Global dynamic optimization approach to predict activation in metabolic pathways

Background

During the last decade, a number of authors have shown that the genetic regulation of metabolic networks may follow optimality principles. Optimal control theory has been succesfully used to compute optimal enzyme profiles considering simple metabolic pathways. However, applying this optimal control framework to more general networks (e.g. branched networks, or networks incorporating enzyme production dynamics) yields problems that are analytically intractable and/or numerically very challenging. Further, these previous studies have only considered a single-objective framework.

Results

In this work we consider a more general multi-objective formulation and we present solutions based on recent developments in global dynamic optimization techniques. We illustrate the performance and capabilities of these techniques considering two sets of problems. First, we consider a set of single-objective examples of increasing complexity taken from the recent literature. We analyze the multimodal character of the associated non linear optimization problems, and we also evaluate different global optimization approaches in terms of numerical robustness, efficiency and scalability. Second, we consider generalized multi-objective formulations for several examples, and we show how this framework results in more biologically meaningful results.

Conclusions

The proposed strategy was used to solve a set of single-objective case studies related to unbranched and branched metabolic networks of different levels of complexity. All problems were successfully solved in reasonable computation times with our global dynamic optimization approach, reaching solutions which were comparable or better than those reported in previous literature. Further, we considered, for the first time, multi-objective formulations, illustrating how activation in metabolic pathways can be explained in terms of the best trade-offs between conflicting objectives. This new methodology can be applied to metabolic networks with arbitrary topologies, non-linear dynamics and constraints.     

Bacterial microcompartments: widespread prokaryotic organelles for isolation and optimization of metabolic pathways

Prokaryotes use subcellular compartments for a variety of purposes. An intriguing example is a family of complex subcellular organelles known as bacterial microcompartments (MCPs). MCPs are widely distributed among bacteria and impact processes ranging from global carbon fixation to enteric pathogenesis. Overall, MCPs consist of metabolic enzymes encased within a protein shell, and their function is to optimize biochemical pathways by confining toxic or volatile metabolic intermediates. MCPs are fundamentally different from other organelles in having a complex protein shell rather than a lipid‐based membrane as an outer barrier. This unusual feature raises basic questions about organelle assembly, protein targeting and metabolite transport. In this review, we discuss the three best‐studied MCPs highlighting atomic‐level models for shell assembly, targeting sequences that direct enzyme encapsulation, multivalent proteins that organize the lumen enzymes, the principles of metabolite movement across the shell, internal cofactor recycling, a potential system of allosteric regulation of metabolite transport and the mechanism and rationale behind the functional diversification of the proteins that form the shell. We also touch on some potential biotechnology applications of an unusual compartment designed by nature to optimize metabolic processes within a cellular context.     

Improving metabolic flux estimation via evolutionary optimization for convex solution space

MOTIVATION: Flux estimation by using (13) C-labeling pattern information of metabolites is currently the only method that can give accurate, detailed quantification of all intracellular fluxes in the central metabolism of a microorganism. In essence, it corresponds to a constrained optimization problem which minimizes a weighted distance between measured and simulated results. Characteristics, such as existence of multiple local minima, non-linear and non-differentiable make this problem a special difficulty. RESULTS: In the present work, we propose an evolutionary-based global optimization algorithm taking advantage of the convex feature of the problem's solution space. Based on the characteristics of convex spaces, specialized initial population and evolutionary operators are designed to solve (13)C-based metabolic flux estimation problem robustly and efficiently. The algorithm was applied to estimate the central metabolic fluxes in Escherichia coli and compared with conventional optimization technique. Experimental results illustrated that our algorithm is capable of achieving fast convergence to good near-optima and maintaining the robust nature of evolutionary algorithms at the same time. AVAILABILITY: Available from the authors upon request.     

