Francisco Montero - Academia.edu (original) (raw)

Papers by Francisco Montero

Research paper thumbnail of Determinism and Contingency Shape Metabolic Complementation in an Endosymbiotic Consortium

Frontiers in microbiology, 2017

Bacterial endosymbionts and their insect hosts establish an intimate metabolic relationship. Bact... more Bacterial endosymbionts and their insect hosts establish an intimate metabolic relationship. Bacteria offer a variety of essential nutrients to their hosts, whereas insect cells provide the necessary sources of matter and energy to their tiny metabolic allies. These nutritional complementations sustain themselves on a diversity of metabolite exchanges between the cell host and the reduced yet highly specialized bacterial metabolism-which, for instance, overproduces a small set of essential amino acids and vitamins. A well-known case of metabolic complementation is provided by the cedar aphid Cinara cedri that harbors two co-primary endosymbionts, Buchnera aphidicola BCc and Ca. Serratia symbiotica SCc, and in which some metabolic pathways are partitioned between different partners. Here we present a genome-scale metabolic network (GEM) for the bacterial consortium from the cedar aphid iBSCc. The analysis of this GEM allows us the confirmation of cases of metabolic complementation pr...

Research paper thumbnail of Metabolic complementation in bacterial communities: necessary conditions and optimality

Bacterial communities may display metabolic complementation, in which different members of the as... more Bacterial communities may display metabolic complementation, in which different members of the association partially contribute to the same biosynthetic pathway. In this way, the end product of the pathway is synthesized by the community as a whole. However, the emergence and the benefits of such complementation are poorly understood. Herein we present a simple model to analyze the metabolic interactions among bacteria, including the host in the case of endosymbiotic bacteria. The model considers two cell populations, with both cell types encoding for the same linear biosynthetic pathway. We have found that, for metabolic complementation to emerge as an optimal strategy, both product inhibition and large permeabilities are needed. In the light of these results, we then consider the patterns found in the case of tryptophan biosynthesis in the endosymbiont consortium hosted by the aphidCinara cedri.Using in-silico computed physicochemical properties of metabolites of this and other bi...

Research paper thumbnail of Nature lessons: the whitefly bacterial endosymbiont is a minimal amino acid factory with unusual energetics

Bacterial lineages that establish obligate symbiotic associations with insect hosts are known to ... more Bacterial lineages that establish obligate symbiotic associations with insect hosts are known to possess highly reduced genomes with streamlined metabolic functions that are commonly focused on amino acid and vitamin synthesis. We constructed a genome-scale metabolic model of the whitefly bacterial endosymbiont Candidatus Portiera aleyrodidarum to study the energy production capabilities using stoichiometric analysis. Strikingly, the results suggest that the energetic metabolism of the bacterial endosymbiont relies on the use of pathways related to the synthesis of amino acids and carotenoids. A deeper insight showed that the ATP production via carotenoid synthesis may also have a potential role in the regulation of amino acid production. The coupling of energy production to anabolism suggest that minimization of metabolic networks as a consequence of genome size reduction does not necessarily limit the biosynthetic potential of obligate endosymbionts.

Research paper thumbnail of Biofísica

Research paper thumbnail of Network organization of cell metabolism: monosaccharide interconversion

Biochemical Journal, 1997

The structural properties of carbohydrate metabolism are being studied. The present contribution ... more The structural properties of carbohydrate metabolism are being studied. The present contribution focuses mainly on those processes involving the transfer of carbon fragments among sugars. It is shown how enzymic activities fix the way the system self-organizes stoichiometrically at the steady state. It is proven that there exists a specific correspondence between the set of all possible enzymic activities, the activity set, and the set of stoichiometrically compatible flux distributions through the pathway. On the one hand, there are enzymic activities that do not allow a stoichiometrically feasible coupling at the steady state of the reactions involved in the conversion. On the other hand, there are enzymic activities that are related to one or more flux distributions at the steady state (i.e. with one or several rate vectors respectively). For this latter group, it can be demonstrated that the structure of the system depends on other non-structural factors, such as boundary constr...

