Direct Measurements of Local Coupling between Myosin Molecules Are Consistent with a Model of Muscle Activation
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{"title"=>"Direct Measurements of Local Coupling between Myosin Molecules Are Consistent with a Model of Muscle Activation", "type"=>"journal", "authors"=>[{"first_name"=>"Sam", "last_name"=>"Walcott", "scopus_author_id"=>"24729488000"}, {"first_name"=>"Neil M.", "last_name"=>"Kad", "scopus_author_id"=>"6603131385"}], "year"=>2015, "source"=>"PLoS Computational Biology", "identifiers"=>{"scopus"=>"2-s2.0-84949211299", "pui"=>"607183849", "sgr"=>"84949211299", "isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "issn"=>"15537358", "pmid"=>"26536123", "doi"=>"10.1371/journal.pcbi.1004599"}, "id"=>"c7e36def-c2cc-3f4c-baeb-779c954a7f78", "abstract"=>"Muscle contracts due to ATP-dependent interactions of myosin motors with thin filaments composed of the proteins actin, troponin, and tropomyosin. Contraction is initiated when calcium binds to troponin, which changes conformation and displaces tropomyosin, a filamentous protein that wraps around the actin filament, thereby exposing myosin binding sites on actin. Myosin motors interact with each other indirectly via tropomyosin, since myosin binding to actin locally displaces tropomyosin and thereby facilitates binding of nearby myosin. Defining and modeling this local coupling between myosin motors is an open problem in muscle modeling and, more broadly, a requirement to understanding the connection between muscle contraction at the molecular and macro scale. It is challenging to directly observe this coupling, and such measurements have only recently been made. Analysis of these data suggests that two myosin heads are required to activate the thin filament. This result contrasts with a theoretical model, which reproduces several indirect measurements of coupling between myosin, that assumes a single myosin head can activate the thin filament. To understand this apparent discrepancy, we incorporated the model into stochastic simulations of the experiments, which generated simulated data that were then analyzed identically to the experimental measurements. By varying a single parameter, good agreement between simulation and experiment was established. The conclusion that two myosin molecules are required to activate the thin filament arises from an assumption, made during data analysis, that the intensity of the fluorescent tags attached to myosin varies depending on experimental condition. We provide an alternative explanation that reconciles theory and experiment without assuming that the intensity of the fluorescent tags varies.", "link"=>"http://www.mendeley.com/research/direct-measurements-local-coupling-between-myosin-molecules-consistent-model-muscle-activation", "reader_count"=>12, "reader_count_by_academic_status"=>{"Researcher"=>3, "Student > Ph. D. Student"=>6, "Student > Master"=>2, "Lecturer"=>1}, "reader_count_by_user_role"=>{"Researcher"=>3, "Student > Ph. D. Student"=>6, "Student > Master"=>2, "Lecturer"=>1}, "reader_count_by_subject_area"=>{"Biochemistry, Genetics and Molecular Biology"=>4, "Mathematics"=>1, "Agricultural and Biological Sciences"=>4, "Physics and Astronomy"=>3}, "reader_count_by_subdiscipline"=>{"Physics and Astronomy"=>{"Physics and Astronomy"=>3}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>4}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>4}, "Mathematics"=>{"Mathematics"=>1}}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/2407125"], "description"=>"<p>A. Experimental set up and raw images for three different conditions: 1. (left) a single myosin bound to the thin filament; 2. (middle) two nearby myosin molecules bound to the thin filament; and 3. (right) three myosin molecules bound to the thin filament, two of which are close together. (Top) A thin filament is suspended between two silica beads (purple spheres) on a glass surface (gray). Variable concentrations of myosin head domains (S1), labeled with a fluorescent tag (GFP), are added to a solution that also contains variable concentrations of ATP and calcium. (Bottom) A camera records the fluorescence. Bound GFP-tagged S1s (GFP-S1s) appear as diffraction limited spots. In each simulated image, single GFP-S1s make a faint spot, while two nearby GFP-S1s make a brighter spot. The red box indicates the position of the thin filament. B. Construction of a kymograph. For each frame of a recorded movie, the pixels along the thin filament are isolated and stacked together, in chronological order, to make a 2-dimensional image. When GFP-S1s bind to the thin filament (inset, white arrows), they either increase the intensity of an existing spot if they bind near a bound GFP-S1 (left arrow), or they create a new spot (right arrow). C. Fitting the data with Gaussians. For a frame of a recorded movie, the pixels along the thin filament are isolated (top), and fluorescence is plotted as a function of position (bottom). Custom code [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.ref052\" target=\"_blank\">52</a>] is used to fit these plots with Gaussians of constant standard deviation, but variable amplitude. Fluorescent intensity as a function of position, and the best-fit Gaussian(s), are shown for each of the different conditions in (A). Two nearby bound GFP-S1s (Peaks 2 and 4) are fit by a Gaussian with roughly twice the amplitude of the single bound GFP-S1 (Peaks 1 and 3). D. Construction of a histogram. For an entire movie, the amplitudes of the best-fit Gaussians of each individual frame are displayed as a histogram. The individual frames shown in (C) generate four amplitudes (red). The histogram is scaled so that the peak has an amplitude of 1. Note: scaled intensity, defined in the text, gives a single GFP-S1 an intensity of 1.