Biomedical subjects

E O Voit

Publications and source records attributed to E O Voit.

At least 19 recordsLinked to original sources

PubMed2006

Regulation of glycolysis in Lactococcus lactis: an unfinished systems biological case study.

The unexpectedly long, and still unfinished, path towards a reliable mathematical model of glycolysis and its regulation in Lactococcus lactis is described. The model of this comparatively simple pathway was to be deduced from in vivo nuclear magnetic resonance time-series measurements of the key glycolytic metabolites. As to be expected from any nonlinear inverse problem, computational challenges were encountered in the numerical determination of parameter values of the model. Some of these were successfully solved, whereas others are still awaiting improved techniques of analysis. In addition, rethinking of the model formulation became necessary, because some generally accepted assumptions during model design are not necessarily valid for in vivo models. Examples include precursor-product relationships and the homogeneity of cells and their responses. Finally, it turned out to be useful to model only some of the metabolites, while using time courses of ubiquitous compounds such as adenosine triphosphate, inorganic phosphate, nicotinamide adenine dinucleotide (oxidised) and nicotinamide adenine dinucleotide (reduced) as unmodelled input functions. With respect to our specific application, the modelling process has come a long way, but it is not yet completed. Nonetheless, the model analysis has led to interesting insights into the design of the pathway and into the principles that govern its operation. Specifically, the widely observed feedforward activation of pyruvate kinase by fructose 1,6-bisphosphate is shown to provide a crucial mechanism for positioning the starving organism in a holding pattern that allows immediate uptake of glucose, as soon as it becomes available.

Computer Simulation↗

PubMed2005

Approximation of delays in biochemical systems.

In the past metabolic pathway analyses have mostly ignored the effects of time delays that may be due to processes that are slower than biochemical reactions, such as transcription, translation, translocation, and transport. We show within the framework of biochemical systems theory (BST) that delay processes can be approximated accurately by augmenting the original variables and non-linear differential equations with auxiliary variables that are defined through a system of linear ordinary differential equations. These equations are naturally embedded in the structure of S-systems and generalized mass action systems within BST and can be interpreted as linear signaling pathways or cascades. We demonstrate the approximation method with the simplest generic modules, namely single delayed steps with and without feedback inhibition. These steps are representative though, because they are easily incorporated into larger systems. We show that the dynamics of the approximated systems reflects that of the original delay systems well, as long as the systems do not operate in very close vicinity of threshold values where the systems lose stability. The accuracy of approximation furthermore depends on the selected number of auxiliary variables. In the most relevant situations where the systems operate at states away from their critical thresholds, even a few auxiliary variables lead to satisfactory approximations.

Biochemistry↗

PubMed2005

Smooth bistable S-systems.

S-systems have been used as models of biochemical systems for over 30 years. One of their hallmarks is that, although they are highly non-linear, their steady states are characterised by linear equations. This allows streamlined analyses of stability, sensitivities and gains as well as objective, mathematically controlled comparisons of similar model designs. Regular S-systems have a unique steady state at which none of the system variables is zero. This makes it difficult to represent switching phenomena, as they occur, for instance, in the expression of genes, cell cycle phenomena and signal transduction. Previously, two strategies were proposed to account for switches. One was based on a technique called recasting, which permits the modelling of any differentiable non-linearities, including bistability, but typically does not allow steady-state analyses based on linear equations. The second strategy formulated the switching system in a piece-wise fashion, where each piece consisted of a regular S-system. A representation gleaned from a simplified form of recasting is proposed and it is possible to divide the characterisation of the steady states into two phases, the first of which is linear, whereas the other is non-linear, but easy to execute. The article discusses a representative pathway with two stable states and one unstable state. The pathway model exhibits strong separation between the stable states as well as hysteresis.

Cell Physiological Phenomena↗

PubMed2001

Assessment of effects of experimental imprecision on optimized biochemical systems.

