the contraction of cardiomyocytes has 
 been studied extensively 
 because it is crucial to proper heart function .
cross - bridges between 
 actin and myosin lead to force generation and subsequently contraction . 

one important regulatory protein in the thin filament complex is troponin 
 ( tn ) .
tn consists of three subunits : troponin c ( tnc ) , troponin i 
 ( tni ) , and troponin t ( tnt ) . upon binding 
 of the signaling ion , ca
, the n - terminal regulatory domain 
 of tnc undergoes a structural reorganization that initiates myofilament 
 contraction .
calcium binding to tnc exposes 
 a hydrophobic patch on tnc s surface that promotes its association 
 with the switch region of troponin i ( tni ) .
this in turn disturbs 
 the interaction of the tni inhibitory region with tropomyosin and 
 actin , hence relieving tni s inhibition of contractile activity .
therefore , ca - binding to the 89 residue n - terminal 
 regulatory domain of tnc presents a crucial step in a chain of events 
 leading to a contractile response . elucidating its structure and dynamics 
 is central to studies of the role of calcium in myofilament contraction .
a plethora of structural studies have been carried out to elucidate 
 the structure and function of the tnc regulatory domain of which nuclear 
 magnetic resonance ( nmr ) has been particularly popular .
three states have been identified that are considered to be important 
 intermediates in the myofilament contraction process : the free ( apo ) 
 state , the ca - bound state , and the ca - tni - switch - peptide - bound 
 state .
additionally , the structures of the tnc regulatory domain in 
 complex with small molecules and mutants 
 of tnc have been elucidated .
the regulatory domain , a highly -helical 
 molecule that constitutes the n - terminal half of the troponin c protein , 
 consists of five -helices ( n , a 
the 
 ef - hands , which are known to be metal - binding sites , are labeled sites 
 i and ii .
in contrast with the c - terminal 
 domain of tnc , which contains two high - affinity ca - binding 
 sites , the sites in the regulatory domain are of considerably lower 
 affinity .
interestingly , in cardiac tnc , site i is completely defunct 
 for calcium binding that is due to several amino acid substitutions 
 with respect to site i in skeletal tnc .
site ii , the low - affinity , ca - specific ca - binding site , is generally considered to be the only site directly 
 involved in calcium regulation of cardiac muscle contraction .
ca - binding to site ii of cardiac 
 tnc does not induce an opening transition akin to skeletal tnc but leaves the structure more or less unperturbed 
 in the closed conformation .
it is believed that 
 the tni switch peptide has to be present to stabilize the open conformation 
 of the ca - bound regulatory domain of cardiac tnc , suggesting that the open conformation may only be a transient state 
 that is sampled by tnc after ca - binding .
in addition 
 to the structural properties of tnc , its calcium exchange 
 kinetics have been the focus of much experimental investigation .
the calcium association rate to site ii of isolated 
 cardiac troponin c has been measured using stopped - flow techniques 
 to be very high .
similarly , stopped - flow techniquesand nmr spectroscopy were able to determine 
 ca - dissociation rates from site ii much faster than the 
 time scale of muscle relaxation .
although a wide variety of 
 experimental techniques have shed light 
 on the structure and function of tnc , atomistic level simulations 
 of tnc structure and dynamics in various states of calcium and tni 
 switch peptide association are necessary for understanding the binding 
 processes involved .
as elucidation of the dynamics of the tnc regulatory 
 domain in response to calcium binding is integral for estimating ca affinity , this work may also provide a platform for computationally 
 calculating association and dissociation rates . additionally , relaxed 
 complex scheme type approaches could 
 be used to generate actionable pharmaceutical leads by docking drug - like 
 small molecules into structurally representative snapshots from molecular 
 dynamics trajectories . in general , therapeutic strategies aim to improve 
 calcium affinity in compromised tissue by changing the thermodynamics 
 and kinetics of ca binding and tni association . in this 
 study , we use conventional and accelerated molecular dynamics ( md ) 
 to elucidate the dynamics of tnc with and without ca bound 
 as well as with the tni switch peptide bound .
comparison of molecular 
 dynamics trajectories with experimentally obtained order parameters is used as an assessment of how well the conformational 
 landscape conducive to ca binding is sampled .
we examine 
 tnc for its ability of binding ca and furthermore determine 
 the molecular contributions to ca binding kinetics .
the 
 results of these studies can provide a framework for understanding 
 impaired ca handling in tnc mutants and knowledge gained 
 from this study will guide the improvement of inotropic pharmaceuticals 
 that target tnc .
the apo system was 
 modeled based on model 13 from pdb entry 1spy ( 89 residues ) .
the ca - bound system was modeled based on model 14 
 from pdb entry 1ap4 ( 89 residues , ca - ion ) .
the ca - tni - bound system was modeled based on model 18 from pdb entry 1mxl ( 106 residues , ca - ion ) .
all systems were neutralized adding na counterions ( 1ap4 : 13 na , 1spy : 15 na , 1mxl : 11 na ) and solvated using a tip3p water box .
the fully solvated systems 
 contained 24  316 ( 1ap4 ) , 26  756 ( 1spy ) , and 25  994 ( 1mxl ) atoms , respectively . 

