Free-Energy Surfaces of Two Cardiac Thin Filament Conformational Changes during Muscle Contraction

Abstract

The troponin core is an important regulatory complex in cardiac sarcomeres. Contraction is initiated by a calcium ion binding to cardiac troponin C (cTnC), initiating a conformational shift within the protein, altering its interactions with cardiac troponin I (cTnI). The change in cTnC–cTnI interactions prompts the C-terminal domain of cTnI to dissociate from actin, allowing tropomyosin to reveal myosin-binding sites on actin. Each of the concerted movements in the cardiac thin filament (CTF) is crucial for allowing the contraction of cardiomyocytes, yet little is known about the free energy associated with each transition, which is vital for understanding contraction on a molecular level. Using metadynamics, we calculated the free-energy surface of two transitions in the CTF: cTnC opening in the presence and absence of Ca²⁺ and cTnI dissociating from actin with both open and closed cTnC. These results not only provide the free-energy surface of the transitions but will also be shown to determine if the order of transitions in the contraction cycle is important. From our calculations, we found that the calcium ion helps stabilize the open conformation of cTnC and that the C-terminus of cTnI is stabilized by cTnC in the open conformation when dissociating from the actin surface.

Graphical Abstract

INTRODUCTION

Cardiac thin filament (CTF), known as the regulatory unit of the cardiac sarcomere, is composed of F-actin, tropomyosin (Tm) coiled coil dimers, and the troponin complex (cTn).¹ The cTn is responsible for initiating a chain of events that ultimately result in the contraction of cardiomyocytes.² It consists of three subunits: cardiac troponin C (cTnC), the calcium binding subunit; cardiac troponin I (cTnI), the inhibitory subunit; and cardiac troponin T (cTnT), the subunit that tethers cTn to Tm and the rest of the CTF. Upon binding of Ca²⁺ to the N-terminal domain of cTnC (N-cTnC), a conformational shift exposes a hydrophobic patch, increasing the affinity for the cTnI switch peptide (residues 149–163). The association of the cTnI switch peptide and N-cTnC hydrophobic patch subsequently decreases the affinity of the cTnI H4 helix (residues 164–188) to actin, permitting the release of cTnI from the myosin-binding site on actin, ultimately resulting in cross-bridge formation with myosin.^2,3

The structure of N-cTnC (residues 1–89) consists of five α-helices (N, A–D; Figure 1), which comprise two EF-hand motifs.^1,4 An EF-hand is a helix–loop–helix structural motif that coordinates Ca²⁺ in calcium-binding proteins. The second EF-hand, known as site II, is known to be a metal-binding site specific to Ca²⁺ and is believed to be solely responsible for the calcium regulation of contraction.⁵ Previous studies have shown that Ca²⁺ binding alone does not induce a large enough conformational perturbation for cTnC to shift into a fully open state. It is believed that the cTnI switch peptide association to the hydrophobic patch has a stabilizing effect on the Ca²⁺-saturated N-cTnC.^2,6–8 This conformational shift of cTnC has been described as an equilibrium of forces that push the protein toward the open conformation and forces that hold it in the initial closed conformation.^9,10

Figure 1.

Conformations of cardiac troponin C (red) in the closed (A) and open (B) states with Ca²⁺ (pink) bound to site II of the N-terminal lobe. The five α-helices of the N-lobe are color coded to highlight the conformational shift between the two states: N-helix (gray; residues 1–11), A-helix (orange; residues 15–27), B-helix (blue; residues 39–49), C-helix (purple; residues 56–64), and D-helix (green; residues 75–85).

The structure of cTnI is composed of a cardiac specific N-terminal domain, two α-helices (H1 and H2) that couple with cTnT to form the IT-arm, and the C-terminal domain residues that extend out of the cTn core. These C-terminal residues include the switch peptide (residues 149–163), the H4 helix (residues 164–188), and the C-terminus (residues 189–210). In a Ca²⁺-unsaturated state, the H4 helix is associated with actin, sterically hindering Tm in a blocked conformation covering the myosin-binding site on the actin surface (Figure 2). Upon Ca²⁺ binding to N-cTnC, the switch peptide has an increased affinity for cTnC, as previously mentioned, while the H4 helix has a decreased affinity for the actin surface.⁸ This allows Tm to traverse the actin surface, shifting from a blocked position to a closed position.¹¹

Figure 2.

