Optimality principles in the regulation of metabolic networks

Optimality of syntactic dependency distances

It is often stated that human languages, as other biological systems, are shaped by cost-cutting pressures but, to what extent? Attempts to quantify the degree of optimality of languages by means of an optimality score have been scarce and focused mostly on English. Here we recast the problem of the optimality of the word order of a sentence as an optimization problem on a spatial network where the vertices are words, arcs indicate syntactic dependencies, and the space is defined by the linear order of the words in the sentence. We introduce a score to quantify the cognitive pressure to reduce the distance between linked words in a sentence. The analysis of sentences from 93 languages representing 19 linguistic families reveals that half of languages are optimized to a 70% or more. The score indicates that distances are not significantly reduced in a few languages and confirms two theoretical predictions: that longer sentences are more optimized and that distances are more likely to be longer than expected by chance in short sentences. We present a hierarchical ranking of languages by their degree of optimization. The score has implications for various fields of language research (dependency linguistics, typology, historical linguistics, clinical linguistics, and cognitive science). Finally, the principles behind the design of the score have implications for network science.

Using optimal control to understand complex metabolic pathways

BACKGROUND

Optimality principles have been used to explain the structure and behavior of living matter at different levels of organization, from basic phenomena at the molecular level, up to complex dynamics in whole populations. Most of these studies have assumed a single-criteria approach. Such optimality principles have been justified from an evolutionary perspective. In the context of the cell, previous studies have shown how dynamics of gene expression in small metabolic models can be explained assuming that cells have developed optimal adaptation strategies. Most of these works have considered rather simplified representations, such as small linear pathways, or reduced networks with a single branching point, and a single objective for the optimality criteria.

RESULTS

Here we consider the extension of this approach to more realistic scenarios, i.e. biochemical pathways of arbitrary size and structure. We first show that exploiting optimality principles for these networks poses great challenges due to the complexity of the associated optimal control problems. Second, in order to surmount such challenges, we present a computational framework which has been designed with scalability and efficiency in mind, including mechanisms to avoid the most common pitfalls. Third, we illustrate its performance with several case studies considering the central carbon metabolism of S. cerevisiae and B. subtilis. In particular, we consider metabolic dynamics during nutrient shift experiments.

CONCLUSIONS

We show how multi-objective optimal control can be used to predict temporal profiles of enzyme activation and metabolite concentrations in complex metabolic pathways. Further, we also show how to consider general cost/benefit trade-offs. In this study we have considered metabolic pathways, but this computational framework can also be applied to analyze the dynamics of other complex pathways, such as signal transduction or gene regulatory networks.

Resource allocation in metabolic networks: kinetic optimization and approximations by FBA

Based on recent theoretical results on optimal flux distributions in kinetic metabolic networks, we explore the congruences and differences between solutions of kinetic optimization problems and results obtained by constraint-based methods. We demonstrate that, for a certain resource allocation problem, kinetic optimization and standard flux balance analysis (FBA) give rise to qualitatively different results. Furthermore, we introduce a variant of FBA, called satFBA, whose predictions are in qualitative agreement with kinetic optimization.

Metabolism at evolutionary optimal States

Metabolism is generally required for cellular maintenance and for the generation of offspring under conditions that support growth. The rates, yields (efficiencies), adaptation time and robustness of metabolism are therefore key determinants of cellular fitness. For biotechnological applications and our understanding of the evolution of metabolism, it is necessary to figure out how the functional system properties of metabolism can be optimized, via adjustments of the kinetics and expression of enzymes, and by rewiring metabolism. The trade-offs that can occur during such optimizations then indicate fundamental limits to evolutionary innovations and bioengineering. In this paper, we review several theoretical and experimental findings about mechanisms for metabolic optimization.

Footprints of optimal protein assembly strategies in the operonic structure of prokaryotes

In this work, we investigate optimality principles behind synthesis strategies for protein complexes using a dynamic optimization approach. We show that the cellular capacity of protein synthesis has a strong influence on optimal synthesis strategies reaching from a simultaneous to a sequential synthesis of the subunits of a protein complex. Sequential synthesis is preferred if protein synthesis is strongly limited, whereas a simultaneous synthesis is optimal in situations with a high protein synthesis capacity. We confirm the predictions of our optimization approach through the analysis of the operonic organization of protein complexes in several hundred prokaryotes. Thereby, we are able to show that cellular protein synthesis capacity is a driving force in the dissolution of operons comprising the subunits of a protein complex. Thus, we also provide a tested hypothesis explaining why the subunits of many prokaryotic protein complexes are distributed across several operons despite the presumably less precise co-regulation.

Enzyme allocation problems in kinetic metabolic networks: optimal solutions are elementary flux modes

The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In particular, the total enzymatic capacity for cellular metabolism is limited by finite resources that are shared between all enzymes, such as cytosolic space, energy expenditure for amino-acid synthesis, or micro-nutrients. While extensive work has been done to study constrained optimization problems based only on stoichiometric information, mathematical results that characterize the optimal flux in kinetic metabolic networks are still scarce. Here, we study constrained enzyme allocation problems with general kinetics, using the theory of oriented matroids. We give a rigorous proof for the fact that optimal solutions of the non-linear optimization problem are elementary flux modes. This finding has significant consequences for our understanding of optimality in metabolic networks as well as for the identification of metabolic switches and the computation of optimal flux distributions in kinetic metabolic networks.