Free-energy landscape of protein oligomerization from atomistic simulations

Significance

Oligomeric proteins, comprising two or more associating polypeptide chains, represent a large fraction of cellular proteins. In particular, many proteins self-associate into homooligomers to gain functional advantages. Our understanding of the oligomerization at the molecular level is currently limited because intermediates that occur in the process are short-lived in most occasions, precluding a direct experimental characterization. Using molecular dynamics simulations, enhanced by a sampling method developed in our group, we obtained an atomistic description of the assembly of an evolutionary-optimized trimeric protein. Our results are in excellent agreement with available experimental data and extend the current view of oligomerization by showing the importance of the apparently contradictory requirements of monomer preorganization and conformational flexibility.

Abstract

In the realm of protein–protein interactions, the assembly process of homooligomers plays a fundamental role because the majority of proteins fall into this category. A comprehensive understanding of this multistep process requires the characterization of the driving molecular interactions and the transient intermediate species. The latter are often short-lived and thus remain elusive to most experimental investigations. Molecular simulations provide a unique tool to shed light onto these complex processes complementing experimental data. Here we combine advanced sampling techniques, such as metadynamics and parallel tempering, to characterize the oligomerization landscape of fibritin foldon domain. This system is an evolutionarily optimized trimerization motif that represents an ideal model for experimental and computational mechanistic studies. Our results are fully consistent with previous experimental nuclear magnetic resonance and kinetic data, but they provide a unique insight into fibritin foldon assembly. In particular, our simulations unveil the role of nonspecific interactions and suggest that an interplay between thermodynamic bias toward native structure and residual conformational disorder may provide a kinetic advantage.

In the cell, proteins most often exist and perform their functions as complexes. In particular, a large percentage of proteins self-associate into homooligomers to gain functional advantages, such as improved thermodynamic stability and regulation of activity (1, 2). Understanding how these oligomeric complexes are assembled is thus a central topic in biophysics and molecular biology. Several studies have investigated the kinetics and thermodynamics of protein oligomerization, and different kinetic mechanisms have been identified (3, 4). However, current understanding of the assembly mechanism is still limited. Indeed, a comprehensive description of these reactions would require the identification and structural characterization of transient intermediates that remain elusive to most experimental techniques.

Molecular dynamics (MD) simulations are an extremely useful tool for unraveling interesting biophysical processes. However, the time scales accessible to MD simulations based on accurate atomistic models are limited by the computational resources currently available. Although great progress has been made with the introduction of distributed computing platforms (5) and specialized hardware (6), the characterization of oligomerization free-energy landscapes with straightforward MD still remains an extremely challenging task, even for dimers (7, 8). This limitation may be circumvented by using advanced sampling algorithms such as metadynamics (9, 10) (MetaD). MetaD is based on the introduction of a history-dependent bias potential that simultaneously enables enhanced sampling and estimation of the free-energy surface (FES) as a function of a few selected collective variables (CVs). Furthermore, MetaD can be seamlessly integrated with other advanced sampling algorithms, such as parallel tempering (PT) (11), with great benefits when studying complex biomolecular processes and large systems.

Here we focus on the oligomerization process of the fibritin foldon domain. Fibritin is a trimeric rod-like structural protein from bacteriophage T4 with a multidomain architecture (12). A small C-terminal globular domain is essential for fibritin folding and assembly both in vivo and in vitro (12, 13). This domain, dubbed “foldon domain,” is an evolutionarily optimized trimerization motif with remarkable properties: it can act as a chaperone during the assembly of trimeric proteins (14), and it can even induce the trimerization of other proteins (15–17). The foldon domain trimer is extremely stable, and its structure has been solved by means of nuclear magnetic resonance (NMR) spectroscopy (18) (Fig. 1A). Each 27-residue monomer is composed of an N-terminal extended structure, a β-hairpin, and a small 3₁₀ helical turn (Fig. 1B). The trimeric structure is stabilized by several intermolecular interactions including hydrophobic packing, backbone–backbone hydrogen bonds (H bonds), and salt bridges. The small size of the foldon domain, its simple fold, and its high stability make it an ideal model for detailed mechanistic studies of an assembly process both experimentally and computationally.