Two structures of the cardiac thin filament used for metadynamics simulations including actin (gray), cTnC (red), cTnI (blue), cTnT (yellow), and bound Ca²⁺ ions (pink spheres). The fully blocked state with cTnC in the closed conformation and cTnI is associated with actin, blocking the binding site of myosin (A). The uninhibited state with cTnC in the open conformation with Ca²⁺ bound in the N-lobe and cTnI lifted off of actin (B).

Recently, cryo-EM reconstructions of the CTF have revealed structures for both the Ca²⁺-saturated and -unsaturated states of the cardiac thin filament.¹² This was the first time that structures of all proteins in the CTF were resolved together and the first time that Ca²⁺ depleted structures were resolved. Following this, studies by both Pavadai et al. and Lehman et al. have since refined certain segments in the models: Tm helical pitch and location¹³ and cTnI placement on actin,¹⁴ respectively. Our group has previously published results using these updated structures while also providing initial locations for unstructured segments not included in the cryo-EM maps to include all of the complete proteins of the CTF.^15,16

Understanding the interactions between proteins in the cTn complex is crucial for understanding contraction at a molecular level. Previous work analyzing the opening of cTnC has shown that binding of Ca²⁺ to site II creates a strain on the protein.¹⁰ This strain is alleviated when cTnC changes conformation and is a sufficient enough perturbation to alter dynamics within the N-lobe. With the new forces, the protein is prompted to explore semi-open conformations, allowing for association with the switch peptide on cTnI, which ultimately stabilizes cTnC. However, there is an energetic cost associated with the exposure of the hydrophobic patch; therefore, the opening of N-cTnC is not favorable.

The conformational changes within cTnC and cTnI occur on timescales (long micro- or millisecond timescales) that make the transitions unattainable by study with standard molecular dynamics. Therefore, an enhanced sampling technique, metadynamics,¹⁷ was utilized to sample the free-energy surface of both cTnC opening and cTnI lifting off of actin. Metadynamics is a method where an external force acts on a selected number of degrees of freedom, collective variables (CV), to encourage the exploration of conformational space and the crossing of large free-energy barriers associated with transitions.^17–19 The force applied is an external history-dependent bias potential that is written as a sum of Gaussians deposited along the trajectory in the CV space. No a priori knowledge of the path is needed, only the initial and final states of the system, making this a favorable technique for studying the CTF transitions. Keeping track of the potential added to create these forces allows the inference of the full free energy surface as the inverse function. Previous work in our group has successfully applied metadynamics to study the free-energy barriers of small Tm segments moving into an open position due to myosin binding.¹⁶ Similarly, metadynamics has been applied to study the recovery stroke of two different isoforms of myosin, again supporting the use of metadynamics to uncover the free-energy profile for conformational transitions.^20,21 Here, we simulated the opening of N-cTnC, both saturated and unsaturated, with Ca²⁺ to determine the effect that ion binding has on the conformational transition. We also simulated the dissociation of cTnI from actin with N-cTnC in both the open and closed conformations to establish if the conformational state of cTnC had an effect on the energetics of the dissociation.

METHODS

Structures utilized in this study were created starting from the cryo-EM structures published by Yamada, Namba, and Fujii,¹² as previously described,^15,16 which provided structures for both Ca²⁺-saturated and -unsaturated conformations of the CTF (PDB 6KN8 and 6KN7, respectively). In the context of saturation of the CTF, a fully saturated system refers to Ca²⁺ bound to site II of cTnC, while unsaturated refers to no Ca²⁺ bound to site II of cTnC. Modifications to the published structures included adding unstructured regions of cTnT and cTnI, which cannot be experimentally resolved, using complete Tm dimers for both the N- and C-terminal sides of the overlap region and adding actin monomers to extend the actin filament so Tm was interacting at all points. To add unstructured regions into the new model, the complete proteins from our previous model, which included all residues, were aligned with the structured portions of cTnI and cTnT, respectively. All structured fragments were aligned and the proteins were subjected to minimization until all bonds and angles were acceptable values. Any clashing of proteins was resolved by rotating dihedral angles in the unstructured regions, as previously described.^15,16 The helical pitch of Tm in the Yamada structure was corrected to agree with the protein docking study by Pavadai et al.,¹³ allowing Tm to span 7 actin monomers instead of the 6 monomers in the original pdb. The structure for the cTnI C-terminal domain of the Ca²⁺-unsaturated state was also corrected to agree with the docking study by Lehman et al.,¹⁴ which found a more energetically favorable location compared to the originally published structure.

