Mathematical modelling of the urea cycle. A numerical investigation into substrate channelling

Temporal multiscale modeling of biochemical regulatory networks: Calcium-regulated hepatocyte lipid and glucose metabolism

Hepatocyte lipid and glucose metabolism is regulated not only by major hormones like insulin and glucagon but also by many other factors, including calcium ions. Recently, mitochondria-associated membrane (MAM) dysfunction combined with incorrect IP3-receptor regulation has been shown to result in abnormal calcium signaling in hepatocytes. This dysfunction could further lead to hepatic metabolism pathology. However, the exact contribution of MAM dysfunction, incorrect IP3-receptor regulation and insulin resistance to the calcium-insulin-glucagon interplay is not understood yet. In this work, we analyze the role of abnormal calcium signaling and insulin dysfunction in hepatocytes by proposing a model of hepatocyte metabolic regulatory network with a detailed focus on the model construction details besides the biological aspect. In this work, we analyze the role of abnormal calcium signaling and insulin dysfunction in hepatocytes by proposing a model of hepatocyte metabolic regulatory network. We focus on the model construction details, model validation, and predictions. We describe the dynamic regulation of signaling processes by sigmoid Hill function. In particular, we study the effect of both the Hill function slope and the distance between Hill function extremes on metabolic processes in hepatocytes as a model of nonspecific insulin dysfunction. We also address the significant time difference between characteristic time of glucose hepatic processing and a typical calcium oscillation period in hepatocytes. Our modeling results show that calcium signaling dysfunction results in an abnormal increase in postprandial glucose levels, an abnormal glucose decrease in fasting, and a decreased amount of stored glycogen. An insulin dysfunction of glucose phosphorylation, glucose dephosphorylation, and glycogen breakdown also cause a noticeable effect. We also get some insight into the so-called hepatic insulin resistance paradox, confirming the hypothesis regarding indirect insulin action on hepatocytes via dysfunctional adipocyte lipolysis.

A mechanobiological mathematical model of liver metabolism

The liver plays a complex role in metabolism and detoxification, and better tools are needed to understand its function and to develop liver-targeted therapies. In this study, we establish a mechanobiological model of liver transport and hepatocyte biology to elucidate the metabolism of urea and albumin, the production/detoxification of ammonia, and consumption of oxygen and nutrients. Since hepatocellular shear stress (SS) can influence the enzymatic activities of liver, the effect of SS on the urea and albumin synthesis are empirically modeled through the mechanotransduction mechanisms. The results demonstrate that the rheology and dynamics of the sinusoid flow can significantly affect liver metabolism. We show that perfusate rheology and blood hematocrit can affect urea and albumin production by changing hepatocyte mechanosensitive metabolism. The model can also simulate enzymatic diseases of the liver such as hyperammonemia I, hyperammonemia II, hyperarginemia, citrollinemia, and argininosuccinicaciduria, which disrupt the urea metabolism and ammonia detoxification. The model is also able to predict how aggregate cultures of hepatocytes differ from single cell cultures. We conclude that in vitro perfusable devices for the study of liver metabolism or personalized medicine should be designed with similar morphology and fluid dynamics as patient liver tissue. This robust model can be adapted to any type of hepatocyte culture to determine how hepatocyte viability, functionality, and metabolism are influenced by liver pathologies and environmental conditions.

Insights into Gene Therapy for Urea Cycle Defects by Mathematical Modeling

Metabolic liver diseases are attractive gene therapy targets that necessitate reconstitution of enzymatic activity in functionally complex biochemical pathways. The levels of enzyme activity required in individual hepatocytes and the proportion of the hepatic cell mass that must be gene corrected for therapeutic benefit vary in a disease-dependent manner that is difficult to predict. While empirical evaluation is inevitably required, useful insights can nevertheless be gained from knowledge of disease pathophysiology and theoretical approaches such as mathematical modeling. Urea cycle defects provide an excellent example. Building on a previously described one-compartment model of the urea cycle, we have constructed a two-compartment model that can simulate liver-targeted gene therapy interventions using the computational program Mathematica. The model predicts that therapeutically effective reconstitution of ureagenesis will correlate most strongly with the proportion of the hepatic cell mass transduced rather than the level of enzyme-encoding transgene expression achieved in individual hepatocytes. Importantly, these predictions are supported by experimental data in mice and human genotype/phenotype correlations. The most notable example of the latter is ornithine transcarbamylase deficiency (X-linked) where impairment of ureagenesis in male and female patients is closely simulated by the one- and two-compartment models, respectively. Collectively, these observations support the practical value of mathematical modeling in evaluation of the disease-specific gene transfer challenges posed by complex metabolic phenotypes.