Fig. 1.

(A) Top view of the fibritin foldon domain native structure (PDB code: 1RFO) which is composed of three separate chains. Each chain of the homotrimer is colored differently. (B) Side view of the fibritin foldon domain native structure. One monomer is colored according to its secondary structure (β-structure in magenta and 3₁₀ helix in orange).

The kinetics of fibritin foldon domain assembly has been characterized by Kiefhaber and coworkers by monitoring Trp fluorescence in stopped-flow experiments (18). At physiological concentration, the oligomerization is a multistep process initiated by the submillisecond formation of an intermediate monomeric species which then dimerizes and finally reaches the native trimeric state through the addition of a third monomer to the preformed dimer. Remarkably, the dimerization and trimerization steps are extremely fast compared with other biomolecular folding reactions. The great efficiency of this process was attributed to the formation of an intermediate monomeric species that is structurally similar to the monomer conformation in the native trimeric structure, thus providing a template for rapid assembly during the dimerization and trimerization steps. Similar mechanisms based on templated growth have been proposed, in the more general context of protein aggregation, to rationalize fibril formation kinetics (19–21).

In the case of fibritin foldon domain, this intuition was supported by the NMR structural characterization of the E5R foldon mutant which has a monomeric fold similar to the monomer configuration in the wild-type trimeric structure (22).

In this study, we used a combination of MetaD and PT (PTMetaD) (23) to fully characterize the assembly of fibritin foldon domain by means of atomistic MD simulations. To make this challenging problem computationally tractable, we took advantage of the multistep nature of the process as revealed by the experimental kinetics data. Thus, we adopt a hierarchical approach, and we divide the assembly of the foldon trimer from unfolded monomers into three different simulations: (i) monomer folding (U → M), (ii) dimerization (M + M → D), and (iii) trimerization (D + M → T). The FES obtained in each of these simulations was used to understand the detailed molecular mechanism of each of these stages of oligomerization.

Results

Monomer Folding.

The simulation of the fibritin foldon monomer was performed using the PTMetaD protocol with MetaD bias applied to three CVs: the radius of gyration (Rgyr), the total number of backbone–backbone H bonds (H_b), and the number of native C_α–C_α contacts defined according to the experimental structure of the wild-type trimer . The FES at 300 K as a function of Rgyr and is characterized by the presence of three main basins (Fig. 2A): the unfolded state (U), a partially folded intermediate (P), and a folded state (N). N is the global free-energy minimum, whereas U and P are slightly less populated (, ). The unfolded basin contains disordered, yet rather compact, structures. The intermediate basin corresponds to configurations in which the C-terminal hairpin is partially formed but does not interact with the yet unstructured, detached N-terminal tail. The global free-energy minimum encompasses conformations which are structurally similar to the monomer in the trimeric wild-type experimental structure (rmsd < 0.2 nm). However, this basin is characterized by a significant degree of flexibility of the N-terminal tail which samples multiple conformations that deviate from the ensemble of the NMR conformers determined for the E5R mutant (Fig. 2B).

Fig. 2.

Monomer folding. (A) FES at 300 K as a function of the total number of native contacts and the Rgyr. Isoenergy lines are drawn every 0.6 kcal/mol. Structures representative of the two free-energy basins I and N (gray) are superimposed on the monomer conformation in the trimeric experimental structure (red). (B) The bundle of the NMR conformers obtained for E5R mutant (blue) is compared with the conformational ensemble corresponding to the N basin (green). An additional cartoon representation of a single NMR conformer is added as a guide for the eye. All of the structures are aligned by superimposing the β-hairpin region (residues 13–23).