</p>", "links"=>[], "tags"=>["actin", "myosin binding sites", "filament", "myosin motors", "tropomyosin", "Muscle Activation Muscle contracts"], "article_id"=>1593696, "categories"=>["Biological Sciences"], "users"=>["Sam Walcott", "Neil M. Kad"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004599.g002", "stats"=>{"downloads"=>4, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cartoons_describing_the_experiments_and_data_analysis_of_Desai_et_al_52_/1593696", "title"=>"Cartoons describing the experiments and data analysis of Desai et al. [52].", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-11-04 03:37:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/2407126"], "description"=>"<p>A. Simulated data (top) reasonably reproduces experimental measurements (bottom), including noise. Simulations include two sources of noise: 1) uniform background noise with zero mean and standard deviation <i>σ</i><sub><i>N</i></sub>; and 2) noise due to temporal fluctuations in fluorescent intensity, with zero mean and standard deviation <i>σ</i><sub><i>F</i></sub>. The standard deviation of a diffraction limited spot, <i>σ</i><sub><i>GFP</i></sub> = 2 pixels, where one pixel is 80 nm. B. Kinetic scheme defining the interaction of a fluorescently-labeled myosin (GFP-S1) with an actin binding site. The scheme comes from [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.ref010\" target=\"_blank\">10</a>], but has been modified to reflect the low myosin concentrations in the experiments [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.ref052\" target=\"_blank\">52</a>]. C. Simulated and measured data generate similar fitting error, suggesting that we have successfully captured signal noise. The plot shows a histogram of root mean squared (RMS) error for each of 500 frames of simulated and measured data. D. By varying the calcium dependent fitting parameter <i>ε</i>, the model reasonably reproduces measurements at low and high calcium. At high calcium (pCa 4, where pCa is the negative log of the calcium concentration) Desai et al. [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.ref052\" target=\"_blank\">52</a>], observed fewer binding events for thin filaments than for actin alone We can replicate this result with <i>ε</i> = 0.5 (top and middle). Binding was almost completely eliminated at very low calcium (pCa 8) [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.ref052\" target=\"_blank\">52</a>], which we can replicate with <i>ε</i> = 0.01 (bottom). Note: for A and C, scaled intensity, defined in the text, gives a single GFP-S1 an intensity of 1. For D, zero is defined as the average minimum fluorescence achieved at each pixel. Here, scaled intensity is non-zero in the absence of GFP-S1, and a single GFP-S1 increases the signal by 1 unit.</p>", "links"=>[], "tags"=>["actin", "myosin binding sites", "filament", "myosin motors", "tropomyosin", "Muscle Activation Muscle contracts"], "article_id"=>1593697, "categories"=>["Biological Sciences"], "users"=>["Sam Walcott", "Neil M. Kad"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004599.g003", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Parameter_estimation_and_validation_/1593697", "title"=>"Parameter estimation and validation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-11-04 03:37:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/2407127"], "description"=>"<p>In plots A-C, measurements [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.ref052\" target=\"_blank\">52</a>] (replotted on a uniformly consistent scale) are at the top of each panel and simulations are at the bottom. The different experimental conditions are A. Increasing myosin (left to right), recorded at <i>f</i> = 10 Hz; B. Increasing calcium (left to right), recorded at <i>f</i> = 3.8 Hz; and C. Decreasing ATP (left to right), recorded at <i>f</i> = 3.8 Hz. D. Simulations reasonably capture mean fluorescence per pixel at variable myosin concentrations. For each myosin concentration, the mean scaled intensity of the measurements is shown, along with the mean and standard deviation of five simulations. The faster-than-linear increase in fluorescence with myosin indicates the presence of local coupling. Note: in all plots, zero is defined as the average minimum fluorescence achieved at each pixel. The scaled intensity, defined in the text, is non-zero in the absence of a myosin, and a single myosin increases the signal by 1 unit. The non-zero fluorescence in the absence of myosin, apparent in plot D, is a reflection of this offset.</p>", "links"=>[], "tags"=>["actin", "myosin binding sites", "filament", "myosin motors", "tropomyosin", "Muscle Activation Muscle contracts"], "article_id"=>1593698, "categories"=>["Biological Sciences"], "users"=>["Sam Walcott", "Neil M. Kad"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004599.g004", "stats"=>{"downloads"=>0, "page_views"=>17, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_model_reproduces_measured_kymographs_both_qualitatively_and_quantitatively_/1593698", "title"=>"The model reproduces measured kymographs both qualitatively and quantitatively.