To define the initial and final positions for cTnC conformational shifts, four separate structures were created, which are referred to the Ca²⁺-saturated-open, Ca²⁺-saturated-closed, Ca²⁺-unsaturated-open, and Ca²⁺-unsaturated-closed states (Figure S1A–D). In the Ca²⁺-saturated-open structure, Ca²⁺ is bound to site II and the N-terminal domain is in the open conformation. The rest of the CTF proteins are in the respective “closed” conformations with the c-terminal domain of cTnI interacting with actin and Tm in the blocked conformation. In the Ca²⁺-saturated-closed structure, Ca²⁺ is bound in site II and the N-terminal domain of cTnC is in the closed conformation. The rest of the CTF proteins are in the respective “closed” conformation, as previously described. These two structures are used as the input for the Ca²⁺-saturated metadynamics simulations.

For the Ca²⁺-unsaturated-open structure, cTnC is in the open conformation, with no Ca²⁺ ions bound in the N-terminal domain. The rest of the CTF proteins are in the closed conformation. Finally, for the Ca²⁺-unsaturated-closed structure, all proteins in the CTF are in the closed conformation and no Ca²⁺ ions are bound in the N-terminal domain of cTnC. These two structures are used as the input for the Ca²⁺-unsaturated metadynamics simulations.

To define the initial and final positions for cTnI release from actin, four separate structures were created, which are referred to as the Ca²⁺-saturated-up, Ca²⁺-saturated-down, Ca²⁺-unsaturated-up, and Ca²⁺-unsaturated-down states (Figure S1B,D–F). In the Ca²⁺-saturated-up state, a fully open cTnC protein with Ca²⁺ bound to site II was combined with cTnI, where the C-terminal domain was lifted off of actin. Tm remained in the blocked conformation. In the Ca²⁺-saturated-down state, a fully open cTnC protein with Ca²⁺ bound to site II was combined with cTnI in a “down” conformation, where the c-terminal domain was associated with actin. These two structures were used as the input for the cTnI moving with cTnC open metadynamics simulations.

For the Ca²⁺-unsaturated-up structure, cTnC was in the closed conformation, with no Ca²⁺ ion bound in the N-terminal domain combined with cTnI, where the C-terminal domain was lifted off of actin. Tm remained in the blocked conformation. In the Ca²⁺-unsaturated-down structure, all proteins were in the fully closed conformations, with no Ca²⁺ ion in the N-terminal domain of cTnC. These two structures were used as the input for the cTnI moving with cTnC closed metadynamics simulations.

All structures were solvated with TIP3P^22,23 waters using the SOLVATE plugin in VMD1.9.3, with the water box extending at least 15 Å from all edges of the protein.²⁴ Potassium and chloride ions were randomly added to a concentration of 0.15 mol/L using the AUTOIONIZE plugin in VMD1.9.3 to prepare the systems for dynamics. All MD simulations were prepared and run with the nanoscale molecular dynamics (NAMD)²⁵ program version 2.13 with the CHARMM36 force field.²⁶ The SHAKE algorithm was used to constrain heavy atom-hydrogen bonds, and all nonbonded interactions were calculated using the Particle Mesh Ewald method with a cutoff of 12 Å. All structures were prepared in the same fashion: starting with an initial minimization of the structures for 5000 steps using the conjugate gradient method, followed by a slow heating at a rate of 1 K/ps to the final temperature of 300 K. Finally, an equilibration of the system in an isobaric– isothermal ensemble (300 K, 1 atm, 690 ps) was performed to produce the final structures used as the input for all metadynamics simulations. Equilibration simulations were calculated using a Langevin piston Nose–Hoover method for the barostat and Langevin dynamics for the thermostat. Visualization and analysis of all trajectories was performed in visual molecular dynamics (VMD) version 1.9.3.

Metadynamics simulations for the Ca²⁺-saturated cTnC opening started with the equilibrated Ca²⁺-saturated-open structure previously created and used the Ca²⁺-saturated-closed structure as the target conformation. The collective variable (CV) chosen for the given simulation was the projection of the difference vector between two coordinate systems. This CV was able to distinctly differentiate between the initial and final states for cTnC, making it an appropriate CV for this simulation. The CV has been previously used to simulate a similar conformational shift in both human myosin and dictyostelium myosin II in previous metadynamics studies performed in our group.^20,21 Therefore, a similar approach was deemed appropriate and utilized for the systems in the current study.