Research paper thumbnail of The Role of Natural Selection and Evolution in the Game of the Pentose Phosphate Cycle

Biomedical and Life Physics, 1996

The pentose phosphate cycle has been presented as a paradigm of optimization in the design of met... more The pentose phosphate cycle has been presented as a paradigm of optimization in the design of metabolic pathways. The hypothesis of simplicity, i.e. the tendency to the least number of both steps and carbons involved in every intermediate, seems to have played a prominent role in its evolution. In fact, the number of steps and carbons of the intermediates affect the values of important characteristics of the system, such as the total flux of the pathway and its transition time.

Research paper thumbnail of An algorithm to study the evolution and selection of auto replicative molecules

Computers & Chemistry, 1984

Computers <£ Chemistry Vol. 8, No. 4. pp. 303-307, 1984 Printed in the USA 0097-84BS/8... more Computers <£ Chemistry Vol. 8, No. 4. pp. 303-307, 1984 Printed in the USA 0097-84BS/84 S3.0Û + .00 Perpamon Press Lid. APPLICATIONS SECTION AN ALGORITHM TO STUDY THE EVOLUTION AND SELECTION OF AUTO REPLICATIVE MOLECULES Federico Moran ...

Research paper thumbnail of Simulating a Model of Metabolic Closure

Biological Theory, 2013

Your article is protected by copyright and all rights are held exclusively by Konrad Lorenz Insti... more Your article is protected by copyright and all rights are held exclusively by Konrad Lorenz Institute for Evolution and Cognition Research. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Research paper thumbnail of Aggregation of the histone h1 from the fruit fly Ceratitis capitata through disulphide bridges. Studies on their complexes with DNA

International Journal of Biochemistry, 1985

Three different major components. BGI, BG2 and BG3, have been obtained when the histone HI from t... more Three different major components. BGI, BG2 and BG3, have been obtained when the histone HI from the fruit fly Ceratitis capitata is oxidized in vitro, separated by gel permeation chromatography and characterized by both amino acid analysis and polyacrylamide electrophoresis. 2. BGI and BG2 correspond to the aggregation products by formation of intermolecular disulphide bridges, while BG3 is a monomeric component which shows the presence of one intramolecular disulphide bridge. 3. Structural studies by both circular dichroism and controlled tryptic digestion on BG1, BG2 and BG3 show the native conformation of HI from the insect changes slightly and in a different range in each component. 4. All the subfractions induce PSI structure in DNA and stabilize the double helix of DNA, although quantitative differences appear.

Research paper thumbnail of Theoretical Approaches to the Evolutionary Optimization of Glycolysis. Thermodynamic and Kinetic Constraints

European Journal of Biochemistry, 1997

It is analyzed whether the structural design of contemporary glycolysis can be explained theoreti... more It is analyzed whether the structural design of contemporary glycolysis can be explained theoretically on the basis of optimization principles originating from natural selection during evolution. Particular attention is paid to the problem of how the kinetic and thermodynamic properties of the glycolytic pathway are related to its stoichiometry with respect to the number and location of ATP-coupling sites. The mathematical analysis of a minimal model of unbranched energy-converting pathways shows that the requirement of high ATP-production rate favours a structural design that includes not only ATP-producing reactions (P-sites) but also ATP-consuming reactions (C-sites). It is demonstrated that, at fixed overall thermodynamic properties of a chain, the ATP-production rate may be enhanced by kinetic optimization. The ATP-production rate is increased if the C-sites are concentrated at the beginning and all the P-sites at the end of the pathway. An optimum is attained, which is characterized by numbers of coupling sites corresponding to those found in glycolysis. Various extensions of the minimal model are considered, which allow the effects of internal feedback-regulations, variable enzyme concentrations, and the symmetric branching of glycolysis at the aldolase step to be considered.

