Herges, T.

Schug, A.

Wenzel, W.

English

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Reproducible Protein Folding with the Stochastic Tunneling MethodA. Schug,1 T. Herges,1 and W. Wenzel11Forschungszentrum Karlsruhe, Institut für Nanotechnologie, 76021 Karlsruhe, GermanyWe report the reproducible folding of the 20 amino-acid protein trp cage using a novel version of the stochastic tunneling method and a recently developed all-atom protein free-energy force field. Six of 25 simulations reached an energy within 1 kcal=mol of the best energy, all of which correctly predicted the native experimental structure of the protein, in total eight simulations converged to the native structure. We find a strong correlation between energy and root-mean-square deviation to the native structure for all simulations.PACS numbers: 87.15.Cc, 02.60.Pn, 02.70.Nsthe stochastic tunneling algorithm is an efficient and form: VhbCOi;NHj  R~rijij; ij where ~rij, ij,Protein structure prediction on the basis of the amino-acid sequence alone remains one of the grand outstandingchallenges of theoretical biophysics [1–3]. In the postge-nomic era, sequence information for proteins abounds,while structural and mechanistic information remainsscarce. While the sequences for hundreds of thousandsof proteins are known, the PDB database contains justover 20 000 entries [4]. Theoretical models may help toclose this gap, and elucidate mechanisms of proteins thatare difficult to handle experimentally (e.g., transmem-brane proteins). With the development of reliable forcefields [5] and robust simulation techniques [6], proteinstructure prediction may assist in the understanding andquantitative analysis of protein-protein or protein-ligandassociation [7] at an atomistic level. Ultimately questionsregarding the dynamics of biological function may beaddressed.While homology based methods have demonstratedsteady progress in the past decade, the assessment ofatomistic de novo prediction strategies has been less fa-vorable [2,3]. De novo prediction strategies at the all-atomlevel are presently rare, in part because of their enormouscomputational cost [8,9]. The prediction of protein terti-ary structure with free-energy force fields may signi-ficantly reduce this cost, because the native structurecan be determined with global optimization methods[2,6,10], without recourse to the folding dynamics, ordersof magnitude faster than with direct simulation methods.We have recently reported the rational development of atransferable all-atom free-energy force field (PFF01) [5]that correctly predicts the native structure of two three-helix proteins, the 36 amino-acid headgroup of villin(pdb-code:1VII) [6,8] and the 40 amino-acid headgroupof the HIV accessory protein (pdb-code:1F4I), as theglobal minimum of the free-energy surface (FES). TheFES of both proteins has several deep and complex fold-ing funnels, with several nontrivial branching points.Optimization methods to efficiently and reliably locatethe low-energy minima of such complex, rugged FES arestill lacking.In this investigation we show that an adapted version ofreliable method for reproducible structure prediction oftrp cage [11,12](pdb-code 1L2Y), one of the fastest fold-ing proteins [13]. Our results demonstrate that the PFF01force field is transferable from the three-helix peptides tosystems with significantly less helical content.Model.—We have recently developed an all-atom (withthe exception of apolar CHn groups) free-energy proteinforce field (PFF01) that models the low-energy conforma-tions of proteins with minimal computational demand[14]. In the folding process at physiological conditionsthe degrees of freedom of a peptide are confined torotations about single bonds. The force field is parame-trized with the following nonbonded interactions:Vf~rig XijVijRijrij122Rijrij6XijqiqjgigjrijXiiAi XhbondsVhb: (1)Here rij denotes the distance between atoms i and j andgi the type of the amino-acid i. The Lennard-Jonesparameters (Vij; Rij for potential depths and equilibriumdistance) depend on the type of the atom pair and wereadjusted to satisfy constraints derived from as a set of 138proteins of the PDB database [14–16]. The nontrivialelectrostatic interactions in proteins are represented viagroup-specific dielectric constants (i depending on theamino acid to which atom i belongs). The partial chargesqi and i were previously derived in a potential-of-mean-force approach [17]. Interactions with the solvent werefirst fit in a minimal solvent accessible surface model [18]parametrized by free energies per unit area i to repro-duce the enthalpies of solvation of the Gly-X-Gly familyof peptides [19]. Ai corresponds to the area of atom i thatis in contact with a fictitious solvent. The i were adjustedto stabilize the native state of the 36-amino acid head-group of villin (pdb-code 1VII) as the global minimum ofthe force field [20]. Hydrogen bonds are described viadipole-dipole interactions included in the electrostaticterms and an additional short range term for backbone-backbone hydrogen bonding (CO to NH) which takes theTABLE I. Energy (in kcal=mol) and RMSB deviation to therelaxed NMR (RMSB-1) and the NMR (RMSB-2) structure of1L2Y for the twenty-five simulations described in the text. Alsoshown is the secondary structure assignment (DSSP) for