Evolutionary Dynamics on Protein Bi-stability Landscapes can Potentially Resolve Adaptive Conflicts
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{"title"=>"Evolutionary Dynamics on Protein Bi-stability Landscapes can Potentially Resolve Adaptive Conflicts", "type"=>"journal", "authors"=>[{"first_name"=>"Tobias", "last_name"=>"Sikosek", "scopus_author_id"=>"35759536200"}, {"first_name"=>"Erich", "last_name"=>"Bornberg-Bauer", "scopus_author_id"=>"6603818279"}, {"first_name"=>"Hue Sun", "last_name"=>"Chan", "scopus_author_id"=>"55663530400"}], "year"=>2012, "source"=>"PLoS Computational Biology", "identifiers"=>{"sgr"=>"84866928115", "doi"=>"10.1371/journal.pcbi.1002659", "pui"=>"365755949", "pmid"=>"23028272", "scopus"=>"2-s2.0-84866928115", "issn"=>"1553734X"}, "id"=>"91723d22-ac82-354a-b104-1b0d94004c8f", "abstract"=>"Experimental studies have shown that some proteins exist in two alternative native-state conformations. It has been proposed that such bi-stable proteins can potentially function as evolutionary bridges at the interface between two neutral networks of protein sequences that fold uniquely into the two different native conformations. Under adaptive conflict scenarios, bi-stable proteins may be of particular advantage if they simultaneously provide two beneficial biological functions. However, computational models that simulate protein structure evolution do not yet recognize the importance of bi-stability. Here we use a biophysical model to analyze sequence space to identify bi-stable or multi-stable proteins with two or more equally stable native-state structures. The inclusion of such proteins enhances phenotype connectivity between neutral networks in sequence space. Consideration of the sequence space neighborhood of bridge proteins revealed that bi-stability decreases gradually with each mutation that takes the sequence further away from an exactly bi-stable protein. With relaxed selection pressures, we found that bi-stable proteins in our model are highly successful under simulated adaptive conflict. Inspired by these model predictions, we developed a method to identify real proteins in the PDB with bridge-like properties, and have verified a clear bi-stability gradient for a series of mutants studied by Alexander et al. (Proc Nat Acad Sci USA 2009, 106:21149-21154) that connect two sequences that fold uniquely into two different native structures via a bridge-like intermediate mutant sequence. Based on these findings, new testable predictions for future studies on protein bi-stability and evolution are discussed.", "link"=>"http://www.mendeley.com/research/evolutionary-dynamics-protein-bistability-landscapes-potentially-resolve-adaptive-conflicts", "reader_count"=>49, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Researcher"=>17, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>13, "Student > Postgraduate"=>2, "Student > Master"=>6, "Other"=>3, "Student > Bachelor"=>2, "Professor"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Researcher"=>17, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>13, "Student > Postgraduate"=>2, "Student > Master"=>6, "Other"=>3, "Student > Bachelor"=>2, "Professor"=>2}, "reader_count_by_subject_area"=>{"Unspecified"=>2, "Biochemistry, Genetics and Molecular Biology"=>8, "Agricultural and Biological Sciences"=>27, "Medicine and Dentistry"=>1, "Physics and Astronomy"=>7, "Chemistry"=>3, "Computer Science"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Chemistry"=>{"Chemistry"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>7}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>27}, "Computer Science"=>{"Computer Science"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>8}, "Unspecified"=>{"Unspecified"=>2}}, "reader_count_by_country"=>{"Canada"=>2, "United States"=>5, "Brazil"=>1, "Mexico"=>1, "Germany"=>1}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/576491"], "description"=>"<p>The negative logarithmic steady-state populations, , of all sequences from two adjacent extended neutral networks (A in blue, B in red, overlap region in magenta; see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#pcbi-1002659-g002\" target=\"_blank\">Figure 2a</a>) in our biophysical protein chain model are plotted against their respective Hamming distances with respect to the most stable bridge protein sequence . A low value corresponds to a high population (probability) at steady state. The and signs of the sequence distance values (horizontal axis) distinguish between the two networks A and B, respectively. Steady state populations were obtained with (black symbols) and without (grey symbols) bridge proteins for an example neutral network pair, under three different selection pressures: (<b>a</b>; strong selection), (<b>b</b>; weak selection), and (<b>c</b>; no selection). The same selection pressure was applied for both selected structures ( and ). The black solid and grey dashed lines indicate the average values as functions of Hamming distance that were simulated, respectively, with and without the bridge sequences. To facilitate comparison, even in cases where bridge proteins were removed from the neutral networks during the evolutionary simulation, Hamming distances are still defined by that between a given sequence and (the removed) .</p>", "links"=>[], "tags"=>["populations", "sequences", "simulated", "adaptive"], "article_id"=>246989, "categories"=>["Biological Sciences", "Biophysics", "Evolutionary Biology"], "users"=>["Tobias Sikosek", "Erich Bornberg-Bauer", "Hue Sun Chan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002659.g004", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Steady_state_populations_of_protein_sequences_after_simulated_evolution_under_adaptive_conflict_/246989", "title"=>"Steady-state populations of protein sequences after simulated evolution under adaptive conflict.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-13 01:56:29"}