Research paper thumbnail of A Simple Self-Maintaining Metabolic System: Robustness, Autocatalysis, Bistability

PLoS Computational Biology, 2010

A living organism must not only organize itself from within; it must also maintain its organizati... more A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts.

Research paper thumbnail of Complex dynamics of a catalytic network having faulty replication into error-species

Physica D: Nonlinear Phenomena, 1993

We examine the dynamics of catalytic networks when error is introduced through faulty self-replic... more We examine the dynamics of catalytic networks when error is introduced through faulty self-replication into a mutant molecular species. The model consists of n species that individually self-replicate through noncatalytic and catalytic action, and catalyze the replication of other species. Faulty replication produces error mutants which are assumed to be kinetically indistinguishable from one another. This aggregate error-species (error-tail) undergoes noncatalyzed self-replication, but has no effect on the catalytic species. A constant-population criterion produces competition among all reactants. The time evolution of the catalytic species can be expressed by a set of ordinary differential equations. We provide a detailed parametric analysis of the dynamics in a computationally tractable reduced model. Kinetic constants K,, controlling the enzymatic reactions can be used as bifurcation parameters to generate a rich repertoire of periodic and complex chaotic dynamics. Except for changes in the parametric position of bifurcation points, system dynamics is stable in response to changes in the quality of replication Q, where 1-Q is the mutation rate, and in the amplification constant A for the catalytic species. At low values of Q, the system falls out of chaotic regimes and into a "random-replication" state at which there are no catalytic species present. There is a similar insensitivity to changes in the amplification factor for the error species, A,, except for A, = 0, at which the chaotic regimes remain stable throughout the full range of Q. We discuss the behavior of our model against one in which error is handled by means of mutual intermutation between the catalytic species. Complex behavior in this intermutation model is extremely sensitive to the mutation rate. Because the error-tail is expressed only in terms of the catalytic species themselves rather than in variables representing the error-species, the error-tail model may provide a useful method with which to examine models of error-utilization in neuronal and other biological systems involving competitive interactions among their constituent parts.

Research paper thumbnail of Structural analyses of a hypothetical minimal metabolism

Philosophical Transactions of the Royal Society B: Biological Sciences, 2007

By integrating data from comparative genomics and large-scale deletion studies, we previously pro... more By integrating data from comparative genomics and large-scale deletion studies, we previously proposed a minimal gene set comprising 206 protein-coding genes. To evaluate the consistency of the metabolism encoded by such a minimal genome, we have carried out a series of computational analyses. Firstly, the topology of the minimal metabolism was compared with that of the reconstructed networks from natural bacterial genomes. Secondly, the robustness of the metabolic network was evaluated by simulated mutagenesis and, finally, the stoichiometric consistency was assessed by automatically deriving the steady-state solutions from the reaction set. The results indicated that the proposed minimal metabolism presents stoichiometric consistency and that it is organized as a complex power-law network with topological parameters falling within the expected range for a natural metabolism of its size. The robustness analyses revealed that most random mutations do not alter the topology of the ne...

Research paper thumbnail of Stoichiometric properties of the non oxidative phase of the pentose phosphate cycle

Nonlinear Analysis: Theory, Methods & Applications, 1997

Research paper thumbnail of Kinetic and thermodynamic constraints for the structural design of glycolysis

Nonlinear Analysis: Theory, Methods & Applications, 1997

Research paper thumbnail of Stoichiometric analysis of self-maintaining metabolisms

Journal of Theoretical Biology, 2008

This paper presents an extension of stoichiometric analysis in systems where the catalytic compou... more This paper presents an extension of stoichiometric analysis in systems where the catalytic compounds (enzymes) are also intermediates of the metabolic network {dual property), so they are produced and degraded by the reaction network itself. To take this property into account, we introduce the definition of enzyme-maintaining mode, a set of reactions that produces its own catalyst and can operate at stationary state. Moreover, an enzyme-maintaining mode is defined as elementary with respect to a given reaction if the removal of any of the remaining reactions causes the cessation of any steady state flux through this reference reaction. These concepts are applied to determine the network structure of a simple self-maintaining system.

