Predicting the adaptive evolution of Thermoanaerobacterium saccharolyticum

A fully evolved metabolic network can be described as a weighted sum of elementary modes where the usage probabilities of modes are distributed according to the Boltzmann distribution law (Srienc and Unrean, 2010). An organism presumably achieves the fully evolved state through adaptive changes in the kinetics of rate-controlling enzymes. Metabolic control analysis identifies reactions catalyzed by such enzymes. Comparison of the experimentally determined metabolic flux distributions of Thermoanaerobacterium saccharolyticum AS411 with the predicted flux distribution of a fully evolved metabolic network identified phosphoglucose isomerase (PGI) as the enzyme with the greatest flux control, the rate-controlling enzyme. The analysis predicts that an increased activity of PGI would enable the metabolic network to approach the fully evolved state and result in a faster specific growth rate. The prediction was confirmed by experimental results that showed an increased specific activity of PGI in a culture of strain AS411 that adaptively evolved over 280 generations. Sequencing of the gene confirmed the occurrence of a group of mutations clustered in the subunit binding domain of the dimeric enzyme. The results indicate that the evolutionary path is predictable as the strain AS411 adapted toward the fully evolved state by increasing the PGI activity. This experimental finding confirms that enzymes with predicted highest metabolic flux control are the targets of adaptive metabolic pathway evolution.     

The fractional contributions of elementary modes to the metabolism of Escherichia coli and their estimation from reaction entropies

The metabolism of a cell can be viewed as a weighted sum of elementary modes. Due to the multiplicity of modes the identification of the individual weights represents a non-trivial problem. To enable the determination of weighting factors we have identified and implemented two gene deletions in combination with defined growth conditions that limit the metabolism from 4374 original elementary modes to 24 elementary modes for a non-PHB synthesizing control and 40 modes for a PHB synthesizing strain. These remaining modes can be further grouped into five families that have the same overall stoichiometry. Thus, the complexity of the problem is significantly reduced, and weighting factors for each family of modes could be determined from the measurement of accumulation rates of metabolites. Moreover, it is shown that individual weights are inversely correlated with the entropy generated by the operation of the used pathways defined in elementary modes. This suggests that evolution developed cellular regulatory patterns that permit diversity of pathways while favoring efficient pathways with low entropy generation. Furthermore, such correlation provides a rational way of estimating metabolic fluxes based on the thermodynamic properties of elementary modes. This is demonstrated with an example in which experimentally determined, intracellular fluxes are shown to be highly correlated with fluxes computed based on elementary modes and reaction entropies. The analysis suggests that the set of elementary modes can be interpreted analogous to a metabolic ensemble of quantum states of a macroscopic system.     

Enzyme kinetics and the maximum entropy production principle

A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition ES?EP in a generalized reversible Michaelis-Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions ES→EP for three types of β-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that β-Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is a completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution.     

小球藻联产油脂和虾青素的基元模式分析

构建了包含虾青素合成途径的小球藻代谢网络模型,集成文献报道同位素标定的小球藻代谢通量数据,估算了胞内代谢通量分布。在正常和缺氮培养条件下,虾青素的代谢通量分别为0.38和0.35。计算得到基元模式共640条,通过最大熵原理算法求取了正常培养和缺氮培养条件下的基元模式概率。存在4条关键基元模式,在2种培养条件下,其基元模式概率之和分别为60.95%和77.53%。虾青素的最大理论合成产率为11.27%,但是这4条关键基元模式并不包括虾青素的合成反应。     

The geometry of the flux cone of a metabolic network

The analysis of metabolic networks has become a major topic in biotechnology in recent years. Applications range from the enhanced production of selected outputs to the prediction of genotype-phenotype relationships. The concepts used are based on the assumption of a pseudo steady-state of the network, so that for each metabolite inputs and outputs are balanced. The stoichiometric network analysis expands the steady state into a combination of nonredundant subnetworks with positive coefficients called extremal currents. Based on the unidirectional representation of the system these subnetworks form a convex cone in the flux-space. A modification of this approach allowing for reversible reactions led to the definition of elementary modes. Extreme pathways are obtained with the same method but splitting up internal reactions into forward and backward rates. In this study, we explore the relationship between these concepts. Due to the combinatorial explosion of the number of elementary modes in large networks, we promote a further set of metabolic routes, which we call the minimal generating set. It is the smallest subset of elementary modes required to describe all steady states of the system. For large-scale networks, the size of this set is of several magnitudes smaller than that of elementary modes and of extreme pathways.     

Flux modules in metabolic networks

The huge number of elementary flux modes in genome-scale metabolic networks makes analysis based on elementary flux modes intrinsically difficult. However, it has been shown that the elementary flux modes with optimal yield often contain highly redundant information. The set of optimal-yield elementary flux modes can be compressed using modules. Up to now, this compression was only possible by first enumerating the whole set of all optimal-yield elementary flux modes. We present a direct method for computing modules of the thermodynamically constrained optimal flux space of a metabolic network. This method can be used to decompose the set of optimal-yield elementary flux modes in a modular way and to speed up their computation. In addition, it provides a new form of coupling information that is not obtained by classical flux coupling analysis. We illustrate our approach on a set of model organisms.     