The picture of the monomer landscape described above is perfectly consistent with several experimental evidences including the paucity of NOE signals measured for the E5R mutant in the N-terminal region (22) and the temperature-dependent behavior of chemical shifts and residual dipolar couplings of wild-type fibritin trimer (24). To quantify the agreement of our results with NMR experiments on the E5R monomer, we back-calculated the chemical shifts from the PTMetaD simulation using two different algorithms [SHIFTX (25) and CamShift (26)]. These observables are particularly sensitive to variations in the local chemical environment, and they play an important and ever-increasing role in the structural determination of disordered and partially disordered proteins (27–29). A reweighting algorithm (30) was used to recover the correct expectation values of the experimental observables from the biased PTMetaD simulations (31). The results for the H_α nuclei showed an excellent agreement between the simulated and the experimental chemical shifts (Table 1). The quality of this agreement does not change if we consider only the structural ensemble corresponding to basin N. Remarkably, the simulations reproduce the experimental chemical shifts better than the NMR-derived structures of the E5R mutant deposited in the Protein Data Bank (PDB) database (PDB code: 2KBL).

Table 1.

Deviation of calculated H_α chemical shifts from experimental values

Deviation*	SHIFTX, ppm	CamShift, ppm
Δ (Exp,PTMetaDAll)	0.17	0.19
Δ (Exp,PTMetaDN)	0.22	0.20
Δ (Exp,NMR conformers)	0.36	0.34

^*Deviations are calculated as rmsd averaged on the H_α chemical shifts of residues 2–27. Chemical shifts were back-calculated from simulations as reweighted averages performed over the entire conformational ensemble (PTMetaD_All) or the folded basin N (PTMetaD_N) which corresponds to the global energy minimum.

Dimerization.

The dimerization process was studied by complementing the PTMetaD scheme with the well-tempered ensemble (WTE) approach (32). This combined algorithm (PTMetaD-WTE) allowed us to further reduce the high computational cost of simulating protein–protein binding with an explicit-solvent model (33). The metadynamics bias was applied to two configurational CVs: the distance between the centers of mass of the monomers and the number of specific monomer–monomer contacts formed in the trimeric experimental structure. As mentioned before, the aim of this simulation is to study the dimerization process of two prefolded monomers. Therefore, we took advantage of our analysis of the monomer landscape and devised structural restraints to limit the sampling of each monomer to the structural ensemble corresponding to basin N. This strategy prevents the complete unfolding of the monomer at the high temperatures used in the PT scheme and thus sampling irrelevant regions of the configurational space. The FES of the dimerization process as a function of and is reported in Fig. 3A. The free-energy landscape is quite rough with a global minimum corresponding to a deep basin at low intermonomer distance . The position of the minimum indicates that monomer–monomer interaction is extremely favored, whereas its extension along coordinate suggests that several intermonomeric arrangements are likely to be thermodynamically accessible. In the structural ensemble corresponding to this broad basin, it is possible to identify configurations which are remarkably similar to the dimer arrangement in the trimeric experimental structure (N in Fig. 3A, rmsd ≃ 0.3 nm). However, maximal thermodynamic stability is achieved by conformers in which the monomer hairpins are almost antiparallel (C in Fig. 3A, rmsd ≃ 0.5–0.6 nm). In absence of a third monomer, this configuration allows the dimer both to minimize the solvent exposure of hydrophobic residues and to form additional intermonomer H bonds.

Fig. 3.

Dimerization and trimerization. (A) FES of the dimerization process as a function of and . Structures representative of the two free-energy basins N and C (gray) are compared with dimer arrangement in the trimeric experimental structure (red and blue). (B) FES of the trimerization process as a function of and . Structures representative of the free-energy basin N (gray) are superimposed on the trimeric experimental structure (red, blue, and green). In both A and B, isolines are drawn every 1.8 kcal/mol.