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-11-04 03:37:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/2407128"], "description"=>"<p>In all plots, histograms from measurements (blue) [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.ref052\" target=\"_blank\">52</a>] are plotted along with histograms from five individual simulations (gray), and histograms of those five simulations pooled together (black). The different experimental conditions are A. Increasing myosin (left to right), 1000 frames recorded at <i>f</i> = 10 Hz; B. Increasing calcium (left to right), 500 frames recorded at <i>f</i> = 3.8 Hz; and C. Decreasing ATP (left to right), 500 frames recorded at <i>f</i> = 3.8 Hz. At each calcium concentration, there is only a single fitting parameter (<i>ε</i>). With the exception of the right panel in C, agreement between simulation and measurement is good. D. For the single case where model and simulation differ, we get good agreement between simulation and measurement with only a 50nM increase in ATP concentration. Differences between simulation and experiment are therefore likely due to the system’s sensitivity to parameters, so that small differences in experimental condition lead to large changes in measurement. Note: To compare simulations with measurements [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.ref052\" target=\"_blank\">52</a>], all plots have units of intensity, which depends on frame rate. For plot A, collected at 10 Hz, the intensity of a single GFP-S1 is <i>I</i><sub>1</sub> = 45 intensity units. For plots B–D, collected at 3.8 Hz, the intensity of a single GFP-S1 is <i>I</i><sub>1</sub> = 118 intensity units.</p>", "links"=>[], "tags"=>["actin", "myosin binding sites", "filament", "myosin motors", "tropomyosin", "Muscle Activation Muscle contracts"], "article_id"=>1593699, "categories"=>["Biological Sciences"], "users"=>["Sam Walcott", "Neil M. Kad"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004599.g005", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_model_reproduces_measured_histograms_/1593699", "title"=>"The model reproduces measured histograms.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-11-04 03:37:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/2407129"], "description"=>"<p>Scaled intensity, defined in the text, gives a single fluorescently-tagged myosin (GFP-S1) an intensity of 1. The observation that each histogram has a peak near 1 suggests that 1) under these three conditions, mostly single GFP-S1s bind; and 2) the emission of an excited GFP is constant and measured fluorescence is inversely proportional to frame rate. This latter is a central assumption of our analysis.</p>", "links"=>[], "tags"=>["actin", "myosin binding sites", "filament", "myosin motors", "tropomyosin", "Muscle Activation Muscle contracts"], "article_id"=>1593700, "categories"=>["Biological Sciences"], "users"=>["Sam Walcott", "Neil M. Kad"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004599.g006", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Histograms_collected_under_three_different_experimental_conditions_52_collapse_upon_rescaling_fluorescence_/1593700", "title"=>"Histograms, collected under three different experimental conditions [52], collapse upon rescaling fluorescence.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-11-04 03:37:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/2407130"], "description"=>"<p>Details of parameter estimation in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.s001\" target=\"_blank\">S1 Supplementary Material</a>. Scaled intensity, defined in the text, gives a single GFP-S1 an intensity of 1.</p><p>Background noise used in simulations.</p>", "links"=>[], "tags"=>["actin", "myosin binding sites", "filament", "myosin motors", "tropomyosin", "Muscle Activation Muscle contracts"], "article_id"=>1593701, "categories"=>["Biological Sciences"], "users"=>["Sam Walcott", "Neil M. Kad"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004599.t001", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Background_noise_used_in_simulations_/1593701", "title"=>"Background noise used in simulations.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-11-04 03:37:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/2407131"], "description"=>"<p>Note: scaled intensity, defined in the text, gives a single fluorescently-labeled myosin an intensity of 1.</p><p>Model parameters.</p>", "links"=>[], "tags"=>["actin", "myosin binding sites", "filament", "myosin motors", "tropomyosin", "Muscle Activation Muscle contracts"], "article_id"=>1593702, "categories"=>["Biological Sciences"], "users"=>["Sam Walcott", "Neil M. Kad"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004599.t002", "stats"=>{"downloads"=>1, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_parameters_/1593702", "title"=>"Model parameters.