Session X41: Focus Session: Physics of Proteins II: Folding and Structure

Simulations of the folding/unfolding of biomolecules under solvent, and pressure perturbations

Proteins exhibit marginal stability, determined by the balance of many competing effects. This stability can be perturbed by changes in temperature, pH, pressure, and other solvent conditions. Osmolytes are small organic compounds that modulate the conformational equilibrium, folded (F) and unfolded (U), of proteins as cosolvents. Protecting osmolytes such as trimethylamine N-oxide (TMAO), glycerol, and sugars that push the equilibrium toward F play a crucial role in maintaining the function of intracellular proteins in extreme environmental conditions. Urea is a denaturing osmolyte that shifts the equilibrium toward U. We will describe calculations of the reversible folding/unfolding equilibrium, under various solution conditions that include urea, high pressure, and different charge states of the Trp-cage miniprotein. The folding/unfolding equilibrium is studied using all-atom Replica exchange MD simulations. For urea, the simulations capture the experimentally observed linear dependence of unfolding free energy on urea concentration. We find that the denaturation is driven by favorable direct interaction of urea with the protein through both electrostatic and van der Waals forces and quantify their contribution. Though the magnitude of direct electrostatic interaction of urea is larger than van der Waals, the difference between unfolded and folded ensembles is dominated by the van der Waals interaction. We also find that hydrogen bonding of urea to the peptide backbone does not play a dominant role in denaturation. The unfolded ensemble sampled depends on urea concentration, with greater urea concentration favoring conformations with greater solvent exposure.   

Accurate prediction of explicit solvent atom distribution in HIV-1 protease and F-ATP synthase by statistical theory of liquids

We have created a simple algorithm for automatically predicting the explicit solvent atom distribution of biomolecules. The explicit distribution is coerced from the 3D continuous distribution resulting from a 3D-RISM calculation. This procedure predicts optimal location of solvent molecules and ions given a rigid biomolecular structure. We show examples of predicting water molecules near KNI-275 bound form of HIV-1 protease and predicting both sodium ions and water molecules near the rotor ring of F-ATP synthase. Our results give excellent agreement with experimental structure with an average prediction error of 0.45-0.65 angstroms. Further, unlike experimental methods, this method does not suffer from the partial occupancy limit. Our method can be performed directly on 3D-RISM output within minutes. It is useful not only as a location predictor but also as a convenient method for generating initial structures for MD calculations.   

Analysis and Interpretation of Single Molecule Protein Unfolding Kinetics

The kinetics of protein unfolding under a stretching force has been extensively studied by atomic force microscopy (AFM) over the past decade [1]. Experimental artifacts at the single molecule level introduce uncertainties in the data analysis that have led to several competing physical models for the unfolding process. For example, the unfolding dynamics of the protein ubiquitin under constant force has been described by probability distributions as diverse as exponential [2,3], a sum of exponentials, log-normal [4], and more recently a function describing static disorder in the Arrhenius model [5]. A new method for data analysis is presented that utilizes maximum likelihood estimation (MLE) combined with other traditional statistical tests to unambiguously rank the consistency of these and other models with the experimental data. These techniques applied to the ubiquitin unfolding data shows that the probability of unfolding is best fit with a stretched exponential distribution, with important implications on the complexity of the mechanism of protein unfolding. \\[4pt] [1] Carrion-Vazquez, et. al. Springer Series in Biophys. 2006 \\[0pt] [2] Fernandez et. al. Science 2004 \\[0pt] [3] Brujic et. al. Nat. Phys 2006 \\[0pt] [4] Garcia-Manyes et. al. Biophys. J. 2007 \\[0pt] [5] Kuo et. al. PNAS 2010   

Investigating protein structure and folding with coherent two-dimensional infrared spectroscopy

We present a new technique to quantitatively determine the secondary structure composition of proteins in solution based on ultrafast two-dimensional infrared (2DIR) spectroscopy. The percentage of residues in alpha-helix, beta-sheet, and unstructured conformations is extracted from a principal component analysis of the measured amide-I 2DIR spectra. We benchmark the method against a library of commercially-available proteins by comparing the predicted structure compositions with the x-ray crystal structures. The new technique offers sub-picosecond time resolution, and can be used to study systems that are difficult to study with conventional methods such as gels, intrinsically disordered peptides, fibers, and aggregates. We use the technique to investigate the structural changes and timescales associated with folding and denaturing of small proteins via equilibrium and transient temperature-jump 2DIR spectroscopy.   

Protein Folding and Functional Dynamics

Proteins are intrinsically flexible and dynamic objects. Thus, protein dynamics are intimately coupled to their function. In many cases, however, it is difficult to directly probe protein conformational dynamics occurring on either very fast or very slow timescales with high spatial resolution. In this talk, several examples will be discussed to show how ensemble and single-molecule spectroscopic methods can be used to follow protein folding events taking place on the nanosecond timescale and slow conformational dynamics associated with function.   

Folding a protein with equal probability of being helix or hairpin

We explore the possibility for the native state of a protein being inherently a multi-conformation state in an ab initio coarse-grained model. Based on the Wang-Landau algorithm, the complete free energy landscape for the designed sequence 2D4X: INYWLAHAKAGYIVHWTA is constructed. It is shown that 2DX4 posesses two nearly degenerate native states: one has a helix structure, while the other has a hairpin structure and their energy difference is less than 2\% of that of local minimums. Furthermore, the hydrogen-bond and dipole-dipole interactions are found to be two major competing mechanims in transforming one conformation into the other. Our results indicate that degenerate native states are stablized by subtle balance between different interactions in proteins; furthermore, degeneracy only happens for small proteins of sizes being around 18 amino acides or 40-50 amino acides. These results provide important clues to the study of native structures of proteins.   

