Probing the Flexibility of Tropomyosin and Its Binding to

1882 Biophysical Journal Volume 105 October 2013 1882–1892

Probing the Flexibility of Tropomyosin and Its Binding to FilamentousActin Using Molecular Dynamics Simulations

Wenjun Zheng,†* Bipasha Barua,‡ and Sarah E. Hitchcock-DeGregori‡†Department of Physics, University at Buffalo, Buffalo, New York; and ‡Department of Pathology and Laboratory Medicine, Robert WoodJohnson Medical School, Rutgers University, Piscataway, New Jersey

ABSTRACT Tropomyosin (Tm) is a coiled-coil protein that binds to filamentous actin (F-actin) and regulates its interactionswith actin-binding proteins like myosin by moving between three positions on F-actin (the blocked, closed, and open positions).To elucidate the molecular details of Tm flexibility in relation to its binding to F-actin, we conducted extensive moleculardynamics simulations for both Tm alone and Tm-F-actin complex in the presence of explicit solvent (total simulationtime >400 ns). Based on the simulations, we systematically analyzed the local flexibility of the Tm coiled coil using multipleparameters. We found a good correlation between the regions with high local flexibility and a number of destabilizing regionsin Tm, including six clusters of core alanines. Despite the stabilization by F-actin binding, the distribution of local flexibility inTm is largely unchanged in the absence and presence of F-actin. Our simulations showed variable fluctuations of individualTm periods from the closed position toward the open position. In addition, we performed Tm-F-actin binding calculations basedon the simulation trajectories, which support the importance of Tm flexibility to Tm-F-actin binding. We identified key residues ofTm involved in its dynamic interactions with F-actin, many of which have been found in recent mutational studies to be function-ally important, and the rest of which will make promising targets for future mutational experiments.

INTRODUCTION

Tropomyosin (Tm) is a prototype a-helical coiled coilcomprised of a sequence of heptad amino acid repeats(abcdefg)n, which is stabilized by hydrophobic core residuesat the a and d positions. However, the canonical hydropho-bic core residues of Tm are subject to irregular interruptionsby destabilizing residues (1), including six clusters of corealanines (so-called Ala clusters (1–3)), and other acidic res-idues (D137 and E218) and polar residues (such as Q263and Y267) (4). The functional role of these destabilizing res-idues has been under active investigation (5). Tm regulatesthe cooperative binding of myosin with filamentous actin(F-actin) in muscle, and the interactions of various actin-binding proteins with F-actin in nonmuscle cells (6). Tofulfill its regulatory function, Tm must adopt a superhelicalconformation to wrap around and bind to the F-actin helix.How Tm attains shape matching with F-actin remainscontroversial. In one view, Tm is preshaped semirigidly tomatch F-actin’s helical shape (7). In an alternative view,Tm may flexibly sample many conformations, some ofwhich match F-actin’s helical shape. A key source of flexi-bility is Tm’s noncanonical destabilizing regions, includingsix Ala clusters (1–3), where, it has been proposed (2,8),local axial staggering between two Tm chains induces localbending of Tm backbones. In addition, side-chain flexibilitymay result from poor packing in the destabilizing regions ofTm (9). In support of high flexibility in Tm, deviations fromthe canonical coiled-coil structure, such as local axial stag-gering and local bending, have been observed in several

Submitted May 2, 2013, and accepted for publication September 4, 2013.

*Correspondence: [email protected]

Editor: Enrique De La Cruz.

� 2013 by the Biophysical Society

0006-3495/13/10/1882/11 $2.00

x-ray structures of Tm fragments (2,4,8,10–12). However,the low-resolution electron microscopy (EM) studies ofthin filaments seem to favor the picture of a curved andsemirigid Tm that adopts three average azimuthal positions(i.e., blocked, closed, and open positions) on the surface ofF-actin (13–18).

Molecular dynamics (MD) is the method of choice forsimulating protein dynamics in the presence of water andions in atomic detail (19). MD simulation can, in principle,resolve the controversy over the role of Tm flexibility inTm-F-actin binding, thanks to its ability to simulate Tmdynamics and Tm-F-actin interactions under physiologicalconditions. MD may also allow detailed simulations ofeffects of mutations on Tm flexibility and binding to F-actin(such as mutations D137L (20), D175N, and E180G (21)).Compared with x-ray crystallography and EM, MD simula-tion is free from the influence of crystal packing and proteinmodifications in x-ray crystallography, and limited resolu-tion (>20 A) and loss of structural variations by helicalaveraging in EM reconstructions. However, for a large bio-molecular system like the Tm-F-actin complex with explicitsolvent, it remains unfeasible to perform MD simulationsfor more than tens of nanoseconds. Recently, an extendedbias-potential MD method named accelerated MD (aMD)(22) has been developed that can reach timescales >1000times greater than those accessible using standard MD(23). We have previously used aMD to observe an allosterictransition of the microsecond timescale in hemoglobin (24).

Previous MD studies by Lehman and co-workers (25–28)suggested that the average Tm conformation is preshapedfor binding F-actin and that Tm flexibility is highly delocal-ized. In particular, they found no significant correlation

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Molecular Dynamics Simulations of Tropomyosin 1883

between Ala clusters and regions with high flexibility (26).Although an all-atom model for the Tm-F-actin complexwas constructed and key Tm-F-actin interactions werepredicted based on that model (28), no extensive MD simu-lations of the dynamic interactions between Tm and F-actinhave been conducted, leaving key questions unanswered.How does F-actin binding affect the Tm flexibility? Howcorrelated are the Tm fluctuations over the surface of F-actininvolving seven quasiequivalent regions (i.e., periodsP1–P7)? How does Tm flexibility affect its binding toF-actin? How do seven Tm periods participate in F-actinbinding with different contributions (5,29)?

To address the above open questions and elucidate thestructural basis of Tm flexibility in relation to Tm-F-actinbinding, we conducted extensive MD/aMD simulations forboth Tm alone and Tm-F-actin complex in the presence ofexplicit solvent and ions. Our simulations are more exten-sive (total simulation time ¼ 440 ns) than previouslypublished MD studies of Tm dynamics (25–28). Based onthe MD/aMD simulations, we analyzed the local flexibilityof the Tm coiled coil using six parameters (see Methods).Contrary to previous MD studies (25–28), we found a clearcorrelation between the regions with high local flexibilityand a number of destabilizing regions of Tm, includingsix Ala clusters. Despite the stabilization by F-actin binding,the distribution of local flexibility in Tm is similar in theabsence and presence of F-actin. Our MD/aMD simulationsalso showed variable fluctuations of individual Tm periodsfrom the closed position toward the open position. In addi-tion, we performed Tm-F-actin binding calculations basedon the MD/aMD simulations, which approximately quantifythe contributions of electrostatic and nonpolar forces toTm-F-actin binding with residue-level details. Thanks toenhanced conformational sampling by aMD, we foundstronger Tm-F-actin binding based on the aMD simulationsthan on the MD simulations, which supports the importanceof Tm flexibility for Tm-F-actin binding. Finally, we identi-fied key residues of Tm involved in its dynamic interactionswith F-actin, many of which were found by recent muta-tional studies to be functionally important, and the rest ofwhich will make promising targets for future mutationalexperiments.

METHODS

System preparation and MD simulation

A model of full-length Tm in complex with a 15-actin filament was con-

structed by Li et al. (28) based on EM data. Starting from this initial model,

we prepared two systems—one for Tm alone (system 1) and the other for

Tm bound with F-actin (system 2). We also prepared another system

(system 3) for Tm alone based on a 7-A x-ray structure of full-length Tm

(PDB ID: 1c1g). The hydrogen atoms are added with the visual molecular

dynamics (VMD) program (30). All systems are immersed in a rectangular

box of water molecules extending up to 8–10 A from the proteins in each

direction using VMD. To ensure a physiological ionic concentration of

0.15 M and zero net charge, Naþ and Cl� ions are added to the systems

by VMD. After adding solvent and ions, systems 1, 2, and 3 have

517,452, 658,781, and 502,573 atoms, respectively.

The systems are refined with two rounds of energy minimization using

the steepest-descent method: first, a 5000-step energy minimization with

harmonic constraints (force constant ¼ 10 kcal/mol/A2) applied to all pro-

tein-backbone heavy atoms (N, Ca, and C), then a 5000-step energy mini-

mization with harmonic constraints (force constant ¼ 0.01 kcal/mol/A2)

applied to Ca atoms only. The systems are then heated to 300 K

over 300 ps by MD with harmonic constraints (force constant ¼0.01 kcal/mol/A2) applied to Ca atoms only. Then the systems are equili-

brated for 500 ps with MD performed in the NVT ensemble with the

same constraints applied in heating. Then the systems are subject to a

20-ns production run with MD performed in the NPT ensemble with

harmonic constraints (force constant ¼ 0.01 kcal/mol/A2) applied to the

Ca atoms of F-actin only. The Nose–Hoover method (31) is used with tem-

perature T ¼ 300 K and pressure P ¼ 1 atm. The periodic boundary condi-

tions are applied to the systems. A 10-A switching distance and a 12-A

cutoff distance are used for nonbonded interactions. The particle mesh

Ewald (PME) method (32) is used to calculate long-range electrostatic

interactions. The SHAKE algorithm (33) is used to constrain the bond

lengths of hydrogen-containing bonds, which allows a time step of 2 fs

for MD simulations. The atomic coordinates of the systems are saved every

2 ps during MD simulations for later analysis. The energy minimization and

MD simulation are carried out with the NAMD program version 2.9b2 (34)

using the CHARMM27 force field (35) and the TIP3P water model (36).