A mechanism for bistability in glycosylation

Glycosyltransferases are a class of enzymes that catalyse the posttranslational modification of proteins to produce a large number of glycoconjugate acceptors from a limited number of nucleotide-sugar donors. The products of one glycosyltransferase can be the substrates of several other enzymes, causing a combinatorial explosion in the number of possible glycan products. The kinetic behaviour of systems where multiple acceptor substrates compete for a single enzyme is presented, and the case in which high concentrations of an acceptor substrate are inhibitory as a result of abortive complex formation, is shown to result in non-Michaelian kinetics that can lead to bistability in an open system. A kinetic mechanism is proposed that is consistent with the available experimental evidence and provides a possible explanation for conflicting observations on the β-1,4-galactosyltransferases. Abrupt switching between steady states in networks of glycosyltransferase-catalysed reactions may account for the observed changes in glycosyl-epitopes in cancer cells.

HepatoDyn: A Dynamic Model of Hepatocyte Metabolism That Integrates 13C Isotopomer Data

The liver performs many essential metabolic functions, which can be studied using computational models of hepatocytes. Here we present HepatoDyn, a highly detailed dynamic model of hepatocyte metabolism. HepatoDyn includes a large metabolic network, highly detailed kinetic laws, and is capable of dynamically simulating the redox and energy metabolism of hepatocytes. Furthermore, the model was coupled to the module for isotopic label propagation of the software package IsoDyn, allowing HepatoDyn to integrate data derived from 13C based experiments. As an example of dynamical simulations applied to hepatocytes, we studied the effects of high fructose concentrations on hepatocyte metabolism by integrating data from experiments in which rat hepatocytes were incubated with 20 mM glucose supplemented with either 3 mM or 20 mM fructose. These experiments showed that glycogen accumulation was significantly lower in hepatocytes incubated with medium supplemented with 20 mM fructose than in hepatocytes incubated with medium supplemented with 3 mM fructose. Through the integration of extracellular fluxes and 13C enrichment measurements, HepatoDyn predicted that this phenomenon can be attributed to a depletion of cytosolic ATP and phosphate induced by high fructose concentrations in the medium.

Applications of NMR spectroscopy to systems biochemistry

The past decades of advancements in NMR have made it a very powerful tool for metabolic research. Despite its limitations in sensitivity relative to mass spectrometric techniques, NMR has a number of unparalleled advantages for metabolic studies, most notably the rigor and versatility in structure elucidation, isotope-filtered selection of molecules, and analysis of positional isotopomer distributions in complex mixtures afforded by multinuclear and multidimensional experiments. In addition, NMR has the capacity for spatially selective in vivo imaging and dynamical analysis of metabolism in tissues of living organisms. In conjunction with the use of stable isotope tracers, NMR is a method of choice for exploring the dynamics and compartmentation of metabolic pathways and networks, for which our current understanding is grossly insufficient. In this review, we describe how various direct and isotope-edited 1D and 2D NMR methods can be employed to profile metabolites and their isotopomer distributions by stable isotope-resolved metabolomic (SIRM) analysis. We also highlight the importance of sample preparation methods including rapid cryoquenching, efficient extraction, and chemoselective derivatization to facilitate robust and reproducible NMR-based metabolomic analysis. We further illustrate how NMR has been applied in vitro, ex vivo, or in vivo in various stable isotope tracer-based metabolic studies, to gain systematic and novel metabolic insights in different biological systems, including human subjects. The pathway and network knowledge generated from NMR- and MS-based tracing of isotopically enriched substrates will be invaluable for directing functional analysis of other 'omics data to achieve understanding of regulation of biochemical systems, as demonstrated in a case study. Future developments in NMR technologies and reagents to enhance both detection sensitivity and resolution should further empower NMR in systems biochemical research.

