thin filaments 
  were isolated from goldfish ( carassius auratus ) in relaxing solution 
  as described in kensler and stewart ( 1989 ) 
  ( 26 ) .
electron micrographs 
  were recorded of negatively stained filaments applied to a thin carbon film 
  support over the holes of holey carbon grids .
the images were collected on a 
  jeol 1200ex at a nominal magnification of 20,000 .
the images were 
  digitized on a nikon coolscan 8000ed with a step size of 6.35 m .
the focal 
  level of the micrographs was such that the 1 minimum in the thon 
  rings was at substantially higher resolution than the final resolution of our 
  analysis ( 35  , see below ) . from an initial dataset of 29 
 
the 
  fourier transforms were computed and the strong 59  actin reflection 
  used to calibrate the magnification and adjust the sampling of each filament 
  to 3.28  / pixel . image processing 
image processing software packages were 
  used as follows : imagic ( 28 ) , 
  the mrc suite of programs 
  ( 60 ) , spider 
  ( 34 ) , and imagej 
  ( 27 ) .
the straightening of 
  filament images , was achieved using the straighten plugin for imagej 
  ( 27 ) .
single particle analysis  the image processing package imagic 
  provided the framework for the single particle analysis 
  ( 28 ) .
adaptations to the 
  standard procedures , specific to filamentous particles , were implemented 
  including the modified back - projection algorithm 
  ( 25 ) .
individual 
  filaments were interactively selected into a large box ( 30004000 
   ) .
the filaments were straightened and subsequently 
  segmented into smaller boxes 850  ( 128  128 
  pixels ) .
particles 
  originating from the same filament should clearly be assigned the same 
  polarity .
the occurrence of erroneously oriented filaments was checked by 
  monitoring the alignment procedure allowing particles that were assigned 
  polarity inconsistent to their originating filament to be identified and 
  subsequently removed from the data .
the consistency of alignment in the final data set was found to be 87% : 
  those segments , which were inconsistently aligned were eliminated prior to 
  calculating the final three - dimensional map . the relatively high level of 
  consistency is characteristic of a strongly polar structure and effective 
  alignment .
the images in each of these classes were summed together to create 
  class averages with an increased signal to noise ratio .
a 
  helical reconstruction was calculated using the mrc helical processing 
  routines from twelve straightened filaments .
anchor set  of reference images which 
  were evenly spaced over the euler sphere .
the  anchor set  of 
  reference images were used to create sinograms , sets of one - dimensional line 
  projections of each image as a function of projection angle , for use in 
  angular reconstitution .
the alternate angle assignment methods of projection 
  matching using reference images generated from the helical reconstruction 
  rotated about the filament axis and analysis of the central section overlap 
  ( 29 ) were tested using the 
  first set of class averages ( generated before any multi - reference alignment 
  was performed ) .
consistency between the three angle assignment methods was a 
  criterion in angle selection to generate the first three - dimensional 
  reconstruction .
in subsequent rounds of angle assignment the angular 
  reconstitution method was employed with an anchor set of 288 references again 
  evenly distributed over the euler sphere .
the class averages were assigned 
  angles with good coverage around the equator of the euler sphere 
  ( fig .
the modified exact 
  filter back projection algorithm 
  ( 25 ) was applied to create a 
  three - dimensional electron density map from two - dimensional class 
  averages . imposing screw symmetry 
a novel method has been implemented 
  to computationally sum the two strands of the thin filament . once converted to 
  a set of cylindrical sections ( cylindrical surfaces flattened out at a fixed 
  radius ) imagic
after 
  processing , the sections were used to create the desired averaged structure . 
  the three - dimensional map consisting of cylindrical sections was then 
  converted back into cartesian coordinates . rendering in pymol
 the three - dimensional model , electron 
  density maps , and protein data bank ( pdb ) structures were rendered using pymol 
  ( 61 ) .
a hybrid method ( using 
  imagic and pymol ) has been established that allows em density maps to be 
  displayed in pymol at a theoretical volume corresponding to a specific 
  molecular weight .
situs version 
  2.2 ( 30 ) and uro 
  ( 31 ) were used to dock the 
  atomic model of actin into our electron density maps . to evaluate the fit , 
  docked pdb files
were viewed in stereo in pymol using the nvidia quadro stereo 
  system and nuvision stereoscopic glasses .
electron density models were created 
  from the aligned pdb files within the uro software package . the pdb models and 
 
the experimental data were converted into the imagic format and low pass 
  filtered to 35  .
the density models of docked f - actin and docked 
  f - actin with docked tropomyosin were used to create the difference 
  datasets .
a , typical 
  goldfish thin filament negatively stained with regularly spaced 
   bumps  of density attributed to troponin .
b , 
  two - dimensional class average and the corresponding one - dimensional density 
  profile .
the arrow indicates a large peak locating the troponin 
  complex in the center of the segment .
the asterisk highlights a 
  second peak due to contributions from the neighboring troponin complex . 
 
