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PubMed2004

A growth kinetic model of Kluyveromyces marxianus cultures on cheese whey as substrate.

This work presents a multi-route, non-structured kinetic model for determination of microbial growth and substrate consumption in an experimental batch bioreactor in which beta-galactosidase is produced by Kluyveromyces marxianus growing on cheese whey. The main metabolic routes for lactose, and oxygen consumption, cell growth, and ethanol production are derived based on experimental data. When these individual rates are combined into a single growth rate, by rewriting the model equations, the model re-interpretation has a complexity similar to that of the usual variations of the Monod kinetic model, available in the literature. Furthermore, the proposed model is in good agreement with the experimental data for different growth temperatures, being acceptable for dynamic simulations, processes optimization, and implementations of model-based control technologies.

Bioreactors↗

PubMed1991

[Urea kinetic model analysis in dialysis: from theory to practice].

Urea kinetic modeling (UKM) has been originally proposed by F. Gotch and J. Sargent as a guide to optimize and individualize the dialysis prescription in uremic patients. In a recent report, the US National Cooperative Dialysis Study group, showed the power of this approach compared to conventional methods. It was also concluded that dialysis adequacy could be predicted with a high success rate by determining three parameters; uremia represented by the Urea Time Averaged Concentration, dialysis dose defined as KT/V ratio, and dietary protein intake calculated from the urea generation rate. In spite of its potential usefulness, UKM has not gained clinical acceptance among nephrologists since it appeared always complicated due to its mathematical formulation or cumbersome to be used routinely in dialyzed patients. In this paper the authors will bring the reader from basic concepts to practical use of UKM to guide dialysis strategy. Limits of validity and difficulty in using this approach are also discussed. It is concluded that UKM by using very simple and basic parameters is a practical, and very powerful tool for assessing the dialysis adequacy and nutritional status of dialyzed patients. Direct quantification from dialysate (or ultrafiltrate) collection appeared a simple and precise method which should avoided multiple blood sampling.

Humans↗

PubMed2006

A new kinetic model for the photopolymerization shrinkage-strain of dental composites and resin-monomers.

OBJECTIVES: The aim of the study was to develop a new kinetic model for the shrinkage-strain rates of dental resin composites. The effect of filler content on the shrinkage-strain kinetics and degree of conversion of dental composites was also investigated. METHODS: A resin matrix containing 65 wt.% Bis-GMA and 35 wt.% TEGDMA was prepared. 0.5 wt.% camphorquinone and 0.5 wt.% dimethyl aminoethyl methacrylate were dissolved in the resin as photo-initiator system. Silanized glass fillers were added in different percentages to the resin-monomers. The shrinkage-strain of the specimens photopolymerized at circa 550 mW/cm2 was measured using the bonded-disc technique at 23, 37 and 45 degrees C for the matrix monomers and 23 degrees C for the composites. Initial shrinkage-strain rates were obtained by numerical differentiation of shrinkage-strain data with respect to time. Degree-of-conversion of the composites containing different filler contents was measured using FTIR spectroscopy. RESULTS: A new kinetic model was developed for the shrinkage-strain rate using the autocatalytic model of Kamal [Kamal MR, Sourour S. Kinetic and thermal characterization of thermoset cure. Polym Eng Sci 1973;13(1):59-64], which is used to describe the reaction kinetics of thermoset resins. The model predictions were in good agreement with the experimental data. The results also showed a linear correlation between the shrinkage-strain (and shrinkage-strain rate) and filler-volume fraction. The filler fraction did not affect the degree-of-conversion of the composites. SIGNIFICANCE: The rate of polymerization, determined via the shrinkage, being invariant with filler-fraction, suggests that only a relatively high filler-surface area, as may be obtained with nano-fillers, will affect the network-forming kinetics of the resin matrix.

Bisphenol A-Glycidyl Methacrylate↗

PubMed1996

Agreement between the classical urea kinetic model and direct dialysis quantification: importance of urea rebound.