Metabolic pathways may be optimized with S-system models that prescribe profiles of control variables leading to optimal output while keeping metabolites and enzyme activities within predefined ranges. Monte Carlo simulations show how much the yield and the corresponding metabolite concentrations would be affected by inaccuracies in the experimental implementation of the prescribed profiles. For a recent model of citric acid production in Aspergillus niger, the yield is roughly normally distributed, whereas the distributions of metabolite concentrations differ greatly in shape and statistical characteristics. Even moderate inaccuracies may lead to constraint violations, which appear to be correlated with high logarithmic gains.

Aspergillus niger↗

PubMed2000

Estimating age-related trends in cross-sectional studies using S-distributions.

Growth trends in children are often based on cross-sectional studies, in which a sample of the population is investigated at one given point in time. Estimating age-related percentiles in such studies involves fitting data distributions, each of which is specific for one age group, and a subsequent smoothing of the percentile curves. The first requirement for this process is the selection of a distributional form that is expected to be consistent with the observed data. If a goodness-of-fit test reveals significant discrepancies between the data and the best-fitting member of this distributional form, an alternative distribution must be found. In practice, there is seldom an objective argument for selecting any particular distribution. Also, different distributions can yield very similar fits, so that any selection is somewhat arbitrary. Finally, the shapes of the observed distributions may change throughout the age range so drastically that no single traditional distribution can fit them all in a satisfactory manner. To overcome these difficulties in population studies, non-parametric smoothing techniques and normalizing transformations have been used to derive percentile curves. In this paper we present an alternative strategy in the form of a flexible parametric family of statistical distributions: the S-distribution. We suggest a method that guides the search for well-fitting S-distributions for groups of observed distributions. The method is first tested with simulated data sets and subsequently applied to actual weight distributions of girls of different ages. As far as the results can be tested, they are consistent with observations and with results from other methods.

Adolescent↗

PubMed2000

Biochemical systems analysis of genome-wide expression data.

MOTIVATION: Modern methods of genomics have produced an unprecedented amount of raw data. The interpretation and explanation of these data constitute a major, well-recognized challenge. RESULTS: Biochemical Systems Theory (BST) is the mathematical basis of a well-established methodological framework for analyzing networks of biochemical reactions. An existing BST model of yeast glycolysis is used here to explain and interpret the glycolytic gene expression pattern of heat shocked yeast. Our analysis demonstrates that the observed gene expression profile satisfies the primary goals of increased ATP, trehalose, and NADPH production, while maintaining intermediate metabolites at reasonable levels. Based on a systematic exploration of alternative, hypothetical expression profiles, we show that the observed profile outperforms other profiles. CONCLUSION: BST is a useful framework for combining DNA microarray data with enzymatic process information to yield new insights into metabolic pathway regulation. AVAILABILITY: All analyses were executed with the software PLAS(Copyright), which is freely available at http://correio.cc.fc.ul.pt/~aenf/plas.html for academic use. CONTACT: VoitEO@MUSC.edu

Computational Biology↗

PubMed2000

Random number generation from right-skewed, symmetric, and left-skewed distributions.

Monte Carlo simulations have become a mainstream technique for environmental and technical risk assessments. Because their results are dependent on the quality of the involved input distributions, it is important to identify distributions that are flexible enough to model all relevant data yet efficient enough to allow thousands of evaluations necessary in a typical simulation analysis. It has been shown in recent years that the S-distribution provides accurate representations for frequency data that are symmetric or skewed to either side. This flexibility makes the S-distribution an ideal candidate for Monte Carlo analyses. To use the distribution effectively, methods must be available for drawing S-distributed random numbers. Such a method is proposed here. It is shown that S-distributed random numbers can be efficiently generated from a simple algebraic formula whose coefficients are tabulated. The method is shown step by step and illustrated with a detailed example. (The tables are accessible in electronic form in the FTP parent directory at http:@www.musc.edu/voiteo/ftp/.)

Algorithms↗

PubMed2000

Utility of Biochemical Systems Theory for the analysis of metabolic effects from low-dose chemical exposure.