c , five columns represent different viewing angles of the filament 
  described by the euler angles (  = 0 ,  = 90 throughout and  
  = -115 , 162 , 144 , 44 , and 89. ( i ) class averages , ( ii ) 
  reprojections , and ( iii ) surface views of the three - dimensional reconstruction 
  are displayed at the corresponding angles .
the cross - correlation coefficient 
  between each of the class averages and the corresponding reprojection are 
  given at the top of each column .
d , fourier shell 
  correlation curve of the single particle reconstruction prior to averaging . 
 
the dotted line gives the 0.5 threshold , and the exponential decay 
  ( dashed ) shows the  bit criteria . where the curve crosses 
  these two thresholds an estimate of the highest significant spatial frequency 
  present can be made and hence the resolution of the data .
e , 
  distribution of euler angles assigned to the 225 class averages generated in 
  the final round of processing and the 38 class averages back - projected to 
  create the final three - dimensional single particle reconstruction .
the largest gap in the angular coverage in euler angle  in the 
  final three - dimensional single particle reconstruction is 12 ( indicated ) . 
 
a gap of 12 taken as the sampling step for an evenly distributed data set 
  tilted about a single axis theoretically could produce a reconstruction of 
  15  ( 59 ) .
using 
  this calculation we can rule out the possibility that angular distribution and 
  the number of class averages used in our reconstruction has limited the 
  resolution .
a , typical 
  goldfish thin filament negatively stained with regularly spaced 
   bumps  of density attributed to troponin .
b , 
  two - dimensional class average and the corresponding one - dimensional density 
  profile . the arrow indicates a large peak locating the troponin 
  complex in the center of the segment .
the asterisk highlights a 
  second peak due to contributions from the neighboring troponin complex . 
 
c , five columns represent different viewing angles of the filament 
  described by the euler angles (  = 0 ,  = 90 throughout and  
  = -115 , 162 , 144 , 44 , and 89. ( i ) class averages , ( ii ) 
  reprojections , and ( iii ) surface views of the three - dimensional reconstruction 
  are displayed at the corresponding angles .
the cross - correlation coefficient 
  between each of the class averages and the corresponding reprojection are 
  given at the top of each column .
d , fourier shell 
  correlation curve of the single particle reconstruction prior to averaging . 
 
the dotted line gives the 0.5 threshold , and the exponential decay 
  ( dashed ) shows the  bit criteria . where the curve crosses 
  these two thresholds an estimate of the highest significant spatial frequency 
  present can be made and hence the resolution of the data .
e , 
  distribution of euler angles assigned to the 225 class averages generated in 
  the final round of processing and the 38 class averages back - projected to 
  create the final three - dimensional single particle reconstruction .
the largest gap in the angular coverage in euler angle  in the 
  final three - dimensional single particle reconstruction is 12 ( indicated ) . 
 
a gap of 12 taken as the sampling step for an evenly distributed data set 
  tilted about a single axis theoretically could produce a reconstruction of 
  15  ( 59 ) . using 
  this calculation we can rule out the possibility that angular distribution and 
  the number of class averages used in our reconstruction has limited the 
  resolution .
two - dimensional class averages of the thin filament  a 
  dataset of 2638 individual particles was selected from straightened thin 
  filament images ( see  experimental procedures  ) .
the samples were 
  prepared in the absence of ca and were negatively stained for 
  electron microscopy .
1a : periodic 
  regions of extra density at a spacing of 385  are clearly visible , 
  allowing particle selection centered on troponin .
after a reference - free 
  alignment procedure , which centered the particles , multivariate statistical 
  analysis , and hierarchical ascendant classification were used to create 
  classes of filament segments 
  ( 13 ) .
the members of each 
  class were averaged to form a class average with increased signal to noise 
  ratio .
two strands of actin subunits twisting around each other , with a 
  crossover repeat of 360  were clearly visible in the 
  two - dimensional class averages ( fig . 
  1c ) .
these features appeared clear and well - defined from 
  the early stages of the analysis .
euler angles were assigned to the class averages using angular reconstitution 
  initially with a reference set of images from the helical reconstruction 
  calculated from the same data ( see below ) and subsequently using the 
  three - dimensional map generated in the previous cycle of processing . as part 
  of the refinement procedure a careful selection of class averages
was made at 
  the stage of three - dimensional reconstruction so as only to include those with 
  a good level of detail which agreed well with two - dimensional reprojections of 
  the three - dimensional map .
this was achieved by visual and statistical 
  comparison between classes and reprojections of the three - dimensional map , 
  taking into account the distribution of assigned angles .
this served to ensure 
  that only well preserved and properly aligned filament segments were used in 
  the analysis .
accordingly , in the final round of refinement 38 classes were 
  selected out of the 225 calculated from the full data set . the distribution of 
  angles assigned to the final 225 class averages , the entire data set , and the 
  38 used in the map provided a good coverage around the equator of the euler 
  sphere ( fig .
model tests 
  have shown that angular reconstitution can be successfully applied using a 
  starting model that deviates from the desired structure : a model of f - actin 
  provides enough information to accurately assign euler angles to projections 
  of a model of the full thin filament 
  ( 25 ) .
alternative angle 
  assignment methods of projection matching using projection images of the 
  helical reconstruction as references and a method based on the extent of 
  correlation between corresponding central sections 
  ( 29 ) provided consistent 
  results .
once euler angles had been assigned , an initial three - dimensional map 
  was calculated using the exact filter back projection algorithm adapted for 
  filamentous macromolecular complexes 
  ( 25 ) .
the euler angles of adjacent segments assigned via projection matching was 
  evaluated and compared with theoretical values calculated for actin filaments 
  with 13/6 symmetry .
the average departure from 13/6 symmetry of adjacent 
  segments was 18.9 while 55% of segments were assigned angles within 
  20 of the expected value and 78% within 40 
  ( supplemental fig .
cumulative angular disorder is known to perturb the 
  total angle traversed by the actin one - start helix j ( after n 
  subunits ) ( 32 ) according to 
  equation 1 . 
 