From a review of the literature regarding kinetic models used for assessing the adequacy of hemodialysis, no definite conclusions can be drawn as to whether the classical urea kinetic model (UKM) or modified direct dialysis quantification (mDDQ) is more reliable. We compared mDDQ with classical UKM and with a modified UKM that employs an equilibrated urea value. From the theoretical viewpoint, no substantial conflict is found between the two models as regards the dialysis dose, if urea rebound is considered. From the practical viewpoint, in our opinion direct quantification lends itself better for experimental purposes whereas for routine Kt/V evaluation UKM is easier and accurate enough, provided that rebound is taken into account.

Female↗

PubMed2002

Temperature dependence of the epidermal growth factor receptor signaling network can be accounted for by a kinetic model.

Stimulation of isolated hepatocytes with epidermal growth factor (EGF) causes rapid tyrosine phosphorylation of the EGF receptor (EGFR) and adapter/target proteins, which was monitored with 1 and 2 s resolution at 37, 20, and 4 degrees C. The temporal responses detected for multiple signaling proteins involve both transient and sustained phosphorylation patterns, which change dramatically at low temperatures. To account quantitatively for complex responses, we employed a mechanistic kinetic model of the EGFR pathway, formulated in molecular terms as cascades of protein interactions and phosphorylation and dephosphorylation reactions. Assuming differential temperature dependencies for different reaction groups, such as SH2 and PTB domain-mediated interactions, the EGFR kinase, and the phosphatases, good quantitative agreement was obtained between computer-simulated and measured responses. The kinetic model demonstrates that, for each protein-protein interaction, the dissociation rate constant, k(off), strongly decreases at low temperatures, whereas this decline may or may not be accompanied by a large decrease in the k(on) value. Temperature-induced changes in the maximal activities of the reactions catalyzed by the EGFR kinase were moderate, compared to such changes in the V(max) of the phosphatases. However, strong changes in both the V(max) and K(m) for phosphatases resulted in moderate changes in the V(max)/K(m) ratio, comparable to the corresponding changes in EGFR kinase activity, with a single exception for the receptor phosphatase at 4 degrees C. The model suggests a significant decrease in the rates of the EGF receptor dimerization and its dephosphorylation at 4 degrees C, which can be related to the phase transition in the membrane lipids. A combination of high-resolution experimental monitoring and molecular level kinetic modeling made it possible to quantitatively account for the temperature dependence of the integrative signaling responses.

Animals↗

PubMed1995

A kinetic model of coronary reactive hyperemic response to transient ischemia.

A kinetic model is proposed to delineate the factors that determine the coronary reactive hyperemic response (RHR) to transient ischemia. The model comprises of myocardial-interstitial (M) and vascular (V) compartments. Vasodilator metabolites (VM) are produced in the M compartment during the interval of coronary occlusion. The rate of VM production is dependent on the flow rate during the ischemic period, the ratio of excess flow above the control level (R) to the loss of flow during occlusion period (D), the amount of oxygen stored and the degree of vasodilation in the V compartment prior to occlusion. Following a complete release of occlusion, VM are transported from the M to V compartment and are washed out or degraded with time. The time course of RHR is determined by the coronary patency which is proportional to VM concentration in the V compartment. Based on a set of numerical constants, the model is tested by simulating RHR to the various occlusion manoeuvres: a pair of 10 sec occlusions separated by brief release, a 15 sec release followed by a second brief occlusion, a brief release of an occlusion followed by restricted inflow and a period of restricted inflow after occlusion. The simulated results fit the experimental R/D and RH durations data of canine hearts. Factors that determine the impairment of RH capacity in coronary stenosis are suggested in terms of the model scheme.

Animals↗

PubMed2006

Kinetic modeling to optimize pentose fermentation in Zymomonas mobilis.