Four MD trajectories were generated for each of systems 1 and 3. Ten

MD trajectories were generated for system 2 to enhance the sampling for

a larger system.

Accelerated MD simulation

To enhance MD simulations of Tm flexibility, we used aMD (22) to simulate

Tm dynamics in the presence of F-actin. aMD accelerates slow conforma-

tional dynamics of proteins by adding a boost potential, DV ¼ ðE� VÞ2=½aþ ðE� VÞ�, to the dihedral potential, V, of the system (22). During an

aMD simulation, the boost potential is turned on if the dihedral potential

energy, V, falls below a threshold energy, E. Another parameter for the boost

potential is the acceleration factor, a, which determines the depth of the

dihedral potential basin below E. Following recommendations from previous

aMD studies (for example, see Pierce et al. (23)), we chose the aMD param-

eters as follows: E is set equal to the average dihedral potential energy

(31,781.6 kcal/mol), obtained froma classicalMDsimulation plus 4 kcal/mol

times the number of solute residues (6193), and a is then set to 1/5 of this

value. The above procedure has yielded E ¼ 56,553.6 kcal/mol and a ¼4954.4 kcal/mol. The NAMD implementation of aMD is used (37). Four

20-ns aMD trajectories were generated for system 2.

Local flexibility analysis of the Tm coiled-coil

In Tm, two a-helical chains (named A and B) form a coiled coil that

displays a seven-amino-acid long heptad periodicity (with seven positions

a-b-c-d-e-f-g). In the hydrophobic core of Tm, a d residue of chain A is

packed between two a residues of chain B (named a0 and a00) in a knob-

into-hole manner (see Fig. 1, inset). To characterize the backbone flexibility

of each d residue in local packing, we use three distances between the Ca

atomic positions of d, a0, and a00 residues (denoted as da0d, da00d, and d a0a00;

see Fig. 1, inset) to calculate the three parameters discussed below.

Dad ¼ ððda0d þ da}dÞÞ=2measures how closely the d residue of chain A is

packed between the a0 and a00 residues of chain B.

DAS ¼ ððd2a0d � d2a}dÞÞ=da0a} measures the axial displacement of the d res-

idue of chain A along the a0-a00 direction, where a large jDASj indicates alarge axial staggering (AS) of this d residue relative to chain B (see Brown

et al. (2)), and a positive/negativeDAS corresponds to an axial displacement

toward the C/N-terminus of Tm.

Biophysical Journal 105(8) 1882–1892

FIGURE 1 Results of local flexibility analysis of Tm in the absence of F-actin (system 1) using six parameters: Dad (a), D�ad (b), DAS (c), Dt (d), AS (e),

and diameter (f). For definitions of these parameters, see Methods. The average and SD of the above parameters as a function of the a and d residue positions

of Tm are shown as symbols ( ) and (X), respectively. The long vertical lines mark the center positions of six Ala clusters (A22, A78, A120, A155, A183, and

A239). The positions of individual core Ala residues are marked by short dashes. The calculations are based on the last 10 ns of four 20-ns MD trajectories of

system 1. (Inset) The hydrophobic interface between chains A and B of the Tm coiled coil is shown. Three core residues in each chain (at the a0, d, and a00

positions) are shown as spheres, and the distances between these residues (da0d , da}d , and da0a}) and the perpendicular distance,Dt, between the d residue and

line a0 -a} are shown by double-headed arrows. The two orthogonal motions (i.e., axial and lateral motion) of the d residue in chain A relative to chain B are

highlighted by two bold arrows. To see this figure in color, go online.

1884 Zheng et al.

Dt measures the perpendicular distance between the d residue of chain

A and the line a0-a00 (see Fig. 1, inset), which is related to the local diameter

of the Tm coiled coil (see Brown (38)).

To probe the side-chain flexibility of the d residue of chain A packed

between the a0 and a00 residues of chain B, we calculate D�ad ¼ ððd�a0dþ

d�a}dÞÞ=2 using the distances between the side-chain centroid positions of

d, a0, and a00 residues (denoted as d�a0d and d�a}d).In a similar way, the above parameters are defined for each a residue of

chain A packed between two adjacent d residues of chain B using the dis-

tances between the three residues.

To assess local bending of Tm based on 500 snapshots of the last 10 ns of

an MD/aMD trajectory, we define the bending angle, qb, at a given residue

position n as the angle between the two vectors ~rm nþ7 �~rmn and~rmn�~rm n�7, where ~rmn, ~rm n�7, and ~rm nþ7 are the Ca atomic positions of

residues n, n � 7, and n þ 7 in snapshot m. Then we average qb over 500

snapshots.

Tm-actin binding calculation

As in our previous papers (39,40), we calculate the Tm-actin binding free

energy DG (not including the entropy contribution) for each of the 5 actin

subunits interacting with periods P2–P6 of Tm (periods P1 and P7 are


excluded because they are in the overlap regions, which are not properly

modeled here). We extract 100 snapshots of the last 10 ns of each MD/

aMD trajectory for system 2 (after stripping all waters and ions), then calcu-

late DG for each snapshot and average DG over 100 snapshots. Following a

continuum solvent model (see Eriksson and Roux (41)), DG is expressed as

DG ¼ DGnp þ DGelec. Here the nonpolar contribution DGnp ¼ aEvdW is

empirically written as a fraction (a < 1) of the van der Waals (vdW) inter-

action energy, EvdW, between Tm and actin, and the electrostatic contribu-

tion DGelec ¼ bDEelec is empirically written as a fraction (b < 1) of the

change in electrostatic energy, DEelec, from unbound Tm and actin to

Tm-actin complex. Eelec is calculated using the Poisson-Boltzmann (PB)

method (42,43). a ¼ 0.158 and b ¼ 0.153 were obtained from the fitting

of kinesin-microtubule binding data (39). For the PB calculation (42,43),

a dielectric constant of εi ¼ 4 is used for the protein interior (44–47). A

dielectric constant of εe ¼ 80 is used for the exterior aqueous environment.

A probe radius of 1.4 A is used to define the molecular surface correspond-

ing to the dielectric boundary. The salt concentration is set to 0.12 M, which

approximately corresponds to a typical buffer condition of 100 mM KCl.

All the PB calculations are performed using the PBEQ module (43,48,49)

of CHARMM program (50). The atomic Born radii used here were previ-

ously calibrated in Nina et al. (49). Next, we used CHARMM to partition

DG, EvdW, and DEelec into contributions from individual Tm residues

(denoted as DGn, EvdW,n, and DEelec,n for residue n). We select a subset


of Tm residues with jDGnj greater than three times its average over all

residues, which are predicted to be important to actin-Tm binding.

RESULTS

MD and aMD simulations of Tm dynamics

To fully explore the dynamics of Tm, we constructed threesystems with explicit solvent and ions (systems 1 and 3 forTm alone using different initial models, and system 2 forTm bound with F-actin; see Methods) and then completedextensive MD and aMD simulations of Tm dynamics,resulting in the following 22 trajectories (total simulationtime ¼ 440 ns): eight 20-ns MD trajectories of Tm alone(systems 1 and 3), ten 20-ns MD trajectories of Tm boundwith F-actin (system 2), and four 20-ns aMD trajectoriesof Tm bound with F-actin (system 2). To our knowledge,this is the most extensive MD study of Tm dynamicsperformed to date. We used the principal componentanalysis to visualize and compare the regions of conforma-tional space sampled by these trajectories (see SupportingMaterial).

We analyzed the root mean-squared deviation (RMSD)relative to the initial model of Tm for each MD/aMD trajec-tory. Despite large fluctuations, most simulations reached astable state within <10 ns (see Fig. S1): the four MD trajec-tories for system 1 stabilize at RMSD 5–9 A (see Fig. S1 a),two out of four MD trajectories for system 3 stabilize atRMSD 4–6 A (see Fig. S1 b), ten MD trajectories for system2 stabilize at RMSD 2–5 A (see Fig. S1 c), and four aMDtrajectories for system 2 stabilize at RMSD 3–6 A (seeFig. S1 d). Based on the RMSD analysis, we selected andcombined the stable conformations visited by the last10 ns of all 20-ns MD/aMD trajectories to generate anextensively sampled structural ensemble for semiquantita-tive analysis of Tm flexibility and Tm-F-actin binding (seebelow). In particular, we analyzed the local flexibility ofTm in relation to its destabilizing regions (includingsix Ala clusters) and critically examined previous pro-posals on Tm flexibility based on x-ray structural data(2,4,8,12,38,51). To make sure the analysis results are insen-sitive to the truncation of trajectories, we repeated the anal-ysis for the last 5 ns of MD trajectories (see Fig. S3). Wealso verified that the analysis results are not affected bythe differences in initial model between systems 1 and 3(see Fig. S4).

