Identifying essential genes in Escherichia coli from a metabolic optimization principle

Comparative genomics hints at dispensability of multiple essential genes in two Escherichia coli L-form strains

Despite the critical role of bacterial cell walls in maintaining cell shapes, certain environmental stressors can induce the transition of many bacterial species into a wall-deficient state called L-form. Long-term induced Escherichia coli L-forms lose their rod shape and usually hold significant mutations that affect cell division and growth. Besides this, the genetic background of L-form bacteria is still poorly understood. In the present study, the genomes of two stable L-form strains of E. coli (NC-7 and LWF+) were sequenced and their gene mutation status was determined and compared with their parental strains. Comparative genomic analysis between two L-forms reveals both unique adaptions and common mutated genes, many of which belong to essential gene categories not involved in cell wall biosynthesis, indicating that L-form genetic adaptation impacts crucial metabolic pathways. Missense variants from L-forms and Lenski's long-term evolution experiment (LTEE) were analyzed in parallel using an optimized DeepSequence pipeline to investigate predicted mutation effects (α) on protein functions. We report that the two L-form strains analyzed display a frequency of 6-10% (0% for LTEE) in mutated essential genes where the missense variants have substantial impact on protein functions (α<0.5). This indicates the emergence of different survival strategies in L-forms through changes in essential genes during adaptions to cell wall deficiency. Collectively, our results shed light on the detailed genetic background of two E. coli L-forms and pave the way for further investigations of the gene functions in L-form bacterial models.

Flux balance analysis-based metabolic modeling of microbial secondary metabolism: Current status and outlook

In microorganisms, different from primary metabolism for cellular growth, secondary metabolism is for ecological interactions and stress responses and an important source of natural products widely used in various areas such as pharmaceutics and food additives. With advancements of sequencing technologies and bioinformatics tools, a large number of biosynthetic gene clusters of secondary metabolites have been discovered from microbial genomes. However, due to challenges from the difficulty of genome-scale pathway reconstruction and the limitation of conventional flux balance analysis (FBA) on secondary metabolism, the quantitative modeling of secondary metabolism is poorly established, in contrast to that of primary metabolism. This review first discusses current efforts on the reconstruction of secondary metabolic pathways in genome-scale metabolic models (GSMMs), as well as related FBA-based modeling techniques. Additionally, potential extensions of FBA are suggested to improve the prediction accuracy of secondary metabolite production. As this review posits, biosynthetic pathway reconstruction for various secondary metabolites will become automated and a modeling framework capturing secondary metabolism onset will enhance the predictive power. Expectedly, an improved FBA-based modeling workflow will facilitate quantitative study of secondary metabolism and in silico design of engineering strategies for natural product production.

Variational kinetic clustering of complex networks

Efficiently identifying the most important communities and key transition nodes in weighted and unweighted networks is a prevalent problem in a wide range of disciplines. Here, we focus on the optimal clustering using variational kinetic parameters, linked to Markov processes defined on the underlying networks, namely, the slowest relaxation time and the Kemeny constant. We derive novel relations in terms of mean first passage times for optimizing clustering via the Kemeny constant and show that the optimal clustering boundaries have equal round-trip times to the clusters they separate. We also propose an efficient method that first projects the network nodes onto a 1D reaction coordinate and subsequently performs a variational boundary search using a parallel tempering algorithm, where the variational kinetic parameters act as an energy function to be extremized. We find that maximization of the Kemeny constant is effective in detecting communities, while the slowest relaxation time allows for detection of transition nodes. We demonstrate the validity of our method on several test systems, including synthetic networks generated from the stochastic block model and real world networks (Santa Fe Institute collaboration network, a network of co-purchased political books, and a street network of multiple cities in Luxembourg). Our approach is compared with existing clustering algorithms based on modularity and the robust Perron cluster analysis, and the identified transition nodes are compared with different notions of node centrality.