Zymomonas mobilis engineered to express four heterologous enzymes required for xylose utilization ferments xylose along with glucose. A network of pentose phosphate (PP) pathway enzymatic reactions interacting with the native glycolytic Entner Doudoroff (ED) pathway has been hypothesized. We have investigated this putative reaction network by developing a kinetic model incorporating all of the enzymatic reactions of the PP and ED pathways, including those catalyzed by the heterologous enzymes. Starting with the experimental literature on in vitro characterization of each enzymatic reaction, we have developed a kinetic model to enable dynamic simulation of intracellular metabolite concentrations along the network of interacting PP and ED metabolic pathways. This kinetic model is useful for performing in silico simulations to predict how varying the different enzyme concentrations will affect intracellular metabolite concentrations and ethanol production rate during continuous fermentation of glucose and xylose mixtures. Among the five enzymes whose concentrations were varied as inputs to the model, ethanol production in the continuous fermentor was optimized when xylose isomerase (XI) was present at the highest level, followed by transaldolase (TAL). Predictions of the model that the interconnecting enzyme phosphoglucose isomerase (PGI) does not need to be overexpressed were recently confirmed through experimental investigations. Through such systematic analysis, we can develop efficient strategies for maximizing the fermentation of both glucose and xylose, while minimizing the expression of heterologous enzymes.

Fermentation↗

PubMed2002

Kinetic modeling in positron emission tomography.

Most PET kinetic modeling approaches have at their basis a compartmental model that has first-order, constant coefficients. The present article outlines the one-, two-, and three-compartment models used to measure cerebral blood flow, cerebral glucose metabolism, and receptor binding, respectively. The number of compartments of each model is based on specific knowledge of the physiological and/or biochemical compartments into which the tracer distributes. Additional physical and biochemical properties of the tracer distribution are considered in specifying the use of first-order rate constants. For example, in cerebral blood flow and receptor binding studies transport across the blood-brain barrier by diffusion can be modeled as a first-order process. A saturable carrier-mediated process or saturable enzyme catalyzed reaction, when tracer doses of the labeled substrate are used and the natural substrate is in steady-state, also results in first-order rate constants, as in glucose metabolism studies. The rate of ligand binding, on the other hand, depends on the concentrations of both substrate and available receptors. In order to appropriately model the reaction as pseudo first-order during a specified experimental interval, protocols are carefully designed to assure that the number of available binding sites remains approximately constant throughout the given interval. A broad array of scanning protocols is employed for kinetic analyses. These include single-scan approaches, which function like their autoradiographic counterparts in animal studies and are often called "autoradiographic" methods, which allow estimation of a single parameter. Dynamic scanning to obtain the time course of tissue activity allows simultaneous estimation of multiple parameters. Scanning may be conducted during a period of tracer uptake or after attainment of steady-state conditions. All quantitative modeling approaches share the common requirement that an arterial input function be measured or an appropriate surrogate be found. A vast array of methods is available for estimation of model parameters, both micro and macro. In the final analysis, it is the interaction among all elements of the PET study, including careful tracer selection, model specification, experimental protocol design, and sound parameter estimation methods, that determines the quantitative accuracy of the estimates of the physiological or biochemical process under study.

Animals↗

PubMed2005

Generalized first-order kinetic model for biosolids decomposition and oxidation during hydrothermal treatment.

The main objective of this study was to develop generalized first-order kinetic models to represent hydrothermal decomposition and oxidation of biosolids within a wide range of temperatures (200-450 degrees C). A lumping approach was used in which oxidation of the various organic ingredients was characterized by the chemical oxygen demand (COD), and decomposition was characterized by the particulate (i.e., nonfilterable) chemical oxygen demand (PCOD). Using the Arrhenius equation (k = k(o)e(-Ea/RT)), activation energy (Ea) levels were derived from 42 continuous-flow hydrothermal treatment experiments conducted at temperatures in the range of 200-450 degrees C. Using predetermined values for k(o) in the Arrhenius equation, the activation energies of the various organic ingredients were separated into 42 values for oxidation and a similar number for decomposition. The activation energy values were then classified into levels representing the relative ease at which the organic ingredients of the biosolids were oxidized or decomposed. The resulting simple first-order kinetic models adequately represented, within the experimental data range, hydrothermal decomposition of the organic particles as measured by PCOD and oxidation of the organic content as measured by COD. The modeling approach presented in the paper provide a simple and general framework suitable for assessing the relative reaction rates of the various organic ingredients of biosolids.

