 +/- 0.02 x 10(9) x l(-1) x min(-1)), and weaning (0.12 +/- 0.06 x 10(9) x l(-1) x min(-1)) phases of ECC. When applied to our differential equation mathematical model, these results predict that neutrophil average age at exit from the bone marrow decreased continually during ECC, resulting in average neutrophil release 8.44 +/- 2.20 h earlier during the weaning phase than at the beginning of ECC sampling. Modeling of concurrent changes in CD10(-)/CD16(low) neutrophil numbers indicates that CD10 expression is directly related to neutrophil mean age and predicts that the proportion of mobilizable postmitotic neutrophils that are CD10(+) increases from 64 to 81% during these sampled 8.4 h of maturation.

Bone Marrow↗

Kinetic model of autotrophic denitrification in sulphur packed-bed reactors.

Autotrophic denitrification of synthetic wastewater by Thiobacillus denitrificans in upflow sulphur packed-bed reactors was studied in order to establish the process kinetics for prediction of effluent concentration. Elemental sulphur particles of different size served as energy substrate as well as the physical support for the microbial biofilm. Experiments were performed under operating conditions of (i) different flow rates at constant influent nitrate concentration; and (ii) different influent nitrate concentrations at constant flow rate. The experimental results show that autotrophic denitrification rates in upflow sulphur packed-bed reactors can be described by a half-order kinetic model for biofilms. It was found that the half-order kinetic constants of upflow packed-bed reactors are 2.94-3.60, 1.47-2.04, and 1.12-1.29 mg1/2/L1/2 h for sulphur particle sizes of 2.8-5.6, 5.6-11.2, and 11.2-16 mm, respectively. The half-order kinetic constants could be related to the specific surface area of the reactor media by a simple equation. Successful application of the half-order reaction rate model was demonstrated for an actual wastewater (nitrified leachate). A comparison with the literature showed that the half-order reaction rate constants for autotrophic denitrification using elemental sulphur are approximately one order of magnitude lower than those of heterotrophic denitrification. An improved stoichiometric equation for autotrophic denitrification using elemental sulphur as electronic donor is also proposed.

Biodegradation, Environmental↗

A steady-state model for the evaluation of disk rotational speed influence on RBC kinetic: model presentation.

The physical and biological mechanisms of attached-biomass growth were analyzed and a steady-state model was proposed to determine the soluble carbonaceous removal in an RBC unit for different organic loading rates in the reactor. The objective of the model was the prediction of the organic loading rate corresponding to the maximum removal capacity in the system. A system of equations was solved where the influent soluble carbonaceous substrate concentration was the main variable. Monod's rate law was used for the growth of microorganism: the soluble carbonaceous substrate was the limiting substrate. Endogenous decay was neglected. The influence of disk rotational speed on the RBC removal capacity was investigated, the disk rotational speed being a parameter acting on oxygen transfer in the biofilm. The criteria for the evaluation of the kinetic parameter in the model were proposed.

Bacteria↗

A kinetic model of the myeloperoxidase-hydrogen peroxide-chloride ion system in phagolysosomes.

A kinetic model has been constructed of the myeloperoxidase-hydrogen peroxide-chloride ion system of mammalian neutrophils. The model includes the reactions that form chlorinated species and those compounds formed through the reactions of phenolic compounds. Model calculations show that N-chlorotaurine is the primary long-lived product of this system, but that tyrosine peroxide is a major secondary product produced by the generation of tyrosyl radicals. While N-chlorotaurine is formed in much larger concentration than tyrosine peroxide, its lower toxicity may mean that tyrosine peroxide may be the more important mediator of toxic stress in the host associated with inflammatory processes. Care must be taken in the interpretation of dityrosine levels as indicating neutrophil derived oxidant damage. Tyrosine peroxide competes with the formation of dityrosine. Therefore, a high level of oxidative stress may be present even in the absence of significant levels of dityrosine.

Animals↗

Activity of human extravascular temocillin concentrations simulated in an in-vitro kinetic model against beta-lactamase producing gram-negative bacilli.

An in-vitro kinetic model was used to demonstrate the bactericidal activity of concentrations of temocillin achieved in extravascular body fluids following a 1 g intravenous dosage in man. Concentrations of temocillin attainable in peripheral lymph were bactericidal for ampicillin-resistant strains of Escherichia coli, Enterobacter cloacae and Klebsiella oxytoca. Likewise, concentrations of temocillin achieved in human blister fluid following a 12-hourly dosage regimen were bactericidal for cultures of Ent. cloacae and K. oxytoca which were resistant, respectively, to simulated blister fluid concentrations of cefotaxime and aztreonam. The bactericidal activity of extravascular concentrations of temocillin against these multiresistant, Gram-negative bacteria was a reflection of the beta-lactamase-stability and good pharmacokinetic properties of temocillin.