The art of adapting to extreme environments: The model system Pseudoalteromonas

Extremophilic microbes have adapted to thrive in ecological niches characterized by harsh chemical/physical conditions such as, for example, very low/high temperature. Living organisms inhabiting these environments have developed peculiar mechanisms to cope with extreme conditions, in such a way that they mark the chemical-physical boundaries of life on Earth. Studying such mechanisms is stimulating from a basic research viewpoint and because of biotechnological applications. Pseudoalteromonas species are a group of marine gamma-proteobacteria frequently isolated from a range of extreme environments, including cold habitats and deep-sea sediments. Since deep-sea floors constitute almost 60% of the Earth's surface and cold temperatures represent the most common of the extreme conditions, the genus Pseudoalteromonas can be considered one of the most important model systems for studying microbial adaptation. Particularly, among all Pseudoalteromonas representatives, P. haloplanktis TAC125 has recently gained a central role. This bacterium was isolated from seawater sampled along the Antarctic ice-shell and is considered one of the model organisms of cold-adapted bacteria. It is capable of thriving in a wide temperature range and it has been suggested as an alternative host for the soluble overproduction of heterologous proteins, given its ability to rapidly multiply at low temperatures. In this review, we will present an overview of the recent advances in the characterization of Pseudoalteromonas strains and, more importantly, in the understanding of their evolutionary and chemical-physical strategies to face such a broad array of extreme conditions. A particular attention will be given to systems-biology approaches in the study of the above-mentioned topics, as genome-scale datasets (e.g. genomics, proteomics, phenomics) are beginning to expand for this group of organisms. In this context, a specific section dedicated to P. haloplanktis TAC125 will be presented to address the recent efforts in the elucidation of the metabolic rewiring of the organisms in its natural environment (Antarctica).

Statistical mechanics for metabolic networks during steady state growth

Which properties of metabolic networks can be derived solely from stoichiometry? Predictive results have been obtained by flux balance analysis (FBA), by postulating that cells set metabolic fluxes to maximize growth rate. Here we consider a generalization of FBA to single-cell level using maximum entropy modeling, which we extend and test experimentally. Specifically, we define for Escherichia coli metabolism a flux distribution that yields the experimental growth rate: the model, containing FBA as a limit, provides a better match to measured fluxes and it makes a wide range of predictions: on flux variability, regulation, and correlations; on the relative importance of stoichiometry vs. optimization; on scaling relations for growth rate distributions. We validate the latter here with single-cell data at different sub-inhibitory antibiotic concentrations. The model quantifies growth optimization as emerging from the interplay of competitive dynamics in the population and regulation of metabolism at the level of single cells.

An introduction to the maximum entropy approach and its application to inference problems in biology

A cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. Both its broad applicability and the success it obtained in different contexts hinge upon its conceptual simplicity and mathematical soundness. Here we try to concisely review the basic elements of the maximum entropy principle, starting from the notion of 'entropy', and describe its usefulness for the analysis of biological systems. As examples, we focus specifically on the problem of reconstructing gene interaction networks from expression data and on recent work attempting to expand our system-level understanding of bacterial metabolism. Finally, we highlight some extensions and potential limitations of the maximum entropy approach, and point to more recent developments that are likely to play a key role in the upcoming challenges of extracting structures and information from increasingly rich, high-throughput biological data.

Constrained Allocation Flux Balance Analysis

New experimental results on bacterial growth inspire a novel top-down approach to study cell metabolism, combining mass balance and proteomic constraints to extend and complement Flux Balance Analysis. We introduce here Constrained Allocation Flux Balance Analysis, CAFBA, in which the biosynthetic costs associated to growth are accounted for in an effective way through a single additional genome-wide constraint. Its roots lie in the experimentally observed pattern of proteome allocation for metabolic functions, allowing to bridge regulation and metabolism in a transparent way under the principle of growth-rate maximization. We provide a simple method to solve CAFBA efficiently and propose an “ensemble averaging” procedure to account for unknown protein costs. Applying this approach to modeling E. coli metabolism, we find that, as the growth rate increases, CAFBA solutions cross over from respiratory, growth-yield maximizing states (preferred at slow growth) to fermentative states with carbon overflow (preferred at fast growth). In addition, CAFBA allows for quantitatively accurate predictions on the rate of acetate excretion and growth yield based on only 3 parameters determined by empirical growth laws.