minimization using sander was performed 
 in two stages : 1000 steps of minimization of solvent and ions ( the 
 protein is restrained using a force constant of 500 kcal / mol /  ) , followed by a 2500 step minimization of the entire system . 
 a short initial 20 ps md simulation with weak restraints ( 10 kcal / mol /  ) on the protein residues was used to heat up the system to 
 a temperature of 300 k. both 
 cmd and amd simulations were performed under the npt ensemble at 300 
 k for all three tnc systems using amber and the ff99sb force field .
periodic 
 boundary conditions were used , along with a nonbonded interaction 
 cutoff of 10  .
bonds involving hydrogen atoms were constrained 
 using the shake algorithm , allowing for 
 a time step of 2 fs . for each system ,
100 ns md trajectories were 
 generated ( for the ca - bound system md a trajectory of 
 even 150 ns ) as well as 50 ns amd trajectories at four different acceleration 
 levels .
acceleration parameters were determined based on average potential 
 and dihedral energies of the equilibrated md simulations .
dual boost 
 amd ( both the dihedral energy and the total potential energy are boosted ) 
 was used .
the acceleration level is defined in terms of eb and  , where eb is 
 the threshold boost energy and  is a tuning parameter that 
 determines the shape of the accelerated potential .
on the basis of a comparative analysis of previous successful 
 amd studies on a variety of systems of different sizes , the optimal 
 boost energy for the torsional amd is usually found to be the average 
 dihedral angle energy plus 3.5 times the number of residues in the 
 solute , and  should be 20% of eb .
similarly the acceleration parameters for the acceleration 
 of the total potential energy are dependent on the number of atoms 
 in the entire simulation cell . for the amd simulations , 
 a new in - house version of pmeamd
the frames were aligned using all c atoms 
 in the protein and subsequently clustered by rmsd using gromos++ conformational 
 clustering .
an rmsd cutoff of 1.6  
 ( 1ap4 ) , 1.7 
  ( 1spy ) and 1.8  ( 1mxl ) was chosen , respectively .
these cutoffs resulted in 7 ( 1ap4 ) , 9 ( 1spy ) , and 8 ( 1mxl ) clusters that represented 
 at least 90% of the respective trajectories .
the central members of 
 each of these clusters were chosen to represent the protein conformations 
 within the cluster and thereby the conformations sampled by the trajectory .
the principal component 
 analysis ( pca ) was performed using the bio3d package in r. a blast profile of the 1ap4 sequence revealed 
 1056 hits . out of the 35 most similar hits ,
29 hits were chosen ( excluding 
 structures with mutations and the recently crystallized cadmium coordinating 
 structure ) , and their experimentally 
 determined structures were obtained from the protein data bank .
the 
 29 structures underwent iterative rounds of structural superposition 
 to determine the invariant core of the protein , a region that exhibits 
 the least structural variance between the protein structures .
subsequently , 
 the experimental structures were superimposed onto this core , and 
 a pca was employed . in this process , a covariance 
 matrix from the coordinates of the superimposed structures is diagonalized . 

the eigenvectors of this matrix represent the principal components 
 of the system ( parts of the structure within which there is the most 
 variety among the set of superimposed experimental structures ) , whereas 
 the eigenvalues are a measure of the variance within the distribution 
 along the respective eigenvectors .
all experimental structures have 
 been projected into the space spanned by principal components one 
 and two ( along which there is the most variance among the structures ) . 

