Folding a viral peptide in different membrane environments: pathway and sampling analyses
Flock House virus (FHV) is a well-characterized model system to study infection mechanisms in non-enveloped viruses. A key stage of the infection cycle is the disruption of the endosomal membrane by a component of the FHV capsid, the membrane active γ peptide. In this study, we perform all-atom molecular dynamics simulations of the 21 N-terminal residues of the γ peptide interacting with membranes of differing compositions. We carry out umbrella sampling calculations to study the folding of the peptide to a helical state in homogenous and heterogeneous membranes consisting of neutral and anionic lipids. From the trajectory data, we evaluate folding energetics and dissect the mechanism of folding in the different membrane environments. We conclude the study by analyzing the extent of configurational sampling by performing time-lagged independent component analysis.
KeywordsProtein folding Flock House virus Molecular dynamics Umbrella sampling Non-enveloped virus Membrane active peptides TICA
Understanding the thermodynamics of peptide association and folding in a membrane environment is critical to deciphering the underlying mechanisms of membrane disruption by membrane active peptides [1, 2, 3, 4, 5, 6, 7]. The transition from an unstructured solution state to an α-helical membrane bound state is a common trait of small amphipathic membrane proteins that have been researched extensively both experimentally [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] and computationally [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]. The thermodynamic driving forces for protein–membrane interactions and stabilization of the folded state are a delicate balance between enthalpic and entropic factors. Consequently, analyzing the peptide folding pathway and energetics in lipid bilayers can provide detailed insight into the biological activity of the peptide. A clear picture of the mode of membrane disruption employed by membrane active peptides has, in general, remained elusive [30, 31].
Over the last two decades computational studies have been instrumental in providing insight into lipid and protein dynamics by utilizing both equilibrium and biased sampling methodologies to study the energetics, thermodynamics, and structural dynamics of amphipathic membrane active proteins [18, 20, 23, 25, 26, 27, 32, 33, 34, 35, 36]. A major area of emphasis in understanding the mechanism of action of membrane active peptides is characterizing the initial stage of membrane association and peptide folding. Previous studies in this area include that of Brooks and coworkers who examined the folding dynamics of the designed WALP peptides in an implicit membrane model using temperature replica exchange molecular dynamics (T-REMD) . Their studies showed that all variants of the WALP peptides penetrated the membrane with the N-terminal regions initiating the insertion and ultimately transitioning to an α-helix trans-membrane configuration consistent with experimental observations. More recently, molecular dynamics (MD) simulations pertaining to the folding and penetration of a single transmembrane WALP peptide were carried out in both all-atom and coarse-grained models . The folding free-energy was determined in the coarse-grained representation as a function of helicity of the peptide using Hamiltonian REMD. Unbiased MD simulations have also been performed to study the folding dynamics of another widely studied membrane active peptide, the antimicrobial peptide melittin. These simulations have revealed that the peptide robustly associates with the membrane in a disordered state and attains helicity parallel to the surface of the membrane causing deformation of the bilayer as it folds . Long time scale (17 μs) unbiased MD simulations have shown that there is a narrow distribution of folded melittin conformers that partition into the membrane interface .
In our previous work , we investigated the thermodynamic aspects of binding and the structural dynamics of the FHV 21 N-terminal residues of the γ peptide (known as γ1) using a multi-scale approach. We examined the binding and folding characteristics of γ1 on pure phosphatidylcholine (PC), pure phosphatidylglycerol (PG) and a 50:50 mixed PC:PG membrane. Our findings from 1 μs equilibrium all-atom simulations were in agreement with experimental measurements of the configuration of γ1 on a PC bilayer, where we observed ~70% helicity of γ1 . On PG membranes, we observed low α-helical content ranging from 0 to 23%. The strong electrostatic interactions between cationic γ1 and negatively charged PG may result in a higher entropy, less ordered bound state, which is consistent with ITC measurements . The folding propensity of γ1 on the 50:50 PC:PG bilayer could not be inferred from the behavior on the homogeneous membranes. γ1 displayed low helical content (16%) on the mixed bilayer, leading us to conclude the correlation between the amount of charge present in the membrane and the folding propensity of the peptide is not linearly related. We also performed simulations starting from the folded state on PC, PG, and the mixed bilayer system, to probe the stability of the γ1 helical conformation. We found that γ1 does not unfold and remains embedded in the membranes throughout 1-μs simulations. From these observations, we proposed that an energy barrier separates the folded state from the low helicity state, and the barrier height has a dependence on the amount of charge in the membrane . Our equilibrium simulations were likely trapped in a metastable state, due to the rough energy landscape, which was insurmountable by conventional simulation approaches. To explore our proposition further, we appeal to enhanced sampling methods to overcome the limited sampling in equilibrium MD to produce barrier crossing events.
