Phosphorelays Provide Tunable Signal Processing Capabilities for the Cell
Publication Date
November 07, 2013
Journal
PLOS Computational Biology
Authors
Varun B. Kothamachu, Elisenda Feliu, Carsten Wiuf, Luca Cardelli, et al
Volume
9
Issue
11
Pages
e1003322
DOI
http://doi.org/10.1371/journal.pcbi.1003322
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1003322
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/24244132
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3820541
Europe PMC
http://europepmc.org/abstract/MED/24244132
Web of Science
000330357200023
Scopus
84888268251
Mendeley
http://www.mendeley.com/research/phosphorelays-provide-tunable-signal-processing-capabilities-cell
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{"title"=>"Phosphorelays Provide Tunable Signal Processing Capabilities for the Cell", "type"=>"journal", "authors"=>[{"first_name"=>"Varun B.", "last_name"=>"Kothamachu", "scopus_author_id"=>"55938257300"}, {"first_name"=>"Elisenda", "last_name"=>"Feliu", "scopus_author_id"=>"36006280300"}, {"first_name"=>"Carsten", "last_name"=>"Wiuf", "scopus_author_id"=>"7003496015"}, {"first_name"=>"Luca", "last_name"=>"Cardelli", "scopus_author_id"=>"7004219785"}, {"first_name"=>"Orkun S.", "last_name"=>"Soyer", "scopus_author_id"=>"10143056500"}], "year"=>2013, "source"=>"PLoS Computational Biology", "identifiers"=>{"doi"=>"10.1371/journal.pcbi.1003322", "pui"=>"370341778", "scopus"=>"2-s2.0-84888268251", "issn"=>"1553734X", "pmid"=>"24244132", "sgr"=>"84888268251"}, "id"=>"8d3b2152-5c06-3369-a4cc-e1de5b695988", "abstract"=>"Author SummaryTwo-component phosphorelays constitute the key signaling pathways in all prokaryotes, lower eukaryotes, and plants, where they underline diverse physiological responses such as virulence, cell-cycle progression and sporulation. Despite such prevalence, our understanding of the dynamics and function of these systems remains incomplete. In particular, it is not clear why all phosphorelays studied to date embed a four-layer architecture and how their dynamics could relate to phenotypic variability in the resulting responses. Here, we use analytical approaches and numerical simulations to analyze all possible phosphorelay topologies of length four and embedding reverse phosphorylation. We find that only two topologies can embed both hyperbolic and sigmoidal signal-response relationships, and that one of these can underlie high noise (i.e. phenotypic variability) in population responses. All of the remaining topologies are either non-functional or can embed only a hyperbolic signal-response relationship. Using analytical solutions of relay dynamics, we find that reverse phosphorylation from the third layer, a topological featured commonly observed in nature, is a necessary condition for sigmoidal signal-response relationship.", "link"=>"http://www.mendeley.com/research/phosphorelays-provide-tunable-signal-processing-capabilities-cell", "reader_count"=>18, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>2, "Researcher"=>5, "Student > Ph. D. Student"=>4, "Student > Master"=>3, "Student > Bachelor"=>4}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>2, "Researcher"=>5, "Student > Ph. D. Student"=>4, "Student > Master"=>3, "Student > Bachelor"=>4}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Unspecified"=>1, "Biochemistry, Genetics and Molecular Biology"=>1, "Agricultural and Biological Sciences"=>12, "Physics and Astronomy"=>1, "Computer Science"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>12}, "Computer Science"=>{"Computer Science"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Unspecified"=>{"Unspecified"=>1}}, "reader_count_by_country"=>{"Colombia"=>1, "United States"=>1, "India"=>1}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1271609"], "description"=>"<p>For each topology, we have sampled 1000 parameter sets (rate constants and total protein concentrations) from a biologically permissible range (<i>Supporting <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi.1003322.s010\" target=\"_blank\">Text S6</a></i>), derived the signal-response curve for each parameter set and classified this curve as hyperbolic or sigmoidal (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#s4\" target=\"_blank\"><i>Methods</i></a>). The topologies are indicated with a binary identification code that indicates the presence (1) or absence (0) of reverse phosphotransfer reactions along the relay, and the presence (1) or absence (0) of hydrolysis reactions at layers 2 and 4 (see <i>Supporting <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi.1003322.s005\" target=\"_blank\">Text S1</a></i> for all possible topologies). The classification results are given as the fraction of parameter sets resulting in a sigmoidal signal-response curve (the rest being classified as hyperbolic) and assuming a monofunctional HK. Classifications are based on the second derivative of the signal-response curve at zero and from sampling all parameters (with equal total protein concentrations at different layers) (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#s4\" target=\"_blank\"><i>Methods</i></a>). For additional results using alternative classification and sampling schemes (different total protein concentrations at different layers) or assuming bifunctional HK, see <i>Supporting <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi.1003322.s007\" target=\"_blank\">Text S3</a></i>.