the principal component space generated based on the similar experimental 
 structures served as basis for projection of the molecular dynamics 
 trajectories . for the analysis of interhelical angles , interhelical 
 angles
on the basis of the md 
 trajectory of the ca - bound system ( 1ap4 ) , chemical shifts 
 for the amide h and the amide n were calculated 
 using the shiftx software .
protein structures 
 were extracted from the trajectory every 20 ps . for each of these 
 structures chemical shifts were calculated and averaged .
backbone 
 n  h order parameters were calculated from the 100 ns molecular 
 dynamics simulation of the apo system ( 1spy ) using the isotropic reorientational 
 eigenmode dynamics ( ired ) approach .
order 
 parameters were calculated by averaging 0.5 ns trajectory windows 
 to ensure that the calculated s parameters 
 do not contain any motions whose time scale exceeds the overall tumbling 
 correlation time of the protein .
the 
 ptraj program was used to generate a list of eigenvalues and eigenvectors 
 from all of the n 
h backbone vectors with the ired method . 
 on the basis of these lists ,
pqr 
 files for representative protein structures determined by a cluster 
 analysis were generated using pdb2pqr .
the calcium pqr file was generated using a charge of + 2 and an ionic 
 radius of 1.14  .
apbs was used 
 to generate the electrostatic fields for the protein and the calcium 
 ion in opendx format .
bd_top was used to generate all necessary input 
 files for the browndye runs . a phantom atom of zero charge and negative 
 radius ( 1.14  )
the phantom atom was placed at the position of the calcium 
 ion from the trajectory frame .
it has no influence on the association 
 rate constant calculation and serves solely to be able to define a 
 reaction criterion that is spherically symmetric around the expected 
 binding position of the calcium .
the reaction criterion was chosen 
 to be 1.2  within the calcium binding site .
we performed 500  000 
 single trajectory simulations on 8 parallel processors using nam_simulation . 

the reaction rate constants were calculated using compute_rate_constant 
 from the browndye package . a weighted average of the rate constants 
 of each of the representative cluster centers yielded an estimate 
 of the overall rate constant for the system .
pca 
 characterizes collective , high - amplitude structural variations based 
 on a set of homologous protein structures .
the predominant modes provide 
 a basis for analyzing large - scale conformational changes anticipated 
 in md simulations . in this study ,
nmr structures of apo - tnc , ca - bound tnc , ca / tni - bound tnc , and tnc in complex 
 with compounds such as bepridil , w7 , and dfbp were used as inputs 
 for pca .
the first two principal components , pc1 and pc2 , are illustrated 
 in figure 1and account for 50.9 and 13.5% , 
 respectively , of the variance associated with known tnc structures . 

as the two components together account for 64.4% of the variance , 
 it was considered to be appropriate to analyze the simulations just 
 in terms of these components .
pc3 accounts for another 10.4% of the 
 variance but was not used for analysis because of its relatively low 
 contribution .
the quadrants along pc1 and pc2 describe apo and ca - bound tnc structures ( lower right , e.g. , 1spy , 1ap4 ) and ca - tni - bound tnc structures ( left side , e.g. , 1mxl , 2l1r ) .
pca plot comparing cmd 
 and amd trajectory sampling for the ca - bound system . 