Our results suggest that the dimer populates a variety of different conformations at room temperature. The lack of any experimental data about the dimer structure prevents a straightforward validation of our results as done previously for the monomer. Nevertheless, we calculated the dimerization absolute binding free energy from , which is in fair agreement with the estimate obtained by fitting kinetic fluorescence experiments . Besides force field inaccuracies, a simulated affinity greater than the experimental one is to be expected here due to the different definitions of the dimer native state between the two approaches. In our calculation, this state encompassed the entire heterogeneous ensemble of the bound monomer–monomer conformations . Instead, only the subensemble of structures which can actually form a trimer is taken into account by the kinetic model.

Trimerization.

To simulate the trimerization process, we used a PTMetaD-WTE approach with a protocol analogous to that adopted in the dimerization study. The metadynamics bias was applied to two CVs: the distance between the centers of mass of the preformed dimer and the monomer and the number of monomer–dimer specific contacts formed in the trimeric experimental structure. The same structural restraints used in the dimerization study were imposed on the monomer, whereas an additional restraint was devised to allow the dimer a structural flexibility roughly corresponding to the global free-energy minimum observed in Fig. 3A.

The FES of the trimerization process as a function of and is reported in Fig. 3B. The funnel-shaped landscape is characterized by a strong bias toward the formation of the experimental trimeric structure. At variance with the dimerization landscape, no local minima corresponding to significantly populated intermediate states can be identified. Conformations belonging to the global free-energy minimum are extremely similar to the trimeric experimental structure (N in Fig. 3B, rmsd ≃ 0.2–0.3 nm). Within this basin, the only structural heterogeneity is due to small differences in the packing of the N-terminal tails.

To further validate our simulations, we recovered the trimerization absolute binding free energy from . The result is in excellent agreement with the experimental free-energy difference corresponding to the formation of the native trimer .

Analysis of the Oligomerization Mechanism.

The enhanced sampling algorithms used here perturb in a nontrivial way the system trajectory due to the introduction of the MetaD bias potential and the replica diffusion in temperature space. Thus, it is not possible to recover directly information about the order of events in the different stages of the multimerization process which are likely to occur through multiple microscopic pathways.

Nevertheless, we could reconstruct the unbiased distribution of any configurational variable by means of the reweighting algorithm mentioned above. This allowed us to shed light on the dimerization and trimerization mechanisms by monitoring the expectation value of properly chosen quantities as a function of and . A similar approach was used to characterize the mechanism of urea-driven denaturation of the GB1 C-terminal β-hairpin (34).

We first investigated the interplay between the formation of specific and nonspecific intermoiety contacts that are formed during the oligomerization. To this aim, we calculated the average number of specific and nonspecific contacts as a function of and during the dimerization (Fig. 4A) and trimerization processes (Fig. 4D), respectively. To highlight the thermodynamically relevant regions, we also report the free energy as a function of (Fig. 4C) and (Fig. 4F).

Fig. 4.

Analysis of the oligomerization mechanism. Dimerization: (A) average number of specific (red) and nonspecific (blue) contacts as a function of , (B) average number of contacts formed by the monomer’s N-flexible tail (residues 1–10; orange) and by the C-terminal more structured part (residues 11–27; green) as a function of , and (C) free-energy dependence on . Trimerization: (D–F) the same quantities are reported as a function of .

This analysis revealed a striking difference between the dimerization and trimerization processes. Although in the former, nonspecific interactions are dominant, in the latter, specific contacts greatly outnumber nonspecific contacts at short distances. This behavior is not unexpected because contact specificity is defined on the basis of the experimental trimeric structure, and the dimerization FES already indicated significant structural diversity. Besides this difference, some significant similarities emerge from this analysis. First, the ratio between specific and nonspecific interactions in both cases reaches its maximum at distances corresponding to the global free-energy minimum. Second, nonspecific contacts are always dominant at large distances, and thus, they are likely to be formed before the specific interactions in the early stages of both processes.