</p>", "links"=>[], "tags"=>["signal-response", "classification", "18", "responsive"], "article_id"=>844064, "categories"=>["Information And Computing Sciences", "Biological Sciences"], "users"=>["Varun B. Kothamachu", "Elisenda Feliu", "Carsten Wiuf", "Luca Cardelli", "Orkun S. Soyer"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003322.t001", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_results_of_the_signal_response_relationship_classification_for_the_18_responsive_topologies_/844064", "title"=>"The results of the signal-response relationship classification for the 18 responsive topologies.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-11-07 03:22:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/1271610"], "description"=>"<p>The results shown are for topologies 14 and 30, assuming monofunctional HK, and sampling all parameters (with equal total protein concentrations at different layers). For additional results using alternative classification and sampling schemes (different total protein concentrations at different layers), assuming bifunctional HK, as well as for results from topologies 16 and 32, see <i>Supporting <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi.1003322.s008\" target=\"_blank\">Text S4</a></i>. Mean values of all parameters as found in parameter sets resulting in hyperbolic and sigmoidal signal-response relationships in topologies 14, 16, 30 and 32 are provided as <i>Supporting <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi.1003322.s009\" target=\"_blank\">Text S5</a></i>.</p>", "links"=>[], "tags"=>["constants", "parameter", "sets", "hyperbolic", "sigmoidal", "signal-response"], "article_id"=>844065, "categories"=>["Information And Computing Sciences", "Biological Sciences"], "users"=>["Varun B. Kothamachu", "Elisenda Feliu", "Carsten Wiuf", "Luca Cardelli", "Orkun S. Soyer"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003322.t002", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mean_minimum_and_maximum_of_the_ratio_of_forward_to_reverse_rate_constants_based_on_parameter_sets_resulting_in_hyperbolic_and_sigmoidal_signal_response_relationship_/844065", "title"=>"Mean, minimum and maximum of the ratio of forward to reverse rate constants based on parameter sets resulting in hyperbolic and sigmoidal signal-response relationship.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-11-07 03:22:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/1271637", "https://ndownloader.figshare.com/files/1271638", "https://ndownloader.figshare.com/files/1271640", "https://ndownloader.figshare.com/files/1271641", "https://ndownloader.figshare.com/files/1271642", "https://ndownloader.figshare.com/files/1271643", "https://ndownloader.figshare.com/files/1271644", "https://ndownloader.figshare.com/files/1271645", "https://ndownloader.figshare.com/files/1271646", "https://ndownloader.figshare.com/files/1271647"], "description"=>"<div><p>Achieving a complete understanding of cellular signal transduction requires deciphering the relation between structural and biochemical features of a signaling system and the shape of the signal-response relationship it embeds. Using explicit analytical expressions and numerical simulations, we present here this relation for four-layered phosphorelays, which are signaling systems that are ubiquitous in prokaryotes and also found in lower eukaryotes and plants. We derive an analytical expression that relates the shape of the signal-response relationship in a relay to the kinetic rates of forward, reverse phosphorylation and hydrolysis reactions. This reveals a set of mathematical conditions which, when satisfied, dictate the shape of the signal-response relationship. We find that a specific topology also observed in nature can satisfy these conditions in such a way to allow plasticity among hyperbolic and sigmoidal signal-response relationships. Particularly, the shape of the signal-response relationship of this relay topology can be tuned by altering kinetic rates and total protein levels at different parts of the relay. These findings provide an important step towards predicting response dynamics of phosphorelays, and the nature of subsequent physiological responses that they mediate, solely from topological features and few composite measurements; measuring the ratio of reverse and forward phosphorylation rate constants could be sufficient to determine the shape of the signal-response relationship the relay exhibits. Furthermore, they highlight the potential ways in which selective pressures on signal processing could have played a role in the evolution of the observed structural and biochemical characteristic in phosphorelays.</p></div>", "links"=>[], "tags"=>["tunable", "capabilities"], "article_id"=>844067, "categories"=>["Information And Computing Sciences", "Biological Sciences"], "users"=>["Varun B. Kothamachu", "Elisenda Feliu", "Carsten Wiuf", "Luca Cardelli", "Orkun S. Soyer"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003322.s001", "https://dx.doi.org/10.1371/journal.pcbi.1003322.s002", "https://dx.doi.org/10.1371/journal.pcbi.1003322.s003", "https://dx.doi.org/10.1371/journal.pcbi.1003322.s004", "https://dx.doi.org/10.1371/journal.pcbi.1003322.s005", "https://dx.doi.org/10.1371/journal.pcbi.1003322.s006", "https://dx.doi.org/10.1371/journal.pcbi.1003322.s007", "https://dx.doi.org/10.1371/journal.pcbi.1003322.s008", "https://dx.doi.org/10.1371/journal.pcbi.1003322.s009", "https://dx.doi.org/10.1371/journal.pcbi.1003322.s010"], "stats"=>{"downloads"=>44, "page_views"=>17, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Phosphorelays_Provide_Tunable_Signal_Processing_Capabilities_for_the_Cell_/844067", "title"=>"Phosphorelays Provide Tunable Signal Processing Capabilities for the Cell", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-11-07 03:22:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/1271606"], "description"=>"<p>Cartoon representation of the general four layered phosphorelay model. Hydrolysis reactions (on aspartate residues found on REC and RR proteins only) and forward and reverse phosphorylation reactions are shown, along with the possibility of the HK being bifunctional. <b>B.