Calmodulin-TFP system preparation and equilibration

To enable extensive sampling of TFP bound to the multitude of C-CaM conformational states, we chose to initiate simulations in a diversity of conformational states. To do so, we obtained the three C-CaM states predicted from simulations of the 3CLN structure [33] in our prior work [5]–states 2, 5 and 6, which correspond to Calmodulin’s binding to partner proteins in shallow, intermediate and deep manner respectively (S1 Fig). The initial TFP positions within each state were generated by alignment of the C-CaM Cɑ to chain A of the 4RJD [25] structure. To account for the reduced ligand diffusivity within the collapsed hydrophobic core of state 2, we obtained an additional TFP initial pose by alignment of the C-CaM Cɑ to chain B of the 4RJD structure.

Each Ca²⁺ bound CaM-TFP complex obtained thereby were placed in a box containing a solution of 22598 water molecules and Na⁺ counter-ions. The system interaction energies were minimized until the maximum force on an atom was < 1000 kJ/mol and equilibrated by a 20 ps NVT ensemble with harmonic restraints of 1000 kJ/mol/nm² applied to protein and TFP atoms. Pressure was then relaxed, and the box scaled using a Berendsen barostat [34] for 20 ps with similar restraints on the protein and TFP atoms.

Replica exchange solute tempering and adaptive sampling simulations

Before initiating the MD simulations for MSM construction, we ran replica exchange solute tempering (REST) simulations [35,36] to quickly explore the CaM-TFP conformational landscape and obtain a wide range of initial configurations to launch the initial round of adaptive sampling simulations. As such, the REST simulations were not run until convergence of the free energy landscape and not used in the MSM analysis. In temperature replica exchange (REMD) simulations, parallel simulations are run at different temperatures with the higher temperatures allowing a faster exploration of conformational states. REST simulations are a modification of the REMD algorithm wherein only a subset of the system is heated to enable a wider temperature span for the same number of replicas, thereby making the method more efficient for state exploration [36]. We initiated three sets of REST simulations from each of the three bound states with 5 replicas run for 500 ns each. Exchanges between adjacent replicas were attempted every 4 ps and the ‘temperature’ span (303.15 K to 330 K) was determined using the temperature predictor of Patriksson and van der Spoel [37] by only considering the CaM-TFP atoms. Efficiency of the REST simulations exchanges was assessed by analyzing the energy overlap between adjacent replicas and exchange probability (S2 Fig). Protein-ligand contacts of the lowest-temperature replica were then projected onto the two slowest degrees of freedom (called ‘tICs’—see ‘Selecting distance-based features and projecting the data onto slow degrees of freedom’). The two tICs were obtained from the continuous REST trajectories. For each CaM-TFP state, 10 points uniformly distributed across the two-dimensional grid spanning the extent of these two tICs were selected–and their representative conformations were used to initiate the first round of 100 ns-long unbiased MD simulations. Doing so ensured the initiation of MD simulations from both free energy basins and barriers with equal probabilities.

For subsequent rounds of adaptive sampling, we used a counts-based method to sample new initial configurations. This was done by first building an MSM (see ‘Construction of a Markov state model’) using the existing unbiased MD simulations and randomly selecting microstates to sample from, based on the stationary distribution over microstates. Specifically, the probability of sampling an initial configuration from a microstate was inversely proportional to its stationary probability [38]. Thus, microstates with a low stationary probability were more likely selected for seeding new simulations. In other words, rarely visited parts of the conformational landscape were more often chosen to launch new simulations. This simple counts-based method has been demonstrated to be efficient for exploring new states [38,39]. Through eight rounds of such adaptive sampling, we accumulated a combined simulation time of 20.8 μs across the initial C-CaM/TFP binding configuration.

Molecular dynamics simulation parameters

The MD simulations were performed using Gromacs 2018 [40] with a timestep of 2 fs. For the REST simulations, we used Plumed 2.3.5 [41,42]. Long-range electrostatic interactions were calculated using the particle mesh Ewald method [43] and hydrogen-bond lengths were constrained using LINCS [44]. Pressure and temperature were maintained through the use of the Parrinello–Rahman barostat [45] (1 bar) and Nose-Hoover (300 K) thermostat [46] respectively. The protein was described using the Charmm36 force field [47], water using the TIP3P model, Ca²⁺-ions using the Charmm27 parameters of Liao et al. [48] and TFP parameters were generated using STaGE [49].

