protein folding

A protein’s function is directly linked to both its chemical nature and 3-dimensional structure. One of the onuses of molecular dynamics simulations is to correctly predict the latter. MD force fields are constantly updated and refined to better match experimentally observed structures, with particular emphasis on populations of various secondary structures as well as the range of disordered structures.

Our lab is interested in the comparing the free energy of secondary structure formation for various MD force fields in order to assess their accuracy in correctly producing experimental distributions of structure populations. Using umbrella sampling with replica exchange molecular dynamics (REMD-US), we are mapping the free energy landscape of small peptides to better understand how small secondary structure motifs form in solution, and then apply these methods to protein folding in vivo.

α-Helices

α-Helices are some of the most common secondary structures found in native protein folds. Understanding the pathway of their formation and their stability in biological processes is necessary step in combating diseases associated with protein misfolding.

Potential of mean force (PMF) calculated for deca-alanine in water and vacuum. Green line shows the least free energy path calculated between the helical and extended states.

Potential of mean force (PMF) calculated for deca-alanine in water and vacuum. Green line shows the least free energy path calculated between the helical and extended states.

We examined the formation α-helix formation using the model peptide, deca-alanine. With many studies using deca-alanine in vacuum as a benchmark for free energy studies, we decided to examine the free energy landscape in explicit water. Although in vacuum, using the end-to-end distance of the peptide was sufficient to capture the important dynamics of the folding process, a second reaction coordinate, α-helical content, was necessary in order to fully characterize the folding process in water. What we observed was a new energy minimum in the extended conformations not seen in vacuum. These results were consistent with the NMR data used to optimized the CHARMM36 force field (used for these simulations), which revealed the PPII structure to be more prevalent in solution than the helix.

We noticed an overall reduction in energy from the vacuum to the solvated system, corresponding to hydrogen bonding with the surrounding water molecules. The extended, non-helical minimum also corresponds with an increase in peptide-water hydrogen bonds during the unfolding process. We ran additional equilibrium simulations to confirm our free energy surface. We were also able to map the equilibrium dynamics to the free energy surface for both the folding and unfolding processes (see below). We observed cooperative folding from the N-terminus towards the C-terminus, and unfolding from the C-terminus towards the N-terminus.

Equilibrium trajectory (right) mapped to the free energy surface (left), starting from an extended, non-helical state.

Equilibrium trajectory (right) mapped to the free energy surface (left), starting from an extended, non-helical state. High quality video here.

Equilibrium trajectory (right) mapped to the free energy surface (left), starting from the helical state.

Equilibrium trajectory (right) mapped to the free energy surface (left), starting from the helical state. High quality video here.

helix_in_ribo

Nascent peptide (yellow) in the ribosomal exit tunnel (red), solvated in a water box (translucent gray).

Using these results as a guide, we extended our study to helices in vivo. Based on the work of Lu & Deutsch (Nat. Struct. Mol. Bio. 12, 12, 2005), we wish to measure the free energy profiles of short alanine-based sequences inserted into the ribosomal exit tunnel. Lu & Deutsch used these sequence to determine where α-helical formation is either enhanced or hindered inside the exit tunnel. Two “folding regions” were observed (1) near the peptidyl transferase center (PTC), where new amino acids are appended to C-terminus of the nascent peptide, and (2) in the exit pore of the tunnel, where the nascent peptide is released from the ribosome. These regions are significant in that the diameter of the tunnel in these regions is twice the diameter at the “constriction point” between the two regions.

7-ALA5_REMD_US_15ns.pmf

PMF of α-helix formation for a 5-alanine sequence placed 7 residues from the PTC in the ribosomal exit tunnel.

We would like to use MD simulations to elucidate if there are other factors enhancing the formation of helices inside the exit tunnel. The image on the right is a PMF of a 5-alanine sequence near the PTC. We observed that there are two basins corresponding to extended and helical conformations, separated by barrier of ~3 kcal/mol. The free energy difference calculated from these simulations seems to slightly favor the helical state, whereas experiments show the extended state is favored over compacted states. Additional free energy calculations will be performed for other sequences tested by Lu & Deutsch, as well as equilibrium simulations, in order to further compare our simulations with their experiments.

β-Sheets

A-beta

Aβ protein in its (A) native structure and (B) misfolded, aggregated β-fold.

β-sheets are prevalent in both native and misfolded protein structures. The formation of fibrils and plaques associated with β-sheet formation are believed to be an underlying cause of many neurodegenerative disorders, such as Alzheimer’s. The problem lies in the fact that β-sheets are a low-energy metastable state for many proteins, which can easily be trapped in these states during the folding process, especially in the presents of other misfolded proteins, resulting in the aggregation of β-sheets into fibrils and plaques.

GB1_3

GB1 shown with backbone shown in color and hydrogen bonds represented by dashed, blue lines.

β-amyloid proteins are used to study the affects of β-sheet aggregation. To begin our study of this process, we performed free energy calculations on the model peptide, GB1 (the C-terminal end of protein G), whose crystal structure is a simple β-turn. Using the frequently used reaction coordinates (1) number of native hydrogen bonds and (2) radius of gyration of the hydrophobic core, we are comparing the free energy surfaces for various force fields (see below). The energy differences can be quite drastic, as is seen for CHARMM36 and CHARMM22*.

We will use the methods developed from our studies of GB1 to study the formation of amyloid fibers composed of Aβ peptides. We hope to elucidate how the free energy surface of Aβ is affected by the presence of other misfolded Aβ peptides, as well as track the progression of fibril formation as additional Aβ peptides are introduced to the growing fiber system.

pmfs_combined_horizontal

PMF of GB1 using native hydrogen bonds and radius of gyration of the hydrophobic core. (Left) CHARMM36. (Right) CHARMM22*.

 

Publications

  1. Thermodynamics of deca-alanine folding in water.
    Anthony Hazel, Christophe Chipot, and James C. Gumbart. Journal of Chemical Theory and Computation. 10:2836-2844, 2014.