Reproducible polypeptide folding and structure prediction using molecular dynamics simulations

The folding of a polypeptide from an extended state to a well-defined conformation is studied using microsecond classical molecular dynamics (MD) simulations and replica exchange molecular dynamics (REMD) simulations in explicit solvent and in vacuo. It is shown that the solvated peptide folds many times in the REMD simulations but only a few times in the conventional simulations. From the folding events in the classical simulations we estimate an approximate folding time of 1-2 micros. The REMD simulations allow enough sampling to deduce a detailed Gibbs free energy landscape in three dimensions. The global minimum of the energy landscape corresponds to the native state of the peptide as determined previously by nuclear magnetic resonance (NMR) experiments. Starting from an extended state it takes about 50 ns before the native structure appears in the REMD simulations, about an order of magnitude faster than conventional MD. The calculated melting curve is in good qualitative agreement with experiment. In vacuo, the peptide collapses rapidly to a conformation that is substantially different from the native state in solvent.     

The Free Energy Profile of Tubulin Straight-Bent Conformational Changes,with Implications for Microtubule Assembly and Drug Discovery

αβ-tubulin dimers need to convert between a ‘bent’ conformation observed for free dimers in solution and a ‘straight’ conformation required for incorporation into the microtubule lattice. Here, we investigate the free energy landscape of αβ-tubulin using molecular dynamics simulations, emphasizing implications for models of assembly, and modulation of the conformational landscape by colchicine, a tubulin-binding drug that inhibits microtubule polymerization. Specifically, we performed molecular dynamics, potential-of-mean force simulations to obtain the free energy profile for unpolymerized GDP-bound tubulin as a function of the ∼12° intradimer rotation differentiating the straight and bent conformers. Our results predict that the unassembled GDP-tubulin heterodimer exists in a continuum of conformations ranging between straight and bent, but, in agreement with existing structural data, suggests that an intermediate bent state has a lower free energy (by ∼1 kcal/mol) and thus dominates in solution. In agreement with predictions of the lattice model of microtubule assembly, lateral binding of two αβ-tubulins strongly shifts the conformational equilibrium towards the straight state, which is then ∼1 kcal/mol lower in free energy than the bent state. Finally, calculations of colchicine binding to a single αβ-tubulin dimer strongly shifts the equilibrium toward the bent states, and disfavors the straight state to the extent that it is no longer thermodynamically populated.     

Folding of apocytochrome c induced by the interaction with negatively charged lipid micelles proceeds via a collapsed intermediate state

Unfolded apocytochrome c acquires an alpha-helical conformation upon interaction with lipid. Folding kinetic results below and above the lipid's CMC, together with energy transfer measurements of lipid bound states, and salt-induced compact states in solution, show that the folding transition of apocytochrome c from the unfolded state in solution to a lipid-inserted helical conformation proceeds via a collapsed intermediate state (I(C)). This initial compact state is driven by a hydrophobic collapse of the polypeptide chain in the absence of the heme group and may represent a heme-free analogue of an early compact intermediate detected on the folding pathway of cytochrome c in solution. Insertion into the lipid phase occurs via an unfolding step of I(C) through a more extended state associated with the membrane surface (I(S)). While I(C) appears to be as compact as salt-induced compact states in solution with substantial alpha-helix content, the final lipid-inserted state (Hmic) is as compact as the unfolded state in solution at pH 5 and has an alpha-helix content which resembles that of native cytochrome c.     

Structure of stable protein folding intermediates by equilibrium phi-analysis: the apoflavodoxin thermal intermediate

Protein intermediates in equilibrium with native states may play important roles in protein dynamics but, in cases, can initiate harmful aggregation events. Investigating equilibrium protein intermediates is thus important for understanding protein behaviour (useful or pernicious) but it is hampered by difficulties in gathering structural information. We show here that the phi-analysis techniques developed to investigate transition states of protein folding can be extended to determine low-resolution three-dimensional structures of protein equilibrium intermediates. The analysis proposed is based solely on equilibrium data and is illustrated by determination of the structure of the apoflavodoxin thermal unfolding intermediate. In this conformation, a large part of the protein remains close to natively folded, but a 40 residue region is clearly unfolded. This structure is fully consistent with the NMR data gathered on an apoflavodoxin mutant designed specifically to stabilise the intermediate. The structure shows that the folded region of the intermediate is much larger than the proton slow-exchange core at 25 degrees C. It also reveals that the unfolded region is made of elements whose packing surface is more polar than average. In addition, it constitutes a useful guide to rationally stabilise the native state relative to the intermediate state, a far from trivial task.     

Development of an extended simulated annealing method: application to the modeling of complementary determining regions of immunoglobulins.

