Filament Compliance Influences Cooperative Activation of Thin Filaments and the Dynamics of Force Production in Skeletal Muscle
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{"title"=>"Filament compliance influences cooperative activation of thin filaments and the dynamics of force production in skeletal muscle", "type"=>"journal", "authors"=>[{"first_name"=>"Bertrand C.W.", "last_name"=>"Tanner", "scopus_author_id"=>"15048854000"}, {"first_name"=>"Thomas L.", "last_name"=>"Daniel", "scopus_author_id"=>"7201677078"}, {"first_name"=>"Michael", "last_name"=>"Regnier", "scopus_author_id"=>"7006076700"}], "year"=>2012, "source"=>"PLoS Computational Biology", "identifiers"=>{"scopus"=>"2-s2.0-84863651301", "isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "doi"=>"10.1371/journal.pcbi.1002506", "pui"=>"365220666", "sgr"=>"84863651301", "issn"=>"1553734X", "pmid"=>"22589710"}, "id"=>"529ba185-5844-394f-85c6-13ede8b3e7a9", "abstract"=>"Striated muscle contraction is a highly cooperative process initiated by Ca²⁺ binding to the troponin complex, which leads to tropomyosin movement and myosin cross-bridge (XB) formation along thin filaments. Experimental and computational studies suggest skeletal muscle fiber activation is greatly augmented by cooperative interactions between neighboring thin filament regulatory units (RU-RU cooperativity; 1 RU = 7 actin monomers+1 troponin complex+1 tropomyosin molecule). XB binding can also amplify thin filament activation through interactions with RUs (XB-RU cooperativity). Because these interactions occur with a temporal order, they can be considered kinetic forms of cooperativity. Our previous spatially-explicit models illustrated that mechanical forms of cooperativity also exist, arising from XB-induced XB binding (XB-XB cooperativity). These mechanical and kinetic forms of cooperativity are likely coordinated during muscle contraction, but the relative contribution from each of these mechanisms is difficult to separate experimentally. To investigate these contributions we built a multi-filament model of the half sarcomere, allowing RU activation kinetics to vary with the state of neighboring RUs or XBs. Simulations suggest Ca²⁺ binding to troponin activates a thin filament distance spanning 9 to 11 actins and coupled RU-RU interactions dominate the cooperative force response in skeletal muscle, consistent with measurements from rabbit psoas fibers. XB binding was critical for stabilizing thin filament activation, particularly at submaximal Ca²⁺ levels, even though XB-RU cooperativity amplified force less than RU-RU cooperativity. Similar to previous studies, XB-XB cooperativity scaled inversely with lattice stiffness, leading to slower rates of force development as stiffness decreased. Including RU-RU and XB-RU cooperativity in this model resulted in the novel prediction that the force-[Ca²⁺] relationship can vary due to filament and XB compliance. Simulations also suggest kinetic forms of cooperativity occur rapidly and dominate early to get activation, while mechanical forms of cooperativity act more slowly, augmenting XB binding as force continues to develop.", "link"=>"http://www.mendeley.com/research/filament-compliance-influences-cooperative-activation-thin-filaments-dynamics-force-production-skele", "reader_count"=>31, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>2, "Student > Doctoral Student"=>8, "Researcher"=>3, "Student > Ph. D. Student"=>8, "Student > Postgraduate"=>1, "Student > Master"=>3, "Other"=>1, "Student > Bachelor"=>1, "Professor"=>3}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>2, "Student > Doctoral Student"=>8, "Researcher"=>3, "Student > Ph. D. Student"=>8, "Student > Postgraduate"=>1, "Student > Master"=>3, "Other"=>1, "Student > Bachelor"=>1, "Professor"=>3}, "reader_count_by_subject_area"=>{"Engineering"=>4, "Unspecified"=>1, "Biochemistry, Genetics and Molecular Biology"=>3, "Agricultural and Biological Sciences"=>10, "Medicine and Dentistry"=>4, "Neuroscience"=>1, "Sports and Recreations"=>2, "Physics and Astronomy"=>3, "Social Sciences"=>1, "Computer Science"=>2}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>4}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>4}, "Neuroscience"=>{"Neuroscience"=>1}, "Social Sciences"=>{"Social Sciences"=>1}, "Sports and Recreations"=>{"Sports and Recreations"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>3}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>10}, "Computer Science"=>{"Computer Science"=>2}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>3}, "Unspecified"=>{"Unspecified"=>1}}, "reader_count_by_country"=>{"Japan"=>1, "Chile"=>1, "Germany"=>1}, "group_count"=>1}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/640468"], "description"=>"<p>Thin-filament transition rates (<i>ξ</i> = 100).