Endotoxin-induced reduction in biliary indocyanine green excretion rate in a chronically catheterized rat model

Using a nonstressed chronically catheterized rat model in which the common bile duct was cannulated, we studied endotoxin-induced alterations in hepatic function by measuring changes in the maximal steady-state biliary excretion rate of the anionic dye indocyanine green (ICG). Biliary excretion of ICG was calculated from direct measurements of biliary ICG concentrations and the bile flow rate during a continuous vascular infusion of ICG. Despite significant elevations in mean peak serum tumor necrosis factor-alpha (TNF-alpha) concentrations (90.9 +/- 16.2 ng/ml), there was no effect on mean rates of bile flow or biliary ICG clearance after administration of 100 microg/kg endotoxin at 6 or 24 h. Significant differences from mean baseline rates of bile flow and biliary ICG excretion did occur after administration of 1,000 microg/kg endotoxin (mean peak TNF-alpha 129.6 +/- 24.4 ng/ml). Furthermore, when rats were treated with up to 16 microg/kg of recombinant TNF-alpha, there was no change in mean rates of bile flow or ICG biliary clearance compared with baseline values. These data suggest that the complex regulation of biliary excretion is not mediated solely by TNF-alpha.     

Mathematical modelling of metabolic pathways affected by an enzyme deficiency. A mathematical model of glycolysis in normal and pyruvate-kinase-deficient red blood cells

A mathematical model of glycolysis in human erythrocytes is proposed to study the influence of a pyruvate kinase deficiency on the energy metabolism. The model takes into account the main regulatory properties of the non-equilibrium enzymes and the magnesium-complex formation by the adenine nucleotides and by 2,3-bisphosphoglycerate. In the normal case (no enzyme defect) the calculated flux rates and metabolite concentrations are in a good agreement with experimental data. It is shown that a severe pyruvate kinase deficiency manifested in a tenfold diminished activity of that enzyme leads to a remarkable decrease of the glycolytic flux and the ATP concentration of about 50% of the normal values. On the other hand a lowering of the pyruvate kinase activity to half of the normal value, characteristic for the heterozygotes, gives no significant alterations of the metabolite concentrations and the flux rates compared with the normal case which is in accordance with the lack of clinical symptoms for a metabolic disease of these probands. For three patients with known alterations of their pyruvate kinase mutants the calculated metabolite concentrations and the control characteristics permit estimation of the degree of disorder of the glycolytic pathway. The resulting classification corresponds well to other independent experimental and clinical findings. In particular, the calculation demonstrates that there is no simple correlation between the lowered enzyme activity and the reduced flux rate through the affected pathway.     

A statistical model to estimate variance in long term-low dose mutation assays: testing of the model in a human lymphoblastoid mutation assay

Long term-low dose mutation assays offer a means to study the genetic effects of environmental mutagens at concentrations relevant to human exposure. These assays involve continuous induction of mutants, serial dilution of cultures and sampling to determine the mutant fraction as a function of time and mutagen concentration. An arithmetic model for the expected variance among identically treated cultures is presented. This model provides means to calculate a predicted variance of the mutant fractions and mutation rates in typical long term-low dose experiments. We have calculated the expected variances of the mutant fraction with this model and compared them to the observed variances among 4 independent experiments in which human lymphoblastoid cells were treated for 5, 10, 15 and 20 days with a non-toxic concentration of the mutagen 4-aminobiphenyl. Mutations at the HPRT locus were measured by determining the 6-thioguanine-resistant mutant fraction. The expected and observed variances of the mutant fractions are in close agreement. This model is adequate to predict the variance of the mutant fraction and should be useful in experimental design and objective evaluation of long term-low dose mutation assays.     

Kinetic model of disaccharide oxidation by Agrobacterium tumefaciens

Disaccharides were microbaially transformed to their corresponding 3-keto-derivatives by resting cells of Agrobacterium tumefaciens NCPPB 396. The kinetics and yield of this highly specific oxidation depend on several factors. The oxygen concentration especially has a major influence on the production of 3-keto-derivatives and was investigated kinetically with respect to low stationary oxygen concentrations in solution. Experiments showed unconventional results that conflicted with normal Michaelis-Menten kinetics. A kinetic model was developed and the kinetic constants were calculated. The model and experimental data for sucrose, maltose, iso-maltulose (palatinose), and leucrose are in good agreement with each other. Initial reaction rates with different sugars using constant oxygen concentrations resulted in a Michaelis-Mentent type function. The complete kinetics, including the effect of disaccharide and oxygen concentrations, are presented. (c) 1995 John Wiley & Sons, Inc.     