Our results on the fibritin monomer folding landscape showed that its folded structure is only marginally stable and significant fluctuations of the N-terminal tail are expected at room temperature. It is thus tempting to investigate the role of this flexible segment in the assembly process. To this aim, we calculated the average number of contacts formed by the N-terminal flexible region (residues 1–10) and the C-terminal more structured part (residues 11–27) of a monomer as a function of and during the dimerization (Fig. 4B) and trimerization process (Fig. 4E), respectively. In both processes, data clearly show that at large distances (, ), the intermolecular interactions formed by the flexible N tail are much more favored than those formed by the structured β-hairpin.

Discussion

By means of enhanced sampling techniques we were able to characterize the oligomerization process of a trimeric protein using an atomistic description of both protein and solvent degrees of freedom. To achieve this goal, we used a hierarchical approach in which the process was modeled in three different steps: folding of the monomer, dimerization, and trimerization. This hierarchical study of the complete process enabled us to obtain results which are in good agreement with all of the available experimental data, and in addition, they provide a deeper insight into the fibritin foldon assembly process.

Our simulations of the monomer provided a description of its conformational ensemble which confirms the picture of a prefolded monomeric intermediate, and it is fully consistent with NMR chemical shifts measured on the E5R mutant. Additionally, our calculation reveals a degree of structural heterogeneity which is not captured by the ensemble of NMR-derived conformers.

The simulation of the oligomerization processes indicated that both the dimerization and trimerization are thermodynamically favored, with binding affinity consistent with the values estimated from fluorescence stopped-flow experiments. However, the two processes are significantly different. The trimerization proceeds through a rather smooth funnel toward a global free-energy minimum which coincides with the experimental structure. Instead, the dimerization leads to a broad ensemble of almost equally populated structures that include configurations observed in the trimeric experimental structure. The most favored dimeric structure, which has been so far elusive to experimental investigation, corresponds to an almost antiparallel packing of the two monomers. This scenario suggests that the addition of a third monomer operates a conformational selection of the dimer ensemble by stabilizing the conformation observed in the native trimer.

Although our simulations could not directly provide dynamical information, we were able to gain a significant insight into the fibritin assembly mechanism by analyzing how interprotomer contacts are formed during the oligomerization processes. First, we quantified the formation of nonspecific interactions, and we showed that they play a major role in the early recognition stage of both dimerization and trimerization. This finding is fully consistent with the general idea that nonspecific encounter complexes are of key importance in accelerating protein–protein binding (35, 36). Transient encounter complexes have been elucidated by paramagnetic relaxation enhancement NMR spectroscopy (37) and studied computationally by means of coarse-grained models (38, 39).

We further investigated the nature of these interactions by identifying the fragments that most likely interact in the early stages of binding. Our analysis indicated that the monomer N-terminal tail has a crucial function in both monomer–monomer and dimer–monomer recognition. As discussed before, both the NMR experiments and our simulations clearly show that the N-terminal tail is the most flexible and disordered region of the monomer. Thus, it is tempting to relate this finding to the “fly-casting” mechanism (40) proposed for intrinsically disordered proteins (IDPs). According to this model, the lack of a well-defined structure in IDPs leads to an increased capture radius and a reduction in free-energy barriers, ultimately resulting in a fast binding kinetics (40, 41). Similarly, here the presence of residual disorder in an almost completely folded monomer might be beneficial in the recognition stage of the binding process.

Fibritin foldon domain shows a remarkably fast assembly kinetics, and it is considered an evolutionarily optimized trimerization motif. In the current view, this property is a consequence of the structural preorganization of single monomers which provide a scaffold for the oligomerization. Our results confirm this picture but suggest that an interplay between thermodynamic bias toward native structure formation and residual flexibility could provide additional kinetic advantage. These findings might be extended to the interactions between other structured proteins and thus pave the way to further investigation in this direction. In conclusion, our study demonstrates that the combination of different enhanced sampling techniques makes MD simulations a powerful computational microscope to investigate complex biomolecular processes such as protein oligomerization.

