In silico model-driven assessment of the effects of single nucleotide polymorphisms (SNPs) on human red blood cell metabolism

Development of a POCT detection platform based on a locked nucleic acid-enhanced ARMS-RPA-GoldMag lateral flow assay

In this study, a novel genotyping point-of-care testing (POCT) rapid detection device, the locked nucleic acid (LNA)-amplification refractory mutation system (ARMS)-recombinase polymerase amplification (RPA)-GoldMag lateral flow assay (LFA) platform, was provided by mining and synthesis based on prior technology. Research methods based on system-integrated innovation and knowledge-integrated generation have become a new trend in technology development. Here, we exploit the combination of LNA-coupled ARMS-RPA and gold nanoparticle probe technology for detection signal amplification, thus pioneering a new tool for accurate, rapid, and cost-effective genotyping. We also performed SNP typing detection and clinical validation of this new assay platform using common glucose-6-phosphate dehydrogenase (G6PD) gene single nucleotide polymorphism (SNP) loci, and the results demonstrated the high sensitivity, specificity, stability, accuracy and feasibility of the LNA-ARMS-RPA-GoldMag lateral flow assay platform. It is hoped that this new technology will make a significant contribution to the field of POCT rapid diagnosis and aim to expand the application space, reflecting its clinical application value and development prospects.

Topological and kinetic determinants of the modal matrices of dynamic models of metabolism

Large-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of metabolic networks. Central to linear analysis methods are two key matrices: the Jacobian matrix (J) and the modal matrix (M-1) arising from its eigendecomposition. The modal matrix M-1 contains dynamically independent motions of the kinetic model near a reference state, and it is sparse in practice for metabolic networks. However, connecting the structure of M-1 to the kinetic properties of the underlying reactions is non-trivial. In this study, we analyze the relationship between J, M-1, and the kinetic properties of the underlying network for kinetic models of metabolism. Specifically, we describe the origin of mode sparsity structure based on features of the network stoichiometric matrix S and the reaction kinetic gradient matrix G. First, we show that due to the scaling of kinetic parameters in real networks, diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures with clear biological interpretations. Then, we show that more complicated modes originate from topologically-connected reactions that have similar reaction elasticities in G. These elasticities represent dynamic equilibrium balances within reactions and are key determinants of modal structure. The work presented should prove useful towards obtaining an understanding of the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions.

A Multi-scale Computational Platform to Mechanistically Assess the Effect of Genetic Variation on Drug Responses in Human Erythrocyte Metabolism

Progress in systems medicine brings promise to addressing patient heterogeneity and individualized therapies. Recently, genome-scale models of metabolism have been shown to provide insight into the mechanistic link between drug therapies and systems-level off-target effects while being expanded to explicitly include the three-dimensional structure of proteins. The integration of these molecular-level details, such as the physical, structural, and dynamical properties of proteins, notably expands the computational description of biochemical network-level properties and the possibility of understanding and predicting whole cell phenotypes. In this study, we present a multi-scale modeling framework that describes biological processes which range in scale from atomistic details to an entire metabolic network. Using this approach, we can understand how genetic variation, which impacts the structure and reactivity of a protein, influences both native and drug-induced metabolic states. As a proof-of-concept, we study three enzymes (catechol-O-methyltransferase, glucose-6-phosphate dehydrogenase, and glyceraldehyde-3-phosphate dehydrogenase) and their respective genetic variants which have clinically relevant associations. Using all-atom molecular dynamic simulations enables the sampling of long timescale conformational dynamics of the proteins (and their mutant variants) in complex with their respective native metabolites or drug molecules. We find that changes in a protein's structure due to a mutation influences protein binding affinity to metabolites and/or drug molecules, and inflicts large-scale changes in metabolism.

Evaluation of rate law approximations in bottom-up kinetic models of metabolism

BACKGROUND

The mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.

RESULTS

In this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.

CONCLUSIONS

Overall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches.