An extended simulated annealing process (ESAP) has been developed in order to obtain an ensemble of conformations of a peptide segment from a protein fluctuating at a given temperature. The annealing process was performed with a fast Monte Carlo method using the scaled collective variables developed by Noguti and Go. The system was divided into two parts: one consists of one or more peptide segments and is flexible around the main-chain and side-chain torsional angles; the other represents the rest of the molecule and was maintained fixed at the atomic positions determined by x-ray experiments. The target function included the nonbonding atomic interactions and a distance function to anchor the N and C terminal ends of each segment to the fixed part. Three systems of complementary determining regions (CDR) of antibodies were tested and compared to x-ray data: L2 loop (7 residues) of the light chain of lambda-type Bence-Jones protein, H1 and the H2 loops (14 residues) of McPC603, and H1 and H2 loops (12 residues) of HyHEL-5. Each state of CDR conformations was characterized at room temperature by the average of their coordinates (average conformation) and the internal energy. With a limited number of annealing processes (10), starting from the extended conformation, we have obtained states with conformations close to the observed x-ray structures, from 1.1 to 1.7 A root mean square deviation (rmsd) of main-chain atoms depending on the system. These states were identical or within 0.25 A rmsd of those of lowest internal energy. For unknown CDR structures the criteria of lowest internal energies from ESAP can be used to predict hypervariable loop structures in antibodies with an accuracy comparable to other methods.     

Free energy landscapes of peptides by enhanced conformational sampling

The free energy landscapes of peptide conformations in water have been observed by the enhanced conformational sampling method, applying the selectively enhanced multicanonical molecular dynamics simulations. The conformations of the peptide dimers, -Gly-Gly-, -Gly-Ala-, -Gly-Ser-, -Ala-Gly-, -Asn-Gly-, -Pro-Gly-, -Pro-Ala-, and -Ala-Ala-, which were all blocked with N-terminal acetyl and C-terminal N-methyl groups, were individually sampled with the explicit TIP3P water molecules. From each simulation trajectory, we obtained the canonical ensemble at 300 K, from which the individual three-dimensional landscape was drawn by the potential of mean force using the three reaction coordinates: the backbone dihedral angle, psi, of the first amino acid, the backbone dihedral angle, phi, of the second amino acid, and the distance between the carbonyl oxygen of the N-terminal acetyl group and the C-terminal amide proton. The most stable state and several meta-stable states correspond to extended conformations and typical beta-turn conformations, and their free energy values were accounted for from the potentials of mean force at the states. In addition, the contributions from the intra-molecular energies of peptides and those from the hydration effects were analyzed. Consequently, the stable beta-turn conformations in the free energy landscape were consistent with the empirically preferred beta-turn types for each amino acid sequence. The thermodynamic values for the hydration effect were decomposed and they correlated well with the empirical values estimated from the solvent accessible surface area of each molecular conformation during the trajectories. The origin of the architecture of protein local fragments was analyzed from the viewpoint of the free energy and its decomposed factors.     

Molecular dynamics method for proteins with ionization-conformation coupling and equilibrium titration

A new realization of the constant pH molecular dynamics simulation is proposed in mean force potential of proton reservoir in constant titration conditions. The MD-pH-ET method is used for a protein in the most probable ionization microstate, which is the state with minimal energy of the current conformation taking into account the correcting ionization potential of mean force considering an equilibrium ensemble of ionization states. The new MD-pH-ET method allows one to carry out an optimization of protein structure and the total free energy of a protein in the aqueous solution at constant pH and to calculate the pH-dependent properties. The MD-pH-ET method possesses the following unique features: (1) it uses the most precise and computationally effective realization of calculation of electrostatic energy of a protein in aqueous solution, the model of continuous dielectric media with Poisson equation, and the generalized Born method with “ideal” Born atomic radii; (2) it uses the same model of the potential energy surface in the ionization-conformation phase space both for calculating the potential energy of the protein and atomic forces and for determining the most probable ionization states; (3) it calculates the total free energy of the protein in the aqueous solution in a proton reservoir under the conditions of equilibrium titration. The workability of the new method MD-pH-ET is demonstrated for a molecule of the BPTI protein.     

A small tripeptide AFA undergoes two state cooperative conformational transitions: implications for conformational biases in unfolded states

It is important to understand the conformational biases that are present in unfolded states to understand protein folding. In this context, it is surprising that even a short tripeptide like AFA samples folded/ordered conformation as demonstrated recently by NMR experiments of the peptide in aqueous solution at 280 K. In this paper, we present molecular dynamics simulation of the peptide in explicit water using OPLS-AA/L all-atom force field. The results are in overall agreement with NMR results and provide some further insights. The peptide samples turn and extended conformational forms corresponding to minima in free energy landscape. Frequent transitions between the minima are observed due to modest free energy barriers. The turn conformation seems to be stabilized by hydrophobic interactions and possibly by bridging water molecules between backbone donors and acceptors. Thus the peptide does not sample conformations randomly, but samples well defined conformations. The peptide served as a model for folding-unfolding equilibrium in the context of peptide folding. Further, implications for drug design are also discussed.     

