A Simple Self-Maintaining Metabolic System: Robustness, Autocatalysis, Bistability
Publication Date
August 05, 2010
Journal
PLOS Computational Biology
Authors
Gabriel Piedrafita, Francisco Montero, Federico Morán, María Luz Cárdenas, et al
Volume
6
Issue
8
Pages
e1000872
DOI
https://dx.plos.org/10.1371/journal.pcbi.1000872
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1000872
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/20700491
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2916848
Europe PMC
http://europepmc.org/abstract/MED/20700491
Web of Science
000281389500005
Scopus
78049445878
Mendeley
http://www.mendeley.com/research/simple-selfmaintaining-metabolic-system-robustness-autocatalysis-bistability
Events
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Mendeley | Further Information

{"title"=>"A simple self-maintaining metabolic system: Robustness, autocatalysis, bistability", "type"=>"journal", "authors"=>[{"first_name"=>"Gabriel", "last_name"=>"Piedrafita", "scopus_author_id"=>"25960312700"}, {"first_name"=>"Francisco", "last_name"=>"Montero", "scopus_author_id"=>"55199205200"}, {"first_name"=>"Federico", "last_name"=>"Morán", "scopus_author_id"=>"7006435621"}, {"first_name"=>"María Luz", "last_name"=>"Cárdenas", "scopus_author_id"=>"7101944459"}, {"first_name"=>"Athel", "last_name"=>"Cornish-Bowden", "scopus_author_id"=>"7005082000"}], "year"=>2010, "source"=>"PLoS Computational Biology", "identifiers"=>{"pmid"=>"20700491", "sgr"=>"78049445878", "doi"=>"10.1371/journal.pcbi.1000872", "scopus"=>"2-s2.0-78049445878", "pui"=>"359882440", "isbn"=>"1553-734X", "issn"=>"1553734X"}, "id"=>"3c155102-f0df-380d-85b7-4608ad94a1e0", "abstract"=>"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.", "link"=>"http://www.mendeley.com/research/simple-selfmaintaining-metabolic-system-robustness-autocatalysis-bistability", "reader_count"=>86, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>8, "Researcher"=>28, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>26, "Student > Postgraduate"=>4, "Student > Master"=>6, "Other"=>1, "Student > Bachelor"=>2, "Professor"=>8}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>8, "Researcher"=>28, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>26, "Student > Postgraduate"=>4, "Student > Master"=>6, "Other"=>1, "Student > Bachelor"=>2, "Professor"=>8}, "reader_count_by_subject_area"=>{"Unspecified"=>2, "Agricultural and Biological Sciences"=>36, "Philosophy"=>2, "Chemical Engineering"=>1, "Chemistry"=>7, "Computer Science"=>8, "Engineering"=>8, "Environmental Science"=>3, "Biochemistry, Genetics and Molecular Biology"=>6, "Medicine and Dentistry"=>2, "Neuroscience"=>2, "Physics and Astronomy"=>8, "Social Sciences"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>2}, "Social Sciences"=>{"Social Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>8}, "Unspecified"=>{"Unspecified"=>2}, "Environmental Science"=>{"Environmental Science"=>3}, "Chemical Engineering"=>{"Chemical Engineering"=>1}, "Engineering"=>{"Engineering"=>8}, "Chemistry"=>{"Chemistry"=>7}, "Neuroscience"=>{"Neuroscience"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>36}, "Computer Science"=>{"Computer Science"=>8}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>6}, "Philosophy"=>{"Philosophy"=>2}}, "reader_count_by_country"=>{"Netherlands"=>6, "Austria"=>1, "United States"=>7, "United Kingdom"=>2, "Italy"=>1, "France"=>1, "Chile"=>2, "Switzerland"=>1, "Germany"=>3, "India"=>1, "Spain"=>1}, "group_count"=>5}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/837894"], "description"=>"<p>(a) , and represent the contributions of the elements , and respectively. (b) The relative contributions of the three elements are illustrated over the same range of values of .</p>", "links"=>[], "tags"=>["convex", "elements", "flux", "degradation", "constants", "defined"], "article_id"=>508258, "categories"=>["Biochemistry", "Medicine"], "users"=>["Gabriel Piedrafita", "Francisco Montero", "Federico Morán", "María Luz Cárdenas", "Athel Cornish-Bowden"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000872.g008", "stats"=>{"downloads"=>3, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Contribution_of_the_convex_basis_elements_to_the_flux_distribution_at_the_steady_state_for_different_values_of_the_degradation_rate_constants_defined_within_the_region_of_bistability_/508258", "title"=>"Contribution of the convex basis elements to the flux distribution at the steady state, for different values of the degradation rate constants defined within the region of bistability.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:10:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/837957"], "description"=>"<p>Non-trivial steady states reached from different seed metabolites.