Pedagogical view of model metabolic cycles

The main purpose of this study was to present a simplified view of model metabolic cycles. Although the models have been elaborated with the Mathematica Program, and using a system of differential equations, the main conclusions were presented in a rather intuitive way, easily understandable by students of general courses of Biochemistry, and without any need of mathematical support. A change in any kinetic constant (Km or Vmax) of only one enzyme affected the metabolic profile of all the substrates of the cycle. In addition, it is shown how an increase in the Km or a decrease in the Vmax values of any particular enzyme promoted an increase of its substrate; the contrary occurred decreasing the Km or increasing the Vmax values.

Stable isotope-resolved metabolomics and applications for drug development

Advances in analytical methodologies, principally nuclear magnetic resonance spectroscopy (NMR) and mass spectrometry (MS), during the last decade have made large-scale analysis of the human metabolome a reality. This is leading to the reawakening of the importance of metabolism in human diseases, particularly cancer. The metabolome is the functional readout of the genome, functional genome, and proteome; it is also an integral partner in molecular regulations for homeostasis. The interrogation of the metabolome, or metabolomics, is now being applied to numerous diseases, largely by metabolite profiling for biomarker discovery, but also in pharmacology and therapeutics. Recent advances in stable isotope tracer-based metabolomic approaches enable unambiguous tracking of individual atoms through compartmentalized metabolic networks directly in human subjects, which promises to decipher the complexity of the human metabolome at an unprecedented pace. This knowledge will revolutionize our understanding of complex human diseases, clinical diagnostics, as well as individualized therapeutics and drug response. In this review, we focus on the use of stable isotope tracers with metabolomics technologies for understanding metabolic network dynamics in both model systems and in clinical applications. Atom-resolved isotope tracing via the two major analytical platforms, NMR and MS, has the power to determine novel metabolic reprogramming in diseases, discover new drug targets, and facilitates ADME studies. We also illustrate new metabolic tracer-based imaging technologies, which enable direct visualization of metabolic processes in vivo. We further outline current practices and future requirements for biochemoinformatics development, which is an integral part of translating stable isotope-resolved metabolomics into clinical reality.

A composite computational model of liver glucose homeostasis. I. Building the composite model

A computational model of the glucagon/insulin-driven liver glucohomeostasis function, focusing on the buffering of glucose into glycogen, has been developed. The model exemplifies an 'engineering' approach to modelling in systems biology, and was produced by linking together seven component models of separate aspects of the physiology. The component models use a variety of modelling paradigms and degrees of simplification. Model parameters were determined by an iterative hybrid of fitting to high-scale physiological data, and determination from small-scale in vitro experiments or molecular biological techniques. The component models were not originally designed for inclusion within such a composite model, but were integrated, with modification, using our published modelling software and computational frameworks. This approach facilitates the development of large and complex composite models, although, inevitably, some compromises must be made when composing the individual models. Composite models of this form have not previously been demonstrated.

13N as a tracer for studying glutamate metabolism

This mini-review summarizes studies my associates and I carried out that are relevant to the topic of the present volume [i.e. glutamate dehydrogenase (GDH)] using radioactive (13)N (t(1/2) 9.96 min) as a biological tracer. These studies revealed the previously unrecognized rapidity with which nitrogen is exchanged among certain metabolites in vivo. For example, our work demonstrated that (a) the t(1/2) for conversion of portal vein ammonia to urea in the rat liver is ∼10-11s, despite the need for five enzyme-catalyzed steps and two mitochondrial transport steps, (b) the residence time for ammonia in the blood of anesthetized rats is ≤7-8s, (c) the t(1/2) for incorporation of blood-borne ammonia into glutamine in the normal rat brain is <3s, and (d) equilibration between glutamate and aspartate nitrogen in rat liver is extremely rapid (seconds), a reflection of the fact that the components of the hepatic aspartate aminotransferase reaction are in thermodynamic equilibrium. Our work emphasizes the importance of the GDH reaction in rat liver as a conduit for dissimilating or assimilating ammonia as needed. In contrast, our work shows that the GDH reaction in rat brain appears to operate mostly in the direction of ammonia production (dissimilation). The importance of the GDH reaction as an endogenous source of ammonia in the brain and the relation of GDH to the brain glutamine cycle is discussed. Finally, our work integrates with the increasing use of positron emission tomography (PET) and nuclear magnetic resonance (NMR) to study brain ammonia uptake and brain glutamine, respectively, in normal individuals and in patients with liver disease or other diseases associated with hyperammonemia.