The projection of the difference vector is defined by

$$p=\sum _{i=1}^n\left(x_i^{\prime }-x_i^{\text{ref}}\right)\cdot \left[U\left(x_i(t)-x_{\text{cog}}(t)\right)-\left(x_i^{\text{ref}}-x_{\text{cog}}^{\text{ref}}\right)\right]$$

where x^ref is the coordinates for the reference, x^cog is the coordinates for the center of geometries of the group of atoms, U is the optimal rotation matrix, and x′ is another set of variables. This CV is analogous to the root-mean-squared deviation (RMSD) between two sets of coordinates but prevents strict boundaries at 0 and 1, allowing negative values to be sampled and therefore more accurate estimates of the CV boundaries. For the current study, a p value of 1, the maximum difference between the two states, represents the cTnC open conformation and implies no overlap between the two states. A p value of 0 represents the cTnC closed conformation and indicates that the two structures completely overlap. The progress of the CV from 0 to 1 was monitored through histogram distributions to determine proper convergence. Convergence was determined to be satisfied when the histogram was the flattest across the entire CV. The same CV and parameters were also utilized for the Ca²⁺-unsaturated metadynamics simulation. For this simulation, the Ca²⁺-unsaturated-open structure was used as the initial input, while the Ca²⁺-unsaturated-closed structure was used as the target conformation. All metadynamics simulations were run using the collective variable module in NAMD with Gaussian biases of 0.5 kcal/mol in height being deposited every 2 ps.

Metadynamics simulations for the dissociation of cTnI from actin were subjected to minimization, heating, and equilibration for all structures, as previously described. The CV chosen to distinguish the initial and final states of the transition was the center of mass of alpha carbons for cTnI residues 147 to 190. For the cTnC open simulation, the initial structure used as the input into the metadynamics simulation was the equilibrated Ca²⁺-saturated-down structure previously described, with the target structure as the Ca²⁺-saturated-up structure. For the cTnC closed simulation, the initial structure was the equilibrated Ca²⁺-unsaturated-down structure, with the target structure as the Ca²⁺-unsaturated-up structure. For both simulations, the collective variable module in NAMD was utilized with Gaussian biases of 1.5 kcal/mol in height being deposited every 2 ps.

Root-mean-squared fluctuations (RMSF) were calculated using alpha carbons of the respective protein in VMD1.9.3.²⁴ Electrostatic interactions were calculated using the SALT BRIDGES plugin in VMD1.9.3, with the oxygen-nitrogen cutoff distance set to the default value (3.2 Å). Similarly, hydrogen bond interactions were calculated in VMD1.9.3 using the HBONDS plugin with default parameters set (3.0 Å donor–acceptor distance, 20° angle cutoff).

RESULTS AND DISCUSSION

Metadynamics simulations were performed to sample the underlying potential energy surface of both the cTnC N-lobe opening and cTnI switch peptide/H4 helix lifting off of actin to determine the overall free-energy change for each conformational transition, respectively. For cTnC, simulations were run both with and without Ca²⁺ bound to site II of the N-lobe to determine the effect the ion binding has on the opening of N-cTnC. To determine how the conformations are affected by the presence or absence of Ca²⁺ occupying site II, a unique CV was defined for each segment of cTnC: Helix N (residues 1–11), N–A linker (residues 12–14), Helix A (residues 15–27), A–B linker (residues 28–38), Helix B (residues 39–49), B–C linker (residues 50–55), Helix C (residues 56–64), C–D linker (residues 65–74), and Helix D (residues 75–85). All nine one-dimensional contributions to the overall free-energy change were determined concurrently (Figures S2–S10), resulting in the overall free-energy surface, as seen in Figure 3.

Figure 3.

Total free-energy change for the conformational shift of both Ca²⁺-saturated (black) and Ca²⁺-unsaturated (red) cTnC. The CV value 1 represents the open state, while the CV value 0 represents the closed state.

For cTnI, simulations were run with cTnC in both the open and closed conformation to determine whether it is energetically (thermodynamically) favorable to have cTnC open prior to cTnI lifting off of actin. The CV was designated as the distance between the center of mass of cTnI residues 147–190 in the initial actin-bound conformation (CV value 13) and the final released conformation (CV value 0). The free-energy surface for the given transition is shown in Figure 4.