Global flexibility analysis

To explore the global flexibility of Tm, we calculated theglobal root mean-squared fluctuation (RMSF) at every resi-due position of Tm based on the last 10 ns of each MD/aMDtrajectory (see Supporting Methods). Then we computed theaverage of the global RMSF over all Tm residues (denotedas hRMSFi) to assess the overall flexibility of Tm. In the

absence of F-actin, Tm is highly flexible in system 1(hRMSFi ¼ 2.47 5 0.17 A), and somewhat more flexiblein system 3 (hRMSFi ¼ 2.92 5 0.06 A) (see Table S1).When bound with F-actin, Tm is less flexible withhRMSFi ¼ 1.57 5 0.09 A during MD simulations and1.79 5 0.06 A during aMD simulations (see Table S1).The higher flexibility of Tm during aMD simulations canbe attributed to enhanced conformational sampling byaMD (23). We also calculated the local RMSF for individualTm periods to demonstrate that the local flexibility of Tm isadequately sampled, which allows a statistically meaningfulanalysis of the local flexibility of Tm (see SupportingMaterial for details).

Local flexibility analysis of the Tm coiled coil

Tm has six Ala clusters that replace canonical leucine orother large nonpolar residues at the hydrophobic interfacebetween the two chains of the Tm coiled coil (1–3). It wasproposed that the Ala clusters induce local axial staggeringbetween two Tm chains, which causes nearby regions of Tmto bend (2,8). However, a recent analysis of Tm x-ray struc-tures and MD trajectories did not find significant correlationbetween the Ala clusters and the regions with large axialdisplacement or local curvature (26). To shed light on thiscontroversy, we analyzed the local flexibility of Tm basedon extensive MD and aMD simulations of Tm dynamics.

To explore various aspects of local flexibility in Tm(including backbone and side-chain flexibility within andbetween two Tm chains), we calculated the following fourparameters at every a/d position of Tm (see Methods):Dad, measuring the closeness of Ca packing at the hydro-phobic interface of the Tm coiled coil; D�

ad, measuring thecloseness of side-chain packing at the hydrophobic interfaceof the Tm coiled coil; DAS, measuring the axial staggeringbetween two Tm chains; and Dt, measuring the lateralseparation between two Tm chains. Using these parameters,we can dissect local motions between two Tm chains interms of two orthogonal motions (see Fig. 1, inset)—anaxial motion parallel to the coiled-coil axis (affecting Dad

and DAS) and a lateral motion perpendicular to the coiled-coil axis (affecting Dad and Dt). We calculated both theaverage and the standard deviation (SD) of the above param-eters based on the last 10 ns of MD/aMD trajectories in theabsence or presence of F-actin.

Tm flexibility in the absence of F-actin

In the absence of F-actin, the average of Dad exhibits sixvalleys (i.e., local minima) corresponding to six Ala clus-ters (A18-A22-A25-K29-A32-S36, A74-A78-A81, A116-A120-S123, A151-A155-A158, A179-A183-S186, andA235-A239-A242; see Minakata et al. (4)) centered at sixcore Ala residues (A22, A78, A120, A155, A183, andA239) (see Fig. 1 a). This is consistent with the close pack-ing of the coiled coil near the Ala clusters due to the small


1886 Zheng et al.

size of Ala residues. To further validate these structural fea-tures, we calculated Dad for several high-resolution x-raystructures of Tm fragments (PDB IDs: 1ic2, 2efr, 2efs,2b9c, and 2d3e). We found similar valleys in Dad near thesix Ala clusters in these structures, although some of themare slightly shifted due to truncation and modification ofTm (see two valleys near A78 and A120 in Fig. 2 a).Notably, unlike the MD trajectories and the x-ray structures,the initial model for our MD simulations as built in Li et al.(28) does not exhibit these valleys in Dad (see Fig. 2 a).Therefore, our MD simulation is able to recover theobserved structural features of Tm not present in the initialmodel. We also analyzed Tm flexibility based on the MDtrajectories starting from a different initial model of Tm(system 3; see Methods), and found a similar distributionof flexibility in Tm (see Fig. S4). Taken together, these find-ings have validated the ability of our MD simulation andflexibility analysis to uncover new structural and dynamicfeatures of Tm independent of the quality of the initialmodel.

As an indicator of backbone flexibility in the hydrophobicinterface of the Tm coiled coil, the SD of Dad exhibits sevenpronounced peaks, six of which align very well with the sixvalleys in the average of Dad (see Fig. 1 a) where the six Alaclusters are located. In addition, a seventh peak is nearanother destabilizing core residue, E218 (see Fig. 1 a).This finding is, to our knowledge, the first dynamicsevidence that supports the colocalization of six Ala clusterswith regions of high local flexibility in Tm, although such acorrelation was proposed based on the comparison of x-raystructures of Tm fragments solved under different crystalli-zation conditions (2,8).

As indicators for side-chain packing and flexibility in thehydrophobic interface of the Tm coiled coil, the average andSD of D�

ad exhibit features similar to those seen for Dad (seeFig. 1 b). The valleys in the average of D�

ad are less pro-nounced than those in Dad, whereas the peaks in the SDof D�

ad are more pronounced than in Dad (see Fig. 1, aand b). Therefore, to adequately describe local flexibilityin the hydrophobic interface of the Tm coiled coil, it isnecessary to take into account side-chain fluctuations inaddition to backbone fluctuations (5). Both contribute tothe high flexibility near the Ala clusters.

The local flexibility in the hydrophobic interface of theTm coiled coil may involve two orthogonal motionsbetween the two Tm chains, an axial motion parallel tothe coiled-coil axis and a lateral motion perpendicular tothe coiled-coil axis (see Fig. 1, inset). To test the proposalthat the axial motion is the main contributor to the local flex-ibility of Ala clusters (2), we analyzed the average and SDof DAS (see Methods). Interestingly, the SD of DAS displaysseven peaks (see Fig. 1 c), which match well with the sevenpeaks in the SD of Dad, including six peaks near the six Alaclusters (see Fig. 1 a). Only some of these peaks are found inthe average of DAS (see Fig. 1 c), suggesting that the axial


staggering in Tm is highly dynamic and thus cannot be fullycaptured by averaging over MD trajectories. To further vali-date the above finding, we also calculated DAS for severalhigh-resolution x-ray structures of Tm fragments and foundsimilar peaks near the Ala clusters (see Fig. 2 b), some ofwhich were also found by a previous structural analysis(4). Taken together, both MD simulations and x-ray struc-tures of Tm support the proposal that the six Ala clustersare hotspots for local axial motion between two Tm chains(2), which may lead to elevated local flexibility, as observedin the SD of Dad (see Fig. 1 a).To assess whether the lateral motion between two Tm

chains also contributes to the local flexibility of Tm, weanalyzed the average and SD of Dt (see Methods).Although the average of Dt exhibits six valleys at the sixAla clusters, the SD of Dt shows no peaks at the Ala clus-ters but a prominent peak at E218 (see Fig. 1 d). Thus, thelateral motion between two Tm chains is not involved inthe high local flexibility near the Ala clusters.

To further check the robustness of our finding based onthe analysis of DAS and Dt, we analyzed two alternativeparameters for measuring the AS and coiled-coil diameterusing the CCbends program (38). Indeed, the distributionsof AS and diameter are very similar to those of DAS andDt, respectively (see Fig. 1, e and f), which confirms ourfinding that the six Ala clusters, corresponding to six peaksin DAS and AS, are hotspots for the axial motion but not thelateral motion between two Tm chains.

In addition to the six Ala clusters, a region near E218 isalso found to be very flexible, with large axial and lateralfluctuations between the two Tm chains (see Fig. 1). Theregion near E218 is known to be structurally unstable,with a noncanonical core residue, E218, at the hydrophobicinterface of the Tm coiled coil (4). Intriguingly, anotherwell-known noncanonical core residue, D137 (52), doesnot correspond to any peak in the SD of DAS, although itis near a minor peak in the SD of Dt (see Fig. 1 d). In addi-tion, the flexibility of D137 and E218 changes differentlyupon the binding of F-actin (see below). Therefore, the localflexibility near D137 and E218 may differ in the structuraldetails. It is unclear how such differences relate to thefinding that the region near D137 (such as R133 andE131; see Moore et al. (20)) is highly susceptible to prote-olysis, whereas the region near E218 is not. We also foundmoderately high flexibility near Q263, corresponding to aminor peak in the SD of Dad and D�

ad (see Fig. 1, aand b). This region was found to be unstable in both solution(53,54) and the crystal structure of a Tm fragment (12).

In sum, we found a clear correlation between the posi-tions of destabilizing residues (including six Ala clustersand two other destabilizing regions near E218 and Q263)and the regions with high local flexibility in the hydrophobicinterface of the Tm coiled coil. The high flexibility in theAla clusters is due to large axial motion between two Tmchains.

FIGURE 2 Results of local flexibility analysis of Tm in the absence of F-actin in comparison with x-ray structures of Tm fragments using four parameters:

Dad (a), DAS (b), Dt (c), and qb (d). The gray vertical lines mark the center positions of six Ala clusters (A22, A78, A120, A155, A183, and A239). The

positions of individual core Ala residues are marked by short dashes. The red vertical lines in d mark peaks of average qb. The data points are represented as

follows: MD simulations of system 1 ( )• , PDB structures 2d3e ( ), 1ic2 ( ), 2efr ( ), 2efs ( ), and 2b9c ( ), and the initial model from Li et al. (28) ( ).Tosee this figure in color, go online.


