The complex folding pathways of protein A suggest a multiple-funnelled energy landscape

Path-sampling strategies for simulating rare events in biomolecular systems

Despite more than three decades of effort with molecular dynamics simulations, long-timescale (ms and beyond) biologically relevant phenomena remain out of reach in most systems of interest. This is largely because important transitions, such as conformational changes and (un)binding events, tend to be rare for conventional simulations (<10μs). That is, conventional simulations will predominantly dwell in metastable states instead of making large transitions in complex biomolecular energy landscapes. In contrast, path sampling approaches focus computing effort specifically on transitions of interest. Such approaches have been in use for nearly 20 years in biomolecular systems and enabled the generation of pathways and calculation of rate constants for ms processes, including large protein conformational changes, protein folding, and protein (un)binding.

Conformational Interconversions of Amino Acid Derivatives

Exhaustive conformational interconversions including transition structure analyses of N-acetyl-l-glycine-N-methylamide as well as its alanine, serine, and cysteine analogues have been investigated at the MP2/6-31G** level, yielding a total of 142 transition states. Improved estimates of relative energies were obtained by separately extrapolating the Hartree-Fock and MP2 energies to the basis set limit and adding the difference between CCSD(T) and MP2 results with the cc-pVDZ basis set to the extrapolated MP2 results. The performance of eight empirical force fields (AMBER94, AMBER14SB, MM2, MM3, MMFFs, CHARMM22_CMAP, OPLS_2005, and AMOEBAPRO13) in reproducing ab initio energies of transition states was tested. Our results indicate that commonly used class I force fields employing a fixed partial charge model for the electrostatic interaction provide mean errors in the ∼10 kJ/mol range for energies of conformational transition states for amino acid conformers. Modern reparametrized versions, such as CHARMM22_CMAP, and polarizable force fields, such as AMOEBAPRO13, have slightly lower mean errors, but maximal errors are still in the 35 kJ/mol range. There are differences between the force fields in their ability for reproducing conformational transitions classified according to backbone/side-chain or regions in the Ramachandran angles, but the data set is likely too small to draw any general conclusions. Errors in conformational interconversion barriers by ∼10 kJ/mol suggest that the commonly used force field may bias certain types of transitions by several orders of magnitude in rate and thus lead to incorrect dynamics in simulations. It is therefore suggested that information for conformational transition states should be included in parametrizations of new force fields.

The OPEP protein model: from single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems

The OPEP coarse-grained protein model has been applied to a wide range of applications since its first release 15 years ago. The model, which combines energetic and structural accuracy and chemical specificity, allows the study of single protein properties, DNA-RNA complexes, amyloid fibril formation and protein suspensions in a crowded environment. Here we first review the current state of the model and the most exciting applications using advanced conformational sampling methods. We then present the current limitations and a perspective on the ongoing developments.

Large loop conformation sampling using the activation relaxation technique, ART-nouveau method

We present an adaptation of the ART-nouveau energy surface sampling method to the problem of loop structure prediction. This method, previously used to study protein folding pathways and peptide aggregation, is well suited to the problem of sampling the conformation space of large loops by targeting probable folding pathways instead of sampling exhaustively that space. The number of sampled conformations needed by ART nouveau to find the global energy minimum for a loop was found to scale linearly with the sequence length of the loop for loops between 8 and about 20 amino acids. Considering the linear scaling dependence of the computation cost on the loop sequence length for sampling new conformations, we estimate the total computational cost of sampling larger loops to scale quadratically compared to the exponential scaling of exhaustive search methods.

Coarse-grain Protein Models

Coarse-graining is a powerful approach for modeling biomolecules that, over the last few decades, has been extensively applied to proteins. Coarse-grain models offer access to large systems and to slow processes without becoming computationally unmanageable. In addition, they are very versatile, enabling both the protein representation and the energy function to be adapted to the biological problem in hand. This review concentrates on modeling soluble proteins and their assemblies. It presents an overview of the coarse-grain representations, of the associated interaction potentials, and of the optimization procedures used to define them. It then shows how coarse-grain models have been used to understand processes involving proteins, from their initial folding to their functional properties, their binary interactions, and the assembly of large complexes.