( eq . 1)\documentclass[10pt]{article } 
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 \begin{document } 
 \begin{equation*}\;\;{\phi}_{{\mathrm{j}}}=n{\bar { { \phi}}}+n^{1/2}{\mathrm{d}}_{{\mathrm{rms}}}\end{equation*}\end{document } 
  the average angle between adjacent subunits is 
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 \begin{document } 
 \begin{equation*}{\bar { { \phi}}}\end{equation*}\end{document } ( 167 ) .
reported values of 
  drms the root mean square angular deviation per subunit 
  for actin are 5-6 
  ( 33 ) .
for adjacent segments 
  centered on troponin complexes ( n = 14 ) the cumulative disorder is 
  thus 19-22 , which compares closely with the value of 18.9 
  observed in our studies .
the regulatory proteins are believed to increase 
  rigidity of the thin filament , but even in this case substantial angular 
  disorder has been observed 
  ( 32 ) .
location of troponin  extra density in the central region of 
  the segments on opposing sides of the filament was apparent in most of the 
  initial class averages : this density can be attributed to troponin .
after 
  subsequent rounds of refinement , as the data became better aligned , the 
  density attributed to troponin became easier to visualize .
the identification 
  of densities attributed to troponin depends primarily on the orientation of 
  the filament around its long axis .
1c , 
   = -115 ) density caused by troponin is less readily visualized in 
  others ( fig .
this can be explained by the orientation of the filament : 
  it was observed that troponin was less readily identified in orientations 
  where it superimposes directly on top of the actin subunits .
it was possible 
  to check the location of troponin in a class average from the one - dimensional 
  density profile ( fig . 
 
the presence of troponin was indicated by a 
  significant peak close to the midpoint .
this approach was used to assess class 
  averages for inclusion in the three - dimensional analysis .
a second peak was 
  also often observed at a distance from the first peak close to the 385- 
  troponin repeat .
comparison of two - dimensional class averages with reprojections of the 
  three - dimensional map 
the level of detail that can be seen in an 
  individual class average was used as the selection criterion for inclusion in 
  the three - dimensional analysis .
another measure of the quality of a class 
  average and the accuracy of its angular assignment was by comparison with the 
  reprojection of the resulting three - dimensional reconstruction at the same 
  viewing angle .
visual similarity was used to assess the accuracy of angular 
  assignment and the effectiveness of classification .
five typical class 
  averages with corresponding reprojections and surface views of the 
  three - dimensional reconstruction are displayed in 
  fig .
1 , ci ) show good 
  visual agreement with reprojections of the three - dimensional reconstruction 
  ( fig .
1 , cii ) as well 
  high levels of correlation ( correlation coefficients 0.9 ) .
refinement of the structure was achieved by iterating over the image 
  processing steps of alignment , classification , angle assignment , 
  three - dimensional reconstruction , and reprojection ( see  experimental 
  procedures  ) until no significant changes in three - dimensional density 
  distribution were observed .
the 38 class averages used in the final 
  three - dimensional reconstruction were taken from a set of 225 : the average 
  number of segments per class in this set was 12 .
the polarity of the 
  segments was checked for consistency with respect to other segments from the 
  same filament : 13% proved to be inconsistent and were removed from the final 
  refinement . the helical arrangement of the troponin complexes was exploited to 
  improve the signal to noise ratio of our analysis .
addition of the two actin 
  strands by translating and rotating along troponin helical path allowed a 
  2-fold averaging of the structure in a novel way ( see experimental 
  procedures ) .
the alignment was refined further using routines in spider 
  ( 34 ) and the two strand 
  averaging repeated .
prior to two - strand averaging , a quantitative assessment 
  of the resolution of the final map was made using the fourier shell 
  correlation criterion .
the 0.5 criteria 
  ( 35 , 
  36 ) returned a resolution of 
  32  and the  bit criteria 
  ( 37 ) returned a resolution of 
  27  ( fig .
these values are close to a qualitative estimate of 35  obtained 
  by visually comparing our final density map to model data filtered to a known 
  resolution .
three - dimensional reconstruction of the thin filament  the 
  three - dimensional reconstruction of the thin filament is displayed in 
  fig .
2 as a surface - rendered 
  map ( 2a ) and a wire mesh ( 2c ) . using the known stoichiometry 
  of binding ( actin / troponin / tropomyosin , 7:1:1 ) , we calculated the expected 
  particle molecular mass ( 1630 kda ) .
maps are contoured to include 125% of 
  this weight assuming a protein density of 0.844 dalton /  .
it 
  has been reported that three - dimensional reconstructions of intermediate 
  resolution frequently require thresholding at a higher molecular weight 
  primarily due to the degree to which the low - spatial frequencies are 
  represented ( 38 , 
  39 ) .
a range of molecular 
  weights were trialled up to 140% and the contours of the three - dimensional map 
  inspected carefully .
an increased molecular mass improved the connectivity of 
  the density attributed to tropomyosin up to a value of 125% . increasing
the filament has an average width of 
  110  7  and at its widest point measures 141  7  
  ( fig .
two strands 
  of actin subunits clearly twist around each other in the well recognized 
  right - handed , long pitch actin helix .
there is an area of localized mass on 
  each actin strand around the midpoint of the reconstruction which can be 
  attributed to the globular part of the troponin complex .
the exact axial 
  stagger of the density peaks attributed to the globular head of troponin was 
  found to be 27.5  through the alignment procedure prior to averaging 
  the two strands .
figure 2.a comparison of the single particle based reconstruction and the helical 
  reconstruction calculated from the same data . a 
c 
  and i , are shown as wire meshes with atomic f - actin models docked . 
 