Research paper thumbnail of From prebiotic chemistry to cellular metabolism—The chemical evolution of metabolism before Darwinian natural selection

Journal of Theoretical Biology, 2008

It is generally assumed that the complex map of metabolism is a result of natural selection worki... more It is generally assumed that the complex map of metabolism is a result of natural selection working at the molecular level. However, natural selection can only work on entities that have three basic features: information, metabolism and membrane. Metabolism must include the capability of producing all cellular structures, as well as energy (ATP), from external sources; information must be established on a material that allows its perpetuity, in order to safeguard the goals achieved; and membranes must be able to preserve the internal material, determining a selective exchange with external material in order to ensure that both metabolism and information can be individualized. It is not difficult to understand that protocellular entities that boast these three qualities can evolve through natural selection. The problem is rather to explain the origin of such features under conditions where natural selection could not work. In the present work we propose that these protocells could be built by chemical evolution, starting from the prebiotic primordial soup, by means of chemical selection. This consists of selective increases of the rates of certain specific reactions because of the kinetic or thermodynamic features of the process, such as stoichiometric catalysis or autocatalysis, cooperativity and others, thereby promoting their prevalence among the whole set of chemical possibilities. Our results show that all chemical processes necessary for yielding the basic materials that natural selection needs to work may be achieved through chemical selection, thus suggesting a way for life to begin.

Research paper thumbnail of Size matters: Influence of stochasticity on the self-maintenance of a simple model of metabolic closure

Journal of Theoretical Biology, 2012

A fundamental landmark in the emergence and maintenance of the first proto-biological systems mus... more A fundamental landmark in the emergence and maintenance of the first proto-biological systems must have been the formation of a "closed" metabolic organization, and this paper describes a stochastic analysis of a simple model of a system that is closed to efficient causation. Although it shows an absorbing barrier corresponding to the trivial solution that implies collapse and extinction, for certain values of the kinetic parameters it can also show a "coexistence state" in which there are non-null populations of its intermediates, which corresponds approximately to a non-trivial deterministic stable steady state. Depending on the initial conditions, fluctuations can drive the system either to the self-maintaining regime or to extinction, with different probabilities. Different lines of equal probability have been obtained and compared with the deterministic results, and the average time for reaching these states (characteristic time) has been estimated. The system shows strong dependence on volume size, and there is a critical volume below which it collapses very rapidly. The characteristic time is also affected by the volume, with faster responses for lower system volumes. All these results are discussed in the context of the origin of living organization.

Research paper thumbnail of Studies on evolutionary and selective properties of hypercycles using a Monte Carlo method

Journal of Molecular Evolution, 1987

The most relevant properties ofhypercycles were previously studied mainly from a theoretical poin... more The most relevant properties ofhypercycles were previously studied mainly from a theoretical point of view. We have developed a Monte Carlo method simulating hypercyclic organization to obtain information about the dynamics of this prebiotic organization. Nucleation, growth, and selective properties have been tested and the results obtained are in good agreement with those of the theoretical predictions. The influence ofhypercyclic organization on the "error threshold" has also been studied. As a consequence of the emergence of a hypercycle, the value of this threshold decreases. The amount of this decrease depends on the population size. Moreover, for some interval of quality factor values, either the hypercycle organization or an error catastrophe can be produced, depending on the initial conditions. The influence of these phenomena on both the dynamic behavior and evolutionary advantages of the hypercycle, as well as their decisive roles on genome size, are discussed.

Research paper thumbnail of A model of an autocatalytic network formed by error-prone self-replicative species

Bulletin of Mathematical Biology, 1993

A generalized model of n catalytically-coupled self-replicative molecules with error-prone replic... more A generalized model of n catalytically-coupled self-replicative molecules with error-prone replication is presented. A generalized mathematical formulation of this model and the outline of its asymptotic behaviour have been developed. Due to the complexity of the model, only in simple situations is it possible to draw general conclusions from the standard analysis. Some complex situations are illustrated by means of numerical integration of particular examples.