Models of the human metabolic network: aiming to reconcile metabolomics and genomics

The metabolic syndrome, inborn errors of metabolism, and drug-induced changes to metabolic states all bring about a seemingly bewildering array of alterations in metabolite concentrations; these often occur in tissues and cells that are distant from those containing the primary biochemical lesion. How is it possible to collect sufficient biochemical information from a patient to enable us to work backwards and pinpoint the primary lesion, and possibly treat it in this whole human metabolic network? Potential analyses have benefited from modern methods such as ultra-high-pressure liquid chromatography, mass spectrometry, nuclear magnetic resonance spectroscopy, and more. A yet greater challenge is the prediction of outcomes of possible modern therapies using drugs and genetic engineering. This exposes the notion of viewing metabolism from a completely different perspective, with focus on the enzymes, regulators, and structural elements that are encoded by genes that specify the amino acid sequences, and hence encode the various interactions, be they regulatory or catalytic. The mainstream view of metabolism is being challenged, so we discuss here the reconciling of traditionally quantitative chemocentric metabolism with the seemingly 'parameter-free' genomic description, and vice versa.

Systems biology of microbial communities

Microbes exist naturally in a wide range of environments in communities where their interactions are significant, spanning the extremes of high acidity and high temperature environments to soil and the ocean. We present a practical discussion of three different approaches for modeling microbial communities: rate equations, individual-based modeling, and population dynamics. We illustrate the approaches with detailed examples. Each approach is best fit to different levels of system representation, and they have different needs for detailed biological input. Thus, this set of approaches is able to address the operation and function of microbial communities on a wide range of organizational levels.

Isotopomer-based metabolomic analysis by NMR and mass spectrometry

Nuclear magnetic resonance (NMR) and mass spectrometry (MS) together are synergistic in their ability to profile comprehensively the metabolome of cells and tissues. In addition to identification and quantification of metabolites, changes in metabolic pathways and fluxes in response to external perturbations can be reliably determined by using stable isotope tracer methodologies. NMR and MS together are able to define both positional isotopomer distribution in product metabolites that derive from a given stable isotope-labeled precursor molecule and the degree of enrichment at each site with good precision. Together with modeling tools, this information provides a rich functional biochemical readout of cellular activity and how it responds to external influences. In this chapter, we describe NMR- and MS-based methodologies for isotopomer analysis in metabolomics and its applications for different biological systems.

Isotopomer subspaces as indicators of metabolic-pathway structure

The relative abundances and rates of formation of particular isotopic isomers (isotopomers) of metabolic intermediates from (13)C-labelled substrates in living cells provide information on the routes taken by the initial (13)C-atoms. When a primary substrate such as [U,(13)C] d-glucose is added to human erythrocytes, the pattern of labels in terminal metabolites is determined by a set of carbon-group exchange reactions in both glycolysis and the pentose phosphate pathway (PPP). Of a given terminal metabolite, not all possible isotopomers will be produced from each possible primary substrate isotopomer. There are only 8 different (13)C-isotopomers of lactate but not all of these are produced when one of the 64 possible (13)C-isotopomers of glucose is used as the input substrate; thus a subset of all 63 glucose isotopomers x 8 lactate isotopomers+1 unlabelled glucose x 1 unlabelled lactate=505 pattern associations, would be produced if a complete experimental analysis were performed with all the glucose variants. The pattern of labelling in this isotopomer subspace reflects the nature of the re-ordering reactions that 'direct' the metabolism. Predicting the combinatorial rearrangements for particular sets of reactions and comparing these with real data should enable conclusions to be drawn about which enzymes are involved in the real metabolic system. An example of the glycolysis-PPP system is discussed in the context of a debate that occurred around the F- and L-type PPPs and which one actually operates in the human RBC. As part of this discussion we introduce the term 'combinatorial deficit' of all possible isotopomers and we show that this deficit is less for the F- than the L-type pathway.