Metabolomics in transfusion medicine

Biochemical investigations on the regulatory mechanisms of red blood cell (RBC) and platelet (PLT) metabolism have fostered a century of advances in the field of transfusion medicine. Owing to these advances, storage of RBCs and PLT concentrates has become a lifesaving practice in clinical and military settings. There, however, remains room for improvement, especially with regard to the introduction of novel storage and/or rejuvenation solutions, alternative cell processing strategies (e.g., pathogen inactivation technologies), and quality testing (e.g., evaluation of novel containers with alternative plasticizers). Recent advancements in mass spectrometry-based metabolomics and systems biology, the bioinformatics integration of omics data, promise to speed up the design and testing of innovative storage strategies developed to improve the quality, safety, and effectiveness of blood products. Here we review the currently available metabolomics technologies and briefly describe the routine workflow for transfusion medicine-relevant studies. The goal is to provide transfusion medicine experts with adequate tools to navigate through the otherwise overwhelming amount of metabolomics data burgeoning in the field during the past few years. Descriptive metabolomics data have represented the first step omics researchers have taken into the field of transfusion medicine. However, to up the ante, clinical and omics experts will need to merge their expertise to investigate correlative and mechanistic relationships among metabolic variables and transfusion-relevant variables, such as 24-hour in vivo recovery for transfused RBCs. Integration with systems biology models will potentially allow for in silico prediction of metabolic phenotypes, thus streamlining the design and testing of alternative storage strategies and/or solutions.

Analysis of genetic variation and potential applications in genome-scale metabolic modeling

Genetic variation is the motor of evolution and allows organisms to overcome the environmental challenges they encounter. It can be both beneficial and harmful in the process of engineering cell factories for the production of proteins and chemicals. Throughout the history of biotechnology, there have been efforts to exploit genetic variation in our favor to create strains with favorable phenotypes. Genetic variation can either be present in natural populations or it can be artificially created by mutagenesis and selection or adaptive laboratory evolution. On the other hand, unintended genetic variation during a long term production process may lead to significant economic losses and it is important to understand how to control this type of variation. With the emergence of next-generation sequencing technologies, genetic variation in microbial strains can now be determined on an unprecedented scale and resolution by re-sequencing thousands of strains systematically. In this article, we review challenges in the integration and analysis of large-scale re-sequencing data, present an extensive overview of bioinformatics methods for predicting the effects of genetic variants on protein function, and discuss approaches for interfacing existing bioinformatics approaches with genome-scale models of cellular processes in order to predict effects of sequence variation on cellular phenotypes.

SBMLSimulator: A Java Tool for Model Simulation and Parameter Estimation in Systems Biology

The identification of suitable model parameters for biochemical reactions has been recognized as a quite difficult endeavor. Parameter values from literature or experiments can often not directly be combined in complex reaction systems. Nature-inspired optimization techniques can find appropriate sets of parameters that calibrate a model to experimentally obtained time series data. We present SBMLsimulator, a tool that combines the Systems Biology Simulation Core Library for dynamic simulation of biochemical models with the heuristic optimization framework EvA2. SBMLsimulator provides an intuitive graphical user interface with various options as well as a fully-featured command-line interface for large-scale and script-based model simulation and calibration. In a parameter estimation study based on a published model and artificial data we demonstrate the capability of SBMLsimulator to identify parameters. SBMLsimulator is useful for both, the interactive simulation and exploration of the parameter space and for the large-scale model calibration and estimation of uncertain parameter values.

Revitalizing personalized medicine: respecting biomolecular complexities beyond gene expression

Despite recent advancements in "omic" technologies, personalized medicine has not realized its fullest potential due to isolated and incomplete application of gene expression tools. In many instances, pharmacogenomics is being interchangeably used for personalized medicine, when actually it is one of the many facets of personalized medicine. Herein, we highlight key issues that are hampering the advancement of personalized medicine and highlight emerging predictive tools that can serve as a decision support mechanism for physicians to personalize treatments.

Evaluation of liver and kidney function in favism patients

BACKGROUND

G6PD deficiency is the most common enzymopathy of red blood cells. The clinical symptoms of favism are jaundice, hematuria and haemolytic anaemia that seem to affect liver and kidney in long term. Thus we evaluate kidney and liver function of favism patients in an endemic area of the disease with a high rate of fava beans cultivation.