Selecting distance-based features and projecting the data onto slow degrees of freedom

To build the MSM, we first determined distance features to describe TFP binding-modes within C-CaM. For this, the minimum distances between the 60 C-CaM residues 88–147 and five TFP atoms (C25, C24, C10, SC4, C16) were calculated. The five atoms were chosen to encompass the ligand’s functional groups (Fig 1C)–the C25 atom is within the aromatic ring while C10 is adjacent to the trifluoromethyl group, and the SC4 Sulphur is situated between the two. The C16 and C24 atoms, on the other hand, are situated within the alkyl linker and piperazine groups respectively. These distances were transformed into quasi-binary contacts, varying cut-offs from 5 to 8 Å, using the following transformations:

To maximize the kinetic variance within the features, we evaluated these eight different feature types using the variational approach for Markov processes (VAMP2) score [50,51]. Each feature type was scored at 5 lag-times (2 ns, 5 ns, 10 ns, 15 ns, 20 ns) using the top ten eigenvalues and 5-fold cross-validation. S3 Fig shows the mean scores for different lag-times. The scores suggested that these feature types yielded MSMs of similar quality. However, the feature type given by a 6 Å cutoff and inverse distances yielded the highest mean VAMP2 score across lag-times, and this feature type was therefore selected for MSM construction.

The data was projected with time-lagged independent component analysis (tICA) [52] using time-lagged correlation matrices (tICA time-lag of 20 ns). A tICA projection provides a low-dimensional representation of the data along the slowest degrees of freedom. Overall, we used the python package MDTraj [53] to compute distance-based features, MSMBuilder [54] for parameter optimization and pyEMMA [55] for scoring the distance-based features, projecting the data, building the MSM and extracting the final macrostates.

Construction of a Markov state model

The Generalized matrix Rayleigh quotient (GMRQ) method was used for MSM hyperparameter selection. S4 Fig shows the GMRQ scores calculated from 5-fold cross-validation, suggesting that the inclusion of the 10 slowest time-lagged independent components (tICs) and 200 microstates is sufficient to describe the Markov model. The 10 slowest time-lagged independent components (tICs) obtained from the full set of simulations were thus used as input to k-means clustering to obtain 200 microstates. To select a Markovian, or memoryless, lag-time for the MSM, we first estimated a set of transition probability matrices at varying lag-times. Each such matrix describes the probability of transitioning between microstates at a specific lag-time. By plotting the implied timescales [56,57] of the obtained transition matrices, we identified a Markovian lag-time where the timescales appear to converge (15 ns–S5 Fig). The final MSM was constructed using this lag-time, and used to assign probability weights (π_i) to each trajectory frame i. Equilibrium averages of any system characteristic O could then be obtained with a weighted sum,

The number of MSM metastable states was selected using eigenvalue spectral analysis of the MSM transition matrix (S6 Fig). PCCA++ spectral clustering [58,59] was then used to estimate the probability of a trajectory frame belonging to each macrostate. Finally, we identified core-states by assigning a trajectory frame to one of the macrostates if the state probability was >80%. The rest of the trajectory frames were left as transition points. The core states allow us to better distinguish the states due to reduced noise in state-definition.

Identification of important residues using machine learning

To pinpoint C-CaM residues participating in important residue-interactions of each identified TFP binding state, we used the demystifying toolkit [60]. This approach is based on explainable artificial intelligence (AI). In short, a machine learning model can be trained to recognize the three major states based on each frame’s internal coordinates and metastable state-assignment. We may then ask the model which input features contributed the most to making a classification (state assignment) decision. Here, the input features were given by the inverse distances between all C-CaM residue pairs which were less than 6.5 Å in at least one frame and more than 6.5 Å in another. It should be noted that this contrasts with the feature types used for MSM construction which considered distances between CaM residues and selected TFP atoms. We trained random forest (RF) models using scikit-learn [61] and default parameters as determined in Fleetwood et al. [60] to recognize each metastable state given the input features and calculated the importance of residue-interactions for distinguishing between states by their Gini-importance [62]. Moreover, we calculated the Kullback-Leibler divergence of inverse residue-distance distributions for comparison. For both models, we trained one model per state in a one-versus-the-rest fashion. Finally, the per-residue importance was calculated as a sum over all the residues’ interactions. The obtained residue importance was normalized between 0 and 1.