Novel metabolic pathways in Archaea

The Archaea harbor many metabolic pathways that differ to previously recognized classical pathways. Glycolysis is carried out by modified versions of the Embden-Meyerhof and Entner-Doudoroff pathways. Thermophilic archaea have recently been found to harbor a bi-functional fructose-1,6-bisphosphate aldolase/phosphatase for gluconeogenesis. A number of novel pentose-degrading pathways have also been recently identified. In terms of anabolic metabolism, a pathway for acetate assimilation, the methylaspartate cycle, and two CO2-fixing pathways, the 3-hydroxypropionate/4-hydroxybutyrate cycle and the dicarboxylate/4-hydroxybutyrate cycle, have been elucidated. As for biosynthetic pathways, recent studies have clarified the enzymes responsible for several steps involved in the biosynthesis of inositol phospholipids, polyamine, coenzyme A, flavin adeninedinucleotide and heme. By examining the presence/absence of homologs of these enzymes on genome sequences, we have found that the majority of these enzymes and pathways are specific to the Archaea.     

Chromokinetics of metabolic pathways.

Some methods to study and intuitively understand steady-state flows in complicated metabolic pathways are discussed. For this purpose, a suitable decomposition of complex metabolic schemes into smaller subsystems is used. These independent subsystems are then interpreted as basic colors of a chromatic coloring scheme. The mixture of these basic colors allows an intuitive picture of how a steady state in a metabolic pathway can be understood. Furthermore, actions of drugs can be more easily investigated on this basis. An anaerobic variant of pyruvate metabolism in rat liver mitochondria is presented as a simple example. This experiment allows measurement of the percentage that each basic color contributes to the steady states resulting from different experimental conditions. Possible implementations of existing algorithms and rational design of new drugs are discussed. A MATHEMATICA program, based on a new algorithm for finding all basic colors of stoichiometric networks, is included.     

Directed evolution of metabolic pathways

The modification of cellular metabolism is of biotechnological and commercial significance because naturally occurring metabolic pathways are the source of diverse compounds used in fields ranging from medicine to bioremediation. Directed evolution is the experimental improvement of biocatalysts or cellular properties through iterative genetic diversification and selection procedures. The creation of novel metabolic functions without disrupting the balanced intracellular pool of metabolites is the primary challenge of pathway manipulation. The introduction of coordinated changes across multiple genetic elements, in conjunction with functional selection, presents an integrated approach for the modification of metabolism with benign physiological consequences. Directed evolution formats take advantage of the dynamic structures of genomes and genomic sub-structures and their ability to evolve in multiple directions in response to external stimuli. The elucidation, design and application of genome-restructuring mechanisms are key elements in the directed evolution of cellular metabolic pathways.     

Glutamate metabolic pathways and retinal function

Glutamate is a major neurotransmitter in the CNS but is also a key metabolite intimately coupled to amino acid production/degradation. We consider the effect of inhibition of two key glutamate metabolic enzymes: glutamine synthetase (GS) and aspartate aminotransferase on retinal function assessed using the electroretinogram to consider photoreceptoral (a-wave) and post-receptoral (b-wave) amplitudes. Quantitative immunocytochemistry was used to assess amino acid levels within photoreceptors, ganglion and Müller cells secondary to GS inhibition. Intravitreal injections of methionine sulfoximine reduced GS immunoreactivity in the rat retina. Additionally, glutamate and its precursor aspartate was reduced in photoreceptors and ganglion cells, but elevated in Müller cells. This reduction in neuronal glutamate was consistent with a deficit in neurotransmission (−75% b-wave reduction). Exogenous glutamine supply completely restored the b-wave, whereas other amino acid substrates (lactate, pyruvate, α-ketoglutarate, and succinate) only partially restored the b-wave (16–20%). Inhibition of the aminotranferases using aminooxyacetic acid had no effect on retinal function. However, aminooxyacetic acid application after methionine sulfoximine further reduced the b-wave (from −75% to −92%). The above data suggest that de novo glutamate synthesis involving aspartate aminotransferase can partially sustain neurotransmission when glutamate recycling is impaired. We also show that altered glutamate homeostasis results in a greater change in amino acid distribution in ganglion cells compared with photoreceptors.