Different enhanced sampling methods offer varied advantages and disadvantages and one should make a well-informed selection of a method most applicable to addressing the scientific scenario being explored. A popular choice of method for studying protein–membrane systems is T-REMD . T-REMD works on the principle that molecules can sample through a rugged energy surface by making repeated swaps among its replicas that are simulated simultaneously at different temperatures. Although replica-exchange is a widely used method, there are some disadvantages to of this approach. The number of replicas required for efficient sampling scale as f1/2 (where f is the degrees of freedom), which for large biological systems with explicit solvent can lead to very high computational costs [40, 41]. Moreover, T-REMD is not an effective method to overcome entropic barriers, which are present in folding transitions . Path sampling techniques such as milestoning , forward flux sampling , and transition path sampling  also offer non-biased simulation approaches that can be employed to study activated processes by exploiting transition path theory and calculating the key transitions in the trajectory space rather than focusing on the stable states. The basis of these methods is to sample the fast-occurring infrequent rare events involving a transition. Other enhanced sampling methods involve application of bias potentials to accelerate the sampling in a desired region of configurational space such as computational flooding , metadynamics (MetaD) , and umbrella sampling (US) . These methods require the user to select an order parameter (collective variable, CV) along which a biasing potential can be applied to surmount free-energy barriers in the landscape. Both computational flooding and MetaD methods rely on biasing potentials being added “on the fly” to the energy landscape of the system with the objective to sample all energy minima, but avoid excessive and re-sampling of local minima.
Umbrella sampling is a mature and heavily utilized method in different biophysics studies including protein folding [49, 50], peptide–peptide interactions [51, 52], protein–DNA interactions , binding energies and interactions with lipid membranes [20, 37, 54, 55], and conformational sampling of small molecules [56, 57], among others. US relies on a stratification strategy; intermediate states along an order parameter are simulated with a restraint potential that keeps the system localized to a chosen point along the order parameter. A series of restrained simulations spanning the entire range of interest along the order parameter are simulated, and provided there are overlapping distributions between the umbrella windows, the probabilities can be unbiased and the potential of mean force (PMF) can be determined. Convergence in US is non-trivial to achieve or to evaluate and there are also choices regarding the restraint spacing and restraint force constant, though these are relatively easy to evaluate and there is significant literature to inform these choices. One important requirement of US is that an initial path needs to be defined. In the limit of infinite sampling, the initial pathway would be irrelevant. Although in practice it can have a significant effect, especially if there are slow degrees of freedom or energy minima states separated by large energy barriers in orthogonal degrees of freedom to the US coordinate. Factors that make US a more robust and advantageous technique are that additional sampling can be carried out where sampling is sparse or in windows which display slow transitions and it is an appropriate method to maximally utilize parallel computing.
Many non-enveloped viruses [58, 59] contain a membrane active component of their capsid that in some systems is an amphipathic peptide, which is disconnected from the capsid. We have been investigating the membrane lytic peptide of the non-enveloped Flock House virus (FHV), which displays characteristics similar to antimicrobial peptides [37, 60, 61]. In our previous study, we employed microsecond equilibrium simulations to examine the folding characteristics of γ1, on membranes of different compositions . For the present study, we aim to calculate the free-energy profile of γ1 folding in the presence of a membrane. We chose to employ US and have chosen helicity of γ1 as the order parameter for these calculations. To study the folding process, one needs to consider two main aspects, the starting conformational state of the peptide and also its orientational features, i.e., the depth and angle of the peptide with respect to the bilayer. Our approach to addressing these initiation concerns was to initiate our simulations from the last snapshot of our previous work containing the bound helical state of γ1 on different membrane compositions . The bound conformations are derived from 1-μs equilibrium simulations, which have sampled the insertion depth of γ1 at a depth consistent with experimental measurements, based upon Trp fluorescence . Initial unfolding pathways were constructed by applying steered molecular dynamics (SMD) to generate γ1 conformations of varying helicity. In addition to evaluating energetic and structural aspects of the folding pathways, we performed additional analyses to evaluate the convergence and uncertainty in the US data. We have utilized time-lagged independent components analysis (TICA) to identify the slowest decorrelating degrees of freedom. By performing projections of the US data into TICA subspaces, we can evaluate the connectivity of the US data and observe if regions in the configurational space are undersampled leading to poor estimates of the free energy surfaces (FES).