Validation of Markov state model and identification of three major metastable states

We projected two-dimensional MSM free-energy landscapes along the three slowest time-dependent independent components (tICs). The best state separation was observed when the data was projected along tIC1-tIC3 (Figs 2A, S7 and S8). This free-energy landscape suggested the presence of three well-defined major local minima. The projection of the TFP-bound C-CaM structures onto the tIC space revealed how the free energy basins obtained using MD simulations compared with experimentally resolved structures: the 4RJD (Chain—or CaM molecule—B) and 1CTR structures indeed differ from 1A29 and 1LIN along tIC3. Interestingly, Chain A of the 4RJD structure is displaced from the other structures along tIC1, located close to a separate free-energy minimum. To further validate these free energy minima, we analyzed the paths taken by the various sampled trajectories and confirmed that we observe multiple transitions between the free-energy basins. Hence, the coverage of the conformational space by the combined set of MD simulations was extensive (S9 Fig).

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Fig 2.

(A) Projection of the Markov state model free-energy surface along the time-lagged independent components tIC1 and tIC3. The projection of the 4RJD (Chains A & B) [25], 1LIN [23], 1A29 [24] and 1CTR [22] crystallographic structures onto the surface are shown as white dots. (B) S₁-S₇ macrostate assignments along the tICs obtained from PCCA++ clustering. Each trajectory frame is represented as a dot within the scatter plot. The stationary probability distributions of the seven macrostates and the associated standard deviations are shown in the inset.

https://doi.org/10.1371/journal.pcbi.1010583.g002

Based on the MSM spectral analysis, we selected and extracted seven metastable states (S6 Fig). Fig 2B shows the resulting clustering, where each dot corresponds to a trajectory frame, colored by its macrostate assignment. The seven states (S₁-S₇), which were validated by Chapman-Kolmogorov tests (S10 Fig), are well separated in the tIC space (S7 and S8 Figs). We note, however, that the three major macrostates (S₅, S₆, S₇) accounted for ~98% of the stationary probability distribution (Fig 2B). We thus proceeded to characterize these three major TFP binding-modes and their effect on C-CaM conformations.

The metastable states represent distinct TFP binding modes

We first identified the coarse molecular features of each metastable state by calculating the ligand root mean square displacement (RMSD) across frames in the state after alignment of the C-CaM Cɑ atoms. The trajectory frame with the lowest mean RMSD was then selected as a representative structure. A visual inspection of the resulting representative binding modes provides an initial explanation of their separation in tIC-space (Fig 3A). The trifluoromethyl (CF₃) moiety of TFP within S₅/S₆ and S₇, for example, is found in reversed orientations, either pointing towards or away from the hydrophobic pocket, respectively. Consistently, the experimentally resolved structures projected onto the free energy basins display similar ‘flipped’ configurations: the CF₃ group points towards the hydrophobic pocket in 4RJD (Chain A) [25], 1A29 [24] and 1LIN [23], and away from the pocket in 4RJD (Chain B) [25] and 1CTR [22].

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Fig 3.

(A) Representative structures of the S₅, S₆ and S₇ macrostates aligned using the Cɑ C-CaM. The flipped orientation that buries the CF₃ moiety within the S₅ and S₆ macrostates is highlighted using an orange circle. The three F92, F141 and M124 residues whose interactions characterize apo- and holo-CaM states are illustrated. (B) Relative contact frequency of the TFP atoms with C-CaM residues compared between the three S₅, S₆ and S₇ macrostates. The flipped orientation that buries the CF₃ moiety within the S₅ and S₆ macrostates is highlighted using an orange circle and the contrasting burying of the C10 atom with S₇ is highlighted using cyan circles. (C) Projection of the centres of the three populated macrostates onto the calculated free-energy surface along time-dependent independent components tIC1 and tIC3. Transition rates representing the mean first passage times between the macrostates and the associated standard deviations are illustrated as arrows.