</b> Hyperbolic and sigmoidal signal-response relationships displayed by a specific topology (topology 30 shown on <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi-1003322-g002\" target=\"_blank\">Figure 2C</a>). The two curves are obtained by choosing specific parameter sets (given in <i>Supporting <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi.1003322.s009\" target=\"_blank\">Text S5</a></i>). The x- and y-axis correspond to the signal and response of the system, which in the model are approximated by the HK auto-phosphorylation rate constant, <i>k<sub>s</sub></i> and by the fraction of phosphorylated RR, respectively.</p>", "links"=>[], "tags"=>["phosphorelay", "topologies"], "article_id"=>844061, "categories"=>["Information And Computing Sciences", "Biological Sciences"], "users"=>["Varun B. Kothamachu", "Elisenda Feliu", "Carsten Wiuf", "Luca Cardelli", "Orkun S. Soyer"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003322.g001", "stats"=>{"downloads"=>1, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_analysis_of_phosphorelay_topologies_and_their_dynamics_A_/844061", "title"=>"The analysis of phosphorelay topologies and their dynamics. A.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-11-07 03:22:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/1271607"], "description"=>"<p>Panels <b>A</b>, <b>B</b>, <b>C</b> and <b>D</b> show topologies 14, 16, 30 and 32 respectively, each corresponding to a specific set of reverse phosphotransfer and hydrolysis reactions being present. Reactions are shown as directional arrows, where thickness of the arrow indicates the relative strength of the reaction. In other words, arrows are weighted by the mean reaction rate constant obtained from all sampled parameter sets producing sigmoidality. For each layer and a given topology, a gray (open) backdrop indicates that the mean of total protein concentration at that layer is high (low), based on all sampled parameter sets producing sigmoidal signal-response curves (see <i>Supporting <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#pcbi.1003322.s009\" target=\"_blank\">Text S5</a></i> for actual mean parameter values and concentrations).</p>", "links"=>[], "tags"=>["representations", "topologies", "allowed", "sigmoidal", "signal-response", "relationships", "sampled", "parameter", "considering", "monofunctional", "hk", "concentrations", "layers"], "article_id"=>844062, "categories"=>["Information And Computing Sciences", "Biological Sciences"], "users"=>["Varun B. Kothamachu", "Elisenda Feliu", "Carsten Wiuf", "Luca Cardelli", "Orkun S. Soyer"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003322.g002", "stats"=>{"downloads"=>1, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cartoon_representations_of_the_four_topologies_that_allowed_sigmoidal_signal_response_relationships_in_a_significant_part_more_than_2_of_the_sampled_parameter_space_when_considering_monofunctional_HK_and_different_total_protein_concentrations_at_differen/844062", "title"=>"Cartoon representations of the four topologies that allowed sigmoidal signal-response relationships in a significant part (more than 2%) of the sampled parameter space when considering monofunctional HK and different total protein concentrations at different layers (see also <b>Table 1</b>, Figure S1 and <i>Supporting Text S3</i>).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-11-07 03:22:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/1271608"], "description"=>"<p>Signal-response curve for topologies 14 (A) and 30 (B). The x-axis corresponds to the signal input to the system, which in the model is approximated by varying the HK auto-phosphorylation rate constant, <i>k<sub>s</sub></i>. The y-axis corresponds to the simulated mean of the fraction of phosphorylated RR, calculated using PRISM model checker (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#s4\" target=\"_blank\"><i>Methods</i></a>). The solid and dashed curves show the results obtained from constraining the system parameters in the hyperbolic and sigmoidal regimes respectively. <b>C & D.</b> Noise levels in phosphorylated RR for topologies 14 (C) and 30 (D). The x-axis shows the signal input to the system, taken to be the HK auto-phosphorylation rate constant, <i>k<sub>s</sub></i>. The y-axis shows the standard deviation over mean of the fraction of phosphorylated RR at steady state, both calculated using PRISM model checker (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003322#s4\" target=\"_blank\"><i>Methods</i></a>). <b>E & F.</b> Box plots showing the distribution of response times for topologies 14 (E) and 30 (F) as measured from hyperbolic and sigmoidal regimes. For each topology, the response time is measured for 100 randomly selected parameter sets from the hyperbolic and sigmoidal regimes.</p>", "links"=>[], "tags"=>["topologies", "14", "30", "assuming", "monofunctional"], "article_id"=>844063, "categories"=>["Information And Computing Sciences", "Biological Sciences"], "users"=>["Varun B. Kothamachu", "Elisenda Feliu", "Carsten Wiuf", "Luca Cardelli", "Orkun S. Soyer"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003322.g003", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Analysis_of_noise_and_response_properties_of_topologies_14_and_30_assuming_monofunctional_HK_A_amp_B_/844063", "title"=>"Analysis of noise and response properties of topologies 14 and 30 assuming monofunctional HK. A & B.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-11-07 03:22:04"}

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