</p>", "links"=>[], "tags"=>["states", "reached"], "article_id"=>508326, "categories"=>["Biochemistry", "Medicine"], "users"=>["Gabriel Piedrafita", "Francisco Montero", "Federico Morán", "María Luz Cárdenas", "Athel Cornish-Bowden"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000872.t001", "stats"=>{"downloads"=>7, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Non_trivial_steady_states_reached_from_different_seed_metabolites_/508326", "title"=>"Non-trivial steady states reached from different seed metabolites.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 00:10:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/837229"], "description"=>"<p>(a) The metabolites shown inside squares (input) are considered to be “external” and to have fixed concentrations. The reactions shown in red constitute the metabolic process, those in blue the replacement process, and in gray the replacement of the replacement catalyst. (b) Expanded version of the model in which each catalyzed reaction is expanded into a cycle of three chemical reactions with explicit rate constants. Each forward rate constant refers to the reaction in the direction of the arrow, and the three degradation reactions, steps 4, 8 and 11, are assumed to be uncatalyzed and irreversible. All rate constants are treated as constant with the values shown, apart from , and , which are varied (but kept equal to one another) in the range 0.0–0.6. The three external reactants S, T and U are assumed to have the constant concentrations shown. All other concentrations are variable. All units are arbitrary, but they are consistent (i.e. the same units of time and quantity of matter apply throughout) and the model can be written in dimensionless form, if desired. In addition, the numerical values assigned to the rate constants and external concentrations are also arbitrary.</p>", "links"=>[], "tags"=>["biochemistry/biocatalysis", "biochemistry/theory and simulation", "computational biology/systems biology"], "article_id"=>507593, "categories"=>["Biochemistry", "Medicine"], "users"=>["Gabriel Piedrafita", "Francisco Montero", "Federico Morán", "María Luz Cárdenas", "Athel Cornish-Bowden"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000872.g001", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_model_of_an_M_R_system_/507593", "title"=>"A model of an (M,R)-system.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:06:40"}
  • {"files"=>["https://ndownloader.figshare.com/files/837704"], "description"=>"<p>The figure shows the time evolution of the system, starting from the stable non-trivial steady state for after the concentrations of all forms of STU (i.e. not only STU itself but also STUS, STUST and STUSU) are abruptly set to zero, as indicated by the arrows at time zero (leaving the others at their values in the non-trivial steady state).</p>", "links"=>[], "tags"=>["catastrophic"], "article_id"=>508076, "categories"=>["Biochemistry", "Medicine"], "users"=>["Gabriel Piedrafita", "Francisco Montero", "Federico Morán", "María Luz Cárdenas", "Athel Cornish-Bowden"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000872.g006", "stats"=>{"downloads"=>1, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Recovery_from_a_catastrophic_loss_of_catalyst_/508076", "title"=>"Recovery from a catastrophic loss of catalyst.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:09:22"}
  • {"files"=>["https://ndownloader.figshare.com/files/837480"], "description"=>"<p>For there is a region of bistability in which both trivial and non-trivial stable steady states are separated by an unstable steady state. When the system is at equilibrium with , the only possible stable steady state is the non-trivial steady state with [ST] = 16, as indicated by the arrows. If the decay constants are increased (proceeding to the right in the plot), the system remains in a non-trivial steady state until it falls abruptly to zero — the trivial steady state — exactly when leaving the bistability region. However, when starting from these final conditions, with every concentration zero, the initial trajectory cannot be reversed, because the system cannot “climb” to the non-trivial steady state until it is close to the equilibrium condition (). Only when approaching this condition can it experience a large jump after the appearance of small fluctuations in the concentrations. In brief, the direction of movement determines the specific behavior: the jump is detected at when going to the left and at when going to the right.</p>", "links"=>[], "tags"=>["biochemistry/biocatalysis", "biochemistry/theory and simulation", "computational biology/systems biology"], "article_id"=>507854, "categories"=>["Biochemistry", "Medicine"], "users"=>["Gabriel Piedrafita", "Francisco Montero", "Federico Morán", "María Luz Cárdenas", "Athel Cornish-Bowden"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000872.g003", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Bifurcation_plot_/507854", "title"=>"Bifurcation plot.