the principal component space generated by 
 known structures of tnc is shown along with molecular dynamics trajectories 
 that are projected into the first versus second principal component 
 space of known tnc structures .
the nmr structures of 1ap4 , 1spy , and 1mxl are shown as filled 
 green , red , and blue circles , respectively .
( b ) projection of the 1ap4 cmd trajectory ( full 
 blue circles ) into the pc space is shown in density coloring where 
 darker shades of blue indicate the more heavily sampled parts of the 
 trajectory .
( c ) projection of the 1ap4 amd trajectory ( full blue circles ) into 
 the pc space is shown in density coloring .
( d ) projections of the 1ap4 cmd trajectory ( full 
 red circles ) and the 1ap4 amd trajectory ( full blue circles ) into the pc space are shown in 
 density coloring , where darker shades of red and blue indicate the 
 more heavily sampled parts of the trajectories .
complete 
 overlap of most heavily sampled regions for the amd trajectory with 
 the cmd trajectory suggests that cmd samples most of the statistically 
 relevant conformations for this system .
pc1 corresponds to a concerted 
 motion of helices b and c opening up the structure and changing the 
 a / b interhelical angle .
it appears that the motion connected to pc1 
 is primarily connected to an opening motion that presents the hydrophobic 
 patch comprising the tnc / tni interface .
the motion associated 
 with pc2 whose amplitude is considerably smaller than that of pc1 
 pulls away helices b and c from helix a. together with the motion 
 represented by pc1 this motion seems to expose the hydrophobic patch 
 even further .
motions associated with first two principal components . 
 a principal 
 component analysis of the conventional md trajectory of the calcium 
 bound tnc regulatory domain ( 1ap4 ) was performed .
the range of motions associated with 
 pc1 ( a ) and pc2 ( b ) is shown as the overlay of two structures .
the 
 biggest difference between pc1 and pc2 is apparent in the movement 
 of helix b. in the motion associated with pc1 , helix b slides with 
 respect to helix a , whereas it is tilted toward helix a in the motion 
 associated with pc2 .
pca gives information about both the main internal 
 protein motions 
 during molecular dynamics simulations as well as about the overall 
 structural space sampled by the simulations .
for all three troponin 
 c systems ( apo , ca - bound , and ca - tni - bound ) , 
 at least 100 ns of conventional md ( cmd ) as well as 50 ns of accelerated 
 md ( amd ) were performed .
prior studies have demonstrated 
 that predominant pca modes are related to low - frequency collective 
 motions ; therefore , we project these data along the pc modes 1 and 
 2 .
figure 1 shows the projection of the 1ap4 cmd and amd trajectories 
 into pc space as well as an overlay of the two .
cmd and amd share 
 the same peak density location at about ( 25  , 5  )
. 
 this minimum coincides with projection of the 1ap4 and 1spy crystal structures , 
 suggesting a significant energetic barrier to sampling the tni - bound 
 state .
the amd trajectory uncovers several regions of intermediate 
 density , most notably a possible secondary minimum around ( 25  , 
 0  ) , thus indicating its efficacy in traversing moderate conformational 
 barriers . in the amd simulation
, we also note a greater sampling of 
 the pc2 conformational motion toward the ca - tni - bound 
 state at about ( 10  , 5  ) .
this suggests that the 
 ca - bound form approaches tni - compatible states in the 
 absence of tni , although there is a risk that the modified potential 
 inherent to amd samples improbable reaction pathways .
whereas cmd 
 samples a lesser extent compared with amd , the vast majority of the 
 sampled population is located within the region of pc space sampled 
 by cmd centered at ( 25  , 5  ) .
additionally 
 the root - mean - square fluctuations ( rmsfs ) were compared 
 between the cmd and amd simulations .
the general trend for both cases 
 is identical in that the most flexible residues are in the n - terminal 
 and c - terminal regions of the protein ( residues 14 , 8789 ) 
 corresponding to flexible loops at the termini .
the most flexible 
 region within the protein is the dysfunctional ca binding 
 site i ( residues 2837 ) . in the cmd simulations , rmsf values 
 for residues 5070 ( including the ca binding site 