METHODS

This study was performed on favism patients and healthy controls referring to Iranshahr central hospital. Liver and kidney function tests were performed.

RESULTS

The results showed a statistically significant difference between these two groups (p <0.05) for liver function tests, (AST, ALT and ALP), but not for renal tests (BUN and creatinine) (p >0.05).

CONCLUSION

Due to abnormalities were seen in the liver function tests of these patients, we suggest that these tests be regularly performed for favism patients who are constantly exposed to oxidant agents.

Path to facilitate the prediction of functional amino acid substitutions in red blood cell disorders--a computational approach

Background

A major area of effort in current genomics is to distinguish mutations that are functionally neutral from those that contribute to disease. Single Nucleotide Polymorphisms (SNPs) are amino acid substitutions that currently account for approximately half of the known gene lesions responsible for human inherited diseases. As a result, the prediction of non-synonymous SNPs (nsSNPs) that affect protein functions and relate to disease is an important task.

Principal Findings

In this study, we performed a comprehensive analysis of deleterious SNPs at both functional and structural level in the respective genes associated with red blood cell metabolism disorders using bioinformatics tools. We analyzed the variants in Glucose-6-phosphate dehydrogenase (G6PD) and isoforms of Pyruvate Kinase (PKLR & PKM2) genes responsible for major red blood cell disorders. Deleterious nsSNPs were categorized based on empirical rule and support vector machine based methods to predict the impact on protein functions. Furthermore, we modeled mutant proteins and compared them with the native protein for evaluation of protein structure stability.

Significance

We argue here that bioinformatics tools can play an important role in addressing the complexity of the underlying genetic basis of Red Blood Cell disorders. Based on our investigation, we report here the potential candidate SNPs, for future studies in human Red Blood Cell disorders. Current study also demonstrates the presence of other deleterious mutations and also endorses with in vivo experimental studies. Our approach will present the application of computational tools in understanding functional variation from the perspective of structure, expression, evolution and phenotype.

Systems-biology approaches for predicting genomic evolution

Is evolution predictable at the molecular level? The ambitious goal to answer this question requires an understanding of the mutational effects that govern the complex relationship between genotype and phenotype. In practice, it involves integrating systems-biology modelling, microbial laboratory evolution experiments and large-scale mutational analyses - a feat that is made possible by the recent availability of the necessary computational tools and experimental techniques. This Review investigates recent progresses in mapping evolutionary trajectories and discusses the degree to which these predictions are realistic.

A systems biology framework for modeling metabolic enzyme inhibition of Mycobacterium tuberculosis

BACKGROUND

Because metabolism is fundamental in sustaining microbial life, drugs that target pathogen-specific metabolic enzymes and pathways can be very effective. In particular, the metabolic challenges faced by intracellular pathogens, such as Mycobacterium tuberculosis, residing in the infected host provide novel opportunities for therapeutic intervention.

RESULTS

We developed a mathematical framework to simulate the effects on the growth of a pathogen when enzymes in its metabolic pathways are inhibited. Combining detailed models of enzyme kinetics, a complete metabolic network description as modeled by flux balance analysis, and a dynamic cell population growth model, we quantitatively modeled and predicted the dose-response of the 3-nitropropionate inhibitor on the growth of M. tuberculosis in a medium whose carbon source was restricted to fatty acids, and that of the 5'-O-(N-salicylsulfamoyl) adenosine inhibitor in a medium with low-iron concentration.

CONCLUSION

The predicted results quantitatively reproduced the experimentally measured dose-response curves, ranging over three orders of magnitude in inhibitor concentration. Thus, by allowing for detailed specifications of the underlying enzymatic kinetics, metabolic reactions/constraints, and growth media, our model captured the essential chemical and biological factors that determine the effects of drug inhibition on in vitro growth of M. tuberculosis cells.

Using in silico models to simulate dual perturbation experiments: procedure development and interpretation of outcomes

Background

A growing number of realistic in silico models of metabolic functions are being formulated and can serve as 'dry lab' platforms to prototype and simulate experiments before they are performed. For example, dual perturbation experiments that vary both genetic and environmental parameters can readily be simulated in silico. Genetic and environmental perturbations were applied to a cell-scale model of the human erythrocyte and subsequently investigated.

