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PubMed1981

Modeling cellular systems and aging processes: I. Mathematics of cell system models-a review.

A review of the literature on mathematical models of populations of cellular systems is presented. Continuous, discrete, and stochastic models are presented in a semihistorical manner as a prelude to answering the question of how to model an asynchronously dividing cellular system. This analysis is then broadened, in an attempt to broach the more general question of modeling the distribution of a set or collection of cell properties through an asynchronously dividing cellular system. Such properties might be cell motility, cell cycle length, time to mitosis, or number of epigenetic particles. It is shown that one fruitful approach to this modeling question is a coupled continuous-probabilistic model. The ramifications of this type of formalism are discussed.

Aging↗

PubMed1992

Modeling of the quantal release at interneuronal synapses: analysis of permissible values of model moments.

A theoretical study of effects of the different factors on fluctuation of post-synaptic potential (PSP) amplitudes was undertaken, using computation of regions of permissible values (RPV) of the ratio between the variance and the mean number of the quanta released (R1) and the ratio between the third moment and the variance (R2). The RPVs of these indexes for the binomial model were compared with regions determined for a number of models incorporating several factors. It has been shown that the involvement of temporal non-uniformity of transmitter release probability, decremental spreading of potentials along dendrites, and failure of spike propagation give the values of skewness index R2 less, compared to the binomial model. Simultaneously, a number of other factors, especially spatial non-uniformity of release probabilities in single release sites, would give amplitude histograms with high positive values of the index. The values of R1 and R2, calculated for 21 samples of sensorimotor EPSP amplitudes, were biased from RPV of these parameters constructed for the binomial model. The scattergram of R1 and R2 can be explained by the presence of two kinds of contacts which release quantum with different probabilities. The same was true for the beta-model based on the assumption that probabilities of quantal release are a sample of values of random variable that has beta-distribution. From analysis of the distribution of individual release probabilities, obtained from evaluation of beta-model parameters, is concluded that a greater part of boutons in the sensorimotor synapses release transmitter with very low probabilities, there being, however, a few boutons with probabilities close to 1.

Animals↗

PubMed1996

Modelling hybridoma cell growth and metabolism--a comparison of selected models and data.

Unstructured models for cell growth (cell specific growth and death rate) and metabolism (cell specific substrate uptake and metabolite production rates) of hybridoma cell lines were compared with special respect to significance, analytical error and range of validity. The diversity of the unstructured models cited reveals their mostly descriptive character compared to structured models. Bearing in mind this limited knowledge, empirical models can still serve as a valuable tool for process design. For understanding of the cell metabolism itself they might have been overemphasized in the past. For proper model design, care has to be taken to cover the whole range of process conditions. In particular if a process is to be run at very low substrate and high metabolite concentrations, chemostat cultures which have mostly been used for the model formulations, are not sufficient and have to be completed by, for example, fed-batch cultures.

Ammonia↗

PubMed2006

Enzymatic hydrolysis of lime-pretreated corn stover and investigation of the HCH-1 Model: inhibition pattern, degree of inhibition, validity of simplified HCH-1 Model.

The inhibition pattern was identified for a reaction system composed of Trichoderma reesei cellulase enzyme complex and lime-pretreated corn stover. Also, the glucose inhibition effect was quantified for the aforementioned reaction system over a range of enzyme loadings and substrate concentrations. Lastly, the range of substrate concentrations and enzyme loadings were identified in which the linear form of the simplified HCH-1 Model is valid. The HCH-1 Model is a modified Michaelis-Menton Model with non-competitive inhibition and the fraction of insoluble substrate available to bind with enzyme. With a high enzyme loading, the HCH-1 Model can be integrated and simplified in such a way that sugar conversion is linearly proportional to the logarithm of enzyme loading. A wide range of enzyme loadings (0.25-50 FPU/g dry biomass) and substrate concentrations (10-100g/L) were investigated. All experiments were conducted with an excess cellobiase loading to ensure the experimental results were not influenced by cellobiose inhibition. A non-competitive inhibition pattern was identified for the corn stover-cellulase reaction system, thereby validating the assumptions of the HCH-1 Model. At a substrate concentration of 10 g/L, glucose inhibition parameters of 0.986 and 0.979 were measured for enzyme loadings of 2 FPU/g dry biomass and 50 FPU/g dry biomass, respectively. At 5 FPU/g dry biomass, glucose inhibition parameters of 0.985 and 0.853 were measured for substrate concentrations of 10 and 100g/L, respectively. The linear form of the HCH-1 Model predicted biomass digestibility for lime-pretreated corn stover over an enzyme loading range of 0.25-50 FPU/g dry biomass and substrate concentration range of 10-100g/L.