Research paper thumbnail of Determinism and Contingency Shape Metabolic Complementation in an Endosymbiotic Consortium

Frontiers in microbiology, 2017

Bacterial endosymbionts and their insect hosts establish an intimate metabolic relationship. Bact... more Bacterial endosymbionts and their insect hosts establish an intimate metabolic relationship. Bacteria offer a variety of essential nutrients to their hosts, whereas insect cells provide the necessary sources of matter and energy to their tiny metabolic allies. These nutritional complementations sustain themselves on a diversity of metabolite exchanges between the cell host and the reduced yet highly specialized bacterial metabolism-which, for instance, overproduces a small set of essential amino acids and vitamins. A well-known case of metabolic complementation is provided by the cedar aphid Cinara cedri that harbors two co-primary endosymbionts, Buchnera aphidicola BCc and Ca. Serratia symbiotica SCc, and in which some metabolic pathways are partitioned between different partners. Here we present a genome-scale metabolic network (GEM) for the bacterial consortium from the cedar aphid iBSCc. The analysis of this GEM allows us the confirmation of cases of metabolic complementation pr...

Research paper thumbnail of Metabolic complementation in bacterial communities: necessary conditions and optimality

Bacterial communities may display metabolic complementation, in which different members of the as... more Bacterial communities may display metabolic complementation, in which different members of the association partially contribute to the same biosynthetic pathway. In this way, the end product of the pathway is synthesized by the community as a whole. However, the emergence and the benefits of such complementation are poorly understood. Herein we present a simple model to analyze the metabolic interactions among bacteria, including the host in the case of endosymbiotic bacteria. The model considers two cell populations, with both cell types encoding for the same linear biosynthetic pathway. We have found that, for metabolic complementation to emerge as an optimal strategy, both product inhibition and large permeabilities are needed. In the light of these results, we then consider the patterns found in the case of tryptophan biosynthesis in the endosymbiont consortium hosted by the aphidCinara cedri.Using in-silico computed physicochemical properties of metabolites of this and other bi...

Research paper thumbnail of Nature lessons: the whitefly bacterial endosymbiont is a minimal amino acid factory with unusual energetics

Bacterial lineages that establish obligate symbiotic associations with insect hosts are known to ... more Bacterial lineages that establish obligate symbiotic associations with insect hosts are known to possess highly reduced genomes with streamlined metabolic functions that are commonly focused on amino acid and vitamin synthesis. We constructed a genome-scale metabolic model of the whitefly bacterial endosymbiont Candidatus Portiera aleyrodidarum to study the energy production capabilities using stoichiometric analysis. Strikingly, the results suggest that the energetic metabolism of the bacterial endosymbiont relies on the use of pathways related to the synthesis of amino acids and carotenoids. A deeper insight showed that the ATP production via carotenoid synthesis may also have a potential role in the regulation of amino acid production. The coupling of energy production to anabolism suggest that minimization of metabolic networks as a consequence of genome size reduction does not necessarily limit the biosynthetic potential of obligate endosymbionts.

Research paper thumbnail of Biofísica

Research paper thumbnail of Network organization of cell metabolism: monosaccharide interconversion

Biochemical Journal, 1997

The structural properties of carbohydrate metabolism are being studied. The present contribution ... more The structural properties of carbohydrate metabolism are being studied. The present contribution focuses mainly on those processes involving the transfer of carbon fragments among sugars. It is shown how enzymic activities fix the way the system self-organizes stoichiometrically at the steady state. It is proven that there exists a specific correspondence between the set of all possible enzymic activities, the activity set, and the set of stoichiometrically compatible flux distributions through the pathway. On the one hand, there are enzymic activities that do not allow a stoichiometrically feasible coupling at the steady state of the reactions involved in the conversion. On the other hand, there are enzymic activities that are related to one or more flux distributions at the steady state (i.e. with one or several rate vectors respectively). For this latter group, it can be demonstrated that the structure of the system depends on other non-structural factors, such as boundary constr...