https://doi.org/10.1371/journal.pcbi.1010583.g003

Clearly, state S₇ represents a separate binding pose compared to S₅ and S₆. A distinct difference between S₅ and S₆ is, however, difficult to assess by visual inspection. Moreover, unlike the static representative structures, the ensembles of microstates provide a dynamic picture of residue movements and interactions with TFP. To account for the conformational heterogeneity within metastable core-states, we therefore analyzed the ensemble of frames assigned to each state. By doing so, we set out to reveal subtle, but important, differences in the interactions between TFP and CaM. First, we validated the pose difference across metastable states by studying the state-dependent interactions between TFP atoms and C-CaM residues. The difference in contact frequencies between the three metastable states is shown in Fig 3B. Consistent with a flipped orientation between S₅/S₆ and S₇, the C10 and C25 atoms located at opposite edges display similar delta contact frequencies within the S₇:S₅ and S₇:S₆ differences. In S₅ and S_6, the C25 atom and the Fluorines are buried to interact with the F89/F92 residues at the base of the hydrophobic pocket (orange circle). Alternatively, in S₇, the C10 atom slots into the hydrophobic pocket and interacts with the buried aromatic residues (cyan circle). The differences between the S₅ and S₆ binding poses, however, remained difficult to characterize. Indeed, these differences are subtle, and the orientation of the phenothiazine tricyclic is identical in both states. The atomistic contact analysis instead suggests that the main difference between the two binding-modes primarily stems from the interactions between C24 and the residues making up the binding pocket.

To depict the dynamics of interconversion between TFP binding modes, we calculated the mean first passage times (MFPT) [63] between the three major macrostates. The results demonstrate that the S₅ and S₆ states interchange on the sub-microsecond timescale while exchanges with the S₇ state occur on a significantly longer timescale, consistent with the structural differences observed above. Interestingly, the MFPTs also show that a transition to S₇ from the S₅ state with the buried TFP typically requires a longer timescale than a transition from the less buried TFP pose in state S₆. This hints that although S₆ is globally more similar to S₅, it may represent an intermediate state with subtle features similar to both S₇ and S₅.

TFP binding-modes alter the C-CaM binding pocket by affecting local interactions at a Ca²⁺-binding site

With the MSM, we were able to identify three major macrostates which agree with the experimentally resolved TFP-bound configurations. However, the backbone conformations of C-CaM in the representative structures are nearly identical, with a maximum Cɑ RMSD of only 1.71 Å between them. Hence, we hypothesize that the effect of TFP binding-modes on C-CaM conformation is instead manifested through subtle state-dependent changes of residue interactions. To pinpoint CaM residues with distinct interaction patterns in the three states, we utilized machine learning and explainable artificial intelligence [60]. Briefly, we used a random forest (RF) classifier to recognize the three major states based on internal coordinates and metastable state-assignment, and then extracted the per-residue accumulated feature importance (see ‘Materials and Methods’).