Figure 4.

Total free-energy change for the dissociation of cTnI from actin with cTnC in both the open state (black) and closed state (red). The CV value 13 represents cTnI fully associated with actin, and the CV value 0 represents cTnI fully dissociated from actin.

The free-energy profile (Figure 3) for Ca²⁺-saturated cTnC shows a ~12 kcal/mol decrease in free energy when transitioning from the initial open (CV value 1) to the final closed (CV value 0) conformations. This conformational shift toward the N-lobe of cTnC closing closes a hydrophobic patch that is energetically favorable due to the reduction of the hydrophobic residue interactions with water, ultimately stabilizing the closed conformation of cTnC. After the initial move away from the “open” conformation (0.9–1.0), a small well suggests that a slight stabilization occurs at that conformation. A significant stabilization is observed at a CV value of 0.4. This stabilization may be due, in part, to several strong hydrogen bond interactions forming between distant regions in the cTnC N-lobe (Ile36–Val72, Thr38–Gly70, Ser84–Leu48 and –Gln50; Figure 5A). These interactions form as cTnC begins to open, helping to stabilize the opening, and do not form in the Ca²⁺-unsaturated simulations (Figure 5B; Table S1).

Figure 5.

Differences in interactions between residues in loop regions of cTnC (red) for Ca²⁺-saturated and -unsaturated simulations (A,B, respectively). The interactions between cTnC and the cTnI switch peptide (blue) for Ca²⁺-saturated and -unsaturated simulations (C,D, respectively). Differences in interactions between N-helix residues in cTnC for Ca²⁺-saturated and -unsaturated simulations (E,F, respectively). Hydrogen bonds between residues are represented by dashed black lines.

As the N-lobe of cTnC opens, the C-helix shifts toward the inhibitory peptide of cTnI. Throughout the simulations, electrostatic interactions between cTnC residue 56 and either cTnI residue 141 or 146 begin to form (Figure 5C). These interactions are either not observed or unstable (>5 Å) when Ca²⁺ is not present (Figure 5D). These interactions are important to initiate the binding of the cTnI inhibitory peptide to cTnC, a crucial step in the contraction cycle that is believed to prompt the dissociation of cTnI from actin, exposing the myosin-binding site. Once the initial binding of cTnI occurs, the association between the two proteins is likely the driving force that makes the overall cTn conformational shifts favorable during contraction.

The free-energy profile (Figure 3) for Ca²⁺-unsaturated cTnC shows a ~25 kcal/mol decrease in free energy when moving from the initial open (CV value 1) to the final closed (CV value 0) conformations. After the initial move away from the “open” structure (0.8–1.0), a small well suggests a slight stabilization of that conformation. The Ca²⁺-unsaturated free-energy surface is relatively flat, with small oscillations after this initial move until a free-energy barrier (~9.5 kcal/mol) at a CV value of 0.1, with a well occurring at a CV value of 0.0. The free-energy barrier observed at a CV value 0.1 is, in part, due to interactions within cTnC beginning to break and the solvent accessible surface area (SASA) of hydrophobic residues increasing. From the calculations, the most stable conformations for Ca²⁺-unsaturated cTnC occur at CV values 0.0 and 0.8; however, the free-energy surface suggests that the fully open conformation is unstable due to the sharp increase in free energy at 0.8–1.0.

Of note, the Ca²⁺-saturated free-energy surface is ~20 kcal/mol above the Ca²⁺-unsaturated free-energy surface, which is due to each of the nine individual one-dimensional contributions strongly favoring one configuration (open or closed). A significant contribution to the free-energy difference between the Ca²⁺-saturated and -unsaturated plots comes from the interactions between helix N (residues 1–11) and the rest of cTnC. For Ca²⁺-unsaturated, Lys6 has strong electrostatic interactions with Glu63 and Glu66 (Figure 5F). For Ca²⁺-saturated, Glu63 forms strong electrostatic interactions with Arg83 (1.75–3 Å), while Glu66 forms hydrogen bonds with Glu76 (1.75–2.5 Å), and when cTnC opens, Glu66 also forms electrostatic interactions with cTnI Lys38 (Figure 5E; Table S1). Residues within the binding pocket and directly adjacent are the most likely to be affected by Ca²⁺ binding. Residue interactions shown in Figure 5 panels E and F differ due to the influence of binding of the calcium ion, which cascades throughout the N-lobe, allowing for more interactions to form between helices and loops in distant parts of the lobe that are not observed in the absence of Ca²⁺. These longer distance interactions are less effective at stabilizing the overall structure; hence, there is an overall upward shift in the potential of mean force, yet the free-energy difference between open and closed is in fact lower for the Ca²⁺ saturated state.