ii ) are slightly more flexible ( rmsf  1.5  ) than the 
 background at 1  .
while leaving the general trend unchanged , 
 the amd simulations increase the background rmsf level slightly ( to 
 1.5  ) and show slightly larger rmsf values for residues 
 5070 , which also include the ca binding site 
 ii .
later , we demonstrate that cmd - sampled states capture the dynamics observed in nmr chemical shift and order parameters .
therefore , we expect that cmd is sufficient for generating thermodynamically relevant 
 information , whereas amd may be required for assessing transient states 
 leading to binding of tni or other small molecule ligands .
pca can be used to 
 compare the different simulated systems ( apo , ca - bound , 
 and ca - tni - bound ) in terms of collective motions bridging 
 the different states . to compare the dynamics of the three systems 
 under investigation
, we plotted the projection of the cmd and amd 
 trajectories into the principal component space . in the cmd simulations , 
 the structures and dynamics of the apo ( 1spy ) and
ca - bound ( 1ap4 ) systems are very 
 similar , as seen by their virtually overlapping projections into pc 
 space ( figure 3 ) .
the amd simulations , however , 
 reveal subtle yet significant differences in the dynamics of the apo 
 and ca - bound forms .
the area sampled in pc space is larger 
 for the ca - bound system .
the simulations of the ca - tni - bound system ( 1mxl ) predominantly sample a different section of the principal 
 component space generated based on known structures of tnc .
these 
 motions are indicative of the open conformation of tnc , facilitated by the binding of tni .
( see figure 3 . ) in particular , residues 3650 are nearly rigid in 
 the tni - free simulation ( rmsf of 1  ) but become highly 
 mobile in the presence of tni with rmsf values ranging between 1.5 
 and 2.5  .
this suggests that the tni - bound structure exists 
 in an energy well that is distinct from the apo and ca - bound forms of tnc .
given that these dynamics were not even observed 
 with amd sampling , we speculate that there is a high energy barrier 
 between the apo and ca - bound states on the one side and 
 tni - bound states on the other .
pca plot comparing conformational dynamics 
 sampling between the 
 apo , ca - bound and ca - tni - bound system .
the 
 principal component space generated by known structures of tnc is 
 shown along with molecular dynamics trajectories that are projected 
 into the first versus second principal component space of known tnc 
 structures .
the nmr structures of 1ap4 , 1spy , and 1mxl are shown as filled green , red , and blue circles , respectively . 

( b ) projections of the ca - bound tnc for the 1ap4 cmd trajectory ( full 
 blue circles ) , the 1spy cmd trajectory ( full red circles ) , and the 1mxl cmd trajectory ( full 
 green circles ) into the pc space are shown in density coloring , where 
 darker shades of blue , red , and green indicate the more heavily sampled 
 parts of the trajectories . ( c )
projections of the ca - bound 
 tnc for the 1ap4 amd trajectory ( full blue circles ) , the 1spy amd trajectory ( full red circles ) , and 
 the 1mxl amd 
 trajectory ( full green circles ) into the pc space are shown in density 
 coloring , where darker shades of blue , red , and green indicate the 
 more heavily sampled parts of the trajectories .
for the conventional 
 molecular dynamics simulations , the principal component space sampled 
 by the apo and ca - bound systems is almost identical indicating 
 similar dynamics . in the amd simulations , however ,
occasional excursions 
 of the ca - bound system into ca - tni - bound - like 
 states are observed .
the ca - tni - bound system , however , 
 samples a different , hardly overlapping region of the pc space , suggesting 
 a change in dynamics upon tni binding .
additionally , to investigate more closely the opening 
 transition 
 believed to be crucial to tni binding , the interhelical angle analysis 
 was performed .
plotting the a / b angle over the course of the simulations 
 has the potential of identifying transitions between open and closed 
 states as well as possibly making a statement about the time scale 
 of helical motions connecting the states . the concerted motion of 
 helices b and c away from helix a presents the most notable structural 
 change involved in exposing the hydrophobic spot on the tnc surface 
 that facilitates tni binding .
therefore , the interhelical a / b angle 
 has been reported as a good indicator of the degree of opening in 
 the tnc protein , with angles around 135 
 corresponding to a closed conformation and angles around 90100 
 characterizing the open conformation .
this is corroborated by comparing the interhelical 
 angle measurements over the course of the cmd simulations ( figure 5 ) .
the interhelical a / b angles fluctuate around 
 an average of 135 for both the apo and ca - bound system and range from 115 to 150. no opening 
 transitions are seen .
the amd simulations , however , reveal subtle 
 yet significant differences in the dynamics of the apo and ca - bound forms .
the area sampled in pc space is larger for 
 the ca - bound system , corresponding to the apo and the 
 ca - bound structures sampling a wider range of angles . 