The intracellular protein levels of exponentially growing bacteria are known to vary strongly with growth conditions, as described by quantitative “growth laws”. This work introduces a computational genome-scale framework (Constrained Allocation Flux Balance Analysis, CAFBA) which incorporates growth laws into canonical Flux Balance Analysis. Upon introducing 3 parameters based on established growth laws for E. coli, CAFBA accurately reproduces empirical results on the growth-rate dependent rate of carbon overflow and growth yield, and generates testable predictions about cellular energetic strategies and protein expression levels. CAFBA therefore provides a simple, quantitative approach to balancing the trade-off between growth and its associated biosynthetic costs at genome-scale, without the burden of tuning many inaccessible parameters.

Quantitative constraint-based computational model of tumor-to-stroma coupling via lactate shuttle

Cancer cells utilize large amounts of ATP to sustain growth, relying primarily on non-oxidative, fermentative pathways for its production. In many types of cancers this leads, even in the presence of oxygen, to the secretion of carbon equivalents (usually in the form of lactate) in the cell’s surroundings, a feature known as the Warburg effect. While the molecular basis of this phenomenon are still to be elucidated, it is clear that the spilling of energy resources contributes to creating a peculiar microenvironment for tumors, possibly characterized by a degree of toxicity. This suggests that mechanisms for recycling the fermentation products (e.g. a lactate shuttle) may be active, effectively inducing a mutually beneficial metabolic coupling between aberrant and non-aberrant cells. Here we analyze this scenario through a large-scale in silico metabolic model of interacting human cells. By going beyond the cell-autonomous description, we show that elementary physico-chemical constraints indeed favor the establishment of such a coupling under very broad conditions. The characterization we obtained by tuning the aberrant cell’s demand for ATP, amino-acids and fatty acids and/or the imbalance in nutrient partitioning provides quantitative support to the idea that synergistic multi-cell effects play a central role in cancer sustainment.

Notes on stochastic (bio)-logic gates: computing with allosteric cooperativity

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called enzyme based logic) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics, and testing quantitatively the resulting findings on the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity).

Cancer-driven dynamics of immune cells in a microfluidic environment

Scope of the present work is to infer the migratory ability of leukocytes by stochastic processes in order to distinguish the spontaneous organization of immune cells against an insult (namely cancer). For this purpose, spleen cells from immunodeficient mice, selectively lacking the transcription factor IRF-8 (IRF-8 knockout; IRF-8 KO), or from immunocompetent animals (wild-type; WT), were allowed to interact, alternatively, with murine B16.F10 melanoma cells in an ad hoc microfluidic environment developed on a LabOnChip technology. In this setting, only WT spleen cells were able to establish physical interactions with melanoma cells. Conversely, IRF-8 KO immune cells exhibited poor dynamical reactivity towards the neoplastic cells. In the present study, we collected data on the motility of these two types of spleen cells and built a complete set of observables that recapitulate the biological complexity of the system in these experiments. With remarkable accuracy, we concluded that the IRF-8 KO cells performed pure uncorrelated random walks, while WT splenocytes were able to make singular drifted random walks that collapsed on a straight ballistic motion for the system as a whole, hence giving rise to a highly coordinate response. These results may provide a useful system to quantitatively analyse the real time cell-cell interactions and to foresee the behavior of immune cells with tumor cells at the tissue level.

Identifying all moiety conservation laws in genome-scale metabolic networks

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.

Anergy in self-directed B lymphocytes: A statistical mechanics perspective

Self-directed lymphocytes may evade clonal deletion at ontogenesis but still remain harmless due to a mechanism called clonal anergy. For B-lymphocytes, two major explanations for anergy developed over the last decades: according to Varela theory, anergy stems from a proper orchestration of the whole B-repertoire, such that self-reactive clones, due to intensive feed-back from other clones, display strong inertia when mounting a response. Conversely, according to the model of cognate response, self-reacting cells are not stimulated by helper lymphocytes and the absence of such signaling yields anergy. Through statistical mechanics we show that helpers do not prompt activation of a sub-group of B-cells: remarkably, the latter are just those broadly interacting in the idiotypic network. Hence Varela theory can finally be reabsorbed into the prevailing framework of the cognate response model. Further, we show how the B-repertoire architecture may emerge, where highly connected clones are self-directed as a natural consequence of ontogenetic learning.