  • {"files"=>["https://ndownloader.figshare.com/files/576393"], "description"=>"<p>In this study, the PDB structures of (PDB code 2FS1) and (PDB code 1PGA) were used as wildtypes (wt) for energy calculations and mutagenesis. There is only sequence identity between wt and wt sequences. Based on the 2FS1 and 1PGA structures, the structures of all intermediate mutants (sequence variants) were constructed by either FoldX or Rosetta in accordance with the published sequences in Alexander et al. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#pcbi.1002659-Alexander1\" target=\"_blank\">[27]</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#pcbi.1002659-Alexander2\" target=\"_blank\">[69]</a>. The sequence labels along the present horizontal axes have the same meaning as those in these references. (<b>a</b>) The average free energy () predicted by the standard free energy scoring function of Rosetta was computed for all sequence variants. The and structures of the sequence variants were also constructed by Rosetta with its FastRelax free energy minimization procedure. The plotted averages (connected by lines that are merely a guide for the eye) were obtained from 25 replicate calculations and all error bars in this and other panels of this figure correspond to one standard deviation from the mean. (<b>b</b>) The FoldX free energy scores relative to that of the wildtype () for all and variants. (<b>c</b>) Bi-stability of each sequence variant is quantified by the difference in predicted free energy between the variant and structures (vertical axis). Free energy differences are computed using either the Rosetta values in (a) (black line with error bars) or the FoldX values in (b) (grey line). (<b>d</b>) Here bi-stability of each sequence is quantified by the difference in hydrophobic contact density (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#s4\" target=\"_blank\">Methods</a>) between the Rosetta/FastRelax-constructed structures of and for the given sequence (same structures as those in (a)). In (<b>c</b>) and (<b>d</b>), the blue area covers sequences that are known experimentally to adopt as their native structure, whereas the red area covers sequences that are known experimentally to adopt as their native structure.</p>", "links"=>[], "tags"=>["folding", "experimentally", "mutational", "indicates", "gradual"], "article_id"=>246892, "categories"=>["Biological Sciences", "Biophysics", "Evolutionary Biology"], "users"=>["Tobias Sikosek", "Erich Bornberg-Bauer", "Hue Sun Chan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002659.g003", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Modeling_the_folding_stability_of_an_experimentally_determined_mutational_path_from_one_real_protein_structure_to_another_indicates_a_gradual_stability_shift_/246892", "title"=>"Modeling the folding stability of an experimentally determined mutational path from one real protein structure to another indicates a gradual stability shift.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-13 01:54:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/304462", "https://ndownloader.figshare.com/files/304484", "https://ndownloader.figshare.com/files/304513", "https://ndownloader.figshare.com/files/304560", "https://ndownloader.figshare.com/files/304647"], "description"=>"<div><p>Experimental studies have shown that some proteins exist in two alternative native-state conformations. It has been proposed that such bi-stable proteins can potentially function as evolutionary bridges at the interface between two neutral networks of protein sequences that fold uniquely into the two different native conformations. Under adaptive conflict scenarios, bi-stable proteins may be of particular advantage if they simultaneously provide two beneficial biological functions. However, computational models that simulate protein structure evolution do not yet recognize the importance of bi-stability. Here we use a biophysical model to analyze sequence space to identify bi-stable or multi-stable proteins with two or more equally stable native-state structures. The inclusion of such proteins enhances phenotype connectivity between neutral networks in sequence space. Consideration of the sequence space neighborhood of bridge proteins revealed that bi-stability decreases gradually with each mutation that takes the sequence further away from an exactly bi-stable protein. With relaxed selection pressures, we found that bi-stable proteins in our model are highly successful under simulated adaptive conflict. Inspired by these model predictions, we developed a method to identify real proteins in the PDB with bridge-like properties, and have verified a clear bi-stability gradient for a series of mutants studied by Alexander et al. (Proc Nat Acad Sci USA 2009, 106:21149–21154) that connect two sequences that fold uniquely into two different native structures via a bridge-like intermediate mutant sequence. Based on these findings, new testable predictions for future studies on protein bi-stability and evolution are discussed.