How does the local flexibility of Ala clusters and otherdestabilizing regions enable Tm to conform to the contoursof F-actin? Brown and co-workers proposed that the localAS between two Tm chains can induce local bending ofTm backbones in nearby regions (2,8). In support of thisproposal, local bending was indeed observed in severalx-ray structures of Tm fragments near the destabilizing re-gions (2,4,8,10–12). However, the occurrence of localbending seems to depend on crystal packing conditions,and whether such local bending is intrinsic to Tm dynamicsin solution remains to be shown.

To test the above proposal, we analyzed the average localbending angle (denoted as qb, see Methods) at each a/d res-idue position of Tm based on the last 10 ns of MD trajec-tories. The distribution of the average qb features multiplepeaks at residues 46, 71, 92, 113, 127, 137, 144, 169, 207,218, and 246 (with average qb > 10�; see Fig. 2 d). It isencouraging that many of these local bending hotspots coin-cide with local bending regions found in several x-ray struc-tures of Tm fragments (such as residues 46, 113, 127, 144,169, 218, and 246; see Fig. 2 d). In particular, Tm is remark-ably bent at E218 in both our MD simulations (see Fig. 2 d)and the x-ray structure of a Tm fragment (PDB ID: 2d3e)(12). Notably, the initial model of our MD simulations asbuilt in Li et al. (28) does not exhibit these peaks in qb(see Fig. 2 d), which only arise from extensive MD simula-tions. Unlike those highly flexible regions identified by theanalysis of Dad and DAS (see Fig. 1, a and c), the localbending hotspots do not coincide with the destabilizing

regions including the six Ala clusters (see Fig. 2 d). Instead,they are mostly located adjacent to the destabilizing resi-dues (within %25 residues). Thus, it is likely that the localaxial motion at Ala clusters may be transmitted over somedistance to induce local bending in nearby regions (2,8).This idea was supported by a recent correlation analysisof helical staggers in Tm (55).

Tm flexibility in the presence of F-actin

For the MD simulations of Tm in the presence of F-actin, thedistribution of local flexibility in Tm remains largelyunchanged compared with Tm alone (see Fig. S5). Theaverages of Dad, D

�ad, and Dt still exhibit six valleys corre-

sponding to six Ala clusters (see Fig. S5, a, b, and d). TheSDs of Dad, D

�ad, and DAS exhibit seven pronounced peaks,

six of which correspond to the six Ala clusters (see Fig. S5,a–c). Notably, F-actin binding greatly reduces the peak atE218 in the SD of Dad, D

�ad, and Dt (see Fig. S5, a, b,

and d). However, D137 remains highly flexible despiteF-actin binding, with a pronounced peak at D137 in theSD of Dt (see Fig. S5 d).

For the aMD simulations of Tm in the presence of F-actin,we found a similar distribution of local flexibility (e.g., peakpositions in the SDs of Dad, D

�ad, DAS, Dt), although aMD

substantially enhances the height of these peaks (seeFig. S6), thanks to enhanced conformational samplingby aMD.

In sum, F-actin binding does not change the distributionof local flexibility in Tm, especially the high flexibility of


1888 Zheng et al.

six Ala clusters. Two destabilizing regions near residuesD137 and E218 remain flexible, although F-actin bindinggreatly reduces the flexibility of E218.

FIGURE 3 Average structures of Tm bound with F-actin in comparison

with the Tm models at the closed and open positions. (a) Global view of

the entire Tm bound with F-actin. (b) Enlarged view of periods P4 and

P5 in Tm. The average structures of Tm from four aMD simulations are

colored blue, red, green, and orange; the Tm model at the closed position

(28) is colored black; and the Tm model at the open position (57) is colored

yellow. Two actin residues (D25 and P307) are shown as reference points

for the closed and open positions of Tm and colored the same as Tm.

Five actin subunits in contact with periods P2–P6 of Tm are colored dark

gray, and those not in contact with Tm are colored light gray. The block

arrow in a indicates the shift of Tm from the closed position to the open

position.

Analysis of Tm fluctuations over the surfaceof F-actin

Thus far, we have focused on the internal flexibility of Tm inthe absence and presence of F-actin. Another key aspect ofTm dynamics is its fluctuations relative to F-actin. In thethree-state steric blocking model (13,56), Tm is thought tomove over the F-actin surface from the blocked positionin the absence of Ca2þ to the closed position and then theopen position in the presence of Ca2þ and strong-bindingmyosin heads. In one scenario, Tm rapidly fluctuatesbetween these positions, and its transient exposure of themyosin-binding site on F-actin would allow myosin tobind and would favor binding of Tm at the open position.To assess this postulate, we analyzed how the periods P2–P6 of Tm fluctuate relative to the closed and open positionsduring the MD/aMD simulations. Our MD/aMD simula-tions start from an initial model of Tm bound with F-actinin the absence of troponin, presumably near the closedposition (28), although it is near the blocked position asmodeled by another EM-based study (17). To measure thedistances between Tm and the closed and open positions(denoted DC and DO), we calculated the minimal Ca-Cadistances between Tm and two representative residues(D25 and P307) on five actin subunits in contact with theperiods P2–P6 of Tm (see Fig. 3). Residues D25 and P307are close to Tm at the closed and open positions, respec-tively (see Fig. 3). We average the minimal distances fromTm to D25 and P307 (corresponding to DC and DO) overthe last 10 ns of each MD/aMD trajectory. Then we subtractthe values of DC and DO as calculated for the initial model(28) to obtain the changes in DC and DO during the MD/aMD simulations (denoted dDC and dDO; see Table S2):as a Tm period moves from the closed position to theopen position, dDC becomes more positive and dDO

becomes more negative.During the ten MD simulations of Tm bound to F-actin,

the periods P2–P6 of Tm fluctuate near the closed position(�3.1 A % dDC % 5.8 A; see Table S2), with a variableshift toward the open position (�5.8 A % dDO % 0 A;see Table S2). Upon averaging over the ten MD trajectories,whereas P4 undergoes the largest shift away from the closedposition (with an average of dDC ~ 1.8 A; see Table S2), P5shows the greatest variation in dDC (with SD of dDC ~2.2 A;see Table S2), highlighting the dynamic role of these periodsin driving the movement of Tm on F-actin. During the fouraMD simulations of Tm bound to F-actin, the periods P2–P6of Tm undergo a larger shift toward the open position(�7.5 A % dDO % �0.1 A; see Table S2 and Fig. 3).Upon averaging over the four aMD trajectories, P5undergoes the largest shift away from the closed position


(with an average for dDC ~3.1 A; see Table S2). Amongthe four aMD trajectories, the largest shift is observedduring the second aMD simulation, where the periods P2–P6 of Tm shift away from the closed position by 1–4.2 Aand toward the open position by 2.5–7.5 A (see Table S2).Notably, some periods of Tm fluctuate more than halfwaybetween the closed and open position (dDO is �11 A forTm at the open position (57)). Therefore, within the time-scales of our MD/aMD simulations, individual periods ofTm are fluctuating variably from the closed position towardthe open position, in contrast with the proposal that Tmmoves over the F-actin surface semirigidly based on EMstudies (13–18). We also used principal component analysisto analyze the relative motions between Tm and F-actin (seethe Supporting Material).

In sum, our MD/aMD simulations showed variable fluctu-ations of individual Tm periods from the closed positiontoward the open position, which may allow transient expo-sure of at least one myosin-binding site on F-actin for strongbinding of myosin and activation of the thin filament. There-fore, the initial binding of myosin during cooperative activa-tion of F-actin-Tmmay be primarily defined by the dynamic


availability of a binding site on F-actin rather than apreferred binding site on F-actin-Tm with reference to theTm sequence. Further simulations are underway to explorethe structural dynamics of Tm bound with both F-actinand myosin near the open position.

Binding calculation between Tm and actinsubunits

Based on the MD/aMD simulations of Tm bound withF-actin, we performed intermolecular binding calculationsbetween Tm and F-actin, which take into account both elec-trostatic and nonpolar contributions to Tm-F-actin bindingwith residue-level detail (see Methods). To this end, wekept 100 snapshots of the last 10 ns of each MD/aMD trajec-tory. For each snapshot, we calculated the binding freeenergy, DG (not including the entropy contribution; seeMethods), between Tm and each of five actin subunits inter-acting with the periods P2–P6 of Tm (see Fig. 3), and thenaveraged the DG values over all snapshots (see Methods).We established and applied this protocol in two recentstudies of the binding between kinesin motor and microtu-bule in three biochemical states (39,40).

The total DG (i.e., the sum of DG over all five actin sub-units) varies significantly between the MD and aMD trajec-tories (see Table S3). Interestingly, the total DG seems tocorrelate with the overall flexibility of Tm (measured byhRMSFi; see Table S1). Tm binds more strongly withF-actin and has higher hRMSFi during the aMD simulationsthan during the MD simulations (see Table S3). This findingsupports the importance of Tm flexibility for its binding toF-actin. Among the four aMD trajectories, the second hasthe highest hRMSFi (see Table S1) and the largest shifttoward the open position (see Table S2), but it also has theweakest binding to F-actin (see Table S3). This may beattributed to the less favorable Tm-F-actin interactions atthe open position in the absence of myosin binding (28).Therefore, the Tm-myosin interactions must be includedto account for the strong binding of Tm to myosin-decoratedF-actin at the open position (57).