</p>", "links"=>[], "tags"=>["rates"], "article_id"=>310965, "categories"=>["Biological Sciences", "Biotechnology", "Biophysics"], "users"=>["Bertrand C. W. Tanner", "Thomas L. Daniel", "Michael Regnier"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002506.t003", "stats"=>{"downloads"=>3, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Thin_filament_transition_rates_958__100_/310965", "title"=>"Thin-filament transition rates (<i>ξ</i> = 100).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-05-10 00:16:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/640173"], "description"=>"<p>(A) Steady-state thin filament activation is plotted against pCa for simulations where standard parameter values were applied (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi-1002506-g003\" target=\"_blank\">Figure 3</a>), in the presence and absence of kinetic forms of cooperativity. XBs produce larger increases in fractional thin filament activation when cooperative kinetics were present, evidenced by the increase in activation in the presence versus absence of XB binding. These XB-dependent increase in thin filament activation are greatest at submaximal pCa levels, shown by the differences between the two curves when kinetic forms of cooperativity were implemented. Symbols represent mean±SE, where error bars reside within the symbol when not visible. (B) Average thin filament activation is plotted against time for simulations near the <i>pCa<sub>50</sub></i> value of the steady-state force-pCa response (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi-1002506-g003\" target=\"_blank\">Figure 3</a>), with (pCa = 5.9) and without (pCa 4.25) kinetic forms of cooperativity. These time series activation traces demonstrate the representative slowing of thin filament activation kinetics and increased magnitude of thin filament activation due to XBs in the presence of cooperativity. All simulations used standard parameter values: <i>ρ<sub>Tn</sub></i> = 1, <i>k<sub>xb</sub></i> = 3 pN nm<sup>−1</sup>, <i>k<sub>fil</sub></i> = <i>k<sub>m</sub></i> = <i>k<sub>a</sub></i> = 1X, and <i>RU<sub>span</sub></i> = 9 actins.</p>", "links"=>[], "tags"=>["binding", "stabilizes", "augments", "filament"], "article_id"=>310668, "categories"=>["Biological Sciences", "Biotechnology", "Biophysics"], "users"=>["Bertrand C. W. Tanner", "Thomas L. Daniel", "Michael Regnier"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002506.g004", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cross_bridge_XB_binding_stabilizes_and_augments_thin_filament_activation_/310668", "title"=>"Cross-bridge (XB) binding stabilizes and augments thin filament activation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-10 00:11:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/640044"], "description"=>"<p>Simulations where Ca<sup>2+</sup> activated thin filament distance (<i>RU<sub>span</sub></i>) varied while co-varying the fraction of troponin complexes capable of binding Ca<sup>2+</sup> (<i>ρ<sub>Tn</sub></i>) show maximal, steady-state force as a function of <i>ρ<sub>Tn</sub></i> (A). Measurements from demembranated rabbit psoas muscle fibers (○ in panel A) show that maximal steady-state force increased with the fraction of troponin capable of binding Ca<sup>2+</sup>, replotted from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi-1002506-g004\" target=\"_blank\">Figure 4</a> of Regnier et al. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi.1002506-Regnier1\" target=\"_blank\">[4]</a>. <i>RU<sub>span</sub></i> also affects the cooperative, steady-state force-pCa relationship (B). All values were normalized to the pCa 4.0 value within each simulation set and symbols represent mean±SE for measured and simulated data, where error bars lay within the symbol when not visible. These simulations combined all possible forms of cooperativity from sources TF3, XB2, or XB3, targeting <i>r<sub>t,12</sub></i> and/or <i>r<sub>t,23</sub></i> when applicable. Shaded underlays represent 95% confidence intervals for maximal force from 3-parameter Hill fits. † denotes where data from <i>RU<sub>span</sub></i> values of 7 and 14 actins differed from <i>RU<sub>span</sub></i> values of 9 and 11 actins (<i>p<0.05</i>). * denotes where data from all <i>RU<sub>span</sub></i> values differed (<i>p<0.05</i>).</p>", "links"=>[], "tags"=>["activation", "span", "affects", "steady-state"], "article_id"=>310537, "categories"=>["Biological Sciences", "Biotechnology", "Biophysics"], "users"=>["Bertrand C. W. Tanner", "Thomas L. Daniel", "Michael Regnier"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002506.g002", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Regulatory_unit_activation_span_affects_steady_state_force_production_/310537", "title"=>"Regulatory unit activation span affects steady-state force production.