Infinite-cis kinetics support the carrier model for erythrocyte glucose transport

It has been claimed that the Km for infinite-cis uptake of glucose in human erythrocytes is so low that the carrier model for transport must be rejected. We redetermined this parameter for three experimental conditions and found instead that the Km values were in good agreement with the model. For each of a variety of cis glucose concentrations, cells were preequilibrated with various concentrations of glucose, and the apparent Km was determined as the intracellular concentration reducing the initial rate of net uptake by half. The dependence of the apparent Km values on the cis glucose was as predicted by the carrier model; the infinite-cis Km was determined from both this concentration dependence and the extrapolated value at infinite cis glucose. The resulting values were 15 mM for fresh blood at 0 degrees C, 39 mM for outdated blood at 0 degrees C, and 11 mM for outdated blood at 25 degrees C. Previous measurements of the Km at room temperature yielded values of 2-3 mM. These earlier studies used a time course procedure that indicated rapid changes in rates during the initial 10 s of uptake but did not directly measure such changes. We examined the uptake of 60 mM glucose at 20 degrees C into cells containing 0 and 5 mM glucose; rapid changes in rates were not observed in the first few seconds, and the time courses were more consistent with our higher Km values. Our new values, together with other initial rate measurements in the literature, support the adequacy of the carrier model to account for the kinetics of glucose transport in human erythrocytes.     

A model of evaporation from the skin while wearing protective clothing

 A simple model was developed to describe the transport of water vapour from subjects working in hot environments while wearing chemical-protective clothing. The goal of the modelling was to obtain a better estimate of evaporative cooling of the subjects, as it was hypothesised that calculations of evaporative heat loss based on changes in dressed weight over-estimate the actual benefit experienced by the subjects. The model employed measured values of vapour pressure within the clothing ensemble to estimate the skin vapour pressure. The resistance of the clothing ensemble to water vapour transport was calculated from measurements of the physical properties of the materials in conjunction with estimates of the resistance of air layers between the clothing layers. The model predicts mean evaporation rates from the skin that are approximately 60% of those calculated from measured changes in dressed weight. Error analysis failed to account for the magnitude of this difference and possible explanations for the difference are advanced. A brief examination of the effect of wicking suggests that some of the difference results from a reduction of the resistance of the garment to water vapour due to wicking of liquid sweat through fabric layers. Received: 4 June 1997 / Accepted: 21 October 1997     

Kinetic study of hybridoma cell growth in continuous culture. I. A model for non-producing cells

The kinetic behavior of a nonproducing hybridoma clone AFP-27-NP was investigated in continuous culture under glucose-limited conditions. A total of more than 21, 000 h of cultures were operated at dilution rates ranging from 0.01 to 0.06 h(-1). The viable cell concentrations, dead cell concentrations, and cell volumes all varied with the dilution rate. A steady-state model was developed based on the biomass concentration and the glucose concentration. The specific growth rate as a function of glucose concentration is described by a model similar to the Monod model with a threshold glucose concentration and a minimum specific growth rate incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. A death rate is included in the model which is described by an inverted Monod-type function of glucose concentration. The yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper region of specific growth rates. No maintenance term for glucose consumption was needed; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepted the specific growth rate axis at a value close to the minimum growth rate. The values for the model parameters were determined from regression analysis of the steady-state data. The model predictions and experimental results fit very well.     

A combined cell-cycle and metabolic model for the growth of hybridoma cells in steady-state continuous culture

The Model presented in this work demonstrates the combination of cell-cycle model with a model describing the growth and conversion kinetics of hybridoma cells in a steady-state continuous culture. The cell-cycle model is based upon a population balance model as described by Cazzador et al. and assumes the existence of a cycling-and apoptotic-cell population, which together form the viable-cell population. In this part the fraction of apoptotic cells, the age distribution of the cycling and apoptotic-cell population, the mean volume and biomass content per cell of the cycling, apoptotic, and viable cells, and the specific growth and death rates of the cells are calculated. The metabolic part consists of a Monod-type growth equation, four elemental balances, an equation assuming a constant yield of ammonia on glutamine, an equation for product formation, and the relation of Glacken for energy production. Furthermore, a maintenance-energy model for the consumption of glucose and glutamine is introduced, which combines the approaches of Herbert and Pirt into one model in a way similar to Beeftink et al. For energy consumption a Pirt model is assumed. The model is capable of predicting trends in steady-state vaues of a large number of variables of interest like specific growth rate, specific death rate, viability, cell numbers, mean viable-cell volume, and concentrations and conversion rates of product, glucose, glutamine, lactate, and ammonia. Also the concentrations and conversion rates of oxygen and carbon dioxide are qualitatively predicted. The values of the model predictions are generally close to experimental data obtained from literature. (c) 1995 John Wiley & Sons, Inc.     