Stochastic reaction-diffusion simulation of enzyme compartmentalization reveals improved catalytic efficiency for a synthetic metabolic pathway

We have demonstrated the accuracy of a spatial stochastic model of Escherichia coli central carbon metabolism using the next subvolume method (NSM), an efficient implementation of the Gillespie direct method of stochastic simulation. Using this model, we demonstrate that compartmentalization of the enzymes comprising an engineered pathway for biosynthesis of R-1,2-propanediol leads to improved kinetic properties for the pathway enzymes, especially when substrate diffusivities are low. Our results suggest that enzyme compartmentalization is a powerful approach for improving the catalytic turnover of a channeled carbon substrate and should be particularly useful when applied to synthetic metabolic pathways that suffer from poor translation efficiency, are present in highly variable copy numbers, and have low turnover for new substrates. Furthermore, this approach represents a generic modeling framework for simultaneously analyzing spatial and stochastic events in cellular metabolism and should enable quantitative evaluation of the effect of enzyme compartmentalization on virtually any recombinant pathway.

Species connectivities and reaction mechanisms from neutral response experiments

We develop a new method for obtaining connectivity data for nonlinear reaction networks, based on linear response experiments. In our approach the linear response is not the result of an approximation procedure but is due to the appropriate design of the response experiments, that is (1) they are carried out with the preservation of constant values for the total (labeled plus unlabeled) input and output fluxes and (2) the labeled compounds obey a neutrality condition (i.e., they have practically the same kinetic and transport properties as the unlabeled compounds). Under these circumstances the linear response equations hold even though the kinetics of the process is highly nonlinear. On the basis of this linear response law, we develop a method for evaluating reaction connectivities in biochemical networks from stationary response experiments. Given a system in a stationary regime, a pulse of a labeled species is introduced (with conservation of the total flux) and then the response of all the species of the network is recorded. The mechanistic information is contained in a connectivity matrix, K, which can be evaluated from the response data by means of differential as well as integral methods. The approach does not require any prior knowledge of the reaction mechanism. We carried out a numerical study of the method, based on a two-step procedure. Starting from a known reaction mechanism, we generated response data sets, to which we add noise; then, we use the noisy data sets for retrieving the connectivity matrix. The calculations were done with two programs written in Mathematica: the urea cycle and the upper part of glycolysis are used as sample biochemical networks. Given enough computer power, there are no limitations concerning the number of species involved in the response experiments; on current desktop systems processing responses of teens of species would take a few hours. The method is limited by the occurrence of experimental errors: if experimental errors in the evaluation of fluxes are larger than 10%, the method may fail to reproduce the correct values of some elements of the connectivity matrix.

Steady-state kinetic behaviour of functioning-dependent structures

A fundamental problem in biochemistry is that of the nature of the coordination between and within metabolic and signalling pathways. It is conceivable that this coordination might be assured by what we term functioning-dependent structures (FDSs), namely those assemblies of proteins that associate with one another when performing tasks and that disassociate when no longer performing them. To investigate a role in coordination for FDSs, we have studied numerically the steady-state kinetics of a model system of two sequential monomeric enzymes, E(1) and E(2). Our calculations show that such FDSs can display kinetic properties that the individual enzymes cannot. These include the full range of basic input/output characteristics found in electronic circuits such as linearity, invariance, pulsing and switching. Hence, FDSs can generate kinetics that might regulate and coordinate metabolism and signalling. Finally, we suggest that the occurrence of terms representative of the assembly and disassembly of FDSs in the classical expression of the density of entropy production are characteristic of living systems.

