A Mathematical Model for the Branched Chain Amino Acid Biosynthetic Pathways of Escherichia coli K12

Self-Organization and Information Processing: From Basic Enzymatic Activities to Complex Adaptive Cellular Behavior

One of the main aims of current biology is to understand the origin of the molecular organization that underlies the complex dynamic architecture of cellular life. Here, we present an overview of the main sources of biomolecular order and complexity spanning from the most elementary levels of molecular activity to the emergence of cellular systemic behaviors. First, we have addressed the dissipative self-organization, the principal source of molecular order in the cell. Intensive studies over the last four decades have demonstrated that self-organization is central to understand enzyme activity under cellular conditions, functional coordination between enzymatic reactions, the emergence of dissipative metabolic networks (DMN), and molecular rhythms. The second fundamental source of order is molecular information processing. Studies on effective connectivity based on transfer entropy (TE) have made possible the quantification in bits of biomolecular information flows in DMN. This information processing enables efficient self-regulatory control of metabolism. As a consequence of both main sources of order, systemic functional structures emerge in the cell; in fact, quantitative analyses with DMN have revealed that the basic units of life display a global enzymatic structure that seems to be an essential characteristic of the systemic functional metabolism. This global metabolic structure has been verified experimentally in both prokaryotic and eukaryotic cells. Here, we also discuss how the study of systemic DMN, using Artificial Intelligence and advanced tools of Statistic Mechanics, has shown the emergence of Hopfield-like dynamics characterized by exhibiting associative memory. We have recently confirmed this thesis by testing associative conditioning behavior in individual amoeba cells. In these Pavlovian-like experiments, several hundreds of cells could learn new systemic migratory behaviors and remember them over long periods relative to their cell cycle, forgetting them later. Such associative process seems to correspond to an epigenetic memory. The cellular capacity of learning new adaptive systemic behaviors represents a fundamental evolutionary mechanism for cell adaptation.

Persister Cells Form in the Plant Pathogen Xanthomonas citri subsp. citri under Different Stress Conditions

Citrus canker disease, caused by the bacterium Xanthomonas citri subsp. citri is a constant threat to citrus-producing areas. Since it has no cure, agricultural practices to restrain its dissemination are essential to reduce the economic damage. Hence, increased knowledge of the basic aspects of X. citri biology could lead to more efficient management practices that can eliminate dormant bacteria in the field. The dormant cells, also referred to as persisters, are phenotypic variants with lowered metabolism, which in turn leads to tolerance to antimicrobials and undermines existing control approaches. We show here that X. citri forms persisters, identifying triggers for this phenotype, including antibiotics, high temperature, and metals (copper and zinc), which increase persistence rates by 10–100 times. The antioxidant N-acetylcysteine reduced copper and zinc-induced persisters, but not those induced by tetracycline, indicating that oxidative stress may be an important inducer of X. citri persistence. In addition, we found that metabolism-independent drugs like cisplatin and mitomycin C are able to eliminate X. citri persistent cells, as well as copper, at high concentrations. Specific amino acids like proline and isoleucine interfered with the physiological balance of the dormancy in X. citri, stimulating or preventing persister resuscitation. Taken together, we discover chemicals that can induce, wake, and kill X. citri persister cells; these results provide insights that should be considered for more efficient integrated control management in the field.

Diversification of Transcriptional Regulation Determines Subfunctionalization of Paralogous Branched Chain Aminotransferases in the Yeast Saccharomyces cerevisiae