Fig 4A–4C show the state-dependent RF importance profiles. A high RF importance indicates large state-dependent changes in the residue’s interaction pattern and thereby suggests movement of the residue relative to its interacting residues. Estimating importance from the Kullback-Leibler divergence between distances’ probability distributions validates these importance profiles by yielding profiles which share main features with the ones obtained by RF (S11 Fig). As expected for S₅/S₆ and S₇ states with opposing orientations, the RF models identify M144 and F92 residues as important for discerning the states. This result is consistent with the C10 atom oriented towards these residues in the respective states [25]. In fact, both F92 and M144 are highly conserved residues [64], often interacting with target-proteins [7]. Earlier work showed that exposure of F92 to solvent favors deep binding to target-proteins [5], and that the F92A mutant is linked to a drop in ion affinity [65]. In addition to F92, we also note that F141, another highly conserved residue [64], has a relatively high importance in the S₇ profile. Not only is F141L a known long QT syndrome (LQTS) mutation which also decreases Ca²⁺-affinity [66,67], but the interaction and stacking of F141 and F92 has been shown to associate with the transition from apo- to holo-like conformations [13]. Moreover, we observe an increased importance of V108 in S₇ (Fig 4A). This residue is indeed important for the packing and repacking of these aromatic residues during the transition from apo- to holo-like conformations [13]. It was also found important to characterize the overall conformational ensemble of C-CaM [60]. Finally, we note that N111 has a relatively high importance in the S₇ profile (Fig 4A). This residue has also been suggested to change interactions upon Ca²⁺-binding [68]. To further rationalize the structural basis of the importance profiles, we calculated the change in mean inter-residue distances between the states (Fig 4B). Consistent with the RF importance predictions, distances between the helices comprising the F92 and F141 residues are further apart in S₇ than in S₆/S₅ (orange circle). The helix comprising the V108 and N111 residues show similar state-dependant differences with distance to the F92 helix farther in S₇ than in S₆/S₅ (cyan circle) and distance to the F141 helix farther in S₆/S₅ than in S₇ (black circle)–a result consistent with the residues’ capability to impede hydrophobic stacking within the C-CaM core.

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Fig 4.

(A) The per-residue importance in discerning the S₅, S₆ and S₇ macrostates calculated using the supervised Random Forest method. Plots represent the mean importance values calculated from five-fold cross-validation and the standard deviations are plotted as error bars. Physiologically important residues and those with high importance values are illustrated using red dotted lines. (B) Relative C-CaM inter-residue distances compared between the S₅, S₆ and S₇ macrostates. The important F92, V108, N111 and F141 residues identified by the Random Forest method are illustrated as dotted lines. The increased distance between the F92-F141 and F92-V108 residue pairs in S₇ are highlighted as orange and cyan circles respectively. The decreased distance between the V108-F141 residues in S₇ is highlighted with a black circle/ (C) Distance between center-of-mass of the N97 and E104 residues making up the Ca²⁺ binding site within the S₅, S₆ and S₇ macrostates. Each violinplot spans the 5th and 95th percentile of distances and densities are weighted by the Markov state model probabilities. The median value for each macrostate is represented as a white dot. The inter-residue distances calculated from apo- (PDB: 1CFD [9]) and holo- (PDB: 1CLL [8]) calmodulin structures are shown as grey and black dotted lines respectively. The mean inter-residue distances within MD simulations [5] of apo- and holo-CaM are shown as grey and black dashed lines respectively. The standard-deviations of the residue distances within the MD simulations are shown as a shaded area.

https://doi.org/10.1371/journal.pcbi.1010583.g004

Next, we detect differences in the importance profiles of S₅ and S₆ (Fig 4A). We find that N97 is important for recognizing S₅, while F92 appears to change its interaction pattern in S₆. Interestingly, the N97I mutant has been shown to lead to a reorientation of the hydrophobic domain [3], while the N97S mutant causes LQTS [67]. The latter has specifically been shown to affect the activation of the voltage-gated ion channel KCNQ1 likely due to the interactions between CaM and the voltage-sensor domain during channel activation [69,70]. The estimated importance of F92 is likely due to its position within the hydrophobic pocket and interaction with TFP (Fig 3A). N97, on the other hand, is on a loop distant from the hydrophobic pocket, and instead coordinates one of the bound Ca²⁺ ions (Fig 1B). To assess the state-dependence of residue interactions within this Ca²⁺-binding site, we computed the distribution of distances between the N97 and its interacting residue E104 for each state (Fig 4C). In the S₅ state, the residues are stable at a spatially close distance, a characteristic of holo CaM. The flipped TFP pose in state S₇, however, disrupts the ion-binding site and leads to a more apo-like conformation with a larger separation of the residues. Incidentally, TFP binding in C-CaM has been suggested to markedly reduce the Ca²⁺ affinity [32], possibly due to such disruptions at the ion binding site. Consistent with the higher affinity of the second Ca²⁺-binding site [71], however, the TFP binding modes display no noticeable disruption on its stability (D129-D133 –S12 Fig).