Inborn errors of metabolism: the flux from Mendelian to complex diseases

Inborn errors of metabolism are characterized by dysregulation of the metabolic networks that underlie development and homeostasis, and constitute an important and expanding group of genetic disorders in humans. Diagnostic methods that are based on molecular genetic tools have a limited ability to correlate phenotypes with subtle changes in metabolic fluxes. We argue that the direct and dynamic measurement of metabolite flux will facilitate the integration of environmental, genetic and biochemical factors with phenotypic information. Ultimately, this integration will lead to new diagnostic and therapeutic approaches that are focused on the manipulation of these pathways.

Simplification and its consequences in biological modelling: conclusions from a study of calcium oscillations in hepatocytes

Systems Biology requires that biological modelling is scaled up from small components to system level. This can produce exceedingly complex models, which obscure understanding rather than facilitate it. The successful use of highly simplified models would resolve many of the current problems faced in Systems Biology. This paper questions whether the conclusions of simple mathematical models of biological systems are trustworthy. The simplification of a specific model of calcium oscillations in hepatocytes is examined in detail, and the conclusions drawn from this scrutiny generalized. We formalize our choice of simplification approach through the use of functional 'building blocks'. A collection of models is constructed, each a progressively more simplified version of a well-understood model. The limiting model is a piecewise linear model that can be solved analytically. We find that, as expected, in many cases the simpler models produce incorrect results. However, when we make a sensitivity analysis, examining which aspects of the behaviour of the system are controlled by which parameters, the conclusions of the simple model often agree with those of the richer model. The hypothesis that the simplified model retains no information about the real sensitivities of the unsimplified model can be very strongly ruled out by treating the simplification process as a pseudo-random perturbation on the true sensitivity data. We conclude that sensitivity analysis is, therefore, of great importance to the analysis of simple mathematical models in biology. Our comparisons reveal which results of the sensitivity analysis regarding calcium oscillations in hepatocytes are robust to the simplifications necessarily involved in mathematical modelling. For example, we find that if a treatment is observed to strongly decrease the period of the oscillations while increasing the proportion of the cycle during which cellular calcium concentrations are rising, without affecting the inter-spike or maximum calcium concentrations, then it is likely that the treatment is acting on the plasma membrane calcium pump.

Towards building the silicon cell: a modular approach

Systems Biology aims to understand quantitatively how properties of biological systems can be understood as functions of the characteristics of, and interactions between their macromolecular components. Whereas, traditional biochemistry focused on isolation and characterization of cellular components, the challenge for Systems Biology lies in integration of this knowledge and the knowledge about molecular interactions. Computer models play an important role in this integration. We here discuss an approach with which we aim to link kinetic models on small parts of metabolism together, so as to form detailed kinetic models of larger chunks of metabolism, and ultimately of the entire living cell. Specifically, we will discuss techniques that can be used to model a sub-network in isolation of a larger network of which it is a part, while still maintaining the dynamics of the larger complete network. We will start by outlining the JWS online system, the silicon cell project, and the type of models we propose. JWS online is a model repository, which can be used for the storage, simulation and analysis of kinetic models. We advocate to integrate a top-down approach, where measurements on the complete system are used to derive fluxes in a detailed structural model, with a bottom-up approach, consisting of the integration of molecular mechanism-based detailed kinetic models into the structural model.

Modeling allosteric regulation of de novo pyrimidine biosynthesis in Escherichia coli

With the emergence of multifaceted bioinformatics-derived data, it is becoming possible to merge biochemical and physiological information to develop a new level of understanding of the metabolic complexity of the cell. The biosynthetic pathway of de novo pyrimidine nucleotide metabolism is an essential capability of all free-living cells, and it occupies a pivotal position relative to metabolic processes that are involved in the macromolecular synthesis of DNA, RNA and proteins, as well as energy production and cell division. This regulatory network in all enteric bacteria involves genetic, allosteric, and physiological control systems that need to be integrated into a coordinated set of metabolic checks and balances. Allosterically regulated pathways constitute an exciting and challenging biosynthetic system to be approached from a mathematical perspective. However, to date, a mathematical model quantifying the contribution of allostery in controlling the dynamics of metabolic pathways has not been proposed. In this study, a direct, rigorous mathematical model of the de novo biosynthesis of pyrimidine nucleotides is presented. We corroborate the simulations with experimental data available in the literature and validate it with derepression experiments done in our laboratory. The model is able to faithfully represent the dynamic changes in the intracellular nucleotide pools that occur during metabolic transitions of the de novo pyrimidine biosynthetic pathway and represents a step forward in understanding the role of allosteric regulation in metabolic control.