For all MD/aMD trajectories, the nonpolar contribution isconsistently greater than the electrostatic contribution.Although this finding is at odds with the previous proposalthat the electrostatic forces dominate Tm-F-actin binding(28,58), it does not downgrade the importance of electro-static forces in Tm-F-actin binding. In fact, the electrostaticcontribution is more important in Tm-F-actin binding(DEelec/EvdW R 0.4; see Table S3) than in myosin-F-actinbinding (DEelec/EvdW % 0.2; see Zheng and Li (59)).Thanks to the flexibility of both Tm and F-actin, Tm movescloser to F-actin during the MD/aMD simulations, formingmore extensive contact than in the initial model. As a result,we found a higher nonpolar contribution to Tm-F-actinbinding than was found in previous calculations, whichdid not fully account for flexibility (28,58). We note that

both nonpolar and charged residues at the Tm-F-actin inter-face are involved in the nonpolar contribution of DG (seeTable S4). Thus, our finding does not contradict the recentfinding that mutations of charged surface residues of Tmhad a larger effect on Tm-F-actin binding than did mutationsof nonpolar residues (60,61). In fact, as predicted by ourbinding calculation, the Tm residues most involved in Tm-F-actin binding are primarily charged and polar residues(see below).

Given the large variations of DG between differenttrajectories and periods of Tm (see Table S3), we cannotdetermine which period contributes the most to Tm-F-actinbinding. Such strong variations in DG are not unexpectedgiven the observed high flexibility of Tm even in the pres-ence of F-actin. More extensive MD/aMD simulations willbe needed to yield statistically meaningful differences inDG between different periods of Tm.

The calculated values of DG are not comparable to exper-imental binding measurements (mM/mM affinity for Tmwithout/with cooperativity) for the following reasons: first,the entropic cost of Tm-F-actin binding is not taken intoaccount (due to large uncertainty in entropy calculation),which would have made jDGj much smaller; second, thehead-to-tail interactions in the overlap regions of Tm,known to be essential for cooperative Tm-F-actin binding,are missing in our simulations (62). Despite such caveats,we should stress that the objective of our binding calculationis not to accurately reproduce the experimental DG, but tosemiquantitatively analyze the contributions of individualTm residues to Tm-F-actin binding and to identify thosekey residues involved in Tm-F-actin binding (see below).

To identify key Tm residues involved in Tm-F-actinbinding, we partitioned DG into contributions from indi-vidual Tm residues (denoted as DGn for residue n; seeMethods and Table S4). To fully sample the dynamic inter-actions between Tm and F-actin, these per-residue contribu-tions are averaged over the last 10 ns of ten MD trajectories.By ranking the per-residue contributions, the followingactin-binding residues of Tm were found (see Table S4and Fig. S9): K37, V44, Q47, K48, K51, E54, D55, D58,K59, and E62 of P2; A86, N89, R90, Q93, L94, E97,D100, R101, and E104 of P3; R125, K128, V129, E131,S132, Q135, K136, E138, and E142 of P4; R160, R167,V170, I171, E173, S174, E177, R178, and E181 of P5;and K198, N202, K205, E208, A209, E212, K213, Q216,D219, and E223 of P6. Among these residues, the highest-contributing residues (with DGn < �0.2; see Table S4)are dominated by basic residues like K48, K51, R90,R125, K128, R160, R167, and K205, along with other polarresidues like Q93, Q135, and Q216, and only one acidicresidue, E212, and one nonpolar residue, V170. Most ofthese residues are located in the first halves of periods P2–P6, in agreement with a recent mutational study (60).Most of the above residues are at b, c, or f positions ofthe coiled-coil surface, although some are at e or g


1890 Zheng et al.

positions (Q47, E54, N89, E131, E138, E173, and E208),which may also be involved in the stabilization of the Tmcoiled coil.

Among the above residues, 21 (underlined residues) werevalidated by recent mutational studies of evolutionarilyconserved residues at the Tm-F-actin interface (60,61),and the rest will serve as targets for future mutationalstudies. Many of the above actin-binding residues werealso predicted by a previous modeling study of the Tm-F-actin complex (28). In addition to what was predicted inLi et al. (28), we predicted many additional actin-bindingresidues in periods P2–P6 of Tm (including K51, D55,K59, A86, N89, Q93, L94, V129, E131, Q135, K136,E138, R160, I171, E173, S174, E177, R178, K198, N202,E212, K213, Q216, and E223), thanks to extensive MD sim-ulations of dynamic interactions between Tm and F-actin.Our finding of more actin-binding residues does not implystronger binding between Tm and F-actin, because mostof the above residues form transient and weak interactionswith F-actin during the MD simulations as Tm fluctuatesover the surface of F-actin. These dynamic interactionscannot be fully captured by a static snapshot of the Tm-F-actin interface and are consistent with the view that the func-tional blocked, closed, and open positions of Tm on F-actinare averages of dynamic structures. We note that our predic-tions are limited to those Tm residues directly involved inthe interactions with F-actin, and our method cannot predictTm residues that are indirectly involved in F-actin bindingvia changes in dynamics or stability.

We also performed DG partition based on the four aMDtrajectories (see Table S4). We found more actin-bindingresidues of Tm based on the aMD simulations in additionto those found based on the MD simulations, includingK49, A83, K118, I146, and L185 (see Table S4). Thisfinding further supports the importance of extensive MD/aMD simulations to the study of Tm-F-actin interactions.

CONCLUSION

By performing total 440-ns MD/aMD simulations of explic-itly solvated Tm in the absence or presence of F-actin, wesuccessfully captured key dynamic features of Tm observedby x-ray crystallography studies but not by previous, lessextensive and/or implicit-solvent-based MD simulations(25–28,63) and normal mode analysis (63). Our finding ofgood correlation between key destabilizing regions of Tm(including six Ala clusters) and regions with high localflexibility has given strong support to the proposal that theseregions are involved in the Tm flexibility that is criticalfor Tm function. Thanks to the enhanced conformationalsampling by aMD, we observed variable fluctuations ofTm from the closed position toward the open position onthe F-actin surface and uncovered new potential interactionsbetween Tm and F-actin that will make good targets forfuture mutational studies.


This study validates the MD-based approach to the inves-tigation of Tm flexibility and the dynamic interactionsbetween Tm and F-actin. In the future, we will use thisapproach to investigate how specific Tm mutations perturbTm dynamics and its interactions with F-actin, and toperform mutational and binding experiments to test thecomputational predictions.

SUPPORTING MATERIAL

Four tables, nine figures and SupportingMethods andResults are available at

http://www.biophysj.org/biophysj/supplemental/S0006-3495(13)01020-5.

We thank Dr. Lehman for sharing the EM-based model of Tm-F-actin com-

plex. The simulations were conducted using the supercomputing cluster of

the Center for Computational Research at the University at Buffalo and the

Biowulf cluster at the National Institutes of Health.

This study was supported by an American Heart Association grant

(0835292N) and a National Science Foundation grant (0952736) to W.Z.

and a National Institutes of Health grant (GM093065) to S.E.H.D.

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Probing the Flexibility of Tropomyosin and Its Binding to Filamentous Actin Using Molecular Dynamics Simulations

Wenjun Zheng,†* Bipasha Barua,‡ and Sarah E. Hitchcock-DeGregori‡ †Department of Physics, University at Buffalo, Buffalo, New York; and ‡Department of Pathology and Laboratory Medicine, Robert Wood Johnson Medical School, Rutgers University, Piscataway, New Jersey

Supporting Information

Methods

Global and local RMSF analysis To assess the global/local flexibility of Tm based on an MD/aMD simulation, we calculate the global or local root mean squared fluctuation (RMSF) as follows: first, we save 500 snapshots of Tm during the last 10 ns of an MD/aMD simulation; second, we superimpose the Cα atomic coordinates of entire Tm or each Tm period (for ranges of residue numbers see Fig 2 of ref (1)) onto the initial Tm model (2) with minimal root mean squared deviation (RMSD); finally, we calculate the following RMSF at residue n:

2

1

1 M

n mn nm

RMSF r rM =

= −∑

, where mnr is the Cα atomic position of residue n in snapshot m, 1

1 M

n mnm

r rM =

= ∑

is the

average Cα atomic position of residue n, M =500 is the total number of snapshots. We assess the overall flexibility of Tm using the following average of global RMSF over all Tm residues:

2

1

1 N

nn

RMSF RMSFN =

= ∑ , where N=568 is the number of residues in the Tm coiled-coil.