Kinetics↗

PubMed2003

Two-dimensional correlation analysis in application to a kinetic model of parallel reactions.

By applying generalized two-dimensional (2D) correlation analysis as reported by Noda, we have systematically studied a kinetic model of parallel reactions. Given the related rate constants and absorption coefficients, the correlation between reactant and products are analyzed. The reactant-reactant, reactant-product, and product-product pairs are found to be synchronously correlated, and their intensities increase with increase of the rate constant and the absorption coefficient. On the other hand, only the reactant-product pairs show in the asynchronous spectra. Their intensities also depend proportionally on the rate constant and the absorption coefficient. The influence of signal-to-noise ratio (S/N) and overlapped spectra are further discussed. The resulting synchronous and asynchronous correlation spectra for the kinetic model appear to be weakly influenced by poor quality of the signal when the reference spectrum is set at zero. The ratio of asynchronous to synchronous correlation intensity yields a coherence spectrum. This spectrum remains a constant intensity for all the correlated peaks, being free from the influence of rate constant and absorption coefficient as well as being weakly disturbed by a small S/N ratio. It also provides a way to evaluate the extent of spectral overlap between two peaks. The coherence spectrum is useful to characterize the type of parallel reactions.

Algorithms↗

PubMed2004

Optimization and kinetic model of condensation of a secondary amine with a uracil derivative in the synthesis of 2-[(1-carbethoxy-4-piperidinyl) (methyl)amino]-1H-pyrimidin-4-one.

A series of experiments was performed in order to determine the reaction conditions of 2-(methylsulfanyl)pyrimidin-4(3H)-one [U] with 4-(methylamino)piperidine [A] affording 2-[(1-carbethoxy-4-piperidinyl)(methyl)amino]-1H-pyrimidin-4-one [P] in a high yield (80%) (Scheme 1). Two theoretical approaches i.e., the reaction response analysis and the modelling of reaction kinetics supported the experimental studies in order to control the reaction conditions.

Algorithms↗

PubMed2002

Kinetic modeling and determination of reaction constants of Alzheimer's beta-amyloid fibril extension and dissociation using surface plasmon resonance.

To establish the kinetic model of the extension and dissociation of beta-amyloid fibrils (f(A)beta) in vitro, we analyzed these reactions using a surface plasmon resonance (SPR) biosensor. Sonicated f(A)beta were immobilized on the surface of the SPR sensor chip as seeds. The SPR signal increased linearly as a function of time after amyloid beta-peptides (Abeta) were injected into the f(A)beta-immobilized chips. The extension of f(A)beta was confirmed by atomic force microscopy. When flow cells were washed with running buffer, the SPR signal decreased with time after the extension reaction. The curve fitting resolved the dissociation reaction into the fast exponential and slow linear decay phases. Kinetic analysis of the effect of Abeta/f(A)beta concentrations on the reaction rate indicated that both the extension reaction and the slow linear phase of the dissociation were consistent with a first-order kinetic model; i.e., the extension/dissociation reactions proceed via consecutive association/dissociation of Abeta onto/from the end of existing fibrils. On the basis of this model, the critical monomer concentration ([M](e)) and the equilibrium association constant (K) were calculated, for the first time, to be 20 nM and 5 x 10(7) M(-1), respectively. Alternatively, [M](e) was directly measured as 200 nM, which may represent the equilibrium between the extension reaction and the fast phase of the dissociation. The SPR biosensor is a useful quantitative tool for the kinetic and thermodynamic study of the molecular mechanisms of f9A)beta formation in vitro.