Mirror images as naturally competing conformations in protein folding

Evolution has selected a protein's sequence to be consistent with the native state geometry, as this configuration must be both thermodynamically stable and kinetically accessible to prevent misfolding and loss of function. In simple protein geometries, such as coiled-coil helical bundles, symmetry produces a competing, globally different, near mirror image with identical secondary structure and similar native contact interactions. Experimental techniques such as circular dichroism, which rely on probing secondary structure content, cannot readily distinguish these folds. Here, we want to clarify whether the native fold and mirror image are energetically competitive by investigating the free energy landscape of three-helix bundles. To prevent a bias from a specific computational approach, the present study employs the structure prediction forcefield PFF01/02, explicit solvent replica exchange molecular dynamics (REMD) with the Amber94 forcefield, and structure-based simulations based on energy landscape theory. We observe that the native fold and its mirror image have a similar enthalpic stability and are thermodynamically competitive. There is evidence that the mirror fold has faster folding kinetics and could function as a kinetic trap. All together, our simulations suggest that mirror images might not just be a computational annoyance but are competing folds that might switch depending on environmental conditions or functional considerations.

The Activation-Relaxation Technique: ART Nouveau and Kinetic ART

The evolution of many systems is dominated by rare activated events that occur on timescale ranging from nanoseconds to the hour or more. For such systems, simulations must leave aside the full thermal description to focus specifically on mechanisms that generate a configurational change. We present here the activation relaxation technique (ART), an open-ended saddle point search algorithm, and a series of recent improvements to ART nouveau and kinetic ART, an ART-based on-the-fly off-lattice self-learning kinetic Monte Carlo method.

Replica exchange molecular dynamics simulations of coarse-grained proteins in implicit solvent

Current approaches aimed at determining the free energy surface of all-atom medium-size proteins in explicit solvent are slow and are not sufficient to converge to equilibrium properties. To ensure a proper sampling of the configurational space, it is preferable to use reduced representations such as implicit solvent and/or coarse-grained protein models, which are much lighter computationally. Each model must be verified, however, to ensure that it can recover experimental structures and thermodynamics. Here we test the coarse-grained implicit solvent OPEP model with replica exchange molecular dynamics (REMD) on six peptides ranging in length from 10 to 28 residues: two alanine-based peptides, the second beta-hairpin from protein G, the Trp-cage and zinc-finger motif, and a dimer of a coiled coil peptide. We show that REMD-OPEP recovers the proper thermodynamics of the systems studied, with accurate structural description of the beta-hairpin and Trp-cage peptides (within 1-2 A from experiments). The light computational burden of REMD-OPEP, which enables us to generate many hundred nanoseconds at each temperature and fully assess convergence to equilibrium ensemble, opens the door to the determination of the free energy surface of larger proteins and assemblies.

The fast-folding HP35 double mutant has a substantially reduced primary folding free energy barrier

The LYS24/29NLE double mutant of villin headpiece subdomain (HP35) is the fastest folding protein known so far with a folding time constant of 0.6 micros. In this work, the folding mechanism of the mutant has been investigated by both conventional and replica exchange molecular dynamics (CMD and REMD) simulations with AMBER FF03 force field and a generalized-Born solvation model. Direct comparison to the ab initio folding of the wild type HP35 enabled a close examination on the mutational effect on the folding process. The mutant folded to the native state, as demonstrated by the 0.50 A C(alpha)-root mean square deviation (RMSD) sampled in both CMD and REMD simulations and the high population of the folded conformation compared with the denatured conformations. Consistent with experiments, the significantly reduced primary folding free energy barrier makes the mutant closer to a downhill folder than the wild type HP35 that directly leads to the faster transition and higher melting temperature. However, unlike the proposed downhill folding which envisages a smooth shift between unfolded and folded states without transition barrier, we observed a well-defined folding transition that was consistent with experiments. Further examination of the secondary structures revealed that the two mutated residues have higher intrinsic helical preference that facilitated the formation of both helix III and the intermediate state which contains the folded segment helix II/III. Other factors contributing to the faster folding include the more favorable electrostatic interactions in the transition state with the removal of the charged NH(3)(+) groups from LYS. In addition, both transition state ensemble and denatured state ensemble are shifted in the mutant.

Quantifying the structural requirements of the folding transition state of protein A and other systems

The B-domain of protein A is a small three-helix bundle that has been the subject of considerable experimental and theoretical investigation. Nevertheless, a unified view of the structure of the transition-state ensemble (TSE) is still lacking. To characterize the TSE of this surprisingly challenging protein, we apply a combination of psi analysis (which probes the role of specific side-chain to side-chain contacts) and kinetic H/D amide isotope effects (which measures hydrogen-bond content), building upon previous studies using mutational phi analysis (which probes the energetic influence of side-chain substitutions). The second helix is folded in the TSE, while helix formation appears just at the carboxy and amino termini of the first and third helices, respectively. The experimental data suggest a homogenous yet plastic TS with a native-like topology. This study generalizes our earlier conclusion, based on two larger alpha/beta proteins, that the TSEs of most small proteins achieve approximately 70% of their native state's relative contact order. This high percentage limits the degree of possible TS heterogeneity and requires a reevaluation of the structural content of the TSE of other proteins, especially when they are characterized as small or polarized.