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-11-04 03:37:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/2407132"], "description"=>"<div><p>Muscle contracts due to ATP-dependent interactions of myosin motors with thin filaments composed of the proteins actin, troponin, and tropomyosin. Contraction is initiated when calcium binds to troponin, which changes conformation and displaces tropomyosin, a filamentous protein that wraps around the actin filament, thereby exposing myosin binding sites on actin. Myosin motors interact with each other indirectly via tropomyosin, since myosin binding to actin locally displaces tropomyosin and thereby facilitates binding of nearby myosin. Defining and modeling this local coupling between myosin motors is an open problem in muscle modeling and, more broadly, a requirement to understanding the connection between muscle contraction at the molecular and macro scale. It is challenging to directly observe this coupling, and such measurements have only recently been made. Analysis of these data suggests that two myosin heads are required to activate the thin filament. This result contrasts with a theoretical model, which reproduces several indirect measurements of coupling between myosin, that assumes a single myosin head can activate the thin filament. To understand this apparent discrepancy, we incorporated the model into stochastic simulations of the experiments, which generated simulated data that were then analyzed identically to the experimental measurements. By varying a single parameter, good agreement between simulation and experiment was established. The conclusion that two myosin molecules are required to activate the thin filament arises from an assumption, made during data analysis, that the intensity of the fluorescent tags attached to myosin varies depending on experimental condition. We provide an alternative explanation that reconciles theory and experiment without assuming that the intensity of the fluorescent tags varies.</p></div>", "links"=>[], "tags"=>["actin", "myosin binding sites", "filament", "myosin motors", "tropomyosin", "Muscle Activation Muscle contracts"], "article_id"=>1593703, "categories"=>["Biological Sciences"], "users"=>["Sam Walcott", "Neil M. Kad"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004599", "stats"=>{"downloads"=>1, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Direct_Measurements_of_Local_Coupling_between_Myosin_Molecules_Are_Consistent_with_a_Model_of_Muscle_Activation_/1593703", "title"=>"Direct Measurements of Local Coupling between Myosin Molecules Are Consistent with a Model of Muscle Activation", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-11-04 03:37:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/2407124"], "description"=>"<p>A. Size scales in muscle. Muscle contracts due to the formation of transient links between thick filaments (made primarily of the protein myosin) and thin filaments (made of the proteins actin, troponin and tropomyosin). Contraction is regulated by troponin and tropomyosin. After binding calcium, troponin moves tropomyosin from a position where myosin binding to actin is obstructed (blue, blocked position) toward a position where myosin binding is unhindered (yellow, open position). B. Assumptions of the continuous flexible chain model [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.ref015\" target=\"_blank\">15</a>–<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004599#pcbi.1004599.ref017\" target=\"_blank\">17</a>]. Troponin-tropomyosin (Tn-Tm) is a slender, infinite, linearly elastic beam constrained to a plane and in a potential well, <i>W</i>(<i>z</i>). Myosin binding to actin induces a displacement of the Tn-Tm beam into the open position (yellow), and locally deforms it. C. Simplifying assumptions of the model. When nearby myosin molecules bind to actin (molecules 2 and 4), they uniformly displace the intervening Tn-Tm beam into the open position. When distant myosin molecules bind to actin (molecules 4 and 7), they each induce independent deformations of the Tn-Tm beam. D. Energy change of the thin filament (Δ<i>E</i>) due to myosin binding, as a function of the distance to a bound myosin (<i>L</i>). When <i>L</i> is small, Tn-Tm is displaced uniformly, and Δ<i>E</i> increases linearly with <i>L</i> (blue region); when <i>L</i> is large, each myosin displaces Tn-Tm independently, and Δ<i>E</i> is independent of <i>L</i> (green region). If the transition between these regimes is abrupt, the curve is defined by two non-dimensional parameters, <math><mi>C</mi></math> and <i>ε</i>. Note: in the presence of calcium, the Tn-Tm beam moves into the closed state (not pictured), which changes <i>ε</i>, but not <math><mi>C</mi></math>.</p>", "links"=>[], "tags"=>["actin", "myosin binding sites", "filament", "myosin motors", "tropomyosin", "Muscle Activation Muscle contracts"], "article_id"=>1593695, "categories"=>["Biological Sciences"], "users"=>["Sam Walcott", "Neil M. Kad"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004599.g001", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cartoons_of_muscle_and_the_model_of_local_coupling_/1593695", "title"=>"Cartoons of muscle and the model of local coupling.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-11-04 03:37:53"}

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{"start_date"=>"2015-01-01T00:00:00Z", "end_date"=>"2015-12-31T00:00:00Z", "subject_areas"=>[]}
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