Saccharomyces cerevisiae harbors BAT1 and BAT2 paralogous genes that encode branched chain aminotransferases and have opposed expression profiles and physiological roles . Accordingly, in primary nitrogen sources such as glutamine, BAT1 expression is induced, supporting Bat1-dependent valine-isoleucine-leucine (VIL) biosynthesis, while BAT2 expression is repressed. Conversely, in the presence of VIL as the sole nitrogen source, BAT1 expression is hindered while that of BAT2 is activated, resulting in Bat2-dependent VIL catabolism. The presented results confirm that BAT1 expression is determined by transcriptional activation through the action of the Leu3-α-isopropylmalate (α-IPM) active isoform, and uncovers the existence of a novel α-IPM biosynthetic pathway operating in a put3Δ mutant grown on VIL, through Bat2-Leu2-Leu1 consecutive action. The classic α-IPM biosynthetic route operates in glutamine through the action of the leucine-sensitive α-IPM synthases. The presented results also show that BAT2 repression in glutamine can be alleviated in a ure2Δ mutant or through Gcn4-dependent transcriptional activation. Thus, when S. cerevisiae is grown on glutamine, VIL biosynthesis is predominant and is preferentially achieved through BAT1; while on VIL as the sole nitrogen source, catabolism prevails and is mainly afforded by BAT2.

Genetics of metabolic resistance

Herbicide resistance has become a major issue for many weeds. Metabolic resistance refers to the biochemical processes within organisms that degrade herbicides to less toxic compounds, resulting in a shift of the dose response curve. This type of resistance involves polygenic inheritance. A model is presented linking the biochemical pathway of amino acid synthesis and the detoxifying pathway of an inhibitor of the key enzyme ALS. From this model, resistance factors for each biotype are derived, which are then applied to a polygenic population genetic model for an annual weed plant. Polygenic inheritance is described by a new approach based on tensor products of heredity matrices. Important results from the model are that low dose regimes favour fast emergence of resistant biotypes and that the emergence of resistant biotypes occurs as abrupt outbreaks. The model is used to evaluate strategies for the management of metabolic resistance.

Composition of the outgrowth medium modulates wake-up kinetics and ampicillin sensitivity of stringent and relaxed Escherichia coli

The transition of Escherichia coli from the exponential into the stationary phase of growth induces the stringent response, which is mediated by the rapid accumulation of the alarmone nucleotide (p)ppGpp produced by the enzyme RelA. The significance of RelA’s functionality during the transition in the opposite direction, i.e. from the stationary phase into new exponential growth, is less well understood. Here we show that the relaxed strain, i.e. lacking the relA gene, displays a relative delay in regrowth during the new exponential growth phase in comparison with the isogenic wild type strain. The severity of the effect is a function of both the carbon source and amino acid composition of the outgrowth media. As a result, the loss of RelA functionality increases E. coli tolerance to the bactericidal antibiotic ampicillin during growth resumption in fresh media in a medium-specific way. Taken together, our data underscore the crucial role of medium composition and growth conditions for studies of the role of individual genes and regulatory networks in bacterial phenotypic tolerance to antibiotics.

Biosynthesis and Regulation of the Branched-Chain Amino Acids†

This review focuses on more recent studies concerning the systems biology of branched-chain amino acid biosynthesis, that is, the pathway-specific and global metabolic and genetic regulatory networks that enable the cell to adjust branched-chain amino acid synthesis rates to changing nutritional and environmental conditions. It begins with an overview of the enzymatic steps and metabolic regulatory mechanisms of the pathways and descriptions of the genetic regulatory mechanisms of the individual operons of the isoleucine-leucine-valine (ilv) regulon. This is followed by more-detailed discussions of recent evidence that global control mechanisms that coordinate the expression of the operons of this regulon with one another and the growth conditions of the cell are mediated by changes in DNA supercoiling that occur in response to changes in cellular energy charge levels that, in turn, are modulated by nutrient and environmental signals. Since the parallel pathways for isoleucine and valine biosynthesis are catalyzed by a single set of enzymes, and because the AHAS-catalyzed reaction is the first step specific for valine biosynthesis but the second step of isoleucine biosynthesis, valine inhibition of a single enzyme for this enzymatic step might compromise the cell for isoleucine or result in the accumulation of toxic intermediates. The operon-specific regulatory mechanisms of the operons of the ilv regulon are discussed in the review followed by a consideration and brief review of global regulatory proteins such as integration host factor (IHF), Lrp, and CAP (CRP) that affect the expression of these operons.