d , e , f , and j , surface - rendered difference maps . d 
  and j , are obtained by subtracting f - actin models from the single 
  particle and helical reconstructions , respectively .
e and f , 
  are composite difference maps which display the difference density calculated 
  by subtracting an f - actin model with docked tropomyosin from the single 
  particle reconstruction and the difference density displayed in d. 
  extra mass in the central region of the single particle reconstruction 
  ( a and c ) surrounds the central actin subunits whereas the 
  helical reconstruction ( g and i ) gives a much tighter fit to 
  the crystal structure .
two actin subunits are encircled in white in each 
  surface - rendered representation ( a and g ) .
the incorrect fit 
  of the inverted f - actin model would give rise to the assignment of actin 
  subunits illustrated in the pink outline ( a and g ) .
the 
  crossover point of the two long pitch actin strands ( arrowed ) , a 
  slight gap surrounded by four high density bright regions ( blue ) and 
  bands of density running diagonally out from the center of the filament 
  ( red ) are visible in the two - dimensional projections of both the 
  single particle and helical reconstructions ( b and h ) .
these 
  features confirm the polarity inferred from fitting of the f - actin model .
the 
  difference density maps d and j calculated from single 
  particle and helical reconstructions respectfully highlight the non - actin 
  density ( orange ) .
this density attributable to tropomyosin and 
  troponin is highly asymmetric in the single particle reconstruction .
the 
  composite difference density maps e and f highlight the 
  contribution of troponin ( magenta ) and tropomyosin ( yellow ) 
  related by a 90 rotation about the filament axis . a comparison of the single particle based reconstruction and the helical 
  reconstruction calculated from the same data .
c 
  and i , are shown as wire meshes with atomic f - actin models docked . 
 
d , e , f , and j , surface - rendered difference maps . d 
  and j , are obtained by subtracting f - actin models from the single 
  particle and helical reconstructions , respectively .
e and f , 
  are composite difference maps which display the difference density calculated 
  by subtracting an f - actin model with docked tropomyosin from the single 
  particle reconstruction and the difference density displayed in d. 
  extra mass in the central region of the single particle reconstruction 
  ( a and c ) surrounds the central actin subunits whereas the 
  helical reconstruction ( g and i ) gives a much tighter fit to 
  the crystal structure .
two actin subunits are encircled in white in each 
  surface - rendered representation ( a and g ) .
the incorrect fit 
  of the inverted f - actin model would give rise to the assignment of actin 
  subunits illustrated in the pink outline ( a and g ) .
the 
  crossover point of the two long pitch actin strands ( arrowed ) , a 
  slight gap surrounded by four high density bright regions ( blue ) and 
  bands of density running diagonally out from the center of the filament 
  ( red ) are visible in the two - dimensional projections of both the 
  single particle and helical reconstructions ( b and h ) .
these 
  features confirm the polarity inferred from fitting of the f - actin model .
the 
  difference density maps d and j calculated from single 
  particle and helical reconstructions respectfully highlight the non - actin 
  density ( orange ) .
this density attributable to tropomyosin and 
  troponin is highly asymmetric in the single particle reconstruction .
the 
  composite difference density maps e and f highlight the 
  contribution of troponin ( magenta ) and tropomyosin ( yellow ) 
  related by a 90 rotation about the filament axis .
agreement with actin  to interpret the structure at a 
  molecular level an f - actin atomic model was computationally docked into the 
  three - dimensional density ( fig . 
 
the 
  docking programs situs ( 30 ) 
  and uro ( 31 ) were both used to 
  evaluate different orientations of this high resolution filamentous model into 
  the low resolution em map .
the best fit recovered in each case was virtually 
  identical , indicating a single solution .
the only alternative fits were 
  discrete subunit translations along the short pitch filament helix . in no case 
  was there a reversal of polarity . as a test
, docking was repeated after 
  rotating the f - actin model by 180 perpendicular to the filament axis . 
 