Alzheimer Disease↗

PubMed1987

[Peptide synthesis catalyzed by proteases. Analysis of a kinetic model for enzymes with acyl-enzyme mechanism of action].

The kinetics of peptide synthesis via transfer of the acyl moiety from activated derivatives of amino acids or peptides (S) to nucleophiles (N) catalyzed by proteases forming an acyl-enzyme intermediate, was analysed. A kinetic model assumes enzymatic hydrolysis of the formed peptide (P), so the kinetic curve for P has a maximum (denoted as pmax). Particular attention was given to the analysis of the effects of the initial concentrations and kinetic constants on pmax. Computer analysis demonstrated that at a given ratio of initial S and N concentrations pmax is affected only by the ratio of the second order rate constants for enzymatic hydrolysis of S and P (alpha) and the ratio of rate constants for an attack of the acyl-enzyme intermediate by nucleophile and water (beta). These conclusions apply regardless of the existence of enzyme forms other than a free enzyme and an acyl-enzyme intermediate. Thus, the kinetically controlled maximum yield of peptide (pmax) can be calculated a priori from the values of alpha and beta which can be readily evaluated from the reference data. Simple explicit expressions were obtained, allowing fairly accurate prediction of pmax for a broad spectrum of S and N initial concentrations.

Acylation↗

PubMed1989

Urea kinetic modelling by partial dialysate collection.

Conventional urea kinetic modelling (UKM) has several drawbacks, in particular the complexity of the required calculations and the need for accurate values of parameters which are difficult to measure, such as dialyzer clearance and blood flow. An alternative method of UKM is proposed based on collecting a small fraction of spent dialysate flow for 3 consecutive dialyses. Application of a urea mass balance to the 7 day period permits neglecting changes in body urea stores. Thus no blood sampling is required for most patients. The required calculations are simple and straightforward. The partial dialysate collection (PDC) method was compared to conventional UKM in a 3 patient, 15 week study. Protein catabolic rate (PCR) from PDC was a smooth curve and consistent with dietary estimation for each patient. Conventional UKM gave variable PCR results which were 17-27% higher on average. This discrepancy was attributed to overestimation of dialyzer clearance. PDC was concluded to be more convenient and accurate than conventional UKM and therefore ideal for routine clinical use.

Adult↗

PubMed1997

Studies on the modulation of DNA damage. 1: A simple kinetic model for radioprotection of DNA in aqueous solution.

A simple kinetic model, based on the assumption that direct and indirect interactions of ionising radiations with DNA lead to formation of DNA-radicals which are precursors of single strand break (ssb) and double strand break (dsb) is presented. Considering accessibility of OH attack on DNA and assuming homogenous kinetics, the model has been validated by using experimental data on radiation-induced strand break formation in presence of methanol (MeOH) and glutathione (GSH). Fitting the D37 values for ssb in aqueous solution of pBR322 DNA in the presence of the predominantly A-T minor groove-ligand Hoechst 33258, the value of the rate constant of OH scavenging by DNA-bound Hoechst was estimated by Martin and his group as 2.7 x 10(11) dm3 mol-1 s-1 (Martin, R.F. and Denison, L. (1992), Int. J. Radiat. Oncol. Biol. Phys., 23, 578-584). Using aqueous solution of calf thymus DNA in the presence of Hoechst this rate constant has been determined by pulse radiolysis as 1.1 x 10(9) dm3 mol-1 s-1. The yield of strand breaks has also been measured by low angle laser light scattering. Using the experimentally measured value of the rate constant of OH scavenging by DNA-bound Hoechst in the model, calculations show that OH scavenging alone could not explain the overall protection provided by Hoechst; there should be quenching of DNA-radicals by Hoechst. Fitting the yield of radiation-induced ssb (G(ssb)) obtained for CT DNA and pBR322 DNA, the rate constant of this DNA-radical quenching has been calculated as 10(6) dm3 mol-1 s-1, which agrees with pulse radiolytic data. Using these rate constant values, calculations show that the protection against radiation-induced dsb formation provided by the combination of Hoechst with GSH is more than that by the combination of MeOH with GSH.