Maximizing efficiency of rumen microbial protein production

Rumen microbes produce cellular protein inefficiently partly because they do not direct all ATP toward growth. They direct some ATP toward maintenance functions, as long-recognized, but they also direct ATP toward reserve carbohydrate synthesis and energy spilling (futile cycles that dissipate heat). Rumen microbes expend ATP by vacillating between (1) accumulation of reserve carbohydrate after feeding (during carbohydrate excess) and (2) mobilization of that carbohydrate thereafter (during carbohydrate limitation). Protozoa account for most accumulation of reserve carbohydrate, and in competition experiments, protozoa accumulated nearly 35-fold more reserve carbohydrate than bacteria. Some pure cultures of bacteria spill energy, but only recently have mixed rumen communities been recognized as capable of the same. When these communities were dosed glucose in vitro, energy spilling could account for nearly 40% of heat production. We suspect that cycling of glycogen (a major reserve carbohydrate) is a major mechanism of spilling; such cycling has already been observed in single-species cultures of protozoa and bacteria. Interconversions of short-chain fatty acids (SCFA) may also expend ATP and depress efficiency of microbial protein production. These interconversions may involve extensive cycling of intermediates, such as cycling of acetate during butyrate production in certain butyrivibrios. We speculate this cycling may expend ATP directly or indirectly. By further quantifying the impact of reserve carbohydrate accumulation, energy spilling, and SCFA interconversions on growth efficiency, we can improve prediction of microbial protein production and guide efforts to improve efficiency of microbial protein production in the rumen.

Attractor metabolic networks

BACKGROUND

The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core) while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity.

METHODOLOGY/PRINCIPAL FINDINGS

In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network.

CONCLUSIONS/SIGNIFICANCE

We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns, modify the efficiency in the connection between the multienzymatic complexes, and stably retain these modifications. Here for the first time, we have introduced the general concept of attractor metabolic network, in which this dynamic behavior is observed.

An in silico model of enterocytic glutamine to citrulline conversion pathway

Enterocyte is one of the main sites of amino acids metabolism and particularly of the citrulline biosynthesis. Working at the cellular scale and applying ordinary differential equations (ODEs) formalism, we have built a mathematical model of the enterocytic glutamine to citrulline conversion in the fasting state. This model enables us to test different physiopathological scenarios of enzyme activity loss. Results from two different approaches were compared: a standard approach (KA) based on the Michaelis-Menten assumptions and an association-dissociation approach (VH) based on the kinetic mass action law. For both approaches, ODEs system was numerically solved using Mathematica™. In both cases, the model correctly predicts the physiological plasma citrulline steady-state, but the two approaches present clear differences for metabolites of enzymes having a complex mechanism, challenging the validity of the KA approach in such cases. When physiopathological scenarios of enzyme activity loss are simulated, both approaches predict a very sharp transition from the physiological citrulline plasma level to the lack of its production: the concentration profiles of these simulations show a clear threshold of which characteristics vary with the involved enzyme. Moreover, amongst all enzymes included in the model, the ornithine aminotransferase (OAT) shows the highest sensitivity in the system whatever the approach used. This model points out the limits of the Michaelis-Menten approach to model complex enzyme mechanisms. It highlights the key role of OAT in the studied citrulline synthesis pathway and also suggests an order of magnitude about the optimal ratio of enzyme concentrations in this pathway.