The Silicon Cell initiative: working towards a detailed kinetic description at the cellular level

The Silicon Cell initiative aims to understand cellular systems on the basis of the characteristics of their components. As a tool to achieve this, detailed kinetic models at the network reaction level are being constructed. Such detailed kinetic models are extremely useful for medical and biotechnological applications and form strong tools for fundamental studies. Several recently constructed detailed kinetic models on metabolism (glycolysis), signal transduction (EGF receptor), and the eukaryotic cell cycle (Saccharomyces cerevisiae) have been used to exemplify the Silicon Cell project. These models are stored and made accessible via the JWS Online Cellular Systems Modeling project, a web-based repository of kinetic models. Using a web-browser the models can be interrogated via a user-friendly graphical interface. The goal of the two projects is to combine models on parts of cellular systems and ultimately to construct detailed kinetic models at the cellular level.

A computational model of mitochondrial deoxynucleotide metabolism and DNA replication

We present a computational model of mitochondrial deoxynucleotide metabolism and mitochondrial DNA (mtDNA) synthesis. The model includes the transport of deoxynucleosides and deoxynucleotides into the mitochondrial matrix space, as well as their phosphorylation and polymerization into mtDNA. Different simulated cell types (cancer, rapidly dividing, slowly dividing, and postmitotic cells) are represented in this model by different cytoplasmic deoxynucleotide concentrations. We calculated the changes in deoxynucleotide concentrations within the mitochondrion during the course of a mtDNA replication event and the time required for mtDNA replication in the different cell types. On the basis of the model, we define three steady states of mitochondrial deoxynucleotide metabolism: the phosphorylating state (the net import of deoxynucleosides and export of phosphorylated deoxynucleotides), the desphosphorylating state (the reverse of the phosphorylating state), and the efficient state (the net import of both deoxynucleosides and deoxynucleotides). We present five testable hypotheses based on this simulation. First, the deoxynucleotide pools within a mitochondrion are sufficient to support only a small fraction of even a single mtDNA replication event. Second, the mtDNA replication time in postmitotic cells is much longer than that in rapidly dividing cells. Third, mitochondria in dividing cells are net sinks of cytoplasmic deoxynucleotides, while mitochondria in postmitotic cells are net sources. Fourth, the deoxynucleotide carrier exerts the most control over the mtDNA replication rate in rapidly dividing cells, but in postmitotic cells, the NDPK and TK2 enzymes have the most control. Fifth, following from the previous hypothesis, rapidly dividing cells derive almost all of their mtDNA precursors from the cytoplasmic deoxynucleotides, not from phosphorylation within the mitochondrion.

Current status and challenges in connecting models of erythrocyte metabolism to experimental reality

Detailed kinetic models of human erythrocyte metabolism have served to summarize the vast literature and to predict outcomes from laboratory and "Nature's" experiments on this simple cell. Mathematical methods for handling the large array of nonlinear ordinary differential equations that describe the time dependence of this system are well developed, but experimental methods that can guide the evolution of the models are in short supply. NMR spectroscopy is one method that is non-selective with respect to analyte detection but is highly specific with respect to their identification and quantification. Thus time courses of metabolism are readily recorded for easily changed experimental conditions. While the data can be simulated, the systems of equations are too complex to allow solutions of the inverse problem, namely parameter-value estimation for the large number of enzyme and membrane-transport reactions operating in situ as opposed to in vitro. Other complications with the modelling include the dependence of cell volume on time, and the rates of membrane transport processes are often dependent on the membrane potential. These matters are discussed in the light of new modelling strategies.