Biomass↗

PubMed2006

In silico ADME modelling 2: computational models to predict human serum albumin binding affinity using ant colony systems.

Modelling of in vitro human serum albumin (HSA) binding data of 94 diverse drugs and drug-like compounds is performed to develop global predictive models that are applicable to the whole medicinal chemistry space. For this aim, ant colony systems, a stochastic method along with multiple linear regression (MLR), is employed to exhaustively search and select multivariate linear equations, from a pool of 327 molecular descriptors. This methodology helped us to derive optimal quantitative structure-property relationship (QSPR) models based on five and six descriptors with excellent predictive power. The best five-descriptor model is based on Kier and Hall valence connectivity index--Order 5 (path), Auto-correlation descriptor (Broto-Moreau) weighted by atomic masses--Order 4, Auto-correlation descriptor (Broto-Moreau) weighted by atomic polarizabilities--Order 5, AlogP98, SklogS (calculated buffer water solubility) [R=0.8942, Q=0.86790, F=62.24 and SE=0.2626]; the best six-variable model is based on Kier and Hall valence connectivity index of Order 3 (cluster), Auto-correlation descriptor (Broto-Moreau) weighted by atomic masses--Order 4, Auto-correlation descriptor (Broto-Moreau) weighted by atomic polarizabilities--Order 5, Atomic-Level-Based AI topological descriptors--AIdsCH, AlogP98, SklogS (calculated buffer water solubility) [R=0.9128, Q=0.89220, F=64.09 and SE=0.2411]. From the analysis of the physical meaning of the selected descriptors, it is inferred that the binding affinity of small organic compounds to human serum albumin is principally dependent on the following fundamental properties: (1) hydrophobic interactions, (2) solubility, (3) size and (4) shape. Finally, as the models reported herein are based on computed properties, they appear to be a valuable tool in virtual screening, where selection and prioritisation of candidates is required.

Algorithms↗

PubMed2004

Equivalence of the microscopic and macroscopic models of chromatography: stochastic-dispersive versus lumped kinetic model.

The microscopic model of chromatography is a stochastic model that consists of two fundamental processes: (i) the random migration of the molecules in the mobile phase, and (ii) the random adsorption-desorption of molecules on the stationary phase contained in a chromatographic column. The diffusion and drift of the molecules in the mobile phase is described with a simple one-dimensional random walk. The adsorption-desorption process is modeled by a Poisson process that assumes exponential sojourn times of the molecules in both the mobile and the stationary phases. The microscopic, or molecular model of chromatography studied here turns out to be identical to the macroscopic lumped kinetic model of chromatography, whose solution is well known in chromatography. A complete equivalence of the two models is established via the identical expressions they provide for the band profiles.

Chromatography↗

PubMed2005

Testing the sequential model of pain processing in irritable bowel syndrome: a structural equation modeling analysis.

Pain, the cardinal feature of irritable bowel syndrome (IBS), is a multidimensional phenomenon with sensory and affective dimensions. Price's pain processing model was used to delineate four a priori sequentially related stages (pain sensation intensity, immediate pain unpleasantness, long-term suffering, and pain-related behavior). Although prior research with both healthy individuals and somatic pain patients supports the model in general, its applicability to IBS is unclear. Our goal was to extend the scope of the sequential model and test its fundamental tenets using structural equation modeling (SEM) with data obtained from 168 Rome II diagnosed IBS patients (19% male, 81% female). A secondary goal was to assess the relationship between a set of contextual factors associated with IBS (age, gender, trait anxiety) and the four pain stages. Results were consistent with a successive order of pain processing such that the pain sensation directly impacts pain unpleasantness, which, in turn, leads to suffering and illness behaviors. However, contrary to a model with strictly successive stages, pain sensation had independent effects on illness behaviors over and above pain affect. The effect of anxiety on illness behavior was mediated by suffering, while psychopathology directly influenced pain sensation and pain unpleasantness but not later stages. Age was related to pain sensation and illness behaviors but not pain affect. Gender tended to be more strongly associated with more distal pain stages (e.g., pain affect) vis-a-vis its effects on pain sensation. These data are generally supportive of a four-stage pain processing model.