APPLICATION OF A GENERALIZED MWC MODEL FOR THE MATHEMATICAL SIMULATION OF METABOLIC PATHWAYS REGULATED BY ALLOSTERIC ENZYMES

In our effort to elucidate the systems biology of the model organism, Escherichia coli, we have developed a mathematical model that simulates the allosteric regulation for threonine biosynthesis pathway starting from aspartate. To achieve this goal, we used kMech, a Cellerator language extension that describes enzyme mechanisms for the mathematical modeling of metabolic pathways. These mechanisms are converted by Cellerator into ordinary differential equations (ODEs) solvable by Mathematica™. In this paper, we describe a more flexible model in Cellerator, which generalizes the Monod, Wyman, Changeux (MWC) model for enzyme allosteric regulation to allow for multiple substrate, activator and inhibitor binding sites. Furthermore, we have developed a model that describes the behavior of the bifunctional allosteric enzyme aspartate kinase I-homoserine dehydrogenase I (AKI-HDHI). This model predicts the partition of enzyme activities in the steady state which paves the way for a more generalized prediction of the behavior of bifunctional enzymes.

The metabolic core and catalytic switches are fundamental elements in the self-regulation of the systemic metabolic structure of cells

BACKGROUND

Experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a metabolic core formed by a set of enzymatic reactions which are always active under all environmental conditions, while the rest of catalytic processes are only intermittently active. The reactions of the metabolic core are essential for biomass formation and to assure optimal metabolic performance. The on-off catalytic reactions and the metabolic core are essential elements of a Systemic Metabolic Structure which seems to be a key feature common to all cellular organisms.

METHODOLOGY/PRINCIPAL FINDINGS

In order to investigate the functional importance of the metabolic core we have studied different catalytic patterns of a dissipative metabolic network under different external conditions. The emerging biochemical data have been analysed using information-based dynamic tools, such as Pearson's correlation and Transfer Entropy (which measures effective functionality). Our results show that a functional structure of effective connectivity emerges which is dynamical and characterized by significant variations of bio-molecular information flows.

CONCLUSIONS/SIGNIFICANCE

We have quantified essential aspects of the metabolic core functionality. The always active enzymatic reactions form a hub--with a high degree of effective connectivity--exhibiting a wide range of functional information values being able to act either as a source or as a sink of bio-molecular causal interactions. Likewise, we have found that the metabolic core is an essential part of an emergent functional structure characterized by catalytic modules and metabolic switches which allow critical transitions in enzymatic activity. Both, the metabolic core and the catalytic switches in which also intermittently-active enzymes are involved seem to be fundamental elements in the self-regulation of the Systemic Metabolic Structure.

Quantitative analysis of cellular metabolic dissipative, self-organized structures

One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life.

Computational modeling with forward and reverse engineering links signaling network and genomic regulatory responses: NF-kappaB signaling-induced gene expression responses in inflammation

Background

Signal transduction is the major mechanism through which cells transmit external stimuli to evoke intracellular biochemical responses. Diverse cellular stimuli create a wide variety of transcription factor activities through signal transduction pathways, resulting in different gene expression patterns. Understanding the relationship between external stimuli and the corresponding cellular responses, as well as the subsequent effects on downstream genes, is a major challenge in systems biology. Thus, a systematic approach is needed to integrate experimental data and theoretical hypotheses to identify the physiological consequences of environmental stimuli.

Results

We proposed a systematic approach that combines forward and reverse engineering to link the signal transduction cascade with the gene responses. To demonstrate the feasibility of our strategy, we focused on linking the NF-κB signaling pathway with the inflammatory gene regulatory responses because NF-κB has long been recognized to play a crucial role in inflammation. We first utilized forward engineering (Hybrid Functional Petri Nets) to construct the NF-κB signaling pathway and reverse engineering (Network Components Analysis) to build a gene regulatory network (GRN). Then, we demonstrated that the corresponding IKK profiles can be identified in the GRN and are consistent with the experimental validation of the IKK kinase assay. We found that the time-lapse gene expression of several cytokines and chemokines (TNF-α, IL-1, IL-6, CXCL1, CXCL2 and CCL3) is concordant with the NF-κB activity profile, and these genes have stronger influence strength within the GRN. Such regulatory effects have highlighted the crucial roles of NF-κB signaling in the acute inflammatory response and enhance our understanding of the systemic inflammatory response syndrome.