2.1 System setup
Simulation system details
No. of PC and/or PG lipids
No. of US windows
Time of simulation
Per window (ns)
2.2 Umbrella sampling
In each of the systems, the peptide was unfolded using SMD with a restraint of 500 kJ/mol and a velocity of 0.001 S α units/ps. Intermediate configurations spaced in 0.1 S α increments were selected for US. An umbrella potential of 500 kJ/mol was applied in each umbrella window. The number of intermediate configurations (windows) for each system and the simulation time associated with each window are reported in Table 1. A total of 30.7 μs of data was collected.
2.3 Trajectory analysis
The trajectory data excluding the first 20 ns from each umbrella window was used for both 1D and 2D weighted histogram analysis method (WHAM)  to calculate the PMFs. Both 1D and 2D WHAM analysis was performed using Alan Grossfield’s code and the PMFs were converged to 10–3 kcal/mol . The GROMACS tool g_mindist was used to calculate the number of contacts between γ1 and lipid molecules within 5 Å radius. To compute the segmental S α in a given conformation, three overlapping regions of γ1 were defined: residues 1–10, residues 6–15, and residues 12–21, described as the N-term, middle, and C-term segments, respectively. The PLUMED plugin was also used for calculating the insertion depth of γ1. For this parameter, the three non-overlapping regions of γ1 are defined as residues 1–7 as N-term, 8–14 as middle, and 15–21 as C-term. An evaluation of the flexibility of the S α restraint to allow the peptide to sample helicity in different regions of the peptide was performed using the compute_dssp utility of MDTraj . For each system, the helicity was calculated in a low (S α = 2), medium (S α = 7), and high (S α = 12) window. The helicity was averaged in 10-ns segments and is presented in Fig. S1, which shows that the restraint does not rigidly fix the helical segments, but allows for some shifting of the conformation within an umbrella sampling window.
2.4 TICA and dTRAM analyses
3 Results and discussion
3.1 Folding energetics
3.2 Folding mechanisms
Overall, our ability to compare the US results with our previous equilibrium simulations is likely hampered by differences in the pathways being sampled. The equilibrium study was initiated from a surface-bound low helicity state in which the middle segment was folded while the N-term and C-term segments were unfolded. In the current study, the pathways were generated from SMD unfolding from a well-equilibrated high-helicity state. The US pathway does not pass through a conformation where the middle segment is folded in the absence of the N-term being folded and therefore the peptide is sampling different regions of the helicity-insertion phase space in comparing the equilibrium and US pathways.
3.3 Sampling analyses
In addition to assessing the reliability of the reconstructed free-energy profile, we utilized TICA analysis to gain information on the mechanism of folding and to evaluate the landscape in the slowest decorrelating degrees of freedom (slowest tICs). TICA has been used on US data previously to analyze protein dynamics and as the basis for adaptive sampling [81, 82]. Our systems were featurized using the distances between all Cα atoms in the peptide, which provides a reduced data set for performing TICA. Therefore, the TICA space is related to but not identical to the US coordinate, which is the S α parameter. We performed a global TICA analysis by combining the systems into a single, master system, which allows us to obtain global tICs, and compare the systems on a consistent basis. The slowest global tIC (tIC1) describes the US coordinate very well as the two are strongly correlated in all three systems. By projecting each US window onto the tIC1-helicity space, it can be observed that the windows are well connected and evenly spaced in the tIC1 coordinate (Fig. S3). Of the three systems, only the mixed system (Fig. S3C), has a substantial gap which occurs around 50 % helicity and may be an indication of inadequate sampling and/or energy barriers in this region.
We have performed US sampling calculations to analyze the folding energetics and mechanisms of the FHV γ1 peptide in homogeneous and mixed bilayer systems. We have estimated the free-energy profile and observe that the different bilayers systems influence the equilibrium probabilities of the highly folded and intermediately folded states. The heterogeneous bilayer system displays several notable differences from the homogeneous systems, including the lack of a stable intermediately folded state, and folding backtracking in the C-term segment. Additional kinetic-based analyses show differences in sampling of the slow degrees of freedom between the homogeneous and mixed systems. In particular, a much narrower pathway is observed for the mixed system in the tIC2 direction and the appearance of multiple pathways and a barrier in the tIC3 direction. While the PMFs appear to be well converged, the TICA analysis could direct a future adaptive sampling approach which could enhance the exploration of configurations away from the initial pathway.
This work has been supported by the National Institutes of Health through grant R35GM119762 to E.R.M. Computational resources have been provided through the University of Connecticut Hornet HPC cluster and NSF XSEDE program (grant number TG-MCB140016). We thank Kevin Boyd for his critical reading and providing constructive suggestions on this manuscript.
This study was funded by NIH (grant number R35GM119762).
Compliance with ethical standard
Conflict of interest
The authors declare that they have no conflict of interest.
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