the most open conformation seen for the apo system still has an angle 
 of 105 , which is inconsistent with a full opening transition , 
 yet there are several structures in the ca - bound simulation 
 where the interhelical a / b angle is very close to the 90 
 of the open conformation .
( see figure 4c . ) 
 this , in agreement with ref ( 2 ) , suggests that binding of calcium subtly changes the dynamics 
 of the system , allowing for opening transitions that are not seen 
 in the apo form .
despite the fact that due to the acceleration we may underestimate 
 the duration the system spends in the open state , this corroborates 
 the notion of the open state being a nonstable transient one that 
 has to be stabilized by the presence of the tni switch peptide .
these results , to the best of our knowledge , are the first time 
 that an opening transition for cardiac tnc has been observed in a 
 molecular dynamics simulation .
it is worth noting that the opening 
 transition is also observed in the pca analysis .
as previously noted , 
 pc 1 corresponds to the motion associated with opening . in the projection 
 of the amd trajectory into pc space ( figure 1c ) , there are multiple structures observed around ( 5  , 
 25  ) , which come very close to the open conformation 
 ( 10  , 5  ) along pc1 , indicating a decreased a / b 
 interhelical angle
. these structures are not present in the projection 
 of the cmd trajectory ( figure 1b ) .
( a ) nmr structure 
 of ca - bound tnc ( 1ap4 ) , ( b ) nmr structure of ca - tni - bound tnc 
 ( 1mxl ) , and 
 ( c ) structure of frame 9840 of the 1ap4 amd simulation are shown .
for the purpose 
 of clarity , the tni switch peptide has been removed from panel b. 
 for all panels , the helix assignment in the regulatory domain of cardiac 
 tnc is shown .
the most n - terminal helix is denoted by n , followed 
 by helices a through d. the interhelical angle between helices a and 
 b is used to measure the degree of openness of the domain . ( a ) ca - bound nmr structure is in the closed state with an a / b interhelical 
 angle of around 135. ( b ) ca - tni - bound nmr structure 
 is in the open state with an a / b interhelical angle of around 90. 
 ( c ) frame 9840 corresponds to the most open conformation sampled during 
 the 1ap4 amd 
 simulation .
the molecule adopts the open conformation with an a / b 
 interhelical angle of 93. evolution of a / b interhelical angle over the course of 
 the simulations . 

the interhelical angle between helices a and b has been calculated 
 for every frame of the tnc simulations . results for the apo cmd simulation 
 ( a ) , the apo amd simulation ( b ) , the ca - bound cmd simulation 
 ( c ) , and the ca - bound amd simulation ( d ) are shown .
the most open conformation ( a / b interhelical angle 93 ) observed 
 in the simulations is labeled with a black circle in panel d. furthermore , a cross - correlation analysis was performed 
 to elucidate 
 intramolecular fluctuations unique to each state .
the cross - correlation 
 analysis of the trajectories ( figure 6 ) revealed 
 positive correlated motion in the strands of the central -sheet 
 ( c35-s37 , t71-d73 ) linking both ef - hands in the apo simulations and 
 the cmd ca - bound simulation , as previously reported in 
 ref ( 44 ) .
this positive 
 correlation is reversed into a negative correlation in the ca - bound amd simulation ( figure 6d ) . 
 whereas this was not observed in ref ( 44 ) , we believe that the relatively short simulation 
 time ( 6 ns ) would not capture longer - time scale motions that could 
 contribute to anticorrelated motions . therefore , we speculate that 
 the disruption of the correlated motion in the -sheet corresponds 
 to helix b pivoting away from helix a as part of an opening event . 