In addition to Ca²⁺ binding affecting structural interactions from binding pocket residues (65–76) to residues in other regions of cTnC, the RMSF of this region significantly changes (Figure 6). When Ca²⁺ is not bound compared to when it is bound, the average RMSF of residues 65–76 is 7.881 and 5.619 Å, respectively. All other regions of cTnC have similar RMSFs for Ca²⁺-unsaturated and -saturated, suggesting that the Ca²⁺ ion acts as a stabilizing agent for the binding pocket as well as the neighboring C-helix and N-terminus of the D-helix (forming the EF hand II). These results indicate that Ca²⁺ has both structural and dynamic effects on N-cTnC, exhibiting the importance of the ion’s binding.

Figure 6.

Root-mean-squared fluctuation plot of the N-terminal lobe residues of cTnC for Ca²⁺-saturated (black) and -unsaturated (red) simulations.

We wish to emphasize that overall changes in the free energy for the Ca²⁺-saturated and -unsaturated disagree with previous MD studies.^7,27 The previous MD studies also disagreed with each other. The first study by Lindert et al. found that the free-energy difference for cTnC opening for Ca²⁺-bound systems was ~8 kcal/mol, while that for the Ca²⁺-unbound system was ~12 kcal/mol. The second study by Bowman and Lindert found that there was no significant difference between Ca²⁺-bound and -unbound systems (11.5 and 11.6 kcal/mol, respectively). Differences are likely due to previous studies simulating only the N-terminal domain of cTnC, neglecting interactions with other proteins in the CTF that are included in the systems used in the present study. Calcium-binding studies have shown significant differences in results when looking at isolated cTnC versus the whole CTF,²⁸ suggesting that all proteins in the complex need to be present for the most accurate results when studying cardiac contraction.

cTnI Moving.

The free-energy profile (Figure 4) for cTnI dissociating from actin with cTnC closed shows a ~17.8 kcal/mol increase in free energy between the initial down (CV value 13) and the final up (CV value 0) conformations of cTnI. A stabilization occurs at a CV value of 11.5; however, the free energy increases from that conformation until cTnI is completely lifted off of actin (CV value 0).

Starting at the beginning conformation, where cTnI is associated with actin (CV value 13), there is a stabilization at a CV value of 11.5, which is due to the switch peptide and H4 helix of cTnI shifting into a more favorable position along actin. Moving from the CV value 11.5 to 1.8, there are three free-energy barriers that are due to interactions between cTnI and actin breaking. The first barrier between the CV value 11.5 to 9.8 is ~10.7 kcal/mol, the second barrier between the CV value 8.9 and 4.8 is ~5.8 kcal/mol, and the third barrier between the CV value 4.8 and 1.8 is ~11 kcal/mol. The most notable breaking of interactions that contribute to the free-energy barriers include several hydrogen bonds formed between the cTnI H4 helix and actin (residue 170–actin residues 167, 149, or 292; cTnI residue 166–actin residues 57, 60, 61; cTnI residue 162–actin residues 93, 56). There are also several strong electrostatic interactions between cTnI and actin that help stabilize the H4 helix in the “down” conformation across actin. Specifically, cTnI residue 165–actin residue 95, cTnI residue 162–actin residues 93 and 56. The salt bridges are all stable at 3–3.5 Å, while cTnI down-interacts with actin. Once cTnI begins to lift off, the salt bridges break, factoring in the increase in free energy seen in Figure 4. Of note, the cTnI residue 162 is a mutational hotspot that may be due to the importance of interactions securing cTnI to actin when the CTF is in the blocked state. As cTnI lifts off of actin, residues 162 and 165 form a salt bridge, helping to stabilizing the helix in the “up” conformation.