Flipping of the TFP molecule affects the hydrophobic pocket and is associated with a changed β-sheet structure content

As mentioned above, the process of binding and unbinding Ca²⁺ is intrinsically associated with CaM conformational changes. In the presence of ions, the lobe undergoes a ‘repacking’ of hydrophobic residues which is characterized by the movement of the F92 residue. This repacking results in a stacking of four aromatic residues (S13 Fig) [13]. Motivated by the findings from the state-dependent RF importance profiles, we therefore investigated how the different TFP binding-modes affect the hydrophobic pocket. To characterize this, we studied the interactions between F92, M124 and F141 –three residues from different helices whose sidechains subtend into the pocket (Fig 1E). In fact, M124, together with M109, M144 and M145, make up the set of highly conserved methionines [64] which often participate in target-protein binding [11,12].

Fig 5A shows the hydrophobic packing along two inter-residue distances–the F92-F141 and F92-M124 distances. In contrast to the other two states, the slotting of the C10 atom with its aromatic ring in S₇ prevents the otherwise advantageous stacking interactions of F92 with the other aromatic residues (Fig 3A). This leads to the adoption of a conformation reminiscent of the crystallographic apo-CaM (Fig 5A). However, the observed binding mode-dependent effects are local. As such, the packing of the methionines lining the pocket is left unaffected (S14 Fig). Viewing the S₇ as a state with local apo-like structural features is consistent with the findings that the transition from apo- to holo-like conformation is mainly characterized by the repacking of aromatic residues rather than changed interactions between the methionines [13,72]. In summary, our results suggest that the F92, F141 and N97 residues play particularly significant roles in the coupling between the hydrophobic domain and Ca²⁺-site, and that the orientation of TFP controls the switch between these apo- and holo-like interactions.

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Fig 5.

(A) Inter-residue distances between the sidechains of the F92, M124 and F141 within the S₅, S₆ and S₇ macrostates. The two-dimensional histograms are weighted by their Markov state model probabilities. The inter-residue distances calculated from apo- (PDB: 1CFD [9]) and holo- (PDB: 1CLL [8]) calmodulin structures are shown as grey and black dots respectively. The mean inter-residue distances within MD simulations [5] of apo- and holo-CaM are shown as grey and black squares respectively. Error bars represent the standard deviations of residue distances within the MD simulations. (B) The per-residue secondary structure of C-CaM within the three populated macrostates compared to their behaviour within simulations of apo-CaM. The Y99 and N137 residues displaying enhanced sheet behaviour are illustrated as dotted lines. (C) The molecular structure of C-CaM illustrating the Y99-N137 antiparallel sheet situated adjacent to the two Ca²⁺ ion binding sites. The bound Ca²⁺ ions are shown as red spheres.

https://doi.org/10.1371/journal.pcbi.1010583.g005

The two Ca²⁺ sites in C-CaM are cooperative with ion-binding at one interface resulting in up to a 10 kJ/mol enhancement in binding at the other interface [5,6]. Moreover, binding Ca²⁺ at the two sites yields a shift in the position of the β-sheet structure within the lobe [5]. To investigate whether the state-dependent TFP-binding can also affect the apo- and holo-like hallmarks of secondary structure content, we compared the per-residue secondary structure frequency in each state with that of the drug-unbound CaM ensemble (Fig 5B) [5].

The ₉₈GYISA₁₀₂ and ₁₃₄GQVNY₁₃₈ loops are adjacent to the two ion-sites and transiently form antiparallel β-sheet structures [73]. Specifically, the Y99 and N137 residues participate more frequently in sheet structures in the S₅ and S₆ states (Fig 5B and 5C). Recent work has shown that Y99 and N137 are important for the functional interactions between CaM and the activated-open state of KCNQ1 [70]. Together, the results provide a hypothesis on the mechanism of Calmodulin inhibition by the varying TFP binding modes. Apart from obstructing the hydrophobic pocket, in the S₅ and S₆ states, TFP could potentially hinder interactions between CaM and target-proteins by locking the crucial Y99 and N137 residues in a β-sheet structure. Conversely, within the S₇ state, TFP functions by enabling a local switch to an apo-like state characterized by differential interactions of the aromatic F89, F92 and F141 residues.