another region of correlated motion that is consistently present in 
 most simulations is the interface between helices n and d. this suggests 
 the presence of strong hydrophobic contacts between the helices possibly 
 stabilizing the fold . on the basis of the simulation results , it is 
 hard to speculate on the time scale of the opening / closing transition , 
 but it is very likely to be well beyond the 100 ns mark .
future work 
 will focus on running longer cmd simulations that reveal several opening / closing 
 transitions and allow for an estimation of the [ open]/[closed ] equilibrium 
 and a free energy difference of the transition .
c-residue 
 cross correlation plots for the ( a ) 
 apo cmd , ( b ) apo amd , ( c ) ca - bound cmd , and ( d ) ca - bound amd simulations .
green regions mark areas of positive 
 cross correlation while red regions specify areas of negative cross 
 correlation .
chemical shifts derived 
 from nmr data describe the local electronic environment about labeled 
 nuclei and serve as a structure determination tool . in this experiment , we predicted chemical shifts from the 
 md trajectories to demonstrate that states analogous to those observed 
 in solution nmr are sampled . to this end
, amide h and n chemical shifts were calculated from the cmd trajectory 
 for the ca - bound tnc system , which are compared with 
 chemical shifts obtained by nmr spectroscopy in figure 7 .
the calculated shifts show surprisingly 
 good agreement with experimental values , as the determined average 
 root - mean - square deviations between the calculated and experimental 
 chemical shifts are 0.4 ppm for the h shifts and 2.9 ppm 
 for the n shifts , compared with the precision of shiftx 
 of 0.49 ppm for amide h chemical shifts and 2.43 ppm for 
 amide n chemical shifts .
chemical shifts were calculated from the amd trajectory as well 
 and are only marginally better with average root - mean - square deviations 
 between the calculated amd and experimental chemical shifts of 0.5 
 ppm for the h shifts and 2.6 ppm for the n shifts .
it is not surprising that no substantial differences between 
 cmd and amd predicted chemical shifts is observed as the simulations 
 identify the same thermodynamically dominant regions on the potential 
 energy surface as demonstrated by pca .
additionally , the majority 
 of the slow time - scale dynamics observed in the simulations are concerned 
 with tertiary structure and not changes in the secondary structure . 

therefore , they may not be picked up by shiftx , an algorithm predominantly 
 based on local sequence and local secondary structure .
residue - by - residue 
 comparison of experimentally determined chemical shifts ( blue ) and 
 chemical shifts calculated from the cmd trajectory of the ca - bound tnc system ( red with error bars ) .
panel a shows the amide h chemical shifts alongside a ribbon representation of tnc , 
 where the residues for which the predicted h chemical 
 shifts deviate more than two standard deviations from the experimental 
 value are labeled in red .
panel b shows the amide n chemical 
 shifts alongside a ribbon representation of tnc where the residues 
 for which the predicted n chemical shifts deviate more 
 than two standard deviations from the experimental value are labeled 
 in red .
figure 7 also shows the 
 residues in the 
 protein for which the chemical shifts deviate the most from experiment . 

chemical shifts of two of the residues whose h and n chemical shifts deviate from experimental values ( 72 and 
 73 ) have been previously reported to be greatly impacted by calcium 
 binding both experimentally and using 
 quantum mechanical calculations . in general , whereas these sites are 
 distributed throughout the entire molecule , there is an increased 
 occurrence of incorrectly predicted shifts in the calcium binding 
 site ii and neighboring regions .
the deviation of the predicted chemical 
 shifts and experimental values can be attributed to a number of possible 
 causes .
it has been suggested that md - generated 
 structures typically give inferior shifts compared with those generated 
 from a molecular mechanics conformational search , even when using 
 quantum mechanical estimates of the nuclear magnetic shieldings .
therefore , 
 it is possible that these simulations still undersample the conformational 
 states contributing to the nmr observable .
more specifically , the 
 deviations close to the calcium binding site could be attributed to 
 shiftx not being well - parametrized for the prediction of metal binding 
 sites in general .
another possible source 
 of error is the use of nonpolarizable force fields in the simulations . 
 for highly charged interactions like the ones between calcium and 
 the negatively charged ef - hand residues , ignoring polarization effects 
 might introduce additional error .
use 
 of polarizable force fields in future calculations may recover some 
 of the error .
backbone order parameters were calculated from 
 the cmd trajectory 
 for the apo tnc system and compared with the experimentally determined 
 order parameters for the apo form of the regulatory domain of human 
 cardiac troponin c. figure 8 shows the overlay of the calculated and experimental order 
 parameters .
the regions of greatest flexibility ( lowest order parameters ) 
 are the two calcium binding loops , calcium binding sites i ( inactive ) 
 and ii ( low affinity binding site ) , as well as the n- and c - terminal 
 residues . the overall agreement of the calculated and experimental 
 data is good with an average deviation of less than 0.03 . in agreement 
 with previous experimental studies ,
the simulations 
 identify positions 26 ( corresponding to residues 6670 ) 
 in both sites i and ii as the most flexible residues of the protein . 