Adverse health outcomes from exposure to chemical agents are of increasing interest in human and ecological risk assessment and require the development of new analytical methods. Such methods must be able to capture the essence of integrated networks of biochemical pathways in a mathematically feasible fashion. Over the past three decades, Biochemical Systems Theory has been successfully applied to numerous biological systems. It is suggested here that S-system models derived from BST can provide the means for assessing chemical exposures and their effects at the metabolic level. This article briefly reviews essential concepts of S-systems and provides generic examples of chemical exposure scenarios. S-system models can be considered mechanistic, since their components are measurable quantities (e.g., concentrations, fluxes, enzyme activities, and rates). As dynamic models, they can be used to assess immediate and long-term metabolic responses to environmental stimuli. Direct mathematical analysis for low exposures leads to simple dose-response relationships, which have the form of power-law functions. Thus, if the S-system model yields an appropriate description of chemical exposure and its metabolic effects, the dose-response relationship for low exposures is linear in logarithmic coordinates. This result includes as a special case the standard linear relationship in Cartesian coordinates with zero intercept.

Dose-Response Relationship, Drug↗

PubMed2000

Canonical modeling: review of concepts with emphasis on environmental health.

The article reviews concepts of canonical modeling in the context of environmental health. Based on biochemical systems theory, the canonical approach was developed over the past thirty years and applied to complex systems primarily in biochemistry and the regulation of gene expression. Canonical modeling is based on nonlinear ordinary differential equations whose right-hand sides consist of products of power-law functions. This structure results from the linearization of complex processes in logarithmic space. The canonical structure has many intriguing features. First, almost any system of smooth functions or ordinary differential equations can be recast equivalently in a canonical model, which demonstrates that the model structure is rich enough to deal with all relevant nonlinearities. Second, a large body of successful applications suggests that canonical models are often valid and accurate representations of quite complex, real-world systems. Third, a set of guidelines supports the modeler in all phases of analysis. These guidelines address model design, algebraic and numerical analysis, and the interpretation of results. Fourth, the structure of canonical models, especially those in S-system form, facilitates algebraic and numerical analyses. Of particular importance is the derivation of steady-state solutions in an explicit symbolic or numerical form, which allows further assessments of stability and robustness. The homogeneous structure of canonical models has also led to the development of very efficient, customized computer algorithms for all steps of a typical analysis. Fifth, a surprising number of models currently used in environmental health research are special cases of canonical models. The traditional models are thus subsumed in one modeling framework, which offers new avenues of analysis and interpretation.

Algorithms↗

PubMed1998

Analysis of abnormalities in purine metabolism leading to gout and to neurological dysfunctions in man.

A modelling approach is used to analyse diseases associated with purine metabolism in man. The specific focus is on deficiencies in two enzymes, hypoxanthine:guanine phosphoribosyltransferase and adenylosuccinate lyase. These deficiencies can lead to a number of symptoms, including neurological dysfunctions and mental retardation. Although the biochemical mechanisms of dysfunctions associated with adenylosuccinate lyase deficiency are not completely understood, there is at least general agreement in the literature about possible causes. Simulations with our model confirm that accumulation of the two substrates of the enzyme can lead to significant biochemical imbalance. In hypoxanthine:guanine phosphoribosyltransferase deficiency the biochemical mechanisms associated with neurological dysfunctions are less clear. Model analyses support some old hypotheses but also suggest new indicators for possible causes of neurological dysfunctions associated with this deficiency. Hypoxanthine:guanine phosphoribosyltransferase deficiency is known to cause hyperuricaemia and gout. We compare the relative importance of this deficiency with other known causes of gout in humans. The analysis suggests that defects in the excretion of uric acid are more consequential than defects in uric acid synthesis such as hypoxanthine:guanine phosphoribosyltransferase deficiency.

AMP Deaminase↗

PubMed1998

Mathematical models of purine metabolism in man.