PCA To identify dominant modes of fluctuations in the Tm or Tm-F-actin complex, we perform the principal component analysis (PCA) based on the last 10ns of MD/aMD trajectories of system 1 and 2: first, we save 500 snapshots during the last 10 ns of each trajectory and combine them to construct a structural ensemble; second, we superimpose the Cα atomic coordinates onto the initial model (2) with minimal RMSD; third, we calculate the co-variance matrix comprised of the

following 3×3 blocks ( ) ( )' ' '1

1 M

nn mn n mn nm

C r r r rM =

= − ⊗ −∑

(see above for definitions of notations); fourth, we

diagonalize the co-variance matrix and keep the two dominant PCA modes with the highest eigenvalues. In addition, by projecting each trajectory onto a plane spanned by these two dominant PCA modes, we can visualize and compare the regions of conformational space sampled by different trajectories.

Results

1

Results of RMSF analysis The distribution of global RMSF, calculated for the entire Tm coiled-coil, varies significantly between the four MD trajectories of system 1 (see Fig S2a), which indicates that the global fluctuations of Tm are not sufficiently sampled by individual 20-ns MD simulations, and the Tm flexibility may be highly delocalized as proposed previously (3-5). In contrast, the distribution of local RMSF, calculated separately for each Tm period (~80 residues of the Tm coiled-coil), exhibits good convergence between the four MD trajectories (see Fig S2b), which indicates that the local fluctuations within the Tm coiled-coil are adequately sampled by each 20-ns MD simulation. Therefore, our 20-ns MD simulations of Tm dynamics have achieved local equilibration (not global equilibration), which allows us to perform a statistically meaningful analysis of the local flexibility of Tm. As indicated by the local RMSF profile, the N- and C-terminal regions of all periods and the middle region of some periods are highly flexible (see Fig S2b). In particular, the two well-known destabilizing core residues D137 (6) and E218 (7) are both near peaks of local RMSF, supporting their involvement in local flexibility of Tm. Nevertheless, most of the six Ala clusters do not co-localize with the peaks of local RMSF (see Fig S2b). Therefore, the RMSF analysis is not very useful in analyzing the involvement of Ala clusters in Tm dynamics. Results of PCA analysis To visualize and compare the regions of conformational space sampled by different MD trajectories, we have projected each trajectory onto a plane spanned by the two dominant PCA modes calculated for system 1 (accounting for 46% and 24% of overall fluctuations) and system 2 (accounting for 26% and 23% of overall fluctuations): For system 1 (see Fig S7a), the four MD trajectories have sampled three distinct regions, and one region overlaps with the initial model of system 3. Additionally, the four trajectories of system 3 have sampled two regions visited by the trajectories of system 1. Therefore, although individual trajectories of system 1 and 3 display diverging behaviors, the regions sampled by the combined trajectories of system 1 and 3 overlap significantly with each other, suggesting some degree of convergence between the MD simulations of the two systems. For system 2 (see Fig S7b), although the first four MD trajectories have sampled four distinct regions, these regions are also partially sampled by the additional six trajectories, suggesting convergence between the two sets of trajectories. To visualize the dominant modes of fluctuations of Tm in the presence of F-actin, we have performed the PCA based on the last 10ns of four aMD trajectories of the Tm-F-actin system (system 2). The overall Cα atomic fluctuations are dominated by the first and second PCA mode (33% and 29%, respectively). In addition to large flexibility within F-actin and Tm, these modes have captured relative motions between Tm and F-actin which may be functionally important: mode 1 depicts the Tm periods P2-P6 sliding relative to F-actin in the same azimuthal direction (see Fig S8), which may lead to the concerted BCO transitions underlying the activation of thin filaments; mode 2 depicts an unconcerted azimuthal sliding of the Tm periods P2-P6 relative to F-actin where the N- and C-terminus of Tm move in the same direction while the middle region moves in the opposite direction (see Fig S8). The coexistence of these two dominant modes is consistent with our finding of highly variable fluctuations of individual Tm periods.

2

Tables Table S1. Average of global RMSF for MD and aMD simulations of Tm

trajectory #

RMSF (Å)

MD of Tm alone MD of Tm bound with F-actin (system 2)

aMD of Tm bound with F-actin (system 2) system 1 system 3

3

1 2 3 4 5 6 7 8 9 10

2.67 2.31 2.53 2.35

2.85 2.98 2.95 2.88

1.64 1.55 1.54 1.57 1.65 1.36 1.50 1.67 1.55 1.63

1.77 1.87 1.72 1.78

average±SD 2.47±0.17 2.92±0.06 1.57±0.09 1.79±0.06

4

Table S2. Results for analysis of Tm fluctuations relative to F-actin involving periods P2-P6 of Tm period average (SD)* of δDC δDO (Å) P2-ac15 P3-ac13 P4-ac11 P5-ac09 P6-ac07 average P2-ac15 P3-ac13 P4-ac11 P5-ac09 P6-ac07 average P2-ac15 P3-ac13 P4-ac11 P5-ac09 P6-ac07 average

MD trajectory #1 MD trajectory #2 MD trajectory #3 MD trajectory #4 MD trajectory #5 2.8(1.1) -5.2(0.9) 1.5(1.5) -4.2(1.0) 2.1(0.9) -3.2(1.2) -1.0(0.6) -0.5(0.8) -2.6(0.9) -0.9(0.7) 0.5 -2.8

2.0(0.7) -0.6(0.7) -0.1(0.4) -3.1(0.9) 1.2(0.3) -1.5(0.6) -0.8(0.4) -1.4(0.6) -1.5(0.7) -3.2(0.9) 0.2 -1.9

1.0(0.6) -0.1(1.0) -0.8(1.1) -2.9(0.6) 1.4(0.4) -1.0(0.7) -0.4(0.3) -1.0(0.7) -1.4(1.3) -1.0(0.8) -0.0 -1.2

-0.0(0.4) -3.0(1.0) 1.0(1.2) -3.6(1.0) 2.0(0.6) -3.3(1.1) 5.8(1.2) -4.6(0.9) 3.3(1.6) -2.4(1.0) 2.4 -3.4

1.7(0.6) -1.0(1.2) -0.4(0.7) -2.8(0.6) 1.1(0.3) -2.5(0.7) 1.7(1.0) -1.8(1.0) -2.1(0.8) -2.3(1.5) 0.4 -2.1

MD trajectory #6 MD trajectory #7 MD trajectory #8 MD trajectory #9 MD trajectory #10 -1.4(0.9) -4.3(0.8) 1.4(0.8) -2.8(1.0) 1.1(0.3) -1.7(0.6) -0.9(0.5) -1.8(1.0) -2.3(0.4) -1.2(0.6) -0.4 -2.4

0.1(0.7) -2.0(1.1) 2.9(1.3) -5.8(0.7) 3.6(1.0) -1.2(0.7) -1.2(0.5) -1.3(0.8) -3.1(0.4) -2.0(0.8) 0.5 -2.5

2.6(1.4) -1.6(0.9) -1.1(1.0) -2.4(1.2) 1.9(0.6) -2.1(0.8) 0.2(0.5) 0.0(1.1) -1.2(0.9) -1.1(0.8) 0.5 -1.4

1.2(0.9) -3.2(0.9) -1.1(1.1) -2.3(0.7) 1.5(1.0) -2.9(1.4) 1.8(1.0) -2.8(0.6) -0.3(0.5) -0.4(0.7) 0.6 -2.3

1.7(1.5) -3.7(2.0) 1.7(1.5) -4.8(1.0) 1.8(0.7) -3.0(0.9) -0.3(0.4) -2.0(1.9) -1.8(0.6) -1.9(0.7) 0.6 -3.1

All MD trajectories aMD trajectory #1 aMD trajectory #2 aMD trajectory #3 aMD trajectory #4 1.2(1.5) -2.5(1.9) 0.5(1.7) -3.5(1.4) 1.8(1.0) -2.2(1.2) 0.5(2.2) -1.7(1.6) -1.3(1.9) -1.6(1.2) 0.5 -2.3

-1.0(0.5) -1.7(1.0) 2.2(1.1) -0.1(1.1) 4.6(0.7) -3.7(2.0) 3.6(1.8) -3.8(1.7) -3.1(0.5) -2.3(0.8) 1.3 -2.3

3.7(1.3) -7.5(2.2) 1.8(0.8) -6.0(0.9) 1.0(0.5) -4.7(1.0) 4.2(1.5) -2.5(2.2) 4.2(1.5) -6.3(1.6) 3.0 -5.4

0.2(2.2) -2.7(1.4) -2.6(0.5) -1.1(1.0) -2.6(0.2) -3.6(1.2) -0.5(0.8) -3.6(1.3) 0.4(1.5) -4.8(1.1) -1.0 -3.2

-1.9(0.4) -0.5(1.2) -2.9(0.4) -2.9(0.9) 1.8(0.9) -4.9(1.9) 5.2(1.8) -3.2(1.1) -2.5(0.5) -4.9(0.8) -0.0 -3.3

P2-ac15 P3-ac13 P4-ac11 P5-ac09 P6-ac07 average

All aMD trajectories 0.3(2.5) -3.1(3.1) -0.3(2.5) -2.5(2.5) 1.2(2.6) -4.2(1.7) 3.1(2.6) -3.3(1.7) -0.3(3.1) -4.6(1.8) 0.8 -3.5

* The average and standard deviation (SD) were calculated for the last 10ns of each MD/aMD trajectory (or all trajectories combined).

