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Ferrer-I-Cancho R, Gómez-Rodríguez C, Esteban JL, Alemany-Puig L. Optimality of syntactic dependency distances. Phys Rev E 2022; 105:014308. [PMID: 35193296 DOI: 10.1103/physreve.105.014308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2020] [Accepted: 11/10/2021] [Indexed: 06/14/2023]
Abstract
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.
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Affiliation(s)
- Ramon Ferrer-I-Cancho
- Complexity and Quantitative Linguistics Lab, LARCA Research Group, Departament de Ciències de la Computació, Universitat Politècnica de Catalunya, Campus Nord, Edifici Omega, Jordi Girona Salgado 1-3 08034 Barcelona, Catalonia, Spain
| | - Carlos Gómez-Rodríguez
- Universidade da Coruña, CITIC, FASTPARSE Lab, LyS Research Group, Departamento de Ciencias de la Computación y Tecnologías de la Información, Facultade de Informática, Elviña, 15071, A Coruña, Spain
| | - Juan Luis Esteban
- Departament de Ciències de la Computació, Universitat Politècnica de Catalunya (UPC), Campus Nord, Edifici Omega, Jordi Girona Salgado 1-3 08034 Barcelona, Catalonia, Spain
| | - Lluís Alemany-Puig
- Complexity and Quantitative Linguistics Lab, LARCA Research Group, Departament de Ciències de la Computació, Universitat Politècnica de Catalunya, Campus Nord, Edifici Omega, Jordi Girona Salgado 1-3 08034 Barcelona, Catalonia, Spain
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Tsiantis N, Banga JR. Using optimal control to understand complex metabolic pathways. BMC Bioinformatics 2020; 21:472. [PMID: 33087041 PMCID: PMC7579911 DOI: 10.1186/s12859-020-03808-8] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 10/13/2020] [Indexed: 12/16/2022] Open
Abstract
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.
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Affiliation(s)
- Nikolaos Tsiantis
- Bioprocess Engineering Group, Spanish National Research Council, IIM-CSIC, C/Eduardo Cabello 6, 36208 Vigo, Spain
- Department of Chemical Engineering, University of Vigo, 36310 Vigo, Spain
| | - Julio R. Banga
- Bioprocess Engineering Group, Spanish National Research Council, IIM-CSIC, C/Eduardo Cabello 6, 36208 Vigo, Spain
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Resource allocation in metabolic networks: kinetic optimization and approximations by FBA. Biochem Soc Trans 2016; 43:1195-200. [PMID: 26614660 DOI: 10.1042/bst20150156] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
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.
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Rabbers I, van Heerden JH, Nordholt N, Bachmann H, Teusink B, Bruggeman FJ. Metabolism at evolutionary optimal States. Metabolites 2015; 5:311-43. [PMID: 26042723 PMCID: PMC4495375 DOI: 10.3390/metabo5020311] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2015] [Revised: 05/20/2015] [Accepted: 05/25/2015] [Indexed: 01/13/2023] Open
Abstract
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.
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Affiliation(s)
- Iraes Rabbers
- Department of Systems Bioinformatics, VU University Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands.
| | - Johan H van Heerden
- Department of Systems Bioinformatics, VU University Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands.
| | - Niclas Nordholt
- Department of Systems Bioinformatics, VU University Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands.
| | - Herwig Bachmann
- Department of Systems Bioinformatics, VU University Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands.
- NIZO Food Research, 6718 ZB Ede, The Netherlands.
- Top Institute Food and Nutrition, 6700 AN Wageningen, The Netherlands.
| | - Bas Teusink
- Department of Systems Bioinformatics, VU University Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands.
| | - Frank J Bruggeman
- Department of Systems Bioinformatics, VU University Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands.
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Ewald J, Kötzing M, Bartl M, Kaleta C. Footprints of optimal protein assembly strategies in the operonic structure of prokaryotes. Metabolites 2015; 5:252-69. [PMID: 25927816 PMCID: PMC4495372 DOI: 10.3390/metabo5020252] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2015] [Revised: 03/27/2015] [Accepted: 04/24/2015] [Indexed: 11/23/2022] Open
Abstract
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.
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Affiliation(s)
- Jan Ewald
- Research Group Theoretical Systems Biology, Friedrich-Schiller-Universität Jena, Leutragraben 1, 07743 Jena, Germany.
| | - Martin Kötzing
- Research Group Theoretical Systems Biology, Friedrich-Schiller-Universität Jena, Leutragraben 1, 07743 Jena, Germany.
| | - Martin Bartl
- Research Group Theoretical Systems Biology, Friedrich-Schiller-Universität Jena, Leutragraben 1, 07743 Jena, Germany.
| | - Christoph Kaleta
- Research Group Theoretical Systems Biology, Friedrich-Schiller-Universität Jena, Leutragraben 1, 07743 Jena, Germany.
- Research Group Medical Systems Biology, Christian-Albrechts-Universität Kiel, Brunswiker Straße 10, 24105 Kiel, Germany.
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Bachmann H, Pronk JT, Kleerebezem M, Teusink B. Evolutionary engineering to enhance starter culture performance in food fermentations. Curr Opin Biotechnol 2015; 32:1-7. [DOI: 10.1016/j.copbio.2014.09.003] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2014] [Revised: 09/05/2014] [Accepted: 09/12/2014] [Indexed: 01/08/2023]
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Müller S, Regensburger G, Steuer R. Enzyme allocation problems in kinetic metabolic networks: optimal solutions are elementary flux modes. J Theor Biol 2013; 347:182-90. [PMID: 24295962 DOI: 10.1016/j.jtbi.2013.11.015] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2013] [Revised: 11/05/2013] [Accepted: 11/21/2013] [Indexed: 01/12/2023]
Abstract
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.
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Affiliation(s)
- Stefan Müller
- Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraße 69, 4040 Linz, Austria; CzechGlobe - Global Change Research Center, Academy of Sciences of the Czech Republic, Belidla 986/4a, 603 00 Brno, Czech Republic.
| | - Georg Regensburger
- Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraße 69, 4040 Linz, Austria.
| | - Ralf Steuer
- Institute for Theoretical Biology, Humboldt University Berlin, Invalidenstraße 43, 10115 Berlin, Germany.
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