Results

The resulting steady state fluxes and concentrations, as well as dynamic responses to the perturbations were analyzed, yielding two important conclusions: 1) that transporters are informative about the internal states (fluxes and concentrations) of a cell and, 2) that genetic variations can disrupt the natural sequence of dynamic interactions between network components. The former arises from adjustments in energy and redox states, while the latter is a result of shifting time scales in aggregate pool formation of metabolites. These two concepts are illustrated for glucose-6 phosphate dehydrogenase (G6PD) and pyruvate kinase (PK) in the human red blood cell.

Conclusion

Dual perturbation experiments in silico are much more informative for the characterization of functional states than single perturbations. Predictions from an experimentally validated cellular model of metabolism indicate that the measurement of cofactor precursor transport rates can inform the internal state of the cell when the external demands are altered or a causal genetic variation is introduced. Finally, genetic mutations that alter the clinical phenotype may also disrupt the 'natural' time scale hierarchy of interactions in the network.

Formulating genome-scale kinetic models in the post-genome era

The biological community is now awash in high-throughput data sets and is grappling with the challenge of integrating disparate data sets. Such integration has taken the form of statistical analysis of large data sets, or through the bottom-up reconstruction of reaction networks. While progress has been made with statistical and structural methods, large-scale systems have remained refractory to dynamic model building by traditional approaches. The availability of annotated genomes enabled the reconstruction of genome-scale networks, and now the availability of high-throughput metabolomic and fluxomic data along with thermodynamic information opens the possibility to build genome-scale kinetic models. We describe here a framework for building and analyzing such models. The mathematical analysis challenges are reflected in four foundational properties, (i) the decomposition of the Jacobian matrix into chemical, kinetic and thermodynamic information, (ii) the structural similarity between the stoichiometric matrix and the transpose of the gradient matrix, (iii) the duality transformations enabling either fluxes or concentrations to serve as the independent variables and (iv) the timescale hierarchy in biological networks. Recognition and appreciation of these properties highlight notable and challenging new in silico analysis issues.

In silico analysis of SNPs and other high-throughput data

The availability and accessibility of high-throughput and biological legacy data have allowed mathematical analyses of genome-scale metabolic networks and models. Model formulation is centered on the conservation principles of mass and charge. Thermodynamic information is generally incorporated by means of reaction reversibility. If further experimental data are available, such as kinetic parameters, models describing system evolution over time can be developed. The type of data available largely determines the type of model (and subsequently the type of analysis) that can be performed. Different modeling approaches offer different advantages. Detailed kinetic models can make specific predictions about network functional states given knowledge about the enzyme parameter variations resulting from single-nucleotide polymorphisms (SNPs). They also require a large amount of experimental data, which is rarely available. On the other hand, although current formulations using the constraint-based optimization framework do not offer information about metabolite concentrations or time-dependent changes, it is a remarkably flexible modeling framework and permits the integration of a large amount of very different data types.

Simulation study of methemoglobin reduction in erythrocytes. Differential contributions of two pathways to tolerance to oxidative stress

Methemoglobin (metHb), an oxidized form of hemoglobin, is unable to bind and carry oxygen. Erythrocytes are continuously subjected to oxidative stress and nitrite exposure, which results in the spontaneous formation of metHb. To avoid the accumulation of metHb, reductive pathways mediated by cytochrome b5 or flavin, coupled with NADH-dependent or NADPH-dependent metHb reductases, respectively, keep the level of metHb in erythrocytes at less than 1% of the total hemoglobin under normal conditions. In this work, a mathematical model has been developed to quantitatively assess the relative contributions of the two major metHb-reducing pathways, taking into consideration the supply of NADH and NADPH from central energy metabolism. The results of the simulation experiments suggest that these pathways have different roles in the reduction of metHb; one has a high response rate to hemoglobin oxidation with a limited reducing flux, and the other has a low response rate with a high capacity flux. On the basis of the results of our model, under normal oxidative conditions, the NADPH-dependent system, the physiological role of which to date has been unclear, is predicted to be responsible for most of the reduction of metHb. In contrast, the cytochrome b5-NADH pathway becomes dominant under conditions of excess metHb accumulation, only after the capacity of the flavin-NADPH pathway has reached its limit. We discuss the potential implications of a system designed with two metHb-reducing pathways in human erythrocytes.