although neither software package managed to invert the f - actin model , the 
  calculated fit for the inverted model is inconsistent with the 
  three - dimensional reconstruction : empty regions in the three - dimensional 
  reconstruction are filled by density from the model and vice versa . 
 
moreover the actin interstrand gap of the model structure was placed inside 
  the actin subunit density of the three - dimensional reconstruction , and the 
  actin subunit density of the model bridged the interstrand gap of the 
  three - dimensional reconstruction ( figs . 
 
these conclusions 
  are strongly supported by comparing the correlation coefficients of the masked 
  fits for the best orientation ( 0.92 ) with that for the inverted orientation 
  ( 0.68 ) .
thus we can be confident in rejecting this alternative orientation of 
  the actin backbone . by viewing the computed fit in stereo
the agreement 
  between the atomic model and our structure is clear as anticipated from the 
  strong correlation between the fitted model and the data .
additionally the 
  bi - lobed appearance of the subunits corresponds directly to the cleft between 
  subdomains 3&4 and 1&2 of the actin subunit 
  ( fig .
further evidence 
  for the polarity assignment in our single particle reconstruction was obtained 
  from a helical reconstruction of the thin filament data .
fourier bessel 
  helical reconstruction ( 41 ) 
  using 13/6 helical symmetry was applied to twelve selected straightened thin 
  filament images .
the relative polarity of each straightened filament was 
  identified . within the helical reconstruction the characteristic asymmetric 
  actin monomer shape , subunit cleft and interstrand gap
the difference between the helical and single particle 
  reconstruction is readily apparent , namely , the substantial extra density 
  halfway along the single particle reconstruction 
  ( fig .
2 , a and 
  c ) , which we attribute to troponin . the same atomic 
  coordinate f - actin structure was docked into both the helical 
  ( fig .
the f - actin fit to the single particle and helical 
  reconstructions are virtually identical with the asymmetric shape of the actin 
  subunit clearly identified in both maps 
  ( fig .
it is 
  necessary to orient the three - dimensional reconstruction in this frame of 
  reference to fully evaluate the biological significance of our results .
the 
  polarity of actin and the thin filament is often described by the 
  directionality and arrow shape that the myosin heads provide with the barbed 
  end of the filament situated at the z - band of the sarcomere .
this convention 
  has been used in figs . 2 , 
  3 , 
  4 .
the order 
  of three distinct features of the filament detailed below characterizes the 
  polarity of the underlying actin , as outlined in previous studies 
  ( 42 ) .
viewing an actin model 
  filtered to 35  in a similar manner highlights the agreement between 
  the atomic coordinates and the two - dimensional projections calculated from our 
  helical reconstruction and the single particle full and half - data set 
  reconstructions ( supplemental fig .
subdomains 1 and 3 form a band of density running 
  diagonally out from the center of the filament . if lines are drawn 
  highlighting these subdomains , a mini arrow - like pattern is seen .
it is noted 
  that this is in the opposite direction to the arrow - like pattern seen when 
  myosin subfragment-1 heads label actin .
two other strong features are visible 
  in projection , the crossover point of the two long pitch strands and a slight 
  gap between the strands .
the crossover is the narrowest point of the projected 
  image and is a high density bright area .
the gap is surrounded by four 
  subunits viewed from the side which results in four small high density bright 
  regions .
2 , b and 
  h ) support the orientation of the docked f - actin model in 
  both of the three - dimensional reconstructions , allowing us to unambiguously 
  determine the polarity of the data , in each case . figure 3.filament width .
b , plot displaying the diameter of the 
  filament against distance along the filament axis .
the widest point of the 
  filament is in the center of the segment ( i = 141  ) the 
  density begins to taper as toward the pointed end of the filament ( ii 
  = 115  ) .
b , plot displaying the diameter of the 
  filament against distance along the filament axis .
the widest point of the 
  filament is in the center of the segment ( i = 141  ) the 
  density begins to taper as toward the pointed end of the filament ( ii 
  = 115  ) .
the 
  docked atomic co - ordinates of f - actin and f - actin with tropomyosin were used 
  to create an electron density models .
the f - actin model was then subtracted 
  from the three - dimensional reconstruction to create a difference map which 
  highlights all non - actin density ( fig . 
 