Conclusion

We successfully identified and distinguished the corresponding signaling profiles among three microarray datasets with different stimuli strengths. In our model, the crucial genes of the NF-κB regulatory network were also identified to reflect the biological consequences of inflammation. With the experimental validation, our strategy is thus an effective solution to decipher cross-talk effects when attempting to integrate new kinetic parameters from other signal transduction pathways. The strategy also provides new insight for systems biology modeling to link any signal transduction pathways with the responses of downstream genes of interest.

Global self-regulation of the cellular metabolic structure

BACKGROUND

Different studies have shown that cellular enzymatic activities are able to self-organize spontaneously, forming a metabolic core of reactive processes that remain active under different growth conditions while the rest of the molecular catalytic reactions exhibit structural plasticity. This global cellular metabolic structure appears to be an intrinsic characteristic common to all cellular organisms. Recent work performed with dissipative metabolic networks has shown that the fundamental element for the spontaneous emergence of this global self-organized enzymatic structure could be the number of catalytic elements in the metabolic networks.

METHODOLOGY/PRINCIPAL FINDINGS

In order to investigate the factors that may affect the catalytic dynamics under a global metabolic structure characterized by the presence of metabolic cores we have studied different transitions in catalytic patterns belonging to a dissipative metabolic network. The data were analyzed using non-linear dynamics tools: power spectra, reconstructed attractors, long-term correlations, maximum Lyapunov exponent and Approximate Entropy; and we have found the emergence of self-regulation phenomena during the transitions in the metabolic activities.

CONCLUSIONS/SIGNIFICANCE

The analysis has also shown that the chaotic numerical series analyzed correspond to the fractional Brownian motion and they exhibit long-term correlations and low Approximate Entropy indicating a high level of predictability and information during the self-regulation of the metabolic transitions. The results illustrate some aspects of the mechanisms behind the emergence of the metabolic self-regulation processes, which may constitute an important property of the global structure of the cellular metabolism.

A scalable and integrative system for pathway bioinformatics and systems biology

MOTIVATION

Progress in systems biology depends on developing scalable informatics tools to predictively model, visualize, and flexibly store information about complex biological systems. Scalability of these tools, as well as their ability to integrate within larger frameworks of evolving tools, is critical to address the multi-scale and size complexity of biological systems.

RESULTS

Using current software technology, such as self-generation of database and object code from UML schemas, facilitates rapid updating of a scalable expert assistance system for modeling biological pathways. Distribution of key components along with connectivity to external data sources and analysis tools is achieved via a web service interface.

AVAILABILITY

All sigmoid modeling software components and supplementary information are available through: http://www.igb.uci.edu/servers/sb.html.

Towards the engineering of in vitro systems

Synthetic biology aims at rationally implementing biological systems from scratch. Given the complexity of living systems and our current lack of understanding of many aspects of living cells, this is a major undertaking. The design of in vitro systems can be considerably easier, because they can consist of fewer constituents, are quasi time invariant, their parameter space can be better accessed and they can be much more easily perturbed and then analysed chemically and mathematically. However, even for simplified in vitro systems, following a comprehensively rational design procedure is still difficult. When looking at a comparatively simple system, such as a medium-sized enzymatic reaction network as it is represented by glycolysis, major issues such as a lack of comprehensive enzyme kinetics and of suitable knowledge on crucial design parameters remain. Nevertheless, in vitro systems are very suitable to overcome these obstacles and therefore well placed to act as a stepping stone to engineering living systems.

Understanding the regulation of aspartate metabolism using a model based on measured kinetic parameters

The aspartate-derived amino-acid pathway from plants is well suited for analysing the function of the allosteric network of interactions in branched pathways. For this purpose, a detailed kinetic model of the system in the plant model Arabidopsis was constructed on the basis of in vitro kinetic measurements. The data, assembled into a mathematical model, reproduce in vivo measurements and also provide non-intuitive predictions. A crucial result is the identification of allosteric interactions whose function is not to couple demand and supply but to maintain a high independence between fluxes in competing pathways. In addition, the model shows that enzyme isoforms are not functionally redundant, because they contribute unequally to the flux and its regulation. Another result is the identification of the threonine concentration as the most sensitive variable in the system, suggesting a regulatory role for threonine at a higher level of integration.