Dynamics of biological systems: role of systems biology in medical research

Cellular systems are networks of interacting components that change with time in response to external and internal events. Studying the dynamic behavior of these networks is the basis for an understanding of cellular functions and disease mechanisms. Quantitative time-series data leading to meaningful models can improve our knowledge of human physiology in health and disease, and aid the search for earlier diagnoses, better therapies and a healthier life. The advent of systems biology is about to take the leap into clinical research and medical applications. This review emphasizes the importance of a dynamic view and understanding of cell function. We discuss the potential for computer-aided mathematical modeling of biological systems in medical research with examples from some of the major therapeutic areas: cancer, cardiovascular, diabetic and neurodegenerative medicine.

Towards multidimensional genome annotation

Our information about the gene content of organisms continues to grow as more genomes are sequenced and gene products are characterized. Sequence-based annotation efforts have led to a list of cellular components, which can be thought of as a one-dimensional annotation. With growing information about component interactions, facilitated by the advancement of various high-throughput technologies, systemic, or two-dimensional, annotations can be generated. Knowledge about the physical arrangement of chromosomes will lead to a three-dimensional spatial annotation of the genome and a fourth dimension of annotation will arise from the study of changes in genome sequences that occur during adaptive evolution. Here we discuss all four levels of genome annotation, with specific emphasis on two-dimensional annotation methods.

Systems biology of the human red blood cell

While the potential possibilities of systems biology appear to hold great promise, there are still many challenges to overcome, notably lack of complete characterization of biological components and their interactions and ways to measure these changes experimentally. The comparative simplicity of the human red cell sidesteps much of these challenges. Detailed models of human red cell metabolism have been developed for the last quarter century and continued development of these models has resulted in the ability to make functional phenotype predictions, in silico. Additionally, existing experimental proteomic and metabolomic technologies now provide the capability to perform individualized characterization of erythrocytes. While an experimentally testable systems biology model of most human cells is presently out of reach, it may be achievable with the red cell.

Uniform sampling of steady-state flux spaces: means to design experiments and to interpret enzymopathies

Reconstruction of genome-scale metabolic networks is now possible using multiple different data types. Constraint-based modeling is an approach to interrogate capabilities of reconstructed networks by constraining possible cellular behavior through the imposition of physicochemical laws. As a result, a steady-state flux space is defined that contains all possible functional states of the network. Uniform random sampling of the steady-state flux space allows for the unbiased appraisal of its contents. Monte Carlo sampling of the steady-state flux space of the reconstructed human red blood cell metabolic network under simulated physiologic conditions yielded the following key results: 1), probability distributions for the values of individual metabolic fluxes showed a wide variety of shapes that could not have been inferred without computation; 2), pairwise correlation coefficients were calculated between all fluxes, determining the level of independence between the measurement of any two fluxes, and identifying highly correlated reaction sets; and 3), the network-wide effects of the change in one (or a few) variables (i.e., a simulated enzymopathy or fixing a flux range based on measurements) were computed. Mathematical models provide the most compact and informative representation of a hypothesis of how a cell works. Thus, understanding model predictions clearly is vital to driving forward the iterative model-building procedure that is at the heart of systems biology. Taken together, the Monte Carlo sampling procedure provides a broadening of the constraint-based approach by allowing for the unbiased and detailed assessment of the impact of the applied physicochemical constraints on a reconstructed network.

Tools for target identification and validation

Reliable technologies for addressing target identification and validation are the foundation of successful drug development. Microarrays have been well utilized in genomics/proteomics approaches for gene/protein expression profiling and tissue/cell-scale target validation. Besides being used as an essential step in analyzing high-throughput experiments such as those involving microarrays, bioinformatics can also contribute to the processes of target identification and validation by providing functional information about target candidates and positioning information to biological networks. Antisense technologies (including RNA interference technology, which is recently very 'hot') enable sequence-based gene knockdown at the RNA level. Zinc finger proteins are a DNA transcription-targeting version of knockdown. Chemical genomics and proteomics are emerging tools for generating phenotype changes, thus leading to target and hit identifications. NMR-based screening, as well as activity-based protein profiling, are trying to meet the requirement of high-throughput target identification.