Generic transition hierarchies of lattice HP protein adsorption: A Wang-Landau study

We have applied Wang-Landau sampling with appropriate trial moves\footnote{T. W\"{u}st and D. P. Landau, Phy. Rev. Lett. \textbf{102}, 178101 (2009).} to investigate the thermodynamics and structural properties of the HP lattice protein model\footnote{K. A. Dill, Biochemistry \textbf{24}, 1501 (1985).} interacting with an attractive substrate. The conformational ``phase transitions'' of several benchmark HP sequences have been identified by a comprehensive canonical analysis of the specific heat and structural observables, e. g. radius of gyration and thermal derivatives of number of surface contacts. Three major ``transitions'': adsorption, hydrophobic core formation, and ``flattening'' of adsorbed structures, are observed. Depending on the surface attractive strength relative to the intra-protein attraction among the H monomers, these processes take place in a different order upon cooling. We identify a small number of generic categories that are sufficient to classify the folding hierarchies for different HP chains consisting of assorted sequences and chain lengths, regardless of the monomer type that the surface attracts. We thus believe that this classification scheme is generally applicable to lattice protein adsorption problems.   

Elucidating Structure and Catalytic Cycles of Anti- or Ferro-magnetic Iron Enzymes from Spin Density Functional Theory

Nature uses metal-containing enzymes to catalyze important biochemical reactions. Some enzymes, such as methane monooxygenase hydroxylase (MMOH), contain (anti)ferromagnetic binuclear iron centers that interact with dioxygen and/or other substrates to facilitate biochemical functions. We have studied the electronic and magnetic structures of several enzyme binuclear iron centers and predicted their spectroscopic properties. We have used spin density functional theory (SDFT) to predict $^{57}$Fe M\"ossbauer and other spectral parameters of MMOH and structurally related iron-containing enzymes. Upon dioxygen binding, the diiron center of MMOH undergoes a ferromagnetic to antiferromagnetic transition which may play an important role in its catalytic activity. In addition, based on our ability to predict spectroscopic data, we have been able to predict the structure of a key reaction intermediate in the MMOH catalytic cycle for which there is no X-ray structure.   

AWSEM-MD: Coarse-grained Protein Structure Prediction Using Physical Potentials and Bioinformatically Based Local Structure Biasing

The Associative memory, Water mediated, Structure and Energy Model (AWSEM) is a coarse-grained protein model. When combined with a sequence alignment method, AWSEM can be used to perform de novo protein structure prediction. Herein we present structure prediction results for a particular choice of sequence alignment method based on short residue sequences called fragments. We demonstrate the model's structure prediction capabilities for three variants on a standard sequence alignment protocol, all of which assume that the structure of the target sequence is not known. We show that the inclusion of structures from homologous sequences in the fragment memory search improves structure prediction only marginally. However, when the fragment search is restricted to only homologous sequences, AWSEM can perform high-resolution structure prediction.   

Combining first principles and replica exchange for the structure of two large peptides: Ac-Ala$_{19}$-LysH$^+$ vs. Ac-LysH$^+$-Ala$_{19}$

Predicting the structure of peptides requires a high accuracy for ``weak'' interactions. We here focus on the predominant structure types of two alanine-based peptides \emph{in vacuo} from first principles and in comparison to experimental IR spectroscopy$^1$: Ac-Ala$_{19}$-LysH$^+$, which is expected to be $\alpha$-helical [1,2], and Ac-LysH$^+$-Ala$_{19}$, where globular monomers, helical dimers, and helices with non-standard protonation sites are expected [2]. Despite supposedly very different conformers, Ac-LysH$^+$-Ala$_{19}$ and Ac-Ala$_{19}$-LysH$^+$ yield very similar experimental IR spectra in the $\approx$1000-2000 cm$^{-1}$ wavenumber range. We utilize a two-stage structure search approach: we begin by a force-field based replica exchange molecular dynamics (REMD) scan followed by further REMD scans based on density functional theory with the van der Waals corrected [3] PBE functional. We suggest plausible candidates for all likely structure prototypes. Helix-turn-helix motifs emerge as the most likely candidates and explain a subtle peak shift in experiment. [1] M. Rossi \textit{et al.}, JPCL \textbf{1}, 3465 (2010); [2] M. Jarrold, PCCP \textbf{9}, 1659 (2007); [3] A. Tkatchenko, M. Scheffler, PRL \textbf{102}, 073005 (2009).   

Enhanced Wang Landau Sampling of Adsorbed Protein Conformations

Using computer simulations to model the folding of proteins into their native states is computationally expensive due to the extraordinarily low degeneracy of the ground state. In this paper, we develop an efficient way to sample these folded conformations using Wang Landau sampling coupled with the configurational bias method (which uses an unphysical ``temperature'' which is between the collapse and folding transition of the protein). This method speeds-up the folding process by roughly an order of magnitude over existing algorithms. We apply this method to study the adsorption of HP protein fragments on a hydrophobic surface, a model which is a close analog of one presented recently by Shea and coworkers. We are able to readily capture the fact that these fragments, which are unstructured in the bulk, acquire secondary structure upon adsorption onto a strong hydrophobic surface. Apparently, the presence of a hydrophobic surface allows these random coil fragments to fold by providing hydrophobic contacts that were lost in protein fragmentation.