</p> </div>", "links"=>[], "tags"=>["evolutionary", "bi-stability", "landscapes", "adaptive", "conflicts"], "article_id"=>120049, "categories"=>["Biological Sciences", "Biophysics", "Evolutionary Biology"], "users"=>["Tobias Sikosek", "Erich Bornberg-Bauer", "Hue Sun Chan"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002659.s001", "https://dx.doi.org/10.1371/journal.pcbi.1002659.s002", "https://dx.doi.org/10.1371/journal.pcbi.1002659.s003", "https://dx.doi.org/10.1371/journal.pcbi.1002659.s004", "https://dx.doi.org/10.1371/journal.pcbi.1002659.s005"], "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Evolutionary_Dynamics_on_Protein_Bi_stability_Landscapes_can_Potentially_Resolve_Adaptive_Conflicts/120049", "title"=>"Evolutionary Dynamics on Protein Bi-stability Landscapes can Potentially Resolve Adaptive Conflicts", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2012-09-13 00:00:49"}
  • {"files"=>["https://ndownloader.figshare.com/files/576673"], "description"=>"<p>Proteins are ordered by increasing stability difference (decreasing bi-stability) and they may be classified into the following functional categories: metabolism (Purine-nucleoside phosphorylase, Camphor 5-monooxygenase, Glycogen phosphorylase, Adenylate kinase, Hydrolase, Cytochrome P450 119, Light-harvesting protein B-875 beta chain), transcriptional regulation (HTH-type transcriptional regulator qacR, Regulatory protein rop), epigenetic regulation (Histone-lysine N-methyltransferase, Chromobox protein homolog 1), signalling (Synapsin-2, Protein enhancer of sevenless 2B, Baculoviral IAP repeat-containing protein 4, Antithrombin-III, Lymphotactin), translation (50S ribosomal protein L11), cytoskeleton (Talin-1, Synapsin-2), and host-pathogen interaction/immune system (Ig epsilon chain C region, Nitrophorin-4, Baculoviral IAP repeat-containing protein 4, Lymphotactin, Capsid protein G8P).</p>a<p>CATH <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#pcbi.1002659-Orengo1\" target=\"_blank\">[64]</a> structural domain identifiers.</p>b<p>Root Mean Square Deviation of backbone atoms; in units of Å.</p>c<p>Rosetta standard free energy score/domain length.</p>", "links"=>[], "tags"=>["proteins", "putative"], "article_id"=>247170, "categories"=>["Biological Sciences", "Biophysics", "Evolutionary Biology"], "users"=>["Tobias Sikosek", "Erich Bornberg-Bauer", "Hue Sun Chan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002659.t002", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Examples_of_proteins_with_putative_high_bi_stability_/247170", "title"=>"Examples of proteins with putative high bi-stability.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-09-13 01:59:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/576243"], "description"=>"<p>(<b>a</b>) Proteins with degenerate native states (two or more structures with maximum stability) can function as connectors between neutral networks. Bi-stability is indicated for a bi-stable protein by a schematic folding funnel with two free energy minima. In an ideal case, the neutral network of sequences for each native-state structure can be reached by a single mutation from a centrally located sequence. This would enable efficient evolutionary transitions between those neutral networks. The frequency of such a bridge protein sequence may be maintained at an appreciable level in populations evolving under adaptive conflicts. Bridge proteins with up to six-fold native-state degeneracy () are illustrated. (<b>b</b>) Box plots of native-state stability (i.e., fractional population ) versus native state degeneracy () of all model sequences with (grey), and the subset of all bridge sequences (magenta). Here we follow the standard convention for box plots in descriptive statistics: For each sample defined by a given value of the variable plotted along the horizontal axis ( for bridge or non-bridge sequences in this case), the lowest and highest bars are, respectively, the lowest and highest values of the property of interest ( in this case) observed for the given sample. The top and bottom of the box are, respectively, the corresponding lower and upper quartiles of the sample, whereas the median of the sample is shown by the line within the box. The box plots here indicate that bridge sequences are significantly more stable than non-bridge sequences (Wilcoxon Rank Sum Test; in all cases, except , where ). In the biophysical protein chain model used here (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#s4\" target=\"_blank\">Methods</a>), the upper bound of , given , is (black dashed line).</p>", "links"=>[], "tags"=>["multi-stable", "proteins", "acting", "evolutionary"], "article_id"=>246737, "categories"=>["Biological Sciences", "Biophysics", "Evolutionary Biology"], "users"=>["Tobias Sikosek", "Erich Bornberg-Bauer", "Hue Sun Chan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002659.g001", "stats"=>{"downloads"=>1, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Bi_stable_and_multi_stable_proteins_acting_as_evolutionary_bridges_/246737", "title"=>"Bi-stable and multi-stable proteins acting as evolutionary bridges.