Parallel analysis of mutant human glucose 6-phosphate dehydrogenase in yeast using PCR colonies

We demonstrate a highly parallel strategy to analyze the impact of single nucleotide mutations on protein function. Using our method, it is possible to screen a population and quickly identify a subset of functionally interesting mutants. Our method utilizes a combination of yeast functional complementation, growth competition of mutant pools, and polymerase colonies. A defined mutant human glucose-6-phosphate-dehydrogenase library was constructed which contains all possible single nucleotide missense mutations in the eight-residue glucose-6-phosphate binding peptide of the enzyme. Mutant human enzymes were expressed in a zwf1 (gene encoding yeast homologue) deletion strain of Saccharomyces cerevisiae. Growth rates of the 54 mutant strains arising from this library were measured in parallel in conditions selective for active hG6PD. Several residues were identified which tolerated no mutations (Asp200, His201 and Lys205) and two (Ile199 and Leu203) tolerated several substitutions. Arg198, Tyr202, and Gly204 tolerated only 1-2 specific substitutions. Generalizing from the positions of tolerated and non-tolerated amino acid substitutions, hypotheses were generated about the functional role of specific residues, which could, potentially, be tested using higher resolution/lower throughput methods.

k-Cone analysis: determining all candidate values for kinetic parameters on a network scale

The absence of comprehensive measured kinetic values and the observed inconsistency in the available in vitro kinetic data has hindered the formulation of network-scale kinetic models of biochemical reaction networks. To meet this challenge we present an approach to construct a convex space, termed the k-cone, which contains all the allowable numerical values of the kinetic constants in large-scale biochemical networks. The definition of the k-cone relies on the incorporation of in vivo concentration data and a simplified approach to represent enzyme kinetics within an established constraint-based modeling approach. The k-cone approach was implemented to define the allowable combination of numerical values for a full kinetic model of human red blood cell metabolism and to study its correlated kinetic parameters. The k-cone approach can be used to determine consistency between in vitro measured kinetic values and in vivo concentration and flux measurements when used in a network-scale kinetic model. k-Cone analysis was successful in determining whether in vitro measured kinetic values used in the reconstruction of a kinetic-based model of Saccharomyces cerevisiae central metabolism could reproduce in vivo measurements. Further, the k-cone can be used to determine which numerical values of in vitro measured parameters are required to be changed in a kinetic model if in vivo measured values are not reproduced. k-Cone analysis could identify what minimum number of in vitro determined kinetic parameters needed to be adjusted in the S. cerevisiae model to be consistent with the in vivo data. Applying the k-cone analysis a priori to kinetic model development may reduce the time and effort involved in model building and parameter adjustment. With the recent developments in high-throughput profiling of metabolite concentrations at a whole-cell scale and advances in metabolomics technologies, the k-cone approach presented here may hold the promise for kinetic characterization of metabolic networks as well as other biological functions at a whole-cell level.

Monte Carlo sampling can be used to determine the size and shape of the steady-state flux space

Constraint-based modeling results in a convex polytope that defines a solution space containing all possible steady-state flux distributions. The properties of this polytope have been studied extensively using linear programming to find the optimal flux distribution under various optimality conditions and convex analysis to define its extreme pathways (edges) and elementary modes. The work presented herein further studies the steady-state flux space by defining its hyper-volume. In low dimensions (i.e. for small sample networks), exact volume calculation algorithms were used. However, due to the #P-hard nature of the vertex enumeration and volume calculation problem in high dimensions, random Monte Carlo sampling was used to characterize the relative size of the solution space of the human red blood cell metabolic network. Distributions of the steady-state flux levels for each reaction in the metabolic network were generated to show the range of flux values for each reaction in the polytope. These results give insight into the shape of the high-dimensional solution space. The value of measuring uptake and secretion rates in shrinking the steady-state flux solution space is illustrated through singular value decomposition of the randomly sampled points. The V(max) of various reactions in the network are varied to determine the sensitivity of the solution space to the maximum capacity constraints. The methods developed in this study are suitable for testing the implication of additional constraints on a metabolic network system and can be used to explore the effects of single nucleotide polymorphisms (SNPs) on network capabilities.