the equivalent difference density map 
  was calculated between the helical reconstruction and the docked actin model 
  ( fig .
a second 
  difference map was calculated using the f - actin tropomyosin density model 
  subtracted from the single particle reconstruction .
the density in the 
  reconstruction with no counterpart in actin or tropomyosin is highlighted : 
  this density can be assigned to troponin .
2 , e and 
  f. in the single particle reconstruction two bulbous areas of density label 
  each strand of actin with a 27.5  axial stagger .
this appearance is 
  similar to the shape of the two regions of density we see in the 
  reconstruction .
the observed density is located halfway along the filament and 
  tapers away toward the pointed end .
we interpret the shape of the complex to mean that 
  the globular part of troponin ( tni , tnc , and tnt2 ) is the extra mass in the 
  central region of the filament and the tapering density running up the 
  filament axis is the tail of troponin ( tnt1 ) .
tnt1 is the 
  ca - invariant anchor point of troponin onto the thin filament 
  through its binding of tropomyosin 
  ( 44 ) . in our interpretation
, 
  the tail of troponin runs toward the pointed end of the filament and is very 
  closely associated with tropomyosin . in the currently accepted model of the 
  thin filament the globular head is thought to bind closer to the pointed end 
  of the actin filament with the tail pointing toward the barbed / z - band end 
  ( 45 ) .
our present structural 
  analysis of the thin filament has resulted in a three - dimensional 
  reconstruction in which the natural interpretation of the observed troponin 
  density is that the polarity of the troponin complex is reversed with respect 
  to this accepted model .
difference density analysis : assignment of tropomyosin  in 
  addition to regions of bulbous density assigned to troponin , continuous 
  strands of density running diagonally up the filament in the cleft of the 
  actin subunit are visible in both the single particle and helical 
  reconstructions ( fig .
this density can be interpreted as tropomyosin and in 
  the helical reconstruction tropomyosin and a smeared out troponin .
tropomyosin 
  in both the helical and single particle reconstructions appears to have slight 
  swellings that repeat with the same repeat as the actin subunits .
we believe 
  that the swellings and the general appearance of tropomyosin is due to the 
  resolution of the maps . by docking the 7- crystal structure of 
  tropomyosin ( pdb code 1c1 g ) ( 2 ) 
  into these regions of density in the single particle map we have traced the 
  likely path of tropomyosin , which is seen to lie over subdomain 1 of actin . 
 
the average position of the docked tropomyosin in both the single particle and 
  helical maps agrees with the blocked or b - state described by refs . 
  9 , 
  10 .
troponin crystal structure orientation  a space - filling model 
  of the skeletal troponin crystal structure in a ca - free state 
  ( 4 ) was manually positioned in 
  the em density envelope .
the dimensions of the crystal structure 
  match the size of the extra density region that we have ascribed to the 
  globular head of the complex .
the -helical coiled - coil formed between 
  tni and tnt ( the it arm ) runs approximately parallel to the filament axis .
the 
  n - terminal lobe of tnc is located over subdomain 1 of actin , resulting in tni 
  96 and tni 117 being almost equidistant from actin 374 at 44  and 47 
   , respectively .
these are close to the distances ( based on fret 
  measurements ) used to create the published atomic model of the thin filament 
  ( 5 ) .
the inherent flexibility of 
  this disordered region allowed us to incorporate a rotation of 30 of 
  the n - terminal lobe relative to the rest of the crystal structure .
the actin atomic model 
  ( 38 ) has been docked into the 
  three - dimensional map ( c atoms in blue ) .
the orientation of 
  the map in c and f is consistent with 
  fig .
the 
  map has been rotated by -80 about the filament axis in a and 
  d and by -40 in b and e with respect to 
  original position shown in c and f. a 
c , space - filling 
  model of the partial troponin crystal structure 
  ( 4 ) ( displayed in 
  magenta , pdb code 1yv0 ) , and the tropomyosin crystal structure 
  ( 2 ) ( displayed in 
  yellow , pdb code 1c1 g ) are docked into the electron density envelope . 
 
d  f , troponin and tropomyosin displayed as a ribbon 
  diagram : the three troponin components are displayed in different colors 
  tnc , green ; tnt2 , pink ; and tni , cyan .
unassigned 
  density ( yellow arrows ) running alongside tropomyosin can be seen in 
  b and e. docking of troponin and tropomyosin structures .
the actin atomic model 
  ( 38 ) has been docked into the 
  three - dimensional map ( c atoms in blue ) .
the orientation of 
  the map in c and f is consistent with 
  fig .
the 
  map has been rotated by -80 about the filament axis in a and 
  d and by -40 in b and e with respect to 
  original position shown in c and f. a 
c , space - filling 
  model of the partial troponin crystal structure 
  ( 4 ) ( displayed in 
  magenta , pdb code 1yv0 ) , and the tropomyosin crystal structure 
  ( 2 ) ( displayed in 
  yellow , pdb code 1c1 g ) are docked into the electron density envelope . 
 