Research paper thumbnail of The Role of Natural Selection and Evolution in the Game of the Pentose Phosphate Cycle

Biomedical and Life Physics, 1996

The pentose phosphate cycle has been presented as a paradigm of optimization in the design of met... more The pentose phosphate cycle has been presented as a paradigm of optimization in the design of metabolic pathways. The hypothesis of simplicity, i.e. the tendency to the least number of both steps and carbons involved in every intermediate, seems to have played a prominent role in its evolution. In fact, the number of steps and carbons of the intermediates affect the values of important characteristics of the system, such as the total flux of the pathway and its transition time.

Research paper thumbnail of An algorithm to study the evolution and selection of auto replicative molecules

Computers & Chemistry, 1984

Computers <£ Chemistry Vol. 8, No. 4. pp. 303-307, 1984 Printed in the USA 0097-84BS/8... more Computers <£ Chemistry Vol. 8, No. 4. pp. 303-307, 1984 Printed in the USA 0097-84BS/84 S3.0Û + .00 Perpamon Press Lid. APPLICATIONS SECTION AN ALGORITHM TO STUDY THE EVOLUTION AND SELECTION OF AUTO REPLICATIVE MOLECULES Federico Moran ...

Research paper thumbnail of Simulating a Model of Metabolic Closure

Biological Theory, 2013

Your article is protected by copyright and all rights are held exclusively by Konrad Lorenz Insti... more Your article is protected by copyright and all rights are held exclusively by Konrad Lorenz Institute for Evolution and Cognition Research. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Research paper thumbnail of Aggregation of the histone h1 from the fruit fly Ceratitis capitata through disulphide bridges. Studies on their complexes with DNA

International Journal of Biochemistry, 1985

Three different major components. BGI, BG2 and BG3, have been obtained when the histone HI from t... more Three different major components. BGI, BG2 and BG3, have been obtained when the histone HI from the fruit fly Ceratitis capitata is oxidized in vitro, separated by gel permeation chromatography and characterized by both amino acid analysis and polyacrylamide electrophoresis. 2. BGI and BG2 correspond to the aggregation products by formation of intermolecular disulphide bridges, while BG3 is a monomeric component which shows the presence of one intramolecular disulphide bridge. 3. Structural studies by both circular dichroism and controlled tryptic digestion on BG1, BG2 and BG3 show the native conformation of HI from the insect changes slightly and in a different range in each component. 4. All the subfractions induce PSI structure in DNA and stabilize the double helix of DNA, although quantitative differences appear.

Research paper thumbnail of Theoretical Approaches to the Evolutionary Optimization of Glycolysis. Thermodynamic and Kinetic Constraints

European Journal of Biochemistry, 1997

It is analyzed whether the structural design of contemporary glycolysis can be explained theoreti... more It is analyzed whether the structural design of contemporary glycolysis can be explained theoretically on the basis of optimization principles originating from natural selection during evolution. Particular attention is paid to the problem of how the kinetic and thermodynamic properties of the glycolytic pathway are related to its stoichiometry with respect to the number and location of ATP-coupling sites. The mathematical analysis of a minimal model of unbranched energy-converting pathways shows that the requirement of high ATP-production rate favours a structural design that includes not only ATP-producing reactions (P-sites) but also ATP-consuming reactions (C-sites). It is demonstrated that, at fixed overall thermodynamic properties of a chain, the ATP-production rate may be enhanced by kinetic optimization. The ATP-production rate is increased if the C-sites are concentrated at the beginning and all the P-sites at the end of the pathway. An optimum is attained, which is characterized by numbers of coupling sites corresponding to those found in glycolysis. Various extensions of the minimal model are considered, which allow the effects of internal feedback-regulations, variable enzyme concentrations, and the symmetric branching of glycolysis at the aldolase step to be considered.

Research paper thumbnail of A Simple Self-Maintaining Metabolic System: Robustness, Autocatalysis, Bistability

PLoS Computational Biology, 2010

A living organism must not only organize itself from within; it must also maintain its organizati... more A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts.