5

Table S3. Results of Tm-F-actin binding calculations involving periods P2-P6 of Tm

period average (SD)* of ∆G EvdW ∆Εelec (kcal/mol) P2c15 P3-a P4-a1 P5-ac P6-a7 sum

P2c15 P3-a P4-a1 P5-ac P6-a7 sum P2c15 P3-a P4-a1 P5-ac P6-a7 sum

MD trajectory #1 MD trajectory #2 MD trajectory #3 MD trajectory #4 MD trajectory #5 -3.9(0.5) -16.9(3.9) -7.9(1.8) -3.2(0.7) -11.1(5.9) -9.6(3.1) -3.9(0.8) -12.6(6.3) -12.4(2.3) -4.5(1.2) -18.8(10 ) -10.1(3.9) -5.5(0.9) -27.7(6.3) -7.4(2.4) -21.0 -87.1 -47.4

-2.1(0.5) -3.3(4.4) -10.6(2.1) -4.9(0.7) -17.2(6.0) -14.2(2.7) -3.6(0.8) -10.7(5.5) -12.5(2.1) -5.1(0.8) -21.0(6.4) -11.8(2.7) -3.4(1.1) -15.7(5.5) -6.0(4.4) -19.2 -68.0 -55.1

-2.6(0.6) -4.7(4.4) -12.0(2.4) -4.5(0.6) -21.7(4.8) -6.9(2.9) -3.4(0.6) -7.3(4.8) -14.4(2.0) -3.7(0.7) -12.6(5.4) -11.4(2.3) -4.6(0.7) -20.0(5.5) -9.2(2.2) -18.7 -66.2 -53.8

-4.4(0.6) -17.9(4.5) -10.5(2.2) -3.8(0.6) -14.2(4.7) -10.2(2.2) -4.5(0.7) -18.1(5.0) -10.8(1.8) -1.5(0.5) -5.0(3.0) -4.6(2.3) -1.8(0.6) -6.9(3.5) -4.5(1.3) -16.0 -62.1 -40.7

-2.1(0.6) -8.5(3.8) -5.1(2.0) -5.4(0.7) -27.1(4.6) -7.2(1.8) -4.7(0.6) -16.9(4.8) -13.5(2.1) -3.0(0.9) -10.8(7.0) -8.3(2.1) -3.5(0.9) -16.2(5.6) -6.1(1.9) -18.7 -79.5 -40.2

MD trajectory #6 MD trajectory #7 MD trajectory #8 MD trajectory #9 MD trajectory #10 -5.7(1.2) -25.2(7.3) -11.1(3.2) -3.2(0.8) -7.1(5.5) -13.7(2.9) -4.3(0.6) -13.4(4.9) -14.5(2.3) -5.6(0.8) -24.0(6.5) -12.1(2.9) -4.3(0.5) -23.5(3.7) -4.0(1.9) -23.2 -93.2 -55.4

-4.0(0.9) -12.7(5.9) -13.2(3.2) -2.8(0.6) -4.0(4.3) -14.3(2.1) -3.0(0.5) -7.8(4.2) -11.9(2.3) -5.7(0.7) -28.9(5.5) -7.4(2.7) -4.8(0.7) -25.2(4.4) -5.6(1.8) -20.4 -78.7 -52.3

-2.3(0.7) -7.4(3.9) -7.3(2.2) -3.7(1.1) -14.5(6.4) -9.0(3.2) -3.1(0.6) -7.4(4.8) -12.5(2.3) -2.0(0.6) -6.4(4.6) -6.8(2.4) -4.0(0.6) -19.6(4.0) -6.2(1.7) -15.1 -55.3 -41.8

-3.9(0.7) -16.0(4.9) -8.9(1.8) -3.7(0.6) -12.9(6.2) -11.0(3.7) -3.6(0.8) -10.9(5.8) -12.0(2.4) -3.8(0.7) -15.3(4.7) -9.1(2.2) -3.8(0.6) -14.3(4.5) -10.0(2.6) -18.8 -69.3 -51.0

-3.1(0.7) -11.6(4.2) -8.2(2.1) -3.2(0.8) -11.8(6.2) -9.1(2.2) -2.9(0.6) -4.1(4.3) -15.0(2.7) -5.5(1.3) -19.6(8.6) -15.4(1.9) -4.2(0.6) -14.1(5.4) -12.6(2.2) -18.9 -61.2 -60.2

All MD trajectories aMD trajectory #1 aMD trajectory #2 aMD trajectory #3 aMD trajectory #4

-3.4(1.3) -12.4(8.0) -9.5(3.3) -3.8(1.1) -14.2(8.4) -10.5(3.8) -3.7(0.9) -10.9(6.6) -12.9(2.6) -4.0(1.7) -16.2(9.7) -9.7(3.9) -4.0(1.2) -18.3(7.6) -7.2(3.5) -19.0(2.8)-72.1(16.9) -49.8(8.7)

-4.4(0.7) -16.7(5.0) -11.8(2.6) -2.5(1.0) -8.0(6.9) -7.9(2.7) -4.8(1.3) -15.8(7.5) -15.2(4.3) -6.1(1.8) -27.4(11) -11.4(2.5) -7.2(1.1) -33.0(7.4) -13.3(2.3) -25.1 -101.1 -59.5

-3.1(0.9) -12.9(6.8) -6.6(2.7) -4.3(0.8) -14.1(5.6) -13.3(2.9) -4.1(0.8) -11.3(5.9) -15.0(2.5) -2.5(0.9) -9.5(6.2) -6.8(2.3) -2.3(0.6) -12.4(4.7) -2.5(2.5) -16.3 -60.1 -44.2

-4.6(0.7) -18.2(5.9) -11.5(3.9) -5.8(0.9) -26.8(6.5) -10.0(2.3) -7.7(0.8) -35.1(5.7) -13.9(3.9) -6.6(0.8) -34.4(5.8) -7.8(2.4) -5.1(0.7) -21.7(6.3) -11.1(3.3) -29.8 -136.1 -54.3

-4.7(0.8) -14.6(6.9) -15.9(3.0) -6.3(0.9) -28.5(5.6) -11.6(2.3) -6.8(1.1) -26.9(7.8) -16.7(2.8) -2.8(0.7) -11.5(4.6) -6.4(2.2) -5.6(0.9) -26.4(7.0) -9.1(3.3) -26.2 -108.0 -59.7

P215 P3 P41 P509 P607 sum

All aMD trajectories -4.2(1.0) -15.6(6.5) -11.5(4.5) -4.7(1.7) -19.4(10.6) -10.7(3.3) -5.8(1.8) -22.3(11.5) -15.2(3.6) -4.5(2.2) -20.7(12.8) -8.1(3.0) -5.1(2.0) -23.4(9.9) -9.0(5.0) -24.3(5.4) -101.3(30.4) -54.4(8.8)

* The average and standard deviation (SD) were calculated for the last 10ns of each MD/aMD trajectory (or all trajectories combined).

6

Table S4. Results of binding free energy partition and predicted actin-binding residues of Tm chain:residue# ∆Gn EvdW,n ∆Εelec,n based on 10 MD simulations (kcal/mol)

chain:residue ∆Gn EvdW,n ∆Eelec,n based on 4 aMD simulations (kcal/mol)

B:K37 -0.05 -0.18 -0.13 B:V44 -0.10 -0.68 0.02 B:Q47 -0.10 -0.59 -0.05 B:K48 -0.29 -0.34 -1.53 B:K51 -0.28 -1.50 -0.25 B:E54 -0.05 -0.29 -0.06 B:D55 -0.07 -0.28 -0.16 B:D58 -0.07 0.57 -1.06 B:K59 -0.08 -0.48 -0.01 B:E62 -0.10 0.42 -1.05 A:A86 -0.08 -0.49 -0.01 A:N89 -0.14 -0.86 -0.02 A:R90 -0.43 -1.77 -0.97 A:Q93 -0.30 -1.94 0.02 A:L94 -0.08 -0.46 -0.03 A:E97 -0.11 0.89 -1.62 A:D100 -0.11 0.81 -1.53 A:R101 -0.08 -0.73 0.24 A:E104 -0.11 0.26 -0.99 B:R125 -0.34 -0.55 -1.66 B:K128 -0.37 -0.79 -1.57 B:V129 -0.07 -0.43 -0.03 B:E131 -0.08 -0.54 0.02 B:S132 -0.15 -0.92 -0.03 B:Q135 -0.21 -1.27 -0.03 B:K136 -0.17 -0.99 -0.10 B:E138 -0.06 -0.09 -0.33 B:E142 -0.06 0.74 -1.18 A:R160 -0.18 -0.46 -0.68 A:R167 -0.56 -2.04 -1.57 A:V170 -0.22 -1.39 -0.03 A:I171 -0.08 -0.49 -0.03 A:E173 -0.08 -0.34 -0.14 A:S174 -0.13 -0.78 -0.06 A:E177 -0.10 0.65 -1.32 A:R178 -0.10 -0.71 0.11 A:E181 -0.06 0.61 -1.05 B:K198 -0.08 -0.37 -0.14 B:N202 -0.16 -1.07 0.08 B:K205 -0.30 -0.64 -1.31 B:E208 -0.08 -0.70 0.22 B:A209 -0.11 -0.67 -0.04 B:E212 -0.21 -1.15 -0.15 B:K213 -0.13 -0.61 -0.21 B:Q216 -0.29 -1.78 -0.08 B:D219 -0.09 0.80 -1.43 B:E223 -0.08 0.01 -0.55