Abdominal Pain↗

PubMed2004

Modelling the fate of persistent organic pollutants in Europe: parameterisation of a gridded distribution model.

A regionally segmented multimedia fate model for the European continent is described together with an illustrative steady-state case study examining the fate of gamma-HCH (lindane) based on 1998 emission data. The study builds on the regionally segmented BETR North America model structure and describes the regional segmentation and parameterisation for Europe. The European continent is described by a 5 degrees x5 degrees grid, leading to 50 regions together with four perimetric boxes representing regions buffering the European environment. Each zone comprises seven compartments including; upper and lower atmosphere, soil, vegetation, fresh water and sediment and coastal water. Inter-regions flows of air and water are described, exploiting information originating from GIS databases and other georeferenced data. The model is primarily designed to describe the fate of Persistent Organic Pollutants (POPs) within the European environment by examining chemical partitioning and degradation in each region, and inter-region transport either under steady-state conditions or fully dynamically. A test case scenario is presented which examines the fate of estimated spatially resolved atmospheric emissions of lindane throughout Europe within the lower atmosphere and surface soil compartments. In accordance with the predominant wind direction in Europe, the model predicts high concentrations close to the major sources as well as towards Central and Northeast regions. Elevated soil concentrations in Scandinavian soils provide further evidence of the potential of increased scavenging by forests and subsequent accumulation by organic-rich terrestrial surfaces. Initial model predictions have revealed a factor of 5-10 underestimation of lindane concentrations in the atmosphere. This is explained by an underestimation of source strength and/or an underestimation of European background levels. The model presented can further be used to predict deposition fluxes and chemical inventories, and it can also be adapted to provide characteristic travel distances and overall environmental persistence, which can be compared with other long-range transport prediction methods.

Climate↗

PubMed2005

Kinetic modeling of lipase catalyzed hydrolysis of (R/S)-1-methoxy-2-propyl-acetate as a model reaction for production of chiral secondary alcohols.

The Candida antarctica lipase B catalyzed kinetic resolution of (R/S)-1-methoxy-2-propyl-acetate was studied as a model system for the biocatalytic production of chiral secondary alcohols. For this purpose, a kinetic model is proposed involving both enantiomers of this reaction using model discrimination and parameter identification. Starting from a ping-pong bi-bi mechanism, a simplified model with sensitive parameters was derived for the R- and S-enantiomer, respectively. It was validated at pH 7.0, using time-course measurements at varying temperatures (30-60 degrees C) and initial substrate conditions (0.05-1.5 M). This model was then used for mechanistic interpretation of the kinetic resolution on a biochemical level. The effect of temperature on kinetic parameters and enantiomeric ratio was investigated and compared to findings from the field of molecular modeling to obtain a better understanding of the reaction system for process design. Values of 21.2 and 9.7 kJmol-1 were determined for the enthalpic (DeltaR-S DeltaH ++ degrees) and the entropic (-T x DeltaR-S DeltaS ++ degrees) contribution of the difference in transition state energy of both enantiomers at 30 degrees C. High enantiomeric ratio's (E of 47-110) especially at lower temperatures, in addition to enzyme activity at a wide pH range, indicate this biotransformation is a promising example for the industrial production of chiral secondary alcohols.

Fungal Proteins↗

PubMed2004

Scalar modeling and analysis of a 3D biochemical reaction model.

For many systems it is advantageous if analysis and modeling can be accomplished from a scalar time series because this greatly facilitates the experimental setup. Moreover, in real-life systems it is hardly true that all the state variables are available for analysis and modeling. Since the late 1980s, techniques have been put forward for building mathematical models from a scalar time series. One of the objectives of this paper is to verify if it is possible to obtain global non-linear models (non-linear differential equations) from scalar time series. Such data are obtained using a model of biochemical reaction with aperiodic (chaotic) oscillations as recently observed in the case of a glycolytic reaction (Nielsen, K., Sorensen, P.G., Hynne, F., 1997. Chaos in glycolysis. J Theor. Biol. 186, 303-306.). The main objective, however, is to investigate which state variable is more convenient for the task in practice. It is shown that observability indices seem to quantify quite well which variable should be preferred as the observable. The validity of the results are established performing rigorous topological analysis on the original system and the obtained models. The influence of noise, always present in experimental time series, on the dynamics underlying such a system is also investigated.