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:08:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/837551"], "description"=>"<p>The calculation refers to . The point shown in green corresponds to the unstable steady state, which is contained in a barrier separating the attraction areas of the trivial steady state (point shown in red) and the non-trivial steady state (point shown in blue). The brown arrows represent a schematic illustration of the orbits followed in approaching the steady states. The inset illustrates schematically that the main plot is a two-dimensional slice of a multidimensional reality.</p>", "links"=>[], "tags"=>["multidimensional"], "article_id"=>507919, "categories"=>["Biochemistry", "Medicine"], "users"=>["Gabriel Piedrafita", "Francisco Montero", "Federico Morán", "María Luz Cárdenas", "Athel Cornish-Bowden"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000872.g004", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Planar_section_of_the_multidimensional_phase_diagram_/507919", "title"=>"Planar section of the multidimensional phase diagram.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:08:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/837811"], "description"=>"<p>(a) The model contains five reaction subsets, consisting of reaction 1 (red), reactions 2 and 3 (magenta), reactions 4, 5, 6 and 7 (blue), reactions 8, 9 and 10 (green); and reaction 11 (gray). (b) There are three elements of the basis, one consisting of reactions 1, 2, 3 and 11 () and thus corresponding to the metabolic pathway, a second consisting of reactions 1, 2, 3, 4, 5, 6 and 7 (), corresponding to both metabolic and replacement cycles, and the last consisting of reactions 1, 8, 9 and 10 (), which is the pathway that replaces the replacement catalyst SU. Note that elements and do not produce STU, and element produces neither SU nor ST, each of which is produced by the other two elements. Thus none of these elements is an enzyme-maintaining mode <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000872#pcbi.1000872-Montero1\" target=\"_blank\">[23]</a>.</p>", "links"=>[], "tags"=>["biochemistry/biocatalysis", "biochemistry/theory and simulation", "computational biology/systems biology"], "article_id"=>508176, "categories"=>["Biochemistry", "Medicine"], "users"=>["Gabriel Piedrafita", "Francisco Montero", "Federico Morán", "María Luz Cárdenas", "Athel Cornish-Bowden"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000872.g007", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Stoichiometric_analysis_of_the_model_/508176", "title"=>"Stoichiometric analysis of the model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:09:56"}
  • {"files"=>["https://ndownloader.figshare.com/files/837366"], "description"=>"<p>The model was simulated for and various values of , the initial concentration of STU, as shown, and allowed to evolve until a steady state was reached. (a) For the trivial steady state was always reached, whereas for the non-trivial stable steady state was reached. (b) The evolution from the red point in panel (a), with is shown. The behavior at very short times is illustrated in the inset. (c) The evolution from the blue point in panel (a), with , is shown. The behavior at very short times is illustrated in the inset. Note that the two insets are qualitatively very similar to one another, but the long-term trends in (b) and (c) are very different.</p>", "links"=>[], "tags"=>["states", "reached"], "article_id"=>507736, "categories"=>["Biochemistry", "Medicine"], "users"=>["Gabriel Piedrafita", "Francisco Montero", "Federico Morán", "María Luz Cárdenas", "Athel Cornish-Bowden"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000872.g002", "stats"=>{"downloads"=>2, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Steady_states_reached_with_the_model_/507736", "title"=>"Steady states reached with the model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:07:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/837624"], "description"=>"<p>Simulations were done with . The initial concentration of ST was 6.6 (red curve) or 7.2 (blue curve), and other concentrations were set to those in the unstable steady state. The inset shows the time dependences at very low times, which are in the opposite directions from the long-term trends.</p>", "links"=>[], "tags"=>["points", "unstable"], "article_id"=>507998, "categories"=>["Biochemistry", "Medicine"], "users"=>["Gabriel Piedrafita", "Francisco Montero", "Federico Morán", "María Luz Cárdenas", "Athel Cornish-Bowden"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000872.g005", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Time_evolution_from_starting_points_close_to_the_unstable_steady_state_/507998", "title"=>"Time evolution from starting points close to the unstable steady state.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:08:54"}

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