Research paper thumbnail of Complex dynamics of a catalytic network having faulty replication into error-species

Physica D: Nonlinear Phenomena, 1993

We examine the dynamics of catalytic networks when error is introduced through faulty self-replic... more We examine the dynamics of catalytic networks when error is introduced through faulty self-replication into a mutant molecular species. The model consists of n species that individually self-replicate through noncatalytic and catalytic action, and catalyze the replication of other species. Faulty replication produces error mutants which are assumed to be kinetically indistinguishable from one another. This aggregate error-species (error-tail) undergoes noncatalyzed self-replication, but has no effect on the catalytic species. A constant-population criterion produces competition among all reactants. The time evolution of the catalytic species can be expressed by a set of ordinary differential equations. We provide a detailed parametric analysis of the dynamics in a computationally tractable reduced model. Kinetic constants K,, controlling the enzymatic reactions can be used as bifurcation parameters to generate a rich repertoire of periodic and complex chaotic dynamics. Except for changes in the parametric position of bifurcation points, system dynamics is stable in response to changes in the quality of replication Q, where 1-Q is the mutation rate, and in the amplification constant A for the catalytic species. At low values of Q, the system falls out of chaotic regimes and into a "random-replication" state at which there are no catalytic species present. There is a similar insensitivity to changes in the amplification factor for the error species, A,, except for A, = 0, at which the chaotic regimes remain stable throughout the full range of Q. We discuss the behavior of our model against one in which error is handled by means of mutual intermutation between the catalytic species. Complex behavior in this intermutation model is extremely sensitive to the mutation rate. Because the error-tail is expressed only in terms of the catalytic species themselves rather than in variables representing the error-species, the error-tail model may provide a useful method with which to examine models of error-utilization in neuronal and other biological systems involving competitive interactions among their constituent parts.

Research paper thumbnail of Structural analyses of a hypothetical minimal metabolism

Philosophical Transactions of the Royal Society B: Biological Sciences, 2007

By integrating data from comparative genomics and large-scale deletion studies, we previously pro... more By integrating data from comparative genomics and large-scale deletion studies, we previously proposed a minimal gene set comprising 206 protein-coding genes. To evaluate the consistency of the metabolism encoded by such a minimal genome, we have carried out a series of computational analyses. Firstly, the topology of the minimal metabolism was compared with that of the reconstructed networks from natural bacterial genomes. Secondly, the robustness of the metabolic network was evaluated by simulated mutagenesis and, finally, the stoichiometric consistency was assessed by automatically deriving the steady-state solutions from the reaction set. The results indicated that the proposed minimal metabolism presents stoichiometric consistency and that it is organized as a complex power-law network with topological parameters falling within the expected range for a natural metabolism of its size. The robustness analyses revealed that most random mutations do not alter the topology of the ne...

Research paper thumbnail of Stoichiometric properties of the non oxidative phase of the pentose phosphate cycle

Nonlinear Analysis: Theory, Methods & Applications, 1997

Research paper thumbnail of Kinetic and thermodynamic constraints for the structural design of glycolysis

Nonlinear Analysis: Theory, Methods & Applications, 1997

Research paper thumbnail of Stoichiometric analysis of self-maintaining metabolisms

Journal of Theoretical Biology, 2008

This paper presents an extension of stoichiometric analysis in systems where the catalytic compou... more This paper presents an extension of stoichiometric analysis in systems where the catalytic compounds (enzymes) are also intermediates of the metabolic network {dual property), so they are produced and degraded by the reaction network itself. To take this property into account, we introduce the definition of enzyme-maintaining mode, a set of reactions that produces its own catalyst and can operate at stationary state. Moreover, an enzyme-maintaining mode is defined as elementary with respect to a given reaction if the removal of any of the remaining reactions causes the cessation of any steady state flux through this reference reaction. These concepts are applied to determine the network structure of a simple self-maintaining system.