Several hydrogen bonds between cTnI and cTnC (cTnI residue 140–cTnC residues 142 and 143; cTnI residue 146 and cTnC residue 56) were observed throughout the trajectory (Table S2). No new salt bridges or hydrogen bonds between cTnI and cTnC formed when cTnI lifted off of actin, suggesting that there was no additional stabilization of the helix from cTnC (Figure 7A). This is supported by the free-energy plot showing a constant increase in free energy from a CV value of 11.5 to 0 from interactions breaking but no new stabilizing interactions forming.

Figure 7.

Difference in interactions between cTnC and cTnI switch peptide when cTnI dissociated from actin with cTnC in the closed and open conformations (A,B, respectively). With cTnC in the closed conformation, Arg141 on cTnI is the only residue that can interact with cTnC. When cTnC is in the open conformation, several strong interactions between cTnI and cTnC are formed, including Arg141.

The free-energy profile (Figure 4) for cTnI lifting off of actin with cTnC open shows a ~14.1 kcal/mol increase in free energy between the initial down (CV value of 13) and the final up (CV value 0) conformations of cTnI. A significant stabilization occurs at a CV value of 2.4, with several other local minima leading up to that conformation from the “down” cTnI conformation.

Beginning with the initial conformation of the CTF with the cTnI switch peptide and H4 helix in the down position, associated to actin, and cTnC in the open Ca²⁺-saturated conformation, the first free energy barrier is between CV values 13 and 10.4 (~6.8 kcal/mol). The next free energy barrier is ~11.4 kcal/mol between the CV values of 10.0 and 7.0. These barriers are due to interactions breaking between cTnI and actin, more precisely the salt bridges between cTnI residue 170–actin residues 167 and 292; cTnI residue 162–actin residue 56; and cTnI residue 165–actin residue 61. All salt bridges are stable at 3–4 Å when cTnI interacts with actin but become unstable and break once cTnI begins to lift off of actin. The breaking of these interactions is the most prominent contribution to the free-energy barriers seen in Figure 4. Once the N-terminus of the switch peptide begins to break interactions with actin, several hydrogen bond interactions between cTnI and cTnC form (cTnI residue 146–cTnC residue 59; cTnI residues 149, 150–cTnC residue 56; cTnI residues 152, 153–cTnC residue 55; Figure 7B), likely leading to the stabilization seen in the free-energy profile at a CV value of 2.4. In addition to the hydrogen bonds that form, there is a salt bridge between cTnI and cTnC that is present in the complete trajectory, similar to findings from the cTnC-closed simulation discussed above: cTnI residue146–cTnC residue 56 (Table S2). Figure 7 shows that when cTnC is in the closed conformation, the protein is too distant from cTnI to form the necessary interactions that lead to the stabilization. Therefore, cTnC needs to be in the open conformation for the dissociation of cTnI from actin to be favorable.

CONCLUSIONS

The enhanced sampling method, metadynamics, has been utilized to simulate two conformational changes within the CTF that are on timescales too long to observe using traditional molecular dynamics. Through these simulations, we were able to determine the effect of Ca²⁺ binding on the conformational shift in cTnC. It was found that binding of Ca²⁺ to N-cTnC stabilized the binding pocket and increased the number of interactions between cTnI and cTnC, which ultimately decreased the change in free-energy between open and closed positions compared to the unsaturated simulation. There was a stabilization of the Ca²⁺ saturated structure at CV 0.4, which suggests that Ca²⁺ binding is responsible for stabilizing cTnC in a semi-open position, while cTnI association to cTnC may be responsible for driving the transition to a fully open conformation. With the cTnI dissociation from the actin surface, metadynamics simulations revealed that cTnC needs to be in an open conformation for the transition to be favorable. If cTnC is in a closed conformation, the C-terminus of cTnI does not get stabilized when dissociating from actin and is therefore not favorable. When cTnC is in the open conformation, the C-terminus of cTnI is continually stabilized until it is almost fully open due to new interactions formed with cTnC. The sharp increase in free energy from CV 0.0 to 0.2 may be due to the secondary structure of the helix losing form, which has been observed in the literature previously.^29,30

Methods introduced in this study were able to uncover important residue–residue interactions within the Tn core for two different steps of the initiation of contraction. Results here help to gain a broader understanding of muscle contraction, specifically the regulation within the CTF, on a molecular level. These techniques can be further applied to different steps of the contraction cycle to help create a complete picture of the free-energy barriers that occur during the contraction of cardiac sarcomeres. Further, mutations can be introduced into structures to study how the dynamics of contraction may be affected, helping to provide a more complete picture of mutational effects in the CTF.