Detection of driver metabolites in the human liver metabolic network using structural controllability analysis

Background

Abnormal states in human liver metabolism are major causes of human liver diseases ranging from hepatitis to hepatic tumor. The accumulation in relevant data makes it feasible to derive a large-scale human liver metabolic network (HLMN) and to discover important biological principles or drug-targets based on network analysis. Some studies have shown that interesting biological phenomenon and drug-targets could be discovered by applying structural controllability analysis (which is a newly prevailed concept in networks) to biological networks. The exploration on the connections between structural controllability theory and the HLMN could be used to uncover valuable information on the human liver metabolism from a fresh perspective.

Results

We applied structural controllability analysis to the HLMN and detected driver metabolites. The driver metabolites tend to have strong ability to influence the states of other metabolites and weak susceptibility to be influenced by the states of others. In addition, the metabolites were classified into three classes: critical, high-frequency and low-frequency driver metabolites. Among the identified 36 critical driver metabolites, 27 metabolites were found to be essential; the high-frequency driver metabolites tend to participate in different metabolic pathways, which are important in regulating the whole metabolic systems. Moreover, we explored some other possible connections between the structural controllability theory and the HLMN, and find that transport reactions and the environment play important roles in the human liver metabolism.

Conclusion

There are interesting connections between the structural controllability theory and the human liver metabolism: driver metabolites have essential biological functions; the crucial role of extracellular metabolites and transport reactions in controlling the HLMN highlights the importance of the environment in the health of human liver metabolism.

Collective behaviours: from biochemical kinetics to electronic circuits

In this work we aim to highlight a close analogy between cooperative behaviors in chemical kinetics and cybernetics; this is realized by using a common language for their description, that is mean-field statistical mechanics. First, we perform a one-to-one mapping between paradigmatic behaviors in chemical kinetics (i.e., non-cooperative, cooperative, ultra-sensitive, anti-cooperative) and in mean-field statistical mechanics (i.e., paramagnetic, high and low temperature ferromagnetic, anti-ferromagnetic). Interestingly, the statistical mechanics approach allows a unified, broad theory for all scenarios and, in particular, Michaelis-Menten, Hill and Adair equations are consistently recovered. This framework is then tested against experimental biological data with an overall excellent agreement. One step forward, we consistently read the whole mapping from a cybernetic perspective, highlighting deep structural analogies between the above-mentioned kinetics and fundamental bricks in electronics (i.e. operational amplifiers, flashes, flip-flops), so to build a clear bridge linking biochemical kinetics and cybernetics.

Energy metabolism and glutamate-glutamine cycle in the brain: a stoichiometric modeling perspective

Background

The energetics of cerebral activity critically relies on the functional and metabolic interactions between neurons and astrocytes. Important open questions include the relation between neuronal versus astrocytic energy demand, glucose uptake and intercellular lactate transfer, as well as their dependence on the level of activity.

Results

We have developed a large-scale, constraint-based network model of the metabolic partnership between astrocytes and glutamatergic neurons that allows for a quantitative appraisal of the extent to which stoichiometry alone drives the energetics of the system. We find that the velocity of the glutamate-glutamine cycle (V_cyc) explains part of the uncoupling between glucose and oxygen utilization at increasing V_cyc levels. Thus, we are able to characterize different activation states in terms of the tissue oxygen-glucose index (OGI). Calculations show that glucose is taken up and metabolized according to cellular energy requirements, and that partitioning of the sugar between different cell types is not significantly affected by V_cyc. Furthermore, both the direction and magnitude of the lactate shuttle between neurons and astrocytes turn out to depend on the relative cell glucose uptake while being roughly independent of V_cyc.

Conclusions

These findings suggest that, in absence of ad hoc activity-related constraints on neuronal and astrocytic metabolism, the glutamate-glutamine cycle does not control the relative energy demand of neurons and astrocytes, and hence their glucose uptake and lactate exchange.

Thermodynamics of biochemical networks and duality theorems

One interesting yet difficult computational issue has recently been posed in biophysics in regard to the implementation of thermodynamic constraints to complex networks. Biochemical networks of enzymes inside cells are among the most efficient, robust, differentiated, and flexible free-energy transducers in nature. How is the second law of thermodynamics encoded for these complex networks? In this article it is demonstrated that for chemical reaction networks in the steady state the exclusion (presence) of closed reaction cycles makes possible (impossible) the definition of a chemical potential vector. Interestingly, this statement is encoded in one of the key results in combinatorial optimization, i.e., the Gordan theorem of the alternatives. From a computational viewpoint, the theorem reveals that calculating a reaction's free energy and identifying infeasible loops in flux states are dual problems whose solutions are mutually exclusive, and this opens the way for efficient and scalable methods to perform the energy balance analysis of large-scale biochemical networks.