Surface pH controls purple-to-blue transition of bacteriorhodopsin. A theoretical model of purple membrane surface.

We have developed a surface model of purple membrane and applied it in an analysis of the purple-to-blue color change of bacteriorhodopsin which is induced by acidification or deionization. The model is based on dissociation and double layer theory and the known membrane structure. We calculated surface pH, ion concentrations, charge density, and potential as a function of bulk pH and concentration of mono- and divalent cations. At low salt concentrations, the surface pH is significantly lower than the bulk pH and it becomes independent of bulk pH in the deionized membrane suspension. Using an experimental acid titration curve for neutral, lipid-depleted membrane, we converted surface pH into absorption values. The calculated bacteriohodopsin color changes for acidification of purple, and titrations of deionized blue membrane with cations or base agree well with experimental results. No chemical binding is required to reproduce the experimental curves. Surface charge and potential changes in acid, base and cation titrations are calculated and their relation to the color change is discussed. Consistent with structural data, 10 primary phosphate and two basic surface groups per bacteriorhodopsin are sufficient to obtain good agreement between all calculated and experimental curves. The results provide a theoretical basis for our earlier conclusion that the purple-to-blue transition must be attributed to surface phenomena and not to cation binding at specific sites in the protein.     

Ovariectomized hamster: a potential model of postmenopausal hypercholesterolemia

A suitable and economical animal model of ovarian hormone deficiency can greatly enhance the understanding of postmenopausal-elevated risk of coronary heart disease. The male Golden Syrian hamster is a well-established small animal model of hypercholesterolemia, but the effect of ovariectomy on lipid profile in the female hamster is unclear. The objective of this study was to determine whether ovariectomized hamsters develop hypercholesterolemia and experience changes in body fat distribution consistent with changes observed in postmenopausal women. Twenty-two 90-day-old female Golden Syrian hamsters were divided into two groups and were either ovariectomized or sham-operated and given free access to a standard cholesterol-free laboratory diet for 65 days. Ovariectomized hamsters had significantly (P < 0.05) elevated serum total cholesterol concentrations (16.6%) as well as abdominal fat mass (56%; P< 0.01) despite equal food intake compared with the sham-operated group. In contrast, the mean intestinal weight and in vivo rate of sterol biosynthesis were significantly (P < 0.002 and P = 0.01, respectively) lower in the ovariectomized compared with the sham-operated group. In vivo rates of hepatic sterol biosynthesis were directionally lower (P = 0.1) in the ovariectomized group. No significant differences were observed in final body weight, serum triglycerides, or liver total cholesterol and lipids between the two groups. In conclusion, ovariectomized hamsters undergo changes in serum cholesterol and fat distribution similar to those experienced by postmenopausal women, and thus may serve as an appropriate model for postmenopausal hypercholesterolemia.     

Comparison of the rates of inactivation and conformational changes of creatine kinase during urea denaturation

The denaturation of creatine kinase in urea solutions of different concentrations has been studied by following the changes in the ultraviolet absorbance and intrinsic fluorescence as well as by the exposure of hidden SH groups. In concentrated urea solutions, the denaturation of the enzyme results in negative peaks at 285 nm with shoulders at 280 and 290 nm and positive peaks at 244 and 302 nm in the denatured minus native enzyme difference spectrum. The fluorescence emission maximum of the enzyme red shifts with increasing intensity in urea solutions of increasing concentrations. At least part of these changes can be attributed to direct effects of urea on the exposed Tyr and Trp residues as shown by experiments with model compounds. The inactivation of this enzyme has been followed and compared with the conformational changes observed during urea denaturation. A marked decrease in enzyme activity is already evident at low urea concentrations before significant conformational changes can be detected by the exposure of hidden SH groups or by ultraviolet absorbance and fluorescence changes. At higher urea concentrations, the enzyme is inactivated at rates 3 orders of magnitude faster than the rates of conformational changes. The above results are in accord with those reported previously for guanidine denaturation of this enzyme [Yao, Q., Hou, L., Zhou, H., & Tsou, C.-L. (1982) Sci. Sin. (Engl. Ed.) 25, 1186-1193] and can best be explained by assuming that the active site of this enzyme is situated near the surface of the enzyme molecule and is sensitive to very slight conformational changes.     