Research paper thumbnail of From prebiotic chemistry to cellular metabolism—The chemical evolution of metabolism before Darwinian natural selection

Journal of Theoretical Biology, 2008

It is generally assumed that the complex map of metabolism is a result of natural selection worki... more It is generally assumed that the complex map of metabolism is a result of natural selection working at the molecular level. However, natural selection can only work on entities that have three basic features: information, metabolism and membrane. Metabolism must include the capability of producing all cellular structures, as well as energy (ATP), from external sources; information must be established on a material that allows its perpetuity, in order to safeguard the goals achieved; and membranes must be able to preserve the internal material, determining a selective exchange with external material in order to ensure that both metabolism and information can be individualized. It is not difficult to understand that protocellular entities that boast these three qualities can evolve through natural selection. The problem is rather to explain the origin of such features under conditions where natural selection could not work. In the present work we propose that these protocells could be built by chemical evolution, starting from the prebiotic primordial soup, by means of chemical selection. This consists of selective increases of the rates of certain specific reactions because of the kinetic or thermodynamic features of the process, such as stoichiometric catalysis or autocatalysis, cooperativity and others, thereby promoting their prevalence among the whole set of chemical possibilities. Our results show that all chemical processes necessary for yielding the basic materials that natural selection needs to work may be achieved through chemical selection, thus suggesting a way for life to begin.

Research paper thumbnail of Size matters: Influence of stochasticity on the self-maintenance of a simple model of metabolic closure

Journal of Theoretical Biology, 2012

A fundamental landmark in the emergence and maintenance of the first proto-biological systems mus... more A fundamental landmark in the emergence and maintenance of the first proto-biological systems must have been the formation of a "closed" metabolic organization, and this paper describes a stochastic analysis of a simple model of a system that is closed to efficient causation. Although it shows an absorbing barrier corresponding to the trivial solution that implies collapse and extinction, for certain values of the kinetic parameters it can also show a "coexistence state" in which there are non-null populations of its intermediates, which corresponds approximately to a non-trivial deterministic stable steady state. Depending on the initial conditions, fluctuations can drive the system either to the self-maintaining regime or to extinction, with different probabilities. Different lines of equal probability have been obtained and compared with the deterministic results, and the average time for reaching these states (characteristic time) has been estimated. The system shows strong dependence on volume size, and there is a critical volume below which it collapses very rapidly. The characteristic time is also affected by the volume, with faster responses for lower system volumes. All these results are discussed in the context of the origin of living organization.

Research paper thumbnail of Studies on evolutionary and selective properties of hypercycles using a Monte Carlo method

Journal of Molecular Evolution, 1987

The most relevant properties ofhypercycles were previously studied mainly from a theoretical poin... more The most relevant properties ofhypercycles were previously studied mainly from a theoretical point of view. We have developed a Monte Carlo method simulating hypercyclic organization to obtain information about the dynamics of this prebiotic organization. Nucleation, growth, and selective properties have been tested and the results obtained are in good agreement with those of the theoretical predictions. The influence ofhypercyclic organization on the "error threshold" has also been studied. As a consequence of the emergence of a hypercycle, the value of this threshold decreases. The amount of this decrease depends on the population size. Moreover, for some interval of quality factor values, either the hypercycle organization or an error catastrophe can be produced, depending on the initial conditions. The influence of these phenomena on both the dynamic behavior and evolutionary advantages of the hypercycle, as well as their decisive roles on genome size, are discussed.

Research paper thumbnail of A model of an autocatalytic network formed by error-prone self-replicative species

Bulletin of Mathematical Biology, 1993

A generalized model of n catalytically-coupled self-replicative molecules with error-prone replic... more A generalized model of n catalytically-coupled self-replicative molecules with error-prone replication is presented. A generalized mathematical formulation of this model and the outline of its asymptotic behaviour have been developed. Due to the complexity of the model, only in simple situations is it possible to draw general conclusions from the standard analysis. Some complex situations are illustrated by means of numerical integration of particular examples.