Experimental and clinical data on purine metabolism are collated and analyzed with three mathematical models. The first model is the result of an attempt to construct a traditional kinetic model based on Michaelis-Menten rate laws. This attempt is only partially successful, since kinetic information, while extensive, is not complete, and since qualitative information is difficult to incorporate into this type of model. The data gaps necessitate the complementation of the Michaelis-Menten model with other functional forms that can incorporate different types of data. The most convenient and established representations for this purpose are rate laws formulated as power-law functions, and these are used to construct a Complemented Michaelis-Menten (CMM) model. The other two models are pure power-law-representations, one in the form of a Generalized Mass Action (GMA) system, and the other one in the form of an S-system. The first part of the paper contains a compendium of experimental data necessary for any model of purine metabolism. This is followed by the formulation of the three models and a comparative analysis. For physiological and moderately pathological perturbations in metabolites or enzymes, the results of the three models are very similar and consistent with clinical findings. This is an encouraging result since the three models have different structures and data requirements and are based on different mathematical assumptions. Significant enzyme deficiencies are not so well modeled by the S-system model. The CMM model captures the dynamics better, but judging by comparisons with clinical observations, the best model in this case is the GMA model. The model results are discussed in some detail, along with advantages and disadvantages of each modeling strategy.

Animals↗

PubMed1997

Derivation of the linear-logistic model and Cox's proportional hazard model from a canonical system description.

The linear-logistic regression model and Cox's proportional hazard model are widely used in epidemiology. Their successful application leaves no doubt that they are accurate reflections of observed disease processes and their associated risks or incidence rates. In spite of their prominence, it is not a priori evident why these models work. This article presents a derivation of the two models from the framework of canonical modeling. It begins with a general description of the dynamics between risk sources and disease development, formulates this description in the canonical representation of an S-system, and shows how the linear-logistic model and Cox's proportional hazard model follow naturally from this representation. The article interprets the model parameters in terms of epidemiological concepts as well as in terms of general systems theory and explains the assumptions and limitations generally accepted in the application of these epidemiological models.

Communicable Diseases↗

PubMed1997

Validation and steady-state analysis of a power-law model of purine metabolism in man.

The paper introduces a model of human purine metabolism in situ. Chosen from among several alternative system descriptions, the model is formulated as a Generalized Mass Action system within Biochemical Systems Theory and validated with analyses of steady-state and dynamic characteristics. Eigenvalue and sensitivity analyses indicate that the model has a stable and robust steady-state. The model quite accurately reproduces numerous biochemical and clinical observations in healthy subjects as well as in patients with disorders of purine metabolism. These results suggest that the model can be used to assess biochemical and clinical aspects of human purine metabolism. It provides a means of exploring effects of enzyme deficiencies and is a potential tool for identifying steps of the pathway that could be the target of therapeutical intervention. Numerous quantitative comparisons with data are given. The model can be used for biomathematical exploration of relationships between enzymic deficiencies and clinically manifested diseases.

Adenine↗

PubMed1996

A pharmacodynamic model for the action of the antibiotic imipenem on Pseudomonas aeruginosa populations in vitro.

The standard method for measuring in vitro antibiotic efficacy is based on a point observation of bacterial activity 18 hours after inoculation. The method, while simple, forgoes significant information by ignoring the dynamics of the interactions between antibiotic and bacteria. This paper proposes a simple dynamic model describing these interactions. The model consists of two non-linear differential equations of the S-system type. Its parameter values are estimated, through the minimization of residual errors, from data on the effect of the carbapenem antibiotic imipenem on Pseudomonas aeruginosa. The model adequately describes the dynamic behavior of the bacterial populations in the presence of the antibiotic: beginning with drug administration, then through the decline of the bacterial population and possibly ending with bacterial resurgence.

Humans↗

PubMed1992

Symmetries of S-systems.