Are organisms committed to lower their rates of entropy production?: Possible relevance to evolution of the Prigogine theorem and the ergodic hypothesis

The physiology at limiting and stress conditions challenges the current view that the overall reaction of metabolic processes is always far from equilibrium and, therefore, that organisms are not committed to lower their rates of entropy production. Plausibly, critical steps of natural selection takes place at limiting conditions, near equilibrium, in the linear range response of entropy production, and consequently the trend to lower the rate of entropy production could be the fitness arrow of biological evolution. The evolutionary relevance of the Prigogine theorem is discussed in connection with the ergodic hypothesis of Boltzmann. The emergence of metabolic strategies to economise carbon/energy resources, of resource-waste systems like active transport and the irreversible increase in the complexity of organisms during evolution may be consequences of a more general trend of metabolic systems to lower the rates of entropy production.     

Analyzing molecular reaction networks

Pathways are typically the central concept in the analysis of biochemical reaction networks. A pathway can be interpreted as a chain of enzymatical reactions performing a specific biological function. A common way to study metabolic networks are minimal pathways that can operate at steady state called elementary modes. The theory of chemical organizations has recently been used to decompose biochemical networks into algebraically closed and self-maintaining subnetworks termed organizations. The aim of this paper is to elucidate the relation between these two concepts. Whereas elementary modes represent the boundaries of the potential behavior of the network, organizations define metabolite compositions that are likely to be present in biological feasible situations. Hence, steady state organizations consist of combinations of elementary modes. On the other hand, it is possible to assign a unique (and possibly empty) set of organizations to each elementary mode, indicating the metabolites accompanying the active pathway in a feasible steady state.     

Analysis of optimal phenotypic space using elementary modes as applied to Corynebacterium glutamicum

Background  

Quantification of the metabolic network of an organism offers insights into possible ways of developing mutant strain for better productivity of an extracellular metabolite. The first step in this quantification is the enumeration of stoichiometries of all reactions occurring in a metabolic network. The structural details of the network in combination with experimentally observed accumulation rates of external metabolites can yield flux distribution at steady state. One such methodology for quantification is the use of elementary modes, which are minimal set of enzymes connecting external metabolites. Here, we have used a linear objective function subject to elementary modes as constraint to determine the fluxes in the metabolic network of Corynebacterium glutamicum. The feasible phenotypic space was evaluated at various combinations of oxygen and ammonia uptake rates.     

Design, construction and performance of the most efficient biomass producing E. coli bacterium

Inverse metabolic engineering based on elementary mode analysis was applied to maximize the biomass yield of Escherchia coli MG1655. Elementary mode analysis was previously employed to identify among 1691 possible pathways for cell growth the most efficient pathway with maximum biomass yield. The metabolic network analysis predicted that deletion of only 6 genes reduces the number of possible elementary modes to the most efficient pathway. We have constructed a strain containing these gene deletions and we evaluated its properties in batch and in chemostat growth experiments. The results show that the theoretical predictions are closely matched by the properties of the designed strain.     

Analysis of growth of Lactobacillus plantarum WCFS1 on a complex medium using a genome-scale metabolic model

A genome-scale metabolic model of the lactic acid bacterium Lactobacillus plantarum WCFS1 was constructed based on genomic content and experimental data. The complete model includes 721 genes, 643 reactions, and 531 metabolites. Different stoichiometric modeling techniques were used for interpretation of complex fermentation data, as L. plantarum is adapted to nutrient-rich environments and only grows in media supplemented with vitamins and amino acids. (i) Based on experimental input and output fluxes, maximal ATP production was estimated and related to growth rate. (ii) Optimization of ATP production further identified amino acid catabolic pathways that were not previously associated with free-energy metabolism. (iii) Genome-scale elementary flux mode analysis identified 28 potential futile cycles. (iv) Flux variability analysis supplemented the elementary mode analysis in identifying parallel pathways, e.g. pathways with identical end products but different co-factor usage. Strongly increased flexibility in the metabolic network was observed when strict coupling between catabolic ATP production and anabolic consumption was relaxed. These results illustrate how a genome-scale metabolic model and associated constraint-based modeling techniques can be used to analyze the physiology of growth on a complex medium rather than a minimal salts medium. However, optimization of biomass formation using the Flux Balance Analysis approach, reported to successfully predict growth rate and by product formation in Escherichia coli and Saccharomyces cerevisiae, predicted too high biomass yields that were incompatible with the observed lactate production. The reason is that this approach assumes optimal efficiency of substrate to biomass conversion, and can therefore not predict the metabolically inefficient lactate formation.     

Two approaches for metabolic pathway analysis?