this is not surprising as these highly charged residues are very labile 
 in the absence of ca .
interestingly the most significant 
 deviations between prediction and experiment are residues 4249 
 ( corresponding to helix b ) , with a general trend of overestimating 
 order parameters ( i.e. , underestimating the dynamics ) .
future work 
 will focus on comparing order parameters calculated from longer simulations 
 to experimental values .
little overall changes can be observed when 
 comparing the calculated order parameters for the ca - bound 
 simulation with the apo simulation ( figure8b ) . in agreement with observations made in ref ( 48 ) ,
the order parameters 
 in the calcium binding site ii decrease , consistent with decreased 
 flexibility due to calcium binding .
h order parameters were calculated for the apo tnc 
 system and are compared with the experimentally determined nmr order 
 parameters .
calculated order parameters for all residues are shown 
 in red , whereas the experimentally determined parameters at 25 c 
 are shown in green .
agreement of calculated and experimental order parameters is particularly 
 striking in the n - terminal part of the protein including the inactive 
 ( around residue 30 ) calcium binding site .
( b ) comparison of calculated 
 order parameters for the apo ( blue ) and ca - bound ( purple ) 
 tnc system .
order parameters generally agree between the systems with 
 the exception of the calcium binding site ii .
the agreement of calculated and experimentally 
 observed chemical 
 shifts and order parameters indicates that the molecular dynamics 
 simulations did cover the relevant dynamics of the isolated protein 
 domain .
therefore , these results provide an important measure of confidence 
 that the dynamics seen in the calculations capture the predominant 
 dynamics of the protein and that other quantities calculated based 
 on the trajectories most likely represent thermodynamically relevant 
 measures as well .
brownian dynamics simulations have been used to estimate the association 
 rate constant for calcium binding to troponin c. for this , the cmd 
 trajectory for the ca - bound tnc system was clustered 
 by rmsd , and seven representative structures ( cluster centers ) that 
 represented more than 90% of the structures seen in the trajectory 
 were extracted .
we performed 500  000 single trajectory brownian 
 dynamics simulations for each of these representative structures . 

the average calcium association rate constant was determined to be 
 with 3.1  10 1/(ms ) .
diffusion - limited association 
 rates have been reported in the literature , for instance , ( 2 to 4 ) 
  10 1/(ms ) , 4  10 1/(ms ) , and 1.4  10 1/(ms ) .
the calculations based on brownian dynamics and the cmd 
 trajectories reproduce the experimentally observed rates well . to 
 investigate whether there was any variation of the association rate 
 over the course of the simulation , calcium association rates were 
 calculated for a structure extracted every 1.5 ns from the trajectory . 
 no appreciable variation in association rate between different structural 
 states
is observed , leading us to speculate that the binding site 
 always assumes on  open  conformation .
furthermore , in agreement with 
 trends reported by ref ( 18 ) , we observe that ln(kon ) decays linearly 
 with the root of ionic strength ( sqrt(i ) ) ( figure 9 ) .
these results underscore that 
 brownian dynamics simulations are an important and viable tool to 
 investigate the calcium association in troponin c. dependence of ionic strength 
 on calcium association rate .
the square 
 root of ionic strength is plotted versus the natural logarithm of 
 calcium association rate . a linear dependence can be observed .
 troponin c ( tnc ) is an important regulatory molecule 
 in cardiomyocytes . 
 
 calcium binding to site ii in tnc initiates a series of molecular 
 events that result in muscle contraction . 
 the most direct change upon 
 ca2 + binding is an opening motion of the molecule that 
 exposes a hydrophobic patch on the surface allowing for troponin i 
 to bind . 
 molecular dynamics simulations were used to elucidate the 
 dynamics of this crucial protein in three different states : apo , ca2 + -bound , and ca2 + -tni - bound . 
 dynamics between the 
 states are compared , and the ca2 + -bound system is investigated 
 for opening motions . 
 on the basis of the simulations , nmr chemical 
 shifts and order parameters are calculated and compared with experimental 
 observables . 
 agreement indicates that the simulations sample the relevant 
 dynamics of the system . 
 brownian dynamics simulations are used to 
 investigate the calcium association of tnc . 
 we find that calcium binding 
 gives rise to correlative motions involving the ef hand and collective 
 motions conducive of formation of the tni - binding interface . 
 we furthermore 
 indicate the essential role of electrostatic steering in facilitating 
 diffusion - limited binding of ca2 + . 
Introduction
Material and Methods
Results & Discussion