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-10 00:08:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/640442"], "description"=>"<p>Hill parameter values are listed as mean±SD.</p>", "links"=>[], "tags"=>["parameters", "steady-state", "filament", "activation", "responses"], "article_id"=>310933, "categories"=>["Biological Sciences", "Biotechnology", "Biophysics"], "users"=>["Bertrand C. W. Tanner", "Thomas L. Daniel", "Michael Regnier"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002506.t002", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Hill_fit_parameters_to_steady_state_force_and_thin_filament_activation_responses_versus_pCa_/310933", "title"=>"Hill-fit parameters to steady-state force and thin filament activation responses versus pCa.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-05-10 00:15:33"}
  • {"files"=>["https://ndownloader.figshare.com/files/640109"], "description"=>"<p>Various combinations of cooperative thin filament activation kinetics affect the steady-state force-pCa response differently, shown for all possible source combinations when <i>r<sub>t,12</sub></i> was targeted (A) versus both <i>r<sub>t,12</sub></i> and <i>r<sub>t,23</sub></i> being targeted in combination (B). Each line depicts the 3-parameter Hill fit to the simulated force-pCa response, while symbols show <i>n<sub>H</sub></i> (C) and <i>pCa<sub>50</sub></i> (D) values for these fits, with error bars representing 95% confidence intervals. All simulations used standard parameter values: <i>ρ<sub>Tn</sub></i> = 1, <i>k<sub>xb</sub></i> = 3 pN nm<sup>−1</sup>, <i>k<sub>fil</sub></i> = <i>k<sub>m</sub></i> = <i>k<sub>a</sub></i> = 1X, and a <i>RU<sub>span</sub></i> of 9 actins. The dashed lines illustrate an example simulation in the absence of cooperative thin filament activation kinetics, which compares well with prior studies <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi.1002506-Chase1\" target=\"_blank\">[25]</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi.1002506-Tanner1\" target=\"_blank\">[27]</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi.1002506-Tanner2\" target=\"_blank\">[43]</a> after adjusting for <i>K′<sub>1</sub></i> (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi-1002506-t003\" target=\"_blank\">Table 3</a>). The shaded underlay in panels A and B represents the measured physiological range from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi-1002506-g002\" target=\"_blank\">Figure 2</a>.</p>", "links"=>[], "tags"=>["forms", "cooperativity", "simulate", "physiological", "force-pca"], "article_id"=>310598, "categories"=>["Biological Sciences", "Biotechnology", "Biophysics"], "users"=>["Bertrand C. W. Tanner", "Thomas L. Daniel", "Michael Regnier"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002506.g003", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Multiple_forms_of_cooperativity_combine_to_simulate_the_physiological_force_pCa_relationship_/310598", "title"=>"Multiple forms of cooperativity combine to simulate the physiological force-pCa relationship.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-10 00:09:58"}
  • {"files"=>["https://ndownloader.figshare.com/files/330396", "https://ndownloader.figshare.com/files/330836", "https://ndownloader.figshare.com/files/330994", "https://ndownloader.figshare.com/files/331125", "https://ndownloader.figshare.com/files/331280"], "description"=>"<div><p>Striated muscle contraction is a highly cooperative process initiated by Ca<sup>2+</sup> binding to the troponin complex, which leads to tropomyosin movement and myosin cross-bridge (XB) formation along thin filaments. Experimental and computational studies suggest skeletal muscle fiber activation is greatly augmented by cooperative interactions between neighboring thin filament regulatory units (RU-RU cooperativity; 1 RU = 7 actin monomers+1 troponin complex+1 tropomyosin molecule). XB binding can also amplify thin filament activation through interactions with RUs (XB-RU cooperativity). Because these interactions occur with a temporal order, they can be considered kinetic forms of cooperativity. Our previous spatially-explicit models illustrated that mechanical forms of cooperativity also exist, arising from XB-induced XB binding (XB-XB cooperativity). These mechanical and kinetic forms of cooperativity are likely coordinated during muscle contraction, but the relative contribution from each of these mechanisms is difficult to separate experimentally. To investigate these contributions we built a multi-filament model of the half sarcomere, allowing RU activation kinetics to vary with