d  f , troponin and tropomyosin displayed as a ribbon 
  diagram : the three troponin components are displayed in different colors 
  tnc , green ; tnt2 , pink ; and tni , cyan .
unassigned 
  density ( yellow arrows ) running alongside tropomyosin can be seen in 
  b and e. the  core  structure 
  ( 4 ) contains 60% of the 
  mass of the troponin complex .
the missing regions include the c terminus of 
  tni ( residues 144181 ) and the whole of tnt1 ( residues 1159 of 
  tnt ) .
docking the core structure and the present difference density analysis 
  highlights areas that are not occupied .
4 , b and 
  e ) , lying alongside tropomyosin , is an obvious location 
  for tnt1 due to the ca invariant interactions known to occur 
  between these two proteins 
  ( 44 ) .
additional unoccupied 
  density appears to  arc  around the face of the actin subunit , 
  which we propose could be the location of the c terminus of tni also missing 
  from the crystallized core structure .
a connection between the two strands of 
  actin via the c terminus of tni has recently been reported 
  ( 46 ) .
we have used electron microscopy and single particle analysis to study the 
  structure of the native muscle thin filament .
the quality of imaging and 
  filament preservation means that regions of density corresponding to the 
  troponin complex were evident from the beginning of our analysis and used for 
  the accurate identification of filament segments centered on the troponin 
  density .
an adapted single particle method 
  ( 25 ) has been applied 
  successfully to reveal the location and shape of troponin in relaxed thin 
  filaments .
this work represents the first reference - free structural analysis 
  of the thin filament ( i.e. with no prior assumptions with respect to 
  the shape or location of troponin ) .
the actin backbone of the filament is well resolved in the single particle 
  three - dimensional reconstruction : docking the atomic model of f - actin into the 
  three - dimensional map emphasizes the agreement between the reconstruction and 
  the model .
the docked f - actin model and the docked tropomyosin crystal 
  structure were used to calculate a difference structure in which mass present 
  in the reconstruction with no counterpart in the f - actin or tropomyosin 
  density is evident ( fig .
2 , e and 
  f ) . the three - dimensional map and difference structure 
  reveal a significant accumulation of density halfway along the filament 
  attributable to the troponin complex .
the density assigned to individual 
  troponin complexes appears bulbous at the barbed end of the filament and 
  tapers along the filament toward the pointed end .
the exact stagger between pairs of troponin complexes was established to be 
  27.5  0.5  confirming the 1972 model proposed by ebashi 
  ( 1 ) .
this arrangement allows 
  the troponin and tropomyosin molecules to make equivalent interactions with 
  actin on both strands .
why this stagger is 27.5  as opposed to 
  alternatives such as a stagger of 3  27.5  is not yet clear .
one 
  possibility is that as the thin filament assembles the positions of the first 
  two troponin molecules on opposite strands may be related to pseudo 2-fold 
  interactions with z - band components . alternatively , binding of the first 
  troponin could make a local conformational change in the actin subunits , which 
  promotes the binding of the next troponin complex 27.5  away on the 
  opposite strand .
subsequent troponin complexes would label the filament at 
  this regular spacing and if binding occurred in the wrong place it might be 
  weak or may result in an unstable filament structure consequently unraveling 
  the filament .
the troponin complex is highly asymmetric and has a specific polarity when 
  bound to the thin filament .
the widely accepted orientation of troponin is 
  such that the rod - like tail of the complex is closer to the z - band than the 
  globular head .
docking the f - actin model allows us to 
  establish the orientation of our reconstruction .
however , this orientation 
  places the widest region of troponin closest to the z - band and troponin tapers 
  off in the direction of the m - band .
this suggests that the rod - like tail of 
  troponin , which we now know to consist mainly of tnt1 , is positioned closer to 
  the m - band than the z - band .
a similar interpretation of troponin polarity can 
  also be inferred from the shape of the thin filament in an electron tomogram 
  of fast frozen stretched rigor insect flight muscle fibers 
  ( 47 ) .
we consider below 
  whether this reverse polarity , as observed in our reconstruction , can be 
  reconciled with the earlier observations .
tropomodulin binds tropomyosin and caps the actin filament at the 
  m - band end ( 48 ) .
this 
  information combined with the identification of tropomodulin binding site at 
  the n - terminal region of tropomyosin provides a polarity for tropomyosin in 
  the thin filament ( 49 ) . 
 
evidence for two well - separated binding sites of troponin on tropomyosin is 
  also well documented .
the globular head region of troponin has been localized 
  to a region spanning residues 150180 of tropomyosin 
  ( 50 ) and in the vicinity of 
  cys-190 ( 51 , 
  52 ) .
the tail region of 
  troponin is known to bind to the c - terminal region of tropomyosin 
  ( 5052 ) . 
  however , there is no direct evidence from these studies showing whether the 
  tail of troponin binds in an anti - parallel or parallel manner to tropomyosin , 
  although the anti - parallel arrangement has generally been assumed 
  ( 7 ) .
individual troponin 
  subfragments were labeled ( 45 ) 
  with antibodies to tnt1 , t2 , c , and i in electron microscope images of 
  isolated assemblies containing i - bands and z - bands .
this gave rise to the idea 
  that tnt1 is closer to the z - band than tnt2 .
antibody striations are evident 
  in the micrographs . however , subsequent work with fab fragments disagreed with 
  the initial findings ( 43 ) . 
 
here it was reported that the staining of tnt1 and tnt2 is in the same 
  position and that possible discrepancies may be due to the size of the 
  antibody .
the estimated length of the troponin complex also increased 
  considerably from 10 nm to 26.5 nm over the period 19681988 .
the 
  initial length measurements were taken from paracrystal data 
  ( 53 , 
  54 ) and later direct 
  measurements were made on rotary shadowed samples 
  ( 7 , 
  43 ) .
this 2-fold increase in 
  length could result in a different interpretation of the early immunoelectron 
  microscopy data , and possibly a reversal in the orientation of troponin on the 
  actin filament .
the geometry of binding of tnt to troponin has been 
  investigated in double diamond co - crystals of tnt and tropomyosin 
  ( 55 , 
  56 ) . despite the relatively 
  similar appearance of the crystals ,
because the distance 
  between identical nodes of the crystal is 400  ( the length of 
  tropomyosin ) carr et al . 
 