An ecomorphological model of the initial hominid dispersal from Africa

We use new data on the timing and extent of the early Pleistocene dispersal of Homo erectus to estimate diffusion coefficients of early Homo from Africa. These diffusion coefficients indicate more rapid and efficient dispersals than those calculated for fossil Macaca sp., Theropithecus darti, and Mesopithecus pentelicus. Increases in home range size associated with changes in ecology, hominid body size, and possibly foraging strategy may underlay these differences in dispersal efficiency. Ecological data for extant primates and human foragers indicate a close relationship between body size, home range size, and diet quality. These data predict that evolutionary changes in body size and foraging behavior would have produced a 10-fold increase in the home range size of H. erectus compared with that of the australopithecines. These two independent datasets provide a means of quantifying aspects of the dispersal of early Homo and suggest that rapid rates of dispersal appear to have been promoted by changes in foraging strategy and body size in H. erectus facilitated by changes in ecosystem structure during the Plio-Pleistocene.     

A biochemically structured model for Saccharomyces cerevisiae.

A biochemically structured model for the aerobic growth of Saccharomyces cerevisiae on glucose and ethanol is presented. The model focuses on the pyruvate and acetaldehyde branch points where overflow metabolism occurs when the growth changes from oxidative to oxido-reductive. The model is designed to describe the onset of aerobic alcoholic fermentation during steady-state as well as under dynamical conditions, by triggering an increase in the glycolytic flux using a key signalling component which is assumed to be closely related to acetaldehyde. An investigation of the modelled process dynamics in a continuous cultivation revealed multiple steady states in a region of dilution rates around the transition between oxidative and oxido-reductive growth. A bifurcation analysis using the two external variables, the dilution rate, D, and the inlet concentration of glucose, S(f), as parameters, showed that a fold bifurcation occurs close to the critical dilution rate resulting in multiple steady-states. The region of dilution rates within which multiple steady states may occur depends strongly on the substrate feed concentration. Consequently a single steady state may prevail at low feed concentrations, whereas multiple steady states may occur over a relatively wide range of dilution rates at higher feed concentrations.     

A mathematical model of the nutrient dynamics of phytoplankton in a nitrate-limited environment

Insofar as saturation kinetics are applicable to the growth of phytoplankton in laboratory experiments and to growth in nature, the computer modeling of intracellular nutrient partitioning in populations of cells can lead to better understanding of the dynamics of natural populations. A three-compartment mathematical model was developed to represent a phytoplankton population having the capability to store nitrogen in a nitrate-limited environment. Parameters were estimated by fitting the model to data from two chemostat experiments reported by Caperon (1968). The model was used to simulate growth dynamics observed in chemostat and batch experiments. The model demonstrated the changes which may occur in the nitrogenous constituents of a phytoplankton population with time and environmental conditions. The model also demonstrates three phenomena which have been observed in field and laboratory experiments but which are not represented by the customary Monod model: (1) uptake rates may significantly exceed not growth rates, (2) high growth rates may be encountered at very low environmental nitrate concentrations, and (3) the ratio of internal nitrogen to population size may change significantly during a study period. It is suggested that the amount of nitorgen in storage may be used as an indicator of the physiological state of a monospecific population. Parameters for the one-compartment Monod model were estimated by customary methods form data generated by the three-compartment model. It was shown that difficulties encountered in estimating the yield coefficient and the decay coefficient may be attributed to the intracellular storage phenomenon. It was also demonstrated that the one-compartment Monod model was inadequate to accurately represent population growth in chemostat experiments when intracellular storage is a significant factor.     

Development of predictive mathematical model for the growth kinetics of Staphylococcus aureus by response surface model

A response surface model was developed for predicting the growth rates of Staphylococcus aureus in tryptic soy broth (TSB) medium as a function of combined effects of temperature, pH, and NaCl. The TSB containing six different concentrations of NaCl (0, 2, 4, 6, 8, and 10%) was adjusted to an initial of six different pH levels (pH 4, 5, 6, 7, 8, 9, and 10) and incubated at 10, 20, 30, and 40 degrees C. In all experimental variables, the primary growth curves were well (r2=0.9000 to 0.9975) fitted to a Gompertz equation to obtain growth rates. The secondary response surface model for natural logarithm transformations of growth rates as a function of combined effects of temperature, pH, and NaCl was obtained by SAS's general linear analysis. The predicted growth rates of the S. aureus were generally decreased by basic (pH 9-10) or acidic (pH 5-6) conditions and higher NaCl concentrations. The response surface model was identified as an appropriate secondary model for growth rates on the basis of correlation coefficient (r=0.9703), determination coefficient (r2=0.9415), mean square error (MSE=0.0185), bias factor (B(f)=1.0216), and accuracy factor (A(f)=1.2583). Therefore, the developed secondary model proved reliable for predictions of the combined effect of temperature, NaCl, and pH on growth rates for S. aureus in TSB medium.     