First steps in computational systems biology: A practical session in metabolic modeling and simulation

A comprehensive understanding of biological functions requires new systemic perspectives, such as those provided by systems biology. Systems biology approaches are hypothesis-driven and involve iterative rounds of model building, prediction, experimentation, model refinement, and development. Developments in computer science are allowing for ever faster numerical simulations of mathematical models. Mathematical modeling plays an essential role in new systems biology approaches. As a complex, integrated system, metabolism is a suitable topic of study for systems biology approaches. However, up until recently, this topic has not been properly covered in biochemistry courses. This communication reports the development and implementation of a practical lesson plan on metabolic modeling and simulation.

Amino Acid Metabolism and Fluxes

By the mid1960s, the pioneering work of Umbarger and Gerhart and Pardee had shown us that carbon flow through a biosynthetic pathway was controlled by allosteric inhibition of the first enzyme of the pathway by its end product; and, studies of the lac operon by Jacob and Monod had established that genes were controlled by an operator-repressor mechanism. During the intervening forty-plus years, knowledge and technologies have continued to explode in unanticipated ways. Today, we understand in great detail the molecular mechanisms of the many levels of metabolic and genetic regulation that control carbon flow through the amino acid biosynthetic pathways. Traditional experimental approaches are not sufficient for the integration and reconstruction of complex biological systems using data mostly generated by high-throughput experiments. Only with computational methods and adequate modeling tools will we be able to reconstruct and query these large and complicated systems. Due to complicated enzyme reaction mechanisms and the frequent lack of rate constant measurements needed for solving differential equations, most investigators have turned their attention to the development of abstract, top-down modeling tools. For example, Palsson and colleagues have used metabolic flux balance analysis (FBA) methods to simulate steady-state metabolite flux through E. coli pathways representing hundreds of enzyme steps. Recently, Yang et al. have developed a bottom-up, enzyme mechanism modeling language, kMech (kinetic mechanism), for the mathematical simulation of metabolic pathways.

An enzyme-centric approach for modelling non-linear biological complexity

Background

The current challenge of Systems Biology is to integrate high throughput data sets for simulating the complexity of biological networks, exploit the evolution of nature-designed networks that maintain the robustness of a biological system, and thereby generate novel, experimentally testable hypotheses. In order to simulate non-linear biological complexities, we have previously developed an Enzyme-Centric mechanistic modeling approach and validated it using metabolic network in E. coli. The idea is to use prior knowledge of catalytic and regulatory mechanisms of each enzyme within the metabolic network to build a dynamic model for investigating the network level regulation and thus understand the nature design principle behind the network.

Results

In this paper, we further demonstrate the application of complex enzyme catalytic and regulatory modules to simulate nonlinear network regulatory patterns vs. simple linear conversion model. We learned and validated that it is essential to incorporate prior knowledge from the literature to simulate non-linear biological complexities. The network expandability is demonstrated and validated with the complex amino acid biosynthetic network with multi-regulations. Also, we demonstrated the compatibility of mechanistic models within close species. Furthermore, the eukaryotic protein factory model for insuring steady mRNA production is simulated and the coupling of RNA transcription and splicing is validated by both mathematical simulation and experimental analysis.

Conclusion

We demonstrated the importance of modeling complex enzyme catalytic and regulatory mechanisms to further understand nonlinear network regulatory patterns. The simulations presented in this paper reveal how a living system maintains homeostasis and its robustness to continue functioning while facing environmental stresses or genetic mutations.