( 56 ) concluded that 
  tropomyosin runs between these identical nodes : as previously observed in the 
  pure tropomyosin bailey crystals .
the n - terminal region of tnt was interpreted 
  as being located at the acute vertex of the double diamond which corresponded 
  with the c - terminal of tropomyosin .
the mutant tnt used by cabral - lily 
  ( 55 ) lacked the n - terminal 
  region . as a result
it was suggested that the c - terminal of tnt must bind at 
  the acute vertex of the diamond , and the n - terminal region of tnt extended 
  into the long - arm of the large diamond to the c - terminal of tropomyosin .
this 
  arrangement is possible if the head to tail overlap of two tropomyosin 
  molecules is placed in the middle of the long arm and not at the nodes of the 
  crystal as favored by carr et al . 
 
nevertheless the 
  polarity of tropomyosin in the double diamond co - crystals has not been 
  established directly , so the relative orientation of tnt and tropomyosin 
  can not be ascertained from these studies .
these apparent inconsistencies bring us to question the evidence behind the 
  previously accepted model of the thin filament leading us to propose a 
  reversed polarity of the troponin complex .
the reversed polarity would imply a 
  parallel arrangement for the interaction between tnt1 and tropomyosin in which 
  troponin would retain its established interaction with the c terminus of 
  tropomyosin while spanning the region between the n terminus and residue 190 
  of the adjacent tropomyosin molecule .
the importance of a reversal in polarity 
  would be paramount when considering the mechanism of regulation .
the 
  conformational changes that occur within troponin and the thin filament when 
  ca binds to tnc hold the key to understanding regulation of 
  muscle contraction . without locating directly the troponin subunits on actin 
  in both the high and low ca states
our novel analysis methods have resulted in two - dimensional class averages 
  and a three - dimensional reconstruction with clear contributions from troponin 
  and tropomyosin .
the region of density that we attribute to troponin in our 
  reconstruction is significantly larger and more continuous than the volume 
  indicated in the 2001 narita map 
  ( 22 ) .
their map could be 
  enclosed in a cylinder with a diameter of 120  , whereas the diameter of 
  the reconstruction presented here at its widest point is 141  .
a 
  model - based single particle approach was taken by pirani et al . in 
  2005
( 23 ) , and the final 
  three - dimensional map strongly resembles the initial model with an additional 
  area of density which was interpreted as the c terminus of tni .
although these 
  observations provide some support for their conclusion , it would be more 
  evident that model bias had been avoided if in each case ( many orientations of 
  the troponin complex were tested ) the same end result was obtained : this 
  apparently was not observed .
the differences between the image processing 
  methods used in our studies and previous analyses of the structure 
  ( 22 , 
  23 ) offer some explanation for 
  a number of the differences in our conclusions .
in particular the objective 
  reference - free alignment procedure used to obtain our first 
  reconstruction .
many issues remain unaddressed concerning the structure of the thin 
  filament . high resolution em structures of the filament at high and low 
  ca are necessary to allow accurate molecular models to be built . 
 
the existing crystal structures of troponin are incomplete and previous em 
  reconstructions have not identified the missing regions . the important role of 
  the 40% of troponin that remains un - crystallized is becoming apparent . as well 
  as the widely reported anchoring function of tnt1 , the activation of 
  actomyosin atpase activity is reported to be mediated by a direct interaction 
  between tnt1 , tropomyosin , and actin 
  ( 57 ) .
the number of mutations 
  in tnt1 identified as causing heart disease is also increasing 
  ( 58 ) .
we need to locate the 
  exact position of these mutations to begin to understand their 
  pathophysiology .
we have identified the likely path of the troponin tail in 
  our reconstruction . in
future work we aim to identify unambiguously the 
  position of tnt1 and all the components in the thin filament at the molecular 
  level .
 the troponin complex on the thin filament plays a crucial role in the 
  regulation of muscle contraction . however , the precise location of troponin 
  relative to actin and tropomyosin remains uncertain . 
 we have developed a 
  method of reconstructing thin filaments using single particle analysis that 
  does not impose the helical symmetry of actin and is independent of a starting 
  model . 
 we present a single particle three - dimensional reconstruction of the 
  thin filament . 
 atomic models of the f - actin filament were fitted into the 
  electron density maps and troponin and tropomyosin located . 
 the structure 
  provides evidence that the globular head region of troponin labels the two 
  strands of actin with a 27.5- axial stagger . 
 the density attributed to 
  troponin appears tapered with the widest point toward the barbed end . 
 this 
  leads us to interpret the polarity of the troponin complex in the thin 
  filament as reversed with respect to the widely accepted model . 
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
Supplementary Material