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-13 01:52:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/576650"], "description"=>"<p>A bi- or multi-stable protein (with a degenerate native state) is a bridge sequence if it has at least two 1-error mutants that fold non-degenerately into at least two different structures among the sequence's multiple native-state structures, i.e., each mutant folds uniquely to a different structure. In other words, there is at least one connection to the core of each of the two or more neutral networks. In total, for sequences with chain length studied here (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#s4\" target=\"_blank\">Methods</a>), there are sequences in the model sequence space, 6349 of which have non-degenerate () native states.</p>", "links"=>[], "tags"=>["proteins", "connectors"], "article_id"=>247146, "categories"=>["Biological Sciences", "Biophysics", "Evolutionary Biology"], "users"=>["Tobias Sikosek", "Erich Bornberg-Bauer", "Hue Sun Chan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002659.t001", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Bridge_proteins_as_connectors_in_sequence_space_/247146", "title"=>"Bridge proteins as connectors in sequence space.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-09-13 01:59:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/576302"], "description"=>"<p>(<b>a</b>) An example of the distribution of bi-stability in a small section of a model sequence space. The difference in the number of hydrophobic contacts, , (stability difference) for the native-state structures and of two adjacent neutral networks and (blue and red, respectively) are depicted by a two-dimensional representation of sequence space (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#s4\" target=\"_blank\">Methods</a>). Nodes represent sequence variants. Node sizes are scaled according to native-state stability (, a larger node size corresponds to a large value). Edges connect sequences that differ by one mutation. The arrow indicates a mutation from a sequence with a stability difference of to a sequence with a stability difference of . In other words, this mutation increases stability for while conserving as the native state. Bridge proteins (magenta squares) are equally stable for both native states and thus have a stability difference of zero. (<b>b</b>) Generalization of smooth bi-stability gradients around bridge proteins. Each box plot gives the distribution (i.e. the entire data range with vertical lines delimiting quartile boundaries as specified in the caption for <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#pcbi-1002659-g001\" target=\"_blank\">Figure 1b</a> above) of 623 average stability differences computed for individual sequences that belong to the same neutral network and can be mutated into a bridge protein with the same given number of mutations (i.e. have the same Hamming distance from a bridge). The stability difference was calculated between the native structures of all 623 pairs of extended neutral networks (that have at least 5 core nodes, and at least one bridge). Data for each pair was counted only once, and the color blue is used in this plot for the larger network of each pair. The further away a sequence is located from a bridge in sequence space, the higher its stability difference towards one of the two structures, and the lower its bi-stability. All differences between box plots were significant (Wilcoxon Rank Sum Test, ).</p>", "links"=>[], "tags"=>["decreases"], "article_id"=>246808, "categories"=>["Biological Sciences", "Biophysics", "Evolutionary Biology"], "users"=>["Tobias Sikosek", "Erich Bornberg-Bauer", "Hue Sun Chan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002659.g002", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Bi_stability_decreases_with_increasing_sequence_distance_from_bridge_proteins_/246808", "title"=>"Bi-stability decreases with increasing sequence distance from bridge proteins.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-13 01:53:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/576597"], "description"=>"<p>In our biophysical protein chain model, and serve as the selection pressures on and , respectively, by setting the minimum required stability for optimal fitness. Here and values are plotted in units of , where is the stability of the (equally stable) native-state structures ( and ) of the most stable bridge protein . The magenta area is the range of and values within which bridge proteins have higher fitness than the specialized prototypes of neutral networks A and B.</p>", "links"=>[], "tags"=>["proteins", "unequal", "pressures", "native-state"], "article_id"=>247090, "categories"=>["Biological Sciences", "Biophysics", "Evolutionary Biology"], "users"=>["Tobias Sikosek", "Erich Bornberg-Bauer", "Hue Sun Chan"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002659.g005", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Bridge_proteins_persist_under_unequal_selection_pressures_for_two_native_state_structures_/247090", "title"=>"Bridge proteins persist under unequal selection pressures for two native-state structures.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-09-13 01:58:10"}

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Relative Metric

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