DNA Damage↗

PubMed1994

Reliability of haemodialysis urea kinetic modelling in children.

The reliability of urea kinetic modelling (UKM) in paediatric haemodialysis was tested by comparing results of the classic variable volume model (UKM3), a recently introduced two-sample modification of this (UKM2) and direct quantification by a partial dialysate collection method (PDC). Urea generation rate (G) was also found from a 1-week collection of dialysate and urine (OWC). Nine children aged 2-18 years and weighing 10.6-39.9 kg were examined over 1 week (25 treatments). UKM3 and UKM2 gave almost identical results, but deviated from PDC and OWC. The two indirect methods overestimated G by 24% and 18%. However, the correlations between the results were very high for all variables and all methods (r > or = 0.96). Repeating UKM3 and UKM2 mid-week for 5 consecutive weeks, the following coefficients of variation were found: for the normalised whole body urea clearance (Kt/V) 10% and 11%, respectively; for normalised protein catabolic rate 17% and 14%. It is concluded that all tested methods can be used, but each method requires its own reference interval. Results of UKM seem to vary somewhat more than in adults. This should be considered when assessing children by such methods.

Adolescent↗

PubMed1993

A computer simulation study on the effects of input function measurement noise in tracer kinetic modeling with positron emission tomography (PET).

Tracer kinetic modeling with positron emission tomography (PET) requires measurements of the time-activity curves in both plasma (PTAC) and tissue (TTAC) to estimate physiological parameters, i.e. to fit the parameters of certain compartmental models using PTAC and TTAC as the model input and output functions, respectively. However, the estimation usually ignores the measurement noise in plasma tracer activity curves. The accuracy and reliability of the physiological parameters estimated by ignoring such noise are not well understood. In this paper, effects of noise in [18F] 2-fluoro-2-deoxy-D-glucose (FDG) tracer plasma concentration measurements on estimation of local cerebral metabolic rates of glucose (LCMRGlc) with PET is investigated systematically. The PTAC modeling approach used in this paper also provides a realistic means to filter out the noise and to improve the physiological parameter accuracy, which can be potentially used in model-based non-invasive measurements of PTAC.

Artifacts↗

PubMed1994

A computer simulation study on the input function sampling schedules in tracer kinetic modeling with positron emission tomography (PET).

Tracer kinetic modeling with positron emission tomography (PET) requires measurements of the time-activity curves in both plasma (PTAC) and tissue (TTAC) to estimate physiological parameters, i.e. to fit the parameters of certain compartmental models using PTAC and TTAC as the model input and output functions, respectively. In this paper, we first explored the optimal blood sampling schedule (OBSS) for the input function, based on the tracer [18F]2-fluoro-2-deoxy-D-glucose (FDG) blood sample experimental data. Then using a 5-parameter FDG model we investigated the effects of the plasma sampling schedule, as well as PTAC measurement noise, on the estimation accuracy and reliability of FDG model macro- and micro-parameters and the physiological parameter local cerebral metabolic rates of glucose (LCMRGlc), using computer simulation. Three different methods were used: (a) estimation of the FDG model parameters ignoring PTAC noise using the traditional PTAC schedule (non-OBSS); (b) estimation of the PTAC model parameters and FDG model parameters simultaneously using both non-OBSS and OBSS; (c) estimation of the PTAC model parameters first, then the FDG model parameters using both non-OBSS and OBSS. The results show that OBSS can provide more reliable estimates and largely simplifies the experiment operations.

Blood Specimen Collection↗