the state of neighboring RUs or XBs. Simulations suggest Ca<sup>2+</sup> binding to troponin activates a thin filament distance spanning 9 to 11 actins and coupled RU-RU interactions dominate the cooperative force response in skeletal muscle, consistent with measurements from rabbit psoas fibers. XB binding was critical for stabilizing thin filament activation, particularly at submaximal Ca<sup>2+</sup> levels, even though XB-RU cooperativity amplified force less than RU-RU cooperativity. Similar to previous studies, XB-XB cooperativity scaled inversely with lattice stiffness, leading to slower rates of force development as stiffness decreased. Including RU-RU and XB-RU cooperativity in this model resulted in the novel prediction that the force-[Ca<sup>2+</sup>] relationship can vary due to filament and XB compliance. Simulations also suggest kinetic forms of cooperativity occur rapidly and dominate early to get activation, while mechanical forms of cooperativity act more slowly, augmenting XB binding as force continues to develop.</p> </div>", "links"=>[], "tags"=>["filament", "influences", "activation", "filaments", "skeletal"], "article_id"=>125251, "categories"=>["Biological Sciences", "Biotechnology", "Biophysics"], "users"=>["Bertrand C. W. Tanner", "Thomas L. Daniel", "Michael Regnier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002506.s001", "https://dx.doi.org/10.1371/journal.pcbi.1002506.s002", "https://dx.doi.org/10.1371/journal.pcbi.1002506.s003", "https://dx.doi.org/10.1371/journal.pcbi.1002506.s004", "https://dx.doi.org/10.1371/journal.pcbi.1002506.s005"], "stats"=>{"downloads"=>2, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Filament_Compliance_Influences_Cooperative_Activation_of_Thin_Filaments_and_the_Dynamics_of_Force_Production_in_Skeletal_Muscle/125251", "title"=>"Filament Compliance Influences Cooperative Activation of Thin Filaments and the Dynamics of Force Production in Skeletal Muscle", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2012-05-10 01:27:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/640407"], "description"=>"<p>Values of <i>RU<sub>span</sub></i> compared to physiological thin filament structures.</p>", "links"=>[], "tags"=>["compared", "physiological", "filament"], "article_id"=>310903, "categories"=>["Biological Sciences", "Biotechnology", "Biophysics"], "users"=>["Bertrand C. W. Tanner", "Thomas L. Daniel", "Michael Regnier"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002506.t001", "stats"=>{"downloads"=>5, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Values_of_RU_span_compared_to_physiological_thin_filament_structures_/310903", "title"=>"Values of <i>RU<sub>span</sub></i> compared to physiological thin filament structures.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-05-10 00:15:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/640342"], "description"=>"<p>Position-dependent free energy differences (A) and transition rates (B–D) for the XB states illustrated in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi-1002506-g001\" target=\"_blank\">Figure 1A</a> are plotted against, x, which represents the position difference between a particular pair of actin and myosin nodes supporting a bound XB. (A) The top horizontal line shows the free energy of the detached state (G<sub>1</sub>(x)), where the difference between the two horizontal lines represents the standard free energy drop over a full XB cycle (ΔG(x)). Each parabolic free energy well G<sub>2</sub>(x) and G<sub>3</sub>(x) represents bound states XB2 and XB3, respectively. For panels B–D, solid lines represent forward transition rates, and dashed lines represent reverse transition rates as formulated in Tanner et al. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi.1002506-Tanner1\" target=\"_blank\">[27]</a>.</p>", "links"=>[], "tags"=>["xb", "kinetics", "pn"], "article_id"=>310837, "categories"=>["Biological Sciences", "Biotechnology", "Biophysics"], "users"=>["Bertrand C. W. Tanner", "Thomas L. Daniel", "Michael Regnier"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002506.g006", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Position_dependent_XB_kinetics_for_k_xb__3_pN_nm_8722_1_/310837", "title"=>"Position dependent XB kinetics for <i>k<sub>xb</sub></i> = 3 pN nm<sup>−1</sup>.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-10 00:13:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/640248"], "description"=>"<p>Simulation results for steady-state magnitude and rate of force development (<i>k<sub>dev</sub></i>) are plotted against pCa as (A–B) XB stiffness (<i>k<sub>xb</sub></i>) varied, (D–E) thick or thin filament stiffness (<i>k<sub>m</sub></i> or <i>k<sub>a</sub></i>) varied independently, or (G–H) both filament stiffness values (<i>k<sub>fil</sub></i>) varied simultaneously. Parameter values from 3 parameter Hill fits to these force-pCa relationships demonstrate that mechanical properties (<i>i.e.