Catalysis↗

PubMed2005

Insights to the minimal model of insulin secretion through a mean-field beta cell model.

The present work introduces an extension of the original minimal model of second phase insulin secretion during the intravenous glucose tolerance test (IVGTT), which can provide both physiological and mathematical insights to the minimal model. The extension is named the mean-field beta cell model since it returns the average response of a large number of nonlinear secretory entities. Several secretion models have been proposed for the IVGTT, and we shall identify two fundamentally different theoretical features of these models. Both features can play a central role during the IVGTT, including the one presented in the mean-field beta cell model.

Animals↗

PubMed2004

LES modelling of flow in a simple airway model.

Detailed information about the flow field pattern is highly important in accurately predicting particle deposition sites in the human airway. Flow in the upper airway during heavy breathing can have a Reynolds number as high as 9300, and therefore presents turbulent features. Although turbulence is believed to have an important effect on the airflow and other transport processes in the bronchial tree, to date both theoretical and numerical studies have predominantly assumed the flow to be laminar. In this paper, transitional/turbulent flow during inspiration is studied using a large eddy simulation (LES) in a single asymmetric bifurcation model of human upper airway. The influence of the non-laminar flow on the patterns and the particle paths is investigated in both 2D and 3D models. Throughout the investigation, comparisons with the laminar and conventional k- models for the same configuration and flow conditions are made. The LES model is also carefully validated against published experimental data in a stenotic tube model. The results demonstrate that the LES model is capable of capturing instantaneous eddy formation and flow separation in (almost) laminar, transitional and turbulent flow regimes, and hence may be used as a powerful and practical tool to provide much of the detailed flow information required for tracing the particle trajectories and particle deposition in human airways.

Computer Simulation↗

PubMed2005

The Authority/Pharmacotherapy Care model: an explanatory model of the drug use process in primary care.

BACKGROUND: Drug utilization studies have proliferated and many variants exist. Few models have been presented that account for all of the different types of studies and approaches. PURPOSE: This article presents the Authority/Pharmacotherapy Care model, a structural-functional model of the drug use process that illustrates the factors involved in drug utilization and the relationships between factors. The concepts of authority and transfer of authority underlie the relationships. METHODS: The drug use process is presented at the microlevel from the viewpoint of an individual who requires treatment with prescription drugs. The various categories of activity/authority (ie, level of patient care) are those of the individual, physician, pharmacist, patient, and drug. Influencing factors, both internal and external, impact upon each level of care. Three aspects must be considered at each level, which are structures, processes, and outcomes, according to Donabedian's model. RESULTS: The result is a structural-functional model that depicts all of the major points in the drug use process, which might be used as a framework to categorize drug utilization studies. CONCLUSIONS: This model may be used to represent the drug use process, identify the types of drug use studies, determine pertinent factors involved in the process, understand the relationships between factors, and help in evaluating drug use.

Drug Therapy↗

PubMed2006

Modelling of the long term fate of pesticide residues in agricultural soils and their surface exchange with the atmosphere: Part I. Model description and evaluation.

Sources of pesticides in the atmosphere can be releases of new material through current use, or emission/reemission from soil residues resulting from historical use. It is the latter aspect, soil residues, that is the focus of this study. This paper describes the application of a simple coupled atmosphere-soil pesticide exchange model that can assist in the interpretation of soil residue and air concentration measurements, and in the projection of short period field measurements to larger spatial scales and longer time periods. Only dry gaseous exchange (emission and deposition) between bare agricultural lands and the atmosphere is modelled. Wet deposition and particle associated deposition of pesticide are not included. Model results are compared with published co-located air and soil pesticide concentration measurements made on agricultural lands in the southern U.S. that have soil residues of lindane and the following six highly persistent pesticides: cis-, trans-chlordane, p,p'-DDE, dieldrin, trans-nonachlor and toxaphene. The study results show: (i) that measured air concentrations of toxaphene and p,p'-DDE above agricultural soils in the southern U.S. can be attributed to emissions due to local soil residues of these pesticides rather than to the regional background air concentrations; (ii) that both soil emissions and background air concentrations of dieldrin contribute significantly to the measured air concentrations; (iii) that measured air concentrations of cis- and trans-chlordane as well as trans-nonachlor and lindane are mainly due to the regional background with little contribution from local soil residues. An analysis of modelled summer day and night average soil-air exchange fluxes shows that toxaphene and p,p'-DDE soil residues are strong sources of emission to the atmosphere during both the day and night while the chlordanes, trans-nonachlor, lindane and dieldrin are deposited from the atmosphere to the soil during the night hours and emitted to the atmosphere during the day time. This result illustrates the model's capability to simulate the processes that lead to the 'grasshopper' effect whereby persistent pesticides in soils can be transported in the atmosphere by successive periods of emission and deposition to terrestrial surfaces. In the second part to this paper, the model is used to study the trends of pesticide residues and air concentrations over a twenty year period.