Metabolic pathway analysis is becoming increasingly important for assessing inherent network properties in (reconstructed) biochemical reaction networks. Of the two most promising concepts for pathway analysis, one relies on elementary flux modes and the other on extreme pathways. These concepts are closely related because extreme pathways are a subset of elementary modes. Here, the common features, differences and applicability of these concepts are discussed. Assessing metabolic systems by the set of extreme pathways can, in general, give misleading results owing to the exclusion of possibly important routes. However, in certain network topologies, the sets of elementary modes and extreme pathways coincide. This is quite often the case in realistic applications. In our opinion, the unification of both approaches into one common framework for metabolic pathway analysis is necessary and achievable.     

Phenotypic characterization of <Emphasis Type="Italic">Corynebacterium glutamicum</Emphasis> using elementary modes towards synthesis of amino acids

Elementary flux mode (EFM) analysis is a powerful tool to represent the metabolic network structure and can be further utilized for flux analysis. The method enables characterization and quantification of feasible phenotypes in microbes. EFM analysis was employed to characterize the phenotype of Corynebacterium glutamicum to yield various amino acids. The metabolic network of C. glutamicum yielded 62 elementary modes by incorporating the accumulation of amino acids namely, lysine, alanine, valine, glutamine and glutamate. The analysis also allowed us to compute the maximum theoretical yield for the synthesis of various amino acids. These 62 elementary modes were further used to obtain optimal phenotypic space towards accumulation of biomass and lysine. The study indicated that the optimal solution space from 62 elementary modes forms a super space which incorporates various mutants including lysine producing strain of C. glutamicum. The analysis was also extended to obtain sensitivity of the network to variation in the stoichiometry of NADP in the definition of biomass.     

RNA bulge entropies in the unbound state correlate with peptide binding strengths for HIV-1 and BIV TAR RNA because of improved conformational access.

For the binding of peptides to wild-type HIV-1 and BIV TAR RNA and to mutants with bulges of various sizes, changes in the DeltaDelta G values of binding were determined from experimental K d values. The corresponding entropies of these bulges are estimated by enumerating all possible RNA bulge conformations on a lattice and then applying the Boltzmann relationship. Independent calculations of entropies from fluctuations are also carried out using the Gaussian network model (GNM) recently introduced for analyzing folded structures. Strong correlations are seen between the changes in free energy determined for binding and the two different unbound entropy calculations. The fact that the calculated entropy increase with larger bulge size is correlated with the enhanced experimental binding free energy is unusual. This system exhibits a dependence on the entropy of the unbound form that is opposite to usual binding models. Instead of a large initial entropy being unfavorable since it would be reduced upon binding, here the larger entropies actually favor binding. Several interpretations are possible: (i) the higher conformational freedom implies a higher competence for binding with a minimal strain, by suitable selection amongst the set of already accessible conformations; (ii) larger bulge entropies enhance the probability of the specific favorable conformation of the bound state; (iii) the increased freedom of the larger bulges contri-butes more to the bound state than to the unbound state; (iv) indirectly the large entropy of the bound state might have an unfavorable effect on the solvent structure. Nonetheless, this unusual effect is interesting.     

Generalized concept of minimal cut sets in biochemical networks

Recently, the concept of minimal cut sets has been introduced for studying structural fragility and identifying knock-out strategies in biochemical reaction networks. A minimal cut set (MCS) has been defined as a minimal set of reactions whose removal blocks the operation of a chosen objective reaction. In this report the theoretical framework of MCSs is refined and extended increasing the practical applicability significantly. An MCS is now defined as a minimal (irreducible) set of structural interventions (removal of network elements) repressing a certain functionality specified by a deletion task. A deletion task describes unambiguously the flux patterns (or the functionality) to be repressed. It is shown that the MCSs can be computed from the set of target modes, which comprises all elementary modes that exhibit the functionality to be attacked. Since a deletion task can be specified by several Boolean rules, MCSs can now be determined for a large variety of complex deletion problems and may be utilized for inhibiting very special flux patterns. It is additionally shown that the other way around is also possible: the elementary modes belonging to a certain functionality can be computed from the respective set of MCSs. Therefore, elementary modes and MCSs can be seen as dual representations of network functions and both can be converted into each other. Moreover, there exist a strong relationship to minimal hitting sets known from set theory: the MCSs are the minimal hitting sets of the collection of target modes and vice versa. Another generalization introduced herein is that MCSs need not to be restricted to the removal of reactions they may also contain network nodes. In the light of the extended framework of MCSs, applications for assessing, manipulating, and designing metabolic networks in silico are discussed.     

Elementary mode analysis: a useful metabolic pathway analysis tool for characterizing cellular metabolism

Elementary mode analysis is a useful metabolic pathway analysis tool to identify the structure of a metabolic network that links the cellular phenotype to the corresponding genotype. The analysis can decompose the intricate metabolic network comprised of highly interconnected reactions into uniquely organized pathways. These pathways consisting of a minimal set of enzymes that can support steady state operation of cellular metabolism represent independent cellular physiological states. Such pathway definition provides a rigorous basis to systematically characterize cellular phenotypes, metabolic network regulation, robustness, and fragility that facilitate understanding of cell physiology and implementation of metabolic engineering strategies. This mini-review aims to overview the development and application of elementary mode analysis as a metabolic pathway analysis tool in studying cell physiology and as a basis of metabolic engineering.