The global, ppGpp-mediated stringent response to amino acid starvation in Escherichia coli

The stringent response to amino acid starvation, whereby stable RNA synthesis is curtailed in favour of transcription of amino acid biosynthetic genes, is controlled by the alarmone ppGpp. To elucidate the extent of gene expression effected by ppGpp, we designed an experimental system based on starvation for isoleucine, which could be applied to both wild-type Escherichia coli and the multiauxotrophic relA spoT mutant (ppGpp(0)). We used microarrays to profile the response to amino acid starvation in both strains. The wild-type response included induction of the general stress response, downregulation of genes involved in production of macromolecular structures and comprehensive restructuring of metabolic gene expression, but not induction of amino acid biosynthesis genes en masse. This restructuring of metabolism was confirmed using kinetic Biolog assays. These responses were profoundly altered in the ppGpp(0) strain. Furthermore, upon isoleucine starvation, the ppGpp(0) strain exhibited a larger cell size and continued growth, ultimately producing 50% more biomass than the wild-type, despite producing a similar amount of protein. This mutant phenotype correlated with aberrant gene expression in diverse processes, including DNA replication, cell division, and fatty acid and membrane biosynthesis. We present a model that expands and functionally integrates the ppGpp-mediated stringent response to include control of virtually all macromolecular synthesis and intermediary metabolism.

In silico analysis of arginine catabolism as a source of nitric oxide or polyamines in endothelial cells

We use a modeling and simulation approach to carry out an in silico analysis of the metabolic pathways involving arginine as a precursor of nitric oxide or polyamines in aorta endothelial cells. Our model predicts conditions of physiological steady state, as well as the response of the system to changes in the control parameter, external arginine concentration. Metabolic flux control analysis allowed us to predict the values of flux control coefficients for all the transporters and enzymes included in the model. This analysis fulfills the flux control coefficient summation theorem and shows that both the low affinity transporter and arginase share the control of the fluxes through these metabolic pathways.

Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tuberculosis, and its application to assessment of drug targets

Background

Targeting persistent tubercule bacilli has become an important challenge in the development of anti-tuberculous drugs. As the glyoxylate bypass is essential for persistent bacilli, interference with it holds the potential for designing new antibacterial drugs. We have developed kinetic models of the tricarboxylic acid cycle and glyoxylate bypass in Escherichia coli and Mycobacterium tuberculosis, and studied the effects of inhibition of various enzymes in the M. tuberculosis model.

Results

We used E. coli to validate the pathway-modeling protocol and showed that changes in metabolic flux can be estimated from gene expression data. The M. tuberculosis model reproduced the observation that deletion of one of the two isocitrate lyase genes has little effect on bacterial growth in macrophages, but deletion of both genes leads to the elimination of the bacilli from the lungs. It also substantiated the inhibition of isocitrate lyases by 3-nitropropionate. On the basis of our simulation studies, we propose that: (i) fractional inactivation of both isocitrate dehydrogenase 1 and isocitrate dehydrogenase 2 is required for a flux through the glyoxylate bypass in persistent mycobacteria; and (ii) increasing the amount of active isocitrate dehydrogenases can stop the flux through the glyoxylate bypass, so the kinase that inactivates isocitrate dehydrogenase 1 and/or the proposed inactivator of isocitrate dehydrogenase 2 is a potential target for drugs against persistent mycobacteria. In addition, competitive inhibition of isocitrate lyases along with a reduction in the inactivation of isocitrate dehydrogenases appears to be a feasible strategy for targeting persistent mycobacteria.

Conclusion

We used kinetic modeling of biochemical pathways to assess various potential anti-tuberculous drug targets that interfere with the glyoxylate bypass flux, and indicated the type of inhibition needed to eliminate the pathogen. The advantage of such an approach to the assessment of drug targets is that it facilitates the study of systemic effect(s) of the modulation of the target enzyme(s) in the cellular environment.