Reconciliation of metabolites and biochemical reactions for metabolic networks

Genome-scale metabolic network reconstructions are now routinely used in the study of metabolic pathways, their evolution and design. The development of such reconstructions involves the integration of information on reactions and metabolites from the scientific literature as well as public databases and existing genome-scale metabolic models. The reconciliation of discrepancies between data from these sources generally requires significant manual curation, which constitutes a major obstacle in efforts to develop and apply genome-scale metabolic network reconstructions. In this work, we discuss some of the major difficulties encountered in the mapping and reconciliation of metabolic resources and review three recent initiatives that aim to accelerate this process, namely BKM-react, MetRxn and MNXref (presented in this article). Each of these resources provides a pre-compiled reconciliation of many of the most commonly used metabolic resources. By reducing the time required for manual curation of metabolite and reaction discrepancies, these resources aim to accelerate the development and application of high-quality genome-scale metabolic network reconstructions and models.

Reaction networks as systems for resource allocation: a variational principle for their non-equilibrium steady states

Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at stationarity the system minimizes a global function of the reaction fluxes with the form of a Hopfield Hamiltonian with Hebbian couplings, that is explicitly seen to correspond to the rate of decay of entropy production over time. Guided by this analogy, we show that reaction networks can be formally re-cast as systems of interacting reactions that optimize the use of the available compounds by competing for substrates, akin to agents competing for a limited resource in an optimal allocation problem. As an illustration, we analyze the scenario that emerges in two simple cases: that of toy (random) reaction networks and that of a metabolic network model of the human red blood cell.

A scalable algorithm to explore the Gibbs energy landscape of genome-scale metabolic networks

The integration of various types of genomic data into predictive models of biological networks is one of the main challenges currently faced by computational biology. Constraint-based models in particular play a key role in the attempt to obtain a quantitative understanding of cellular metabolism at genome scale. In essence, their goal is to frame the metabolic capabilities of an organism based on minimal assumptions that describe the steady states of the underlying reaction network via suitable stoichiometric constraints, specifically mass balance and energy balance (i.e. thermodynamic feasibility). The implementation of these requirements to generate viable configurations of reaction fluxes and/or to test given flux profiles for thermodynamic feasibility can however prove to be computationally intensive. We propose here a fast and scalable stoichiometry-based method to explore the Gibbs energy landscape of a biochemical network at steady state. The method is applied to the problem of reconstructing the Gibbs energy landscape underlying metabolic activity in the human red blood cell, and to that of identifying and removing thermodynamically infeasible reaction cycles in the Escherichia coli metabolic network (iAF1260). In the former case, we produce consistent predictions for chemical potentials (or log-concentrations) of intracellular metabolites; in the latter, we identify a restricted set of loops (23 in total) in the periplasmic and cytoplasmic core as the origin of thermodynamic infeasibility in a large sample (10(6)) of flux configurations generated randomly and compatibly with the prior information available on reaction reversibility.

Optimal fluxes, reaction replaceability, and response to enzymopathies in the human red blood cell

Characterizing the capabilities, key dependencies, and response to perturbations of genome-scale metabolic networks is a basic problem with important applications. A key question concerns the identification of the potentially most harmful reaction knockouts. The integration of combinatorial methods with sampling techniques to explore the space of viable flux states may provide crucial insights on this issue. We assess the replaceability of every metabolic conversion in the human red blood cell by enumerating the alternative paths from substrate to product, obtaining a complete map of he potential damage of single enzymopathies. Sampling the space of optimal steady state fluxes in the healthy and in the mutated cell reveals both correlations and complementarity between topologic and dynamical aspects.

Flux balance analysis accounting for metabolite dilution

Flux balance analysis is a common method for predicting steady-state flux distributions within metabolic networks, accounting for the growth demand for the synthesis of a predefined set of essential biomass precursors. Ignoring the growth demand for the synthesis of intermediate metabolites required for balancing their dilution leads flux balance analysis to false predictions in some cases. Here, we present metabolite dilution flux balance analysis, which addresses this problem, resulting in improved metabolic phenotype predictions.