B:K37 -0.08 -0.29 -0.20 B:V44 -0.19 -1.24 0.01 B:Q47 -0.11 -0.65 -0.07 B:K48 -0.44 -1.08 -1.75 B:K49 -0.06 -0.18 -0.24 B:K51 -0.27 -1.70 0.02 B:D55 -0.12 -0.04 -0.76 B:D58 -0.09 0.51 -1.09 B:K59 -0.13 -0.93 0.12 B:E62 -0.11 0.32 -1.04 A:A83 -0.09 -0.65 0.05 A:A86 -0.10 -0.62 -0.01 A:N89 -0.11 -0.64 -0.04 A:R90 -0.58 -2.10 -1.62 A:Q93 -0.31 -1.89 -0.05 A:L94 -0.18 -1.12 -0.03 A:E97 -0.15 0.52 -1.50 A:D100 -0.07 0.46 -0.97 A:R101 -0.13 -1.03 0.24 B:K118 -0.17 -0.24 -0.86 B:R125 -0.51 -1.47 -1.83 B:K128 -0.41 -1.42 -1.20 B:V129 -0.11 -0.66 -0.03 B:S132 -0.17 -1.05 -0.01 B:Q135 -0.26 -1.63 -0.02 B:K136 -0.17 -1.10 0.02 B:E139 -0.11 1.18 -1.96 B:E142 -0.10 0.32 -0.96 B:I146 -0.11 -0.70 0.02 A:R160 -0.13 -0.27 -0.57 A:R167 -0.51 -1.70 -1.56 A:V170 -0.28 -1.75 -0.01 A:I171 -0.18 -1.15 -0.02 A:S174 -0.14 -0.80 -0.06 A:E177 -0.10 0.23 -0.87 A:R178 -0.11 -0.80 0.09 A:E181 -0.08 0.11 -0.65 A:L185 -0.08 -0.49 0.01 B:K198 -0.08 -0.37 -0.17 B:N202 -0.16 -1.11 0.11 B:K205 -0.31 -1.19 -0.78 B:S206 -0.08 -0.39 -0.11 B:E208 -0.08 -0.16 -0.33 B:A209 -0.18 -1.06 -0.05 B:E212 -0.22 -0.99 -0.40 B:K213 -0.18 -1.06 -0.07 B:Q216 -0.35 -2.16 -0.03 B:D219 -0.13 0.38 -1.24 B:E223 -0.09 0.42 -1.03

7

Figures

Figure S1. RMSD as a function of time for the following trajectories: (a) four MD trajectories of Tm alone (system 1), (b) four MD trajectories of Tm alone (system 3), (c) ten MD trajectories of Tm bound with F-actin (system 2), (d) four aMD trajectories of Tm bound with F-actin (system 2). The curves for trajectory 1, 2, 3, 4 are colored red, green, blue, purple, respectively. More colors (cyan, yellow, black, orange, gray etc) are used in panel (c). The RMSD is measured for Cα atoms relative to the initial model of Tm in unit of Å. The simulation time is in unit of ns.

8

Figure S2. Results of RMSF analysis for: (a) the entire Tm coiled-coil; (b) individual Tm periods separately. The calculations are based on the last 10 ns of four 20-ns MD trajectories of Tm in the absence of F-actin (system 1). The RMSF curves of trajectory 1, 2, 3, 4 are colored red, green, blue, purple, respectively. RMSF is measured for Cα atoms in unit of Å. In panel (b), the gray vertical lines mark the center positions of six Ala clusters (A22, A78, A120, A155, A183, A239), and the black vertical lines separate the periods P1-P7 of Tm.

P1 P2 P3 P4 P5 P6 P7

9

Figure S3. Supplemental results of local flexibility analysis of Tm in the absence of F-actin (system 1) using the following six parameters: (a) adD , (b) *

adD , (c) ASD , (d) D⊥ , (e) AS, (f) diameter. For definitions of these parameters, see Methods. The average and SD of the above parameters as a function of a/d residue positions of Tm are shown as points colored in blue and red, respectively. The long vertical lines mark the center positions of six Ala clusters (A22, A78, A120, A155, A183, A239). The positions of individual core Ala residues are marked by short dashes. The calculations are based on the last 5 ns of four 20-ns MD trajectories of Tm in the absence of F-actin.

10

Figure S4. Supplemental results of local flexibility analysis of Tm in the absence of F-actin (system 3) using the following six parameters: (a) adD , (b) *

adD , (c) ASD , (d) D⊥ , (e) AS, (f) diameter. For definitions of these parameters, see Methods. The average and SD of the above parameters as a function of a/d residue positions of Tm are shown as points colored in blue and red, respectively. The long vertical lines mark the center positions of six Ala clusters (A22, A78, A120, A155, A183, A239). The positions of individual core Ala residues are marked by short dashes. The calculations are based on the last 10 ns of four 20-ns MD trajectories of Tm starting from an X-ray structure of Tm (PDB id: 1c1g).

11

Figure S5. Results of local flexibility analysis of Tm in the presence of F-actin (system 2) using the following six parameters: (a) adD , (b) *

adD , (c) ASD , (d) D⊥ , (e) AS, (f) diameter. The average and SD of the above parameters as a function of a/d residue positions of Tm are shown as points colored in blue and red, respectively. The long vertical lines mark the center positions of six Ala clusters (A22, A78, A120, A155, A183, A239). The positions of individual core Ala residues are marked by short dashes. The calculations are based on the last 10 ns of ten 20-ns MD trajectories of Tm in the presence of F-actin.

12

Figure S6. Results of local flexibility analysis of Tm in the presence of F-actin (system 2) using the following six parameters: (a) adD , (b) *

adD , (c) ASD , (d) D⊥ , (e) AS, (f) diameter. The average and SD of the above parameters as a function of a/d residue positions of Tm are shown as points colored in blue and red, respectively. The long vertical lines mark the center positions of six Ala clusters (A22, A78, A120, A155, A183, A239). The positions of individual core Ala residues are marked by short dashes. The calculations are based on the last 10 ns of four 20-ns aMD trajectories of Tm in the presence of F-actin.

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Figure S7. Projection of MD trajectories onto the plane spanned by the two dominant PCA modes calculated for system 1 (a) and system 2 (b). In panel (a), the four MD trajectories of system 1 are colored red, green, blue and purple; the MD trajectories of system 3 are colored black; three regions sampled by MD trajectories are circled. In panel (b), the first four MD trajectories of system 2 are colored red, green, blue and purple; the additional six MD trajectories are colored black. The initial models correspond to the cyan dots.

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Figure S8. Relative sliding of Tm with respect to F-actin as captured by the first and second PCA mode with the following color scheme: F-actin (gray), Tm at initial position (blue), Tm after being displaced along the first PCA mode (red), Tm after being displaced along the second PCA mode (green). The arrows indicate the movements of residue 1 and 180 (depicted as two balls) along the azimuthal direction. The internal conformational changes within Tm/F-actin are not shown. The C-terminal 100 residues of Tm are not shown for clarity.

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Figure S9. A structural view of actin-binding residues from periods P2-P6 of Tm at the Tm-F-actin interface: Actins and Tm are colored gray and cyan, respectively. The actin-binding residues of Tm are labeled and colored according to residue type (basic, acidic, polar and non-polar residues are colored blue, red, green and white, respectively). Three segments of actin residues (23-28, 144-147, 325-345) involved in Tm binding are colored yellow.

Supporting References* 1. Barua, B., M. C. Pamula, and S. E. Hitchcock-DeGregori. 2011. Evolutionarily conserved surface

residues constitute actin binding sites of tropomyosin. Proc Natl Acad Sci U S A 108:10150-10155. 2. Li, X. E., L. S. Tobacman, J. Y. Mun, R. Craig, S. Fischer, and W. Lehman. 2011. Tropomyosin

position on F-actin revealed by EM reconstruction and computational chemistry. Biophys J 100:1005-1013.

3. Li, X. E., K. C. Holmes, W. Lehman, H. Jung, and S. Fischer. 2010. The shape and flexibility of tropomyosin coiled coils: implications for actin filament assembly and regulation. Journal of molecular biology 395:327-339.

4. Li, X. E., W. Lehman, S. Fischer, and K. C. Holmes. 2010. Curvature variation along the tropomyosin molecule. Journal of structural biology 170:307-312.

5. Li, X. E., W. Lehman, and S. Fischer. 2010. The relationship between curvature, flexibility and persistence length in the tropomyosin coiled-coil. Journal of structural biology 170:313-318.

6. Sumida, J. P., E. Wu, and S. S. Lehrer. 2008. Conserved Asp-137 imparts flexibility to tropomyosin and affects function. J Biol Chem 283:6728-6734.

7. Nitanai, Y., S. Minakata, K. Maeda, N. Oda, and Y. Maeda. 2007. Crystal structures of tropomyosin: flexible coiled-coil. Adv Exp Med Biol 592:137-151.

* The above references were also listed and cited in the main text.

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Probing the Flexibility of Tropomyosin and Its Binding to