Mathematical modeling of polyamine metabolism in mammals

Polyamines are considered as essential compounds in living cells, since they are involved in cell proliferation, transcription, and translation processes. Furthermore, polyamine homeostasis is necessary to cell survival, and its deregulation is involved in relevant processes, such as cancer and neurodegenerative disorders. Great efforts have been made to elucidate the nature of polyamine homeostasis, giving rise to relevant information concerning the behavior of the different components of polyamine metabolism, and a great amount of information has been generated. However, a complex regulation at transcriptional, translational, and metabolic levels as well as the strong relationship between polyamines and essential cell processes make it difficult to discriminate the role of polyamine regulation itself from the whole cell response when an experimental approach is given in vivo. To overcome this limitation, a bottom-up approach to model mathematically metabolic pathways could allow us to elucidate the systemic behavior from individual kinetic and molecular properties. In this paper, we propose a mathematical model of polyamine metabolism from kinetic constants and both metabolite and enzyme levels extracted from bibliographic sources. This model captures the tendencies observed in transgenic mice for the so-called key enzymes of polyamine metabolism, ornithine decarboxylase, S-adenosylmethionine decarboxylase and spermine spermidine N-acetyl transferase. Furthermore, the model shows a relevant role of S-adenosylmethionine and acetyl-CoA availability in polyamine homeostasis, which are not usually considered in systemic experimental studies.

A comprehensive view of polyamine and histamine metabolism to the light of new technologies

Polyamines and histamine are biogenic amines with multiple biological roles. In spite of the evidence for the involvement of both polyamines and histamine metabolism impairment in several highly prevalent pathological conditions, multiple questions concerning the molecular processes behind these effects remain to be elucidated. More comprehensive and systemic studies integrating molecular biology, biophysical and bioinformatics tools could contribute to accelerate the advances in this research area. This review is designed to underscore the main questions to be answered in polyamine and histamine research and how these new systemic approaches could help to find these answers.

Glucose transport to the brain: a systems model

Glucose transport to the brain involves sophisticated interactions of solutes, transporters, enzymes, and cell signaling processes, within an intricate spatial architecture. The dynamics of the transport are influenced by the adaptive nature of the blood-brain barrier (BBB), the semi-impermeable membranes of brain capillaries. As both the gate and the gatekeeper between blood-borne nutrients and brain tissue, the BBB helps govern brain homeostasis. Glucose in the blood must cross the BBB's luminal and abluminal membranes to reach neural tissue. A robust representation of the glucose transport mechanism can highlight a target for brain therapeutic intervention, help characterize mechanisms behind several disease phenotypes, or suggest a new delivery route for drugs. The challenge for researchers is understanding the relationships between influential physiological variables in vivo, and using that knowledge to predict how alterations or interventions affect glucose transport. This paper reviews factors influencing glucose transport and approaches to representing blood-to-brain glucose transport including in vitro, in vivo, and kinetic models. Applications for different models are highlighted, while their limitations in answering arising questions about the human in vivo BBB lead to a discussion of an alternate approach. A developing complex systems simulation is introduced, initiating a single platform to represent the dynamics of glucose transport across the adapting human blood-brain barrier.

Application of a generalized MWC model for the mathematical simulation of metabolic pathways regulated by allosteric enzymes

In our effort to elucidate the systems biology of the model organism, Escherichia coli, we have developed a mathematical model that simulates the allosteric regulation for threonine biosynthesis pathway starting from aspartate. To achieve this goal, we used kMech, a Cellerator language extension that describes enzyme mechanisms for the mathematical modeling of metabolic pathways. These mechanisms are converted by Cellerator into ordinary differential equations (ODEs) solvable by Mathematica. In this paper, we describe a more flexible model in Cellerator, which generalizes the Monod, Wyman, Changeux (MWC) model for enzyme allosteric regulation to allow for multiple substrate, activator and inhibitor binding sites. Furthermore, we have developed a model that describes the behavior of the bifunctional allosteric enzyme aspartate Kinase I-Homoserine Dehydrogenase I (AKI-HDHI). This model predicts the partition of enzyme activities in the steady state which paves a way for a more generalized prediction of the behavior of bifunctional enzymes.