Anti-Bacterial Agents↗

Numerical solutions to a kinetic model for the plasma-sheath problem with charge exchange collisions of ions.

A kinetic model of the plasma-sheath problem is presented that includes the effects of charge-exchange collisions of the ion. The collisions are modeled as a sink for accelerated ions and as a source of cold ions. Solutions are obtained by numerical integration of Poisson's equation from a point near the plasma midplane to the wall. In the quasineutral region, these solutions agree with earlier analytic work. As the mean free path is decreased, the current density at the wall decreases and the potential profile in the quasineutral region shows a smooth transition from a parabolic profile to a nearly cubic profile determined by the ion mobility. An approximate expression is found for the ion flux to the wall in the collisional limit.

Journal Article↗

Bacterial energetics, stoichiometry, and kinetic modeling of 2,4-dinitrotoluene biodegradation in a batch respirometer.

A stoichiometric equation and kinetic model were developed and validated using experimental data from batch respirometer studies on the biodegradation of 2,4-dinitrotoluene (DNT). The stoichiometric equation integrates bacterial energetics and is revised from that in a previous study by including the mass balance of phosphorus (P) in the biomass. Stoichiometric results on O2 consumption, CO2 evolution, and nitrite evolution are in good agreement with respirometer data. However, the optimal P requirement is significantly higher than the stoichiometrically derived P, implying potentially limited bioavailability of P and the need for buffering capacity in the media to mitigate the adverse pH effect for optimal growth of DNT-degrading bacteria. An array of models was evaluated to fit the O2/CO2 data acquired experimentally and the DNT depletion data calculated from derived stoichiometric coefficients and cell yield. The deterministic, integrated Monod model provides the goodness of fit to the test data on DNT depletion, and the Monod model parameters (Ks, X0, mumax, and Y) were estimated by nonlinear regression. Further analyses with an equilibrium model (MINTEQ) indicate the interrelated nature of medium chemical compositions in controlling the rate and extent of DNT biodegradation. Results from the present batch respirometer study help to unravel some key factors in controlling DNT biodegradation in complex remediation systems, in particular the interactions between acidogenic DNT bacteria and various parameters, including pH and P, the latter of which could serve as a nutrient, a buffer, and a controlling factor on the bioavailable fractions of minerals (Ca, Fe, Zn, and Mo) in the medium.

Aerobiosis↗

Maximum likelihood inference and bootstrap methods for plant organ growth via multi-phase kinetic models and their application to maize.

BACKGROUND AND AIMS: Fitting the parameters of models of plant organ growth is a means to investigate how environmental conditions affect plant architecture. The aim of this article is to evaluate some non-linear methods for fitting the parameters of multi-phase models of the kinetics of extension of plant organs such as laminae, sheaths and internodes. * METHODS: A set of computational procedures was developed allowing parameter-fitting of multi-phase models, using the maximum likelihood criterion, in which phases are identified with reference to ontogenic processes. Two bootstrap methods were compared to assess the precision of the estimates of fitted parameters, and of functions of these parameters such as the final leaf length, and the duration and rate of the rapid extension phase. Methods were applied to an experimental dataset, representing the kinetics of laminae, sheaths and internodes along the maize shoot, for two contrasting densities. * KEY RESULTS: A set of multi-phase models was proposed to describe the extension of laminae, sheaths and internodes along the shoot. The distinguishable phases differed between laminae, sheaths and internodes. For sheaths and laminae, but not for internodes, the same model could be fitted to all phytomers along the shoot. The variation of parameters along the shoot and between density treatments, as well as derived functions such as the durations of the phases of extension, are presented for laminae. It was the duration of the fast extension period, rather than its rate, which determined the difference in final length between treatments. * CONCLUSIONS: Such methods permit a large degree of objectivity and facilitate the analysis of such rather complicated but co-ordinated datasets. The work also illustrates some natural limitations of maximum likelihood methods, and viable ways of overcoming them by including a priori knowledge in the model fitting method are discussed.

Likelihood Functions↗

A kinetic model for comparing proteolytic processing activity and inhibitor resistance potential of mutant HIV-1 proteases.