thelowest energy conformation of each simulation (C  coil, H helix, T  turn, S  sheet). The first two lines give the data forthe original/relaxed NMR structure, respectively.Energy RMSB-1 RMSB-2 Secondary structure19.29 2.61 0.00 CHHHHHHHCCCCTTHHHHTC25:73 0.00 2.61 CHHHHHHHHTHHHHTSCCCC25:79 1.81 2.83 CHHHHHHHHTHHHHTCCSCC25:31 2.52 3.05 CHHHHHHHHTHHHHTCTTTC25:25 2.55 3.13 CHHHHHHHHTHHHHTCTTTC25:25 3.30 4.26 CHHHHHHHHTCHHHHCTTTC25:24 2.56 3.13 CHHHHHHHHTHHHHTCTTTC25:15 2.57 3.13 CHHHHHHHHHHHHHTCTTTC24:15 3.98 4.80 CHHHHHHHHTCSCTTSSSCC24:06 4.43 4.73 CHHHHHHHHTSSCSSSTTTC23:99 4.50 4.95 CHHHHHHHHTCSSTTSTTTC23:64 3.50 3.86 CHHHHHCTTHHHHHTCTTTC23:64 3.70 4.54 CHHHHHHHHHCTTTSSCSCC23:45 2.58 3.18 CHHHHHHHHTHHHHTCTTTC23:30 2.96 3.83 CHHHHHHHHTCHHHHCTTTC23:27 2.51 2.72 CHHHHHHHHTHHHHTCTTTC22:82 4.67 4.73 CHHHHHHHHSSCCTTCTTTC22:53 3.66 4.37 CHHHHHHTTSHHHHHCCSCC22:49 5.10 4.87 CHHHHHHHHTCCSSSSCCCC22:45 4.01 4.59 CHHHHHHHHHCSSTTCTTTC22:23 4.68 5.08 CHHHHHHHHTSSSTTSTTTC21:27 3.43 2.88 CHHHHHHHHTHHHHTCSCCC20:31 5.63 5.77 CHHHHHHHHHSSCTTCSSCC20:20 3.57 4.37 CHHHHHHHHHCSSTTSSSCC20:16 3.22 3.31 CHHHHHHHHSCHHHHCTTTC19:82 3.78 3.89 CHHHHHHHHHCTTTCCCSCC18:70 4.64 4.83 CHHHHHHSSSHHHHTCCSCCand ij designate the OH distance,  is the angle betweenN, H, and O along the bond, and  is the angle betweenthe CO and NH axis. R and  were fitted as a correctivepotential of mean force to the same set of proteins de-scribed above [15].Optimization Technique.—The stochastic tunnelingtechnique (STUN) [21] was proposed as a generic globaloptimization method for complex rugged potential en-ergy surfaces (PES). For a number of problems, includingthe prediction of receptor-ligand complexes for drug de-velopment [22,23], this technique proved superior tocompeting stochastic optimization methods. In STUNthe dynamical process explores not the original, but atransformed PES, which dynamically adapts and simpli-fies during the simulation. The idea behind the methodis to flatten the potential energy surface in all regionsthat lie significantly above the best estimate for the mini-mal energy (E0). Even at finite temperature the dynamicsof the system then becomes diffusive at energies aboveE  E0 independent of the relative energy differencesof the high-energy conformations involved. On the un-transformed PES, STUN thus permits the simulation to‘‘tunnel’’ through energy barriers of arbitrary height.The original transformation proposed for STUN [21] ishelpful for many PES, but leads to failure for peptidesimulations, where the first pair of atoms clashing con-verts the transformed PES to a ‘‘golf-course’’ landscape.Further clashes then cost no extra energy and the entireclashing conformational space is transformed into asingle featureless plateau with no guiding force to a non-clashing conformation. Applied to proteins, this defi-ciency limited the applicability of the original STUN torelatively short peptides.For the peptide simulations reported here we replacethe original transformation [21] with:ESTUN  lnxx2  1p (2)with x  E  E0, where E is the energy, E0 the best energy found so far. The problem-dependent transfor-mation parameter [21]  controls the steepness of the transformation [we used   0:5kcal=mol1]. The transformation in Eq. (2) ameliorates the difficulties as-sociated with the original transformation, becauseESTUN / lnE=kT continues to grow slowly for large energies. Even so, the fictitious temperature of STUN must be dynamically adjusted in order to accelerate con-vergence. STUN works best if its dynamical process alternates between low-temperature ‘‘local-search’’ and high-temperature ‘‘tunneling’’ phases.Results.—We performed 25 simulations of 12:5  106 energy evaluations each of the 1L2Ypeptide starting from randomized dihedral angle conditions. 1L2Y is a de-signed 20-residue Trp-cage protein [11] that folds sponta-neously into a globular fold which exhibits a stable secondary/tertiary structure not often found in proteins of this size [12]. Its secondary structure contains both an helix extending from residue 2-8 and an 3-10 helix inresidues 11-14. The presence of three proline residues nearthe C terminus of the peptide prohibits the existence ofsecondary structure in this region. In experiment, theprotein autonomously folds into a tertiary structure inwhich the proline residues pack against Tyr-3 and Trp-6near the N terminus. Each of the starting conformationshad a large backbone root mean square deviation (RMSB)from the native configuration and a large positive energy.We have independently confirmed that the native state ofthe protein is close to a local minimum of the force field(RMSB  2:61 A, throughout this Letter the first of 20reported NMR structures are used [11]). This deviationsets the scale on which the similarity of the resultingstructures can be judged. The minimal energy andRMSB to the original/relaxed NMR structure are shownin Table I. The estimate of the best energies still spans awide energy window, emphasizing the fact that presentlylittle can be learned about the global minimum of suchcomplex potential energy surfaces from a single isolated

Reproducible protein folding with the stochastic tunneling method

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Reproducible protein folding with the stochastic tunneling method

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