A computer model of gluconeogenesis and lipid metabolism in the perfused liver

A mathematical model of the perfused rat liver was developed to predict intermediate metabolite concentrations and fluxes in response to changes in various substrate concentrations in the perfusion medium. The model simulates gluconeogenesis in the liver perfused separately with lactate and pyruvate and the combination of these substrates with fatty acids (oleate). The model consists of key reactions representing gluconeogenesis, glycolysis, fatty acid metabolism, tricarboxylic acid cycle, oxidative phosphorylation, and ketogenesis. Michaelis-Menten-type kinetic expressions, with control by ATP/ADP, are used for many of the reactions. For key regulated reactions (fructose-1,6-bisphosphatase, phosphofructokinase, pyruvate carboxylase, pyruvate dehydrogenase complex, and pyruvate kinase), rate expressions were developed that incorporate allosteric effectors, specific substrate relationships (e.g., cooperative binding), and/or phosphorylation/dephosphorylation using in vitro enzyme activity data and knowledge of the specific mechanisms. The model was independently validated by comparing model predictions with 10 sets of experimental data from 7 different published works, with no parameter adjustments. The simulations predict the same trends, in terms of stimulation of substrate uptake by fatty acid addition, as observed experimentally. In general, the major metabolic indicators calculated by the model are in good agreement with experimental results. For example, the simulated glucose/pyruvate mass yield is 43% compared with the average of 45% reported in the literature. The model accurately predicts the specific time constants of the glucose response (2.5-4 min) and the dynamic behavior of substrate and product fluxes. It is expected that this model will be a useful tool for analyzing the complex relationships between carbohydrate and fat metabolism.     

Application of the ADM1 model to advanced anaerobic digestion

In this paper the ADM1 model that has been developed by the IWA Task Group for Mathematical Modelling of Anaerobic Digestion Processes is summarized. The model was applied to a variety of anaerobic digestion scenarios that are presented in the literature and for each data set the model predictions were compared to experimental values. Based upon the model applications it was apparent that for accurate model simulations the influent sludge should be well characterized in terms of biodegradable and recalcitrant COD and also nitrogenous compounds. In almost all cases the model was able to reflect the trends that were observed in the experimental data however the concentrations of VFAs were consistently over-predicted in digesters with short SRTs. It would appear that the inhibition functions associated with low pH values tend to overestimate the impact of pH on biokinetic rates for the acid-consuming bacteria. Application of the model with flow through of active biomass between digesters in series in temperature-phased systems needs to be further evaluated in the future.     

Incorporating harvest rates into the sex-age-kill model for white-tailed deer

Although monitoring population trends is an essential component of game species management, wildlife managers rarely have complete counts of abundance. Often, they rely on population models to monitor population trends. As imperfect representations of real-world populations, models must be rigorously evaluated to be applied appropriately. Previous research has evaluated population models for white-tailed deer (Odocoileus virginianus); however, the precision and reliability of these models when tested against empirical measures of variability and bias largely is untested. We were able to statistically evaluate the Pennsylvania sex-age-kill (PASAK) population model using realistic error measured using data from 1,131 radiocollared white-tailed deer in Pennsylvania from 2002 to 2008. We used these data and harvest data (number killed, age-sex structure, etc.) to estimate precision of abundance estimates, identify the most efficient harvest data collection with respect to precision of parameter estimates, and evaluate PASAK model robustness to violation of assumptions. Median coefficient of variation (CV) estimates by Wildlife Management Unit, 13.2% in the most recent year, were slightly above benchmarks recommended for managing game species populations. Doubling reporting rates by hunters or doubling the number of deer checked by personnel in the field reduced median CVs to recommended levels. The PASAK model was robust to errors in estimates for adult male harvest rates but was sensitive to errors in subadult male harvest rates, especially in populations with lower harvest rates. In particular, an error in subadult (1.5-yr-old) male harvest rates resulted in the opposite error in subadult male, adult female, and juvenile population estimates. Also, evidence of a greater harvest probability for subadult female deer when compared with adult (≥2.5-yr-old) female deer resulted in a 9.5% underestimate of the population using the PASAK model. Because obtaining appropriate sample sizes, by management unit, to estimate harvest rate parameters each year may be too expensive, assumptions of constant annual harvest rates may be necessary. However, if changes in harvest regulations or hunter behavior influence subadult male harvest rates, the PASAK model could provide an unreliable index to population changes. © 2012 The Wildlife Society.