</i> stiffness) of they myofilament lattice can influence cooperativity (<i>n<sub>H</sub></i>; panel C) and Ca<sup>2+</sup> sensitivity (<i>pCa<sub>50</sub></i>; panel F) of force production. The rates of XB cycling or turnover directly correlate with ATPase values (I). All relative values were normalized to results for the standard parameter values (solid black circle) of <i>k<sub>xb</sub></i> = 3 pN nm<sup>−1</sup>, <i>k<sub>fil</sub></i> = <i>k<sub>m</sub></i> = <i>k<sub>a</sub></i> = 1X, <i>RU<sub>span</sub></i> = 9 actins, and all possible forms of cooperativity were implemented for all simulations. Symbols represent mean±SE in all panels except C and F, and error bars reside within the symbol when not visible. Symbols in panels C and D depict predicted parameter values with error bars representing 95% confidence intervals.</p>", "links"=>[], "tags"=>["properties", "myofilament", "lattice", "maximal", "xb"], "article_id"=>310732, "categories"=>["Biological Sciences", "Biotechnology", "Biophysics"], "users"=>["Bertrand C. W. Tanner", "Thomas L. Daniel", "Michael Regnier"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002506.g005", "stats"=>{"downloads"=>2, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mechanical_properties_of_the_myofilament_lattice_influence_cooperative_force_production_and_maximal_XB_turnover_/310732", "title"=>"Mechanical properties of the myofilament lattice influence cooperative force production and maximal XB turnover.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-10 00:12:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/639949"], "description"=>"<p>(A) Basic model kinetics combine two three-state cycles describing thin filament regulatory unit (RU) activation and cross-bridge (XB) binding <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002506#pcbi.1002506-Tanner1\" target=\"_blank\">[27]</a>. Thin filament transition rates (<i>r<sub>t,ij</sub></i>) between states TF1–TF3 represent spatial and kinetic behaviors consistent with troponin binding Ca<sup>2+</sup> and tropomyosin movement to activate RUs, which allows myosin binding to actin. Dashed lines between TF2 and TF3, illustrate exposure of available binding sites along the thin filament. XB transition rates (<i>r<sub>x,ij</sub></i>) are strain dependent between states XB1–XB3, representing transitions between unbound, bound pre-power stroke, and bound post-power stroke states. Cooperative pathways (dashed arrows) are layered upon basic model kinetics, amplifying thin filament activation kinetics at neighboring RUs. These layered, kinetic forms of cooperativity represent potential pathways where activation (TF3) or XB binding (XB2 or XB3) can act as a source of cooperativity to augment RU activation kinetics at neighboring RUs via targets <i>r<sub>t,12</sub></i> or <i>r<sub>t,23</sub></i>. (B) Adjacent RUs run along each of the helices that compose the thin filament. Thus, adjacent RUs along one helix face opposing thick filaments every ∼37 nm. Consistently, adjacent co-linear interactions between a thick and thin filament pair occur on alternate helices of the thin filament. (C) Therefore, certain regions of the thin filament can have RUs activated on both helices, either of the two helices, or neither of the two helices. (D) Similar to a finite element models, mechanics are simulated using a network of linear springs where forces balance at thick and thin filament nodes each time-step. The mechanical network comprises tunable spring constants <i>k<sub>m</sub></i>, <i>k<sub>a</sub></i>, and <i>k<sub>xb</sub></i>, representing thick filament, thin filament, and myosin XB stiffness, respectively. Potential interactions for a co-linear thick and thin filament pair depict available thin filament nodes as shown in panel C. Those XBs extending from thick filament nodes occupy the co-linear plane, while XBs extending from neighboring thick filament nodes (not shown) lie outside of this plane.</p>", "links"=>[], "tags"=>["forms", "cooperativity", "layered"], "article_id"=>310441, "categories"=>["Biological Sciences", "Biotechnology", "Biophysics"], "users"=>["Bertrand C. W. Tanner", "Thomas L. Daniel", "Michael Regnier"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002506.g001", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kinetic_forms_of_cooperativity_are_layered_upon_basic_model_kinetics_/310441", "title"=>"Kinetic forms of cooperativity are layered upon basic model kinetics.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-10 00:07:21"}

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