NMR characterization of the energy landscape of SUMO-1 in the native-state ensemble

Characterizing the low energy excited states in the energy landscape of a protein is one of the exciting and demanding problems in structural biology at the present time. These describe the adaptability of the protein structure to external perturbations. In this context, we used here non-linear dependence of amide proton chemical shifts on temperature to identify residues accessing alternative conformations in SUMO-1 in the native state as well as in the near-native states created by sub-denaturing concentrations of urea. The number of residues accessing alternative conformations increases and the profiles of curved temperature dependence also change with increasing urea concentration. In every case these alternative conformations lie within 2 kcal/mol from the ground state, and are separated from it by low energy barriers. The residues that access alternative conformations span the length of the protein chain but are located at particular regions on the protein structure. These include many of the loops, beta2 and beta5 strands, and some edges of the helices. We observed that some of the regions of the protein structure that exhibit such fluctuations coincide with the protein's binding surfaces with different substrate like GTPase effector domain (GED) of dynamin, SUMO binding motifs (SBM), E1 (activating enzyme, SAE1/SAE2) and E2 (conjugating enzyme, UBC9) enzymes of sumoylation machinery, reported earlier. We speculate that this would have significant implications for the binding of diversity of targets by SUMO-1 for the variety of functions it is involved in.     

Growth and shortening of microtubules: a two-state model approach

In this study, a two-state mechanochemical model is presented to describe the dynamic instability of microtubules (MTs) in cells. The MT switches between two states, the assembly and disassembly states. In assembly state, the growth of MTs includes two processes: free GTP-tubulin binding to the tip of protofilament (PF) and conformation change of PF, during which the first tubulin unit that curls outwards is rearranged onto the MT surface, using the energy released from the hydrolysis of GTP in the penultimate tubulin unit. In the disassembly state, the shortening of MTs also includes two processes, the release of GDP-tubulin from the tip of PF and the curling of one new tubulin unit out of the MT surface. Switches between these two states, which are usually called rescue and catastrophe, happen stochastically with external force-dependent rates. Using this two-state model with parameters obtained by fitting the recent experimental data, detailed properties of MT growth are obtained. I find that MT is mainly in the assembly state, its mean growth velocity increases with both the external force and the GTP-tubulin concentration, and an MT will shorten on average without an external force. To know more about the external force and GTP-tubulin concentration-dependent properties of MT growth, and for future experimental verification of this two-state model, 11 critical forces are defined and discussed numerically.     

How maltose influences structural changes to bind to maltose‐binding protein: Results from umbrella sampling simulation

A well‐studied periplasmic‐binding protein involved in the abstraction of maltose is maltose‐binding protein (MBP), which undergoes a ligand‐induced conformational transition from an open (ligand‐free) to a closed (ligand‐bound) state. Umbrella sampling simulations have been us to estimate the free energy of binding of maltose to MBP and to trace the potential of mean force of the unbinding event using the center‐of‐mass distance between the protein and ligand as the reaction coordinate. The free energy thus obtained compares nicely with the experimentally measured value justifying our theoretical basis. Measurement of the domain angle (N‐terminal‐domain – hinge – C‐terminal‐domain) along the unbinding pathway established the existence of three different states. Starting from a closed state, the protein shifts to an open conformation during the initial unbinding event of the ligand then resides in a semi‐open conformation and later resides predominantly in an open‐state. These transitions along the ligand unbinding pathway have been captured in greater depth using principal component analysis. It is proposed that in mixed‐model, both conformational selection and an induced‐fit mechanism combine to the ligand recognition process in MBP. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Energy landscape of a peptide consisting of alpha-helix, 3(10)-helix, beta-turn, beta-hairpin, and other disordered conformations

The energy landscape of a peptide [Ace-Lys-Gln-Cys-Arg-Glu-Arg-Ala-Nme] in explicit water was studied with a multicanonical molecular dynamics simulation, and the AMBER parm96 force field was used for the energy calculation. The peptide was taken from the recognition helix of the DNA-binding protein, c-MYB: A rugged energy landscape was obtained, in which the random-coil conformations were dominant at room temperature. The CD spectra of the synthesized peptide revealed that it is in the random state at room temperature. However, the 300 K canonical ensemble, Q(300K), contained alpha-helix, 3(10)-helix, beta-turn, and beta-hairpin structures with small but notable probabilities of existence. The complete alpha-helix, imperfect alpha-helix, and random-coil conformations were separated from one another in the conformational space. This means that the peptide must overcome energy barriers to form the alpha-helix. The overcoming process may correspond to the hydrogen-bond rearrangements from peptide-water to peptide-peptide interactions. The beta-turn, imperfect 3