Agriculture↗

PubMed1999

Assessment of technical skills transfer from the bench training model to the human model.

BACKGROUND: This study examines whether technical skills learned on a bench model are transferable to the human cadaver model. METHODS: Twenty-three first-year residents were randomly assigned to three groups receiving teaching on six procedures. For each procedure, one group received training on a cadaver model, one received training on a bench model, and one learned independently from a prepared text. Following training, all residents were assessed on their ability to perform the six procedures. RESULTS: Repeated measures analysis of variance revealed a significant effect of training modality for both checklist scores (F(2,44) = 3.49, P <0.05) and global scores (F(2,44) = 7.48, P <0.01). Post-hoc tests indicated that both bench and cadaver training were superior to text learning and that bench and cadaver training were equivalent. CONCLUSIONS: Training on a bench model transfers well to the human model, suggesting strong potential for transfer to the operating room.

Cadaver↗

PubMed2001

Barrel-stave model or toroidal model? A case study on melittin pores.

Transmembrane pores induced by amphiphilic peptides, including melittin, are often modeled with the barrel-stave model after the alamethicin pore. We examine this assumption on melittin by using two methods, oriented circular dichroism (OCD) for detecting the orientation of melittin helix and neutron scattering for detecting transmembrane pores. OCD spectra of melittin were systematically measured. Melittin can orient either perpendicularly or parallel to a lipid bilayer, depending on the physical condition and the composition of the bilayer. Transmembrane pores were detected when the helices oriented perpendicularly to the plane of the bilayers, not when the helices oriented parallel to the bilayers. The evidence that led to the barrel-stave model for alamethicin and that to the toroidal model for magainin were reviewed. The properties of melittin pores are closely similar to that of magainin but unlike that of alamethicin. We conclude that, among naturally produced peptides that we have investigated, only alamethicin conforms to the barrel-stave model. Other peptides, including magainins, melittin and protegrins, all appear to induce transmembrane pores that conform to the toroidal model in which the lipid monolayer bends continuously through the pore so that the water core is lined by both the peptides and the lipid headgroups.

Animals↗

PubMed2004

Biomimetic model of skeletal muscle isometric contraction: I. an energetic-viscoelastic model for the skeletal muscle isometric force twitch.

This paper describes a revision of the Hill-type muscle model so that it will describe the chemo-mechanical energy conversion process (energetic) and the internal-element stiffness variation (viscoelastic) during a skeletal muscle isometric force twitch contraction. The derivation of this energetic-viscoelastic model is described by a first-order linear ordinary differential equation with constant energetic and viscoelastic coefficients. The model has been implemented as part of a biomimetic model, which describes the excitation-contraction coupling necessary to drive the energetic-viscoelastic model. Finally, the energetic-viscoelastic model is validated by comparing its isometric force-time profile with that of various muscles reported in the literature.

Calcium↗

PubMed1996

Comparing non-hierarchical models: application to non-linear mixed effects modeling.

There is no method available to compare the fit of two non-hierarchical non-linear mixed effects models, although the common practice is to select the model with the lower objective function. Bootstrapping the log-likelihood differences (LLDs) of non-hierarchical models and constructing a bootstrap confidence interval on the LLDs is proposed for comparing the goodness-of-fit of such models. This is illustrated with different parameterizations of clearance models for an anti-infective agent in a longitudinal pharmacokinetic study which are compared. Additive and exponential models of creatinine clearance as a predictor of clearance are used as examples.

Adult↗