Materials and Methods

General Setup.

All of the simulations were performed using GROMACS4 MD code (42) and PLUMED plugin (43). The Amber99SB-ILDN (44) and TIP3P (45) models were used for protein and water molecules, respectively. Initial conformations were obtained from the trimeric NMR structure of fibritin foldon domain (PDB code: 1RFO). All of the simulations were performed using a rhombic dodecahedral box with periodic boundary conditions. Well-tempered MetaD (46) was used to accelerate sampling in all of the steps of the oligomerization process in combination with PT, as described below. The PT replica temperatures were chosen according to the distribution proposed in ref. (47). Additional details of the MD parameters and system equilibration are provided in Supporting Information, Simulation Details.

Monomer Folding.

Fibritin monomer was solvated in 3,461 water molecules corresponding to an equilibrated box size of 110.9 nm³. In the PTMetaD scheme, 80 replicas were simulated in the temperature range 275–650 K with a resulting exchange acceptance probability of ≃0.2. The simulation was carried out for 85 ns, corresponding to an aggregated simulation time of 6.8 μs. The MetaD bias was applied to three CVs. The first CV was the radius of gyration of the C_α atoms of the monomer. H_b was calculated using a sum of switching functions:

where was set to 0.25 nm and n and m were set to 6 and 12, respectively. The sum runs over all of the pairs of hydrogen and oxygen backbone atoms with a sequence separation equal to or larger than four residues. The same functional form was used to evaluate the number of native contact . In this case, was set to 0.85 nm, n and m were set to 6 and 12, and the sum included all of the C_α–C_α atom pairs which are closer than 0.9 nm in the experimental structure and separated by more than four residues in sequence.

Dimerization and Trimerization.

Both systems were solvated in 8,419 water molecules corresponding to equilibrated box sizes of 265.0 nm³ for the dimerization and 270.5 nm³ for the trimerization. The PTMetaD-WTE scheme was applied using 16 replicas distributed in the temperature range 290–656 K. First, the bias in the energy space was converged for all of the replicas in 20 ns. This protocol allowed us to significantly increase the potential energy fluctuations and to obtain an average exchange acceptance probability of ≃0.2 for both systems. The MetaD bias was then applied to two configurational variables to enhance sampling: and for the dimerization and and for the trimerization. and were calculated as the distance between the centers of mass of the two monomers (dimerization) and between the dimer and the monomer (trimerization). The total number of specific contacts formed by the dimer and the trimer was calculated analogously to but taking into account only contacts between the two monomers and between the monomer and the dimer, respectively. The length of the PTMetaD-WTE simulation was 140 ns for the dimerization and 200 ns for the trimerization. As discussed previously, structural restraints were implemented to focus sampling in the most relevant regions of the configurational space. These restraints included the following: (i) in both dimerization and trimerization, two restraints on each monomer in the rmsd space to avoid monomer unfolding while allowing significant fluctuation of the N-terminal tail and (ii) in the trimerization, a restraint on the dimer in space to limit its sampling to basins N and C (Fig. 3).

Analysis.

The equilibrium probability distributions of all quantities other than the MetaD CVs were reconstructed using a reweighting algorithm (30). In the dimerization process, the monomers can actually be arranged into two symmetric, native-like structures (AB and BA). These conformations are degenerate but characterized by distinct sets of interchain contacts ( and ). Hence, a symmetrized definition of , i.e., , was used in all of our analyses. In the analysis of the dimerization and trimerization mechanism (Fig. 4), the contacts were calculated as the total number of monomer–monomer and monomer–dimer residue pairs with a C_α–C_α distance smaller than a sharp cutoff (0.75 nm).