A kinetic model is presented for the comparison of potential proteolytic processing activities of wild-type and mutant human immunodeficiency virus proteases in the presence and absence of protease inhibitors. The protease processing of gag substrate in the immature virions is assessed by the kinetic parameters, kcat, Km and Ki. The relationship of the estimated potential processing activities to the viability of the HIV mutants and their tendencies to resist inhibitors also are discussed. A fully developed model has the potential to stimulate the results of inhibitor resistance either in vivo or in cell culture.

Drug Resistance, Microbial↗

A kinetic model describing the processivity of myosin-V.

The precise details of how myosin-V coordinates the biochemical reactions and mechanical motions of its two head elements to engineer effective processive molecular motion along actin filaments remain unresolved. We compare a quantitative kinetic model of the myosin-V walk, consisting of five basic states augmented by two further states to allow for futile hydrolysis and detachments, with experimental results for run lengths, velocities, and dwell times and their dependence on bulk nucleotide concentrations and external loads in both directions. The model reveals how myosin-V can use the internal strain in the molecule to synchronize the motion of the head elements. Estimates for the rate constants in the reaction cycle and the internal strain energy are obtained by a computational comparison scheme involving an extensive exploration of the large parameter space. This scheme exploits the fact that we have obtained analytic results for our reaction network, e.g., for the velocity but also the run length, diffusion constant, and fraction of backward steps. The agreement with experiment is often reasonable but some open problems are highlighted, in particular the inability of such a general model to reproduce the reported dependence of run length on ADP concentration. The novel way that our approach explores parameter space means that any confirmed discrepancies should give new insights into the reaction network model.

Actin Cytoskeleton↗

Experimental application of a multistep kinetic model for natural cytotoxicity: determination of rate constants for lytic programming and killer-cell-independent lysis.

A multistep kinetic model for natural cytotoxicity reactions in vitro is described that includes consideration of the effect of nonlytic target-binding lymphocytes on the experimentally determined kinetic parameters. The expression for the maximal velocity, Vmax, obtained using this model is essentially identical to that obtained using simpler models, whereas the expression for the apparent Michaelis constant, KappM, is considerably more complex. As a first step in the application of this model, experiments were designed to determine the relative contribution of some of the component terms to the value of KappM. Methods were developed that allow for experimental determination of the rate constants for both lytic programming and killer-cell-independent lysis (KCIL) steps in the cytolytic process. The results obtained support lytic programming as the rate-determining step in natural cytotoxicity reactions and demonstrate that terms related to nonlytic target-binding lymphocytes contribute significantly to experimentally determined values for KappM. In addition, the methods developed for the determination of the rates of lytic programming and KCIL should prove useful for various studies of the mechanism of cytotoxicity and the effects of drugs and disease on such phenomena.

Adult↗

Voltage dependence of sodium-calcium exchange: predictions from kinetic models.

Voltage effects on the Na-Ca exchange system are analyzed on the basis of two kinetic models, a "consecutive" and a "simultaneous" reaction scheme. The voltage dependence of a given rate constant is directly related to the amount of charge which is translocated in the corresponding reaction step. Charge translocation may result from movement of an ion along the transport pathway, from displacement of charged ligand groups of the ion-binding site, or from reorientation of polar residues of the protein in the course of a conformational transition. The voltage dependence of ion fluxes is described by a set of coefficients reflecting the dielectric distances over which charge is translocated in the individual reaction steps. Depending on the charge of the ligand system and on the values of the dielectric coefficients, the flux-voltage curve can assume a variety of different shapes. When part of the transmembrane voltage drops between aqueous solution and binding site, the equilibrium constant of ion binding becomes a function of membrane potential. By studying the voltage dependence of ion fluxes in a wide range of sodium and calcium concentrations, detailed information on the microscopic properties of the transport system may be obtained.

Animals↗

A kinetic model for the sodium conductance system in squid axon.

We describe a kinetic reaction sequence for the sodium conductance system in the squid axon. It closely matches the original Hodgkin and Huxley model for voltage clamp experiments but it generates an action potential without a bump on the falling phase. When calcium ions are included in the reaction, this model faithfully reproduces the experimental observations of Frankenhaeuser and Hodgkin on the effects of altered calcium in the medium. The fit to experiment is much better than when a voltage shift in rate constants is assumed. The gating currents recently observed by Armstrong and Bezanilla are not compatible with the Hodgkin and Huxley model but can be reprocuced in considerable detail by the kinetic model. Thus it appears that the kinetic model differs from that of Hodgkin and Huxley perhaps in an important and fundamental way that makes it more realistic.

Animals↗