Network-based analysis of metabolic regulation in the human red blood cell

Reconstruction of cell-scale metabolic networks is now possible. A description of allowable metabolic network functions can be obtained using extreme pathways, which are the convex basis vectors of the solution space containing all steady state flux distributions. However, only a portion of these allowable network functions are physiologically possible due to kinetic and regulatory constraints. Methods are now needed that enable us to take a defined metabolic network and deduce candidate regulatory structures that control the selection of these physiologically relevant states. One such approach is the singular value decomposition (SVD) of extreme pathway matrices (P), which allows for the characterization of steady state solution spaces. Eigenpathways, which are the left singular vectors from the SVD of P, can be described and categorized by their biochemical function. SVD of P for the human red blood cell showed that the first five eigenpathways, out of a total of 23, effectively characterize all the relevant physiological states of red blood cell metabolism calculated with a detailed kinetic model. Thus, with five degrees of freedom the magnitude and nature of the regulatory needs are defined. Additionally, the dominant features of these first five eigenpathways described key metabolic splits that are indeed regulated in the human red blood cell. The extreme pathway matrix is derived directly from network topology and only knowledge of Vmax values is needed to reach these conclusions. Thus, we have implemented a network-based analysis of regulation that complements the study of individual regulatory events. This topological approach may provide candidate regulatory structures for metabolic networks with known stoichiometry but poorly characterized regulation.

Reconstructing metabolic flux vectors from extreme pathways: defining the alpha-spectrum

The move towards genome-scale analysis of cellular functions has necessitated the development of analytical (in silico) methods to understand such large and complex biochemical reaction networks. One such method is extreme pathway analysis that uses stoichiometry and thermodynamic irreversibly to define mathematically unique, systemic metabolic pathways. These extreme pathways form the edges of a high-dimensional convex cone in the flux space that contains all the attainable steady state solutions, or flux distributions, for the metabolic network. By definition, any steady state flux distribution can be described as a nonnegative linear combination of the extreme pathways. To date, much effort has been focused on calculating, defining, and understanding these extreme pathways. However, little work has been performed to determine how these extreme pathways contribute to a given steady state flux distribution. This study represents an initial effort aimed at defining how physiological steady state solutions can be reconstructed from a network's extreme pathways. In general, there is not a unique set of nonnegative weightings on the extreme pathways that produce a given steady state flux distribution but rather a range of possible values. This range can be determined using linear optimization to maximize and minimize the weightings of a particular extreme pathway in the reconstruction, resulting in what we have termed the alpha-spectrum. The alpha-spectrum defines which extreme pathways can and cannot be included in the reconstruction of a given steady state flux distribution and to what extent they individually contribute to the reconstruction. It is shown that accounting for transcriptional regulatory constraints can considerably shrink the alpha-spectrum. The alpha-spectrum is computed and interpreted for two cases; first, optimal states of a skeleton representation of core metabolism that include transcriptional regulation, and second for human red blood cell metabolism under various physiological, non-optimal conditions.

Parallel competition analysis of Saccharomyces cerevisiae strains differing by a single base using polymerase colonies

We describe a strategy to analyze the impact of single nucleotide mutations on protein function. Our method utilizes a combination of yeast functional complementation, growth competition of mutant pools and polyacrylamide gel immobilized PCR. A system was constructed in which the yeast PGK1 gene was expressed from a plasmid-borne copy of the gene in a PGK1 deletion strain of Saccharomyces cerevisiae. Using this system, we demonstrated that the enrichment or depletion of PGK1 point mutants from a mixed culture was consistent with the expected results based on the isolated growth rates of the mutants. Enrichment or depletion of individual point mutants was shown to result from increases or decreases, respectively, in the specific activities of the encoded proteins. Further, we demonstrate the ability to analyze the functional effect of many individual point mutations in parallel. By functional complementation of yeast deletions with human homologs, our technique could be readily applied to the functional analysis of single nucleotide polymorphisms in human genes of medical interest.