An S-system is a set of first-order nonlinear differential equations that all have the same structure: The derivative of a variable is equal to the difference of two products of power-law functions. S-systems have been used as models for a variety of problems, primarily in biology. In addition, S-systems possess the interesting property that large classes of differential equations can be recast exactly as S-systems, a feature that has been proven useful in statistics and numerical analysis. Here, simple criteria are introduced that determine whether an S-system possesses certain types of symmetries and how the underlying transformation groups can be constructed. If a transformation group exists, families of solutions can be characterized, the number of S-system equations necessary for solution can be reduced, and some boundary value problems can be reduced to initial value problems.

Models, Biological↗

PubMed1990

Comparison of isoeffect relationships in radiotherapy.

Irradiation affects numerous physiological processes within cells and tissues and can lead to damage or death. If the damage is not too severe, cells have the ability to repair and regenerate. Many small injuries are repaired more easily than ones causing extensive damage and, consequently, tissues typically respond differently to one large dose of radiation than to many small doses, separated in time. In the radiotherapy of tumors, the choice of the fractionation regimen of dose over time is therefore as crucial as the total radiation dose. The interdependence between total dose, fractionation regimen, and radiation effect has been described mathematically with various isoeffect relationships. These relationships appear to be fundamentally distinct and have been considered unrelated; some even claim that one class of isoeffect relationships is appropriate whereas other relationships are rather useless. We examine how alternative isoeffect models relate to each other and test the reliability of estimating parameter values of one model from the other.

Animals↗

PubMed1988

Estimation of cell cycle parameters from double labeling experiments.

Double labeling of cell populations with radioactive thymidine yields two types of differently labeled nuclei. Their numbers and the number of unlabeled nuclei can be used to estimate doubling times, T, and S-phase lengths, S. As of yet, such estimations have been performed either for stationary populations in which proliferation and losses are in balance, or for exponentially growing populations in which all cells have the same cycle duration. We calculate S and T for the more general type of cell population with arbitrarily distributed frequencies of cycle durations. The calculations do not require more mathematical or computational effort. We obtain three main results: (i) The estimation of T and S does not require explicit knowledge of the frequency distribution of cycle durations; (ii) in particular, equivalent estimates for T and S are obtained for both types of growing cell populations without losses, one with arbitrarily distributed cycle durations and one with the same cycle duration for all cells; and (iii) for small labeling indices, the estimate for S from the general model approaches the S-phase length of a stationary population and the estimate for T from the general model approaches the generation time of a stationary population, multiplied by the constant factor 1n(2). These relationships are valuable tools for reinterpreting results derived under the assumption of stationarity, which are considerably easier to obtain.

Animals↗

PubMed1987

Accuracy of alternative representations for integrated biochemical systems.

The Michaelis-Menten formalism often provides appropriate representations of individual enzyme-catalyzed reactions in vitro but is not well suited for the mathematical analysis of complex biochemical networks. Mathematically tractable alternatives are the linear formalism and the power-law formalism. Within the power-law formalism there are alternative ways to represent biochemical processes, depending upon the degree to which fluxes and concentrations are aggregated. Two of the most relevant variants for dealing with biochemical pathways are treated in this paper. In one variant, aggregation leads to a rate law for each enzyme-catalyzed reaction, which is then represented by a power-law function. In the other, aggregation produces a composite rate law for either net rate of increase or net rate of decrease of each system constituent; the composite rate laws are then represented by a power-law function. The first variant is the mathematical basis for a method of biochemical analysis called metabolic control, the latter for biochemical systems theory. We compare the accuracy of the linear and of the two power-law representations for networks of biochemical reactions governed by Michaelis-Menten and Hill kinetics. Michaelis-Menten kinetics are always represented more accurately by power-law than by linear functions. Hill kinetics are in most cases best modeled by power-law functions, but in some cases linear functions are best. Aggregation into composite rate laws for net increase or net decrease of each system constituent almost always improves the accuracy of the power-law representation. The improvement in accuracy is one of several factors that contribute to the wide range of validity of this power-law representation. Other contributing factors that are discussed include the nonlinear character of the power-law formalism, homeostatic regulatory mechanisms in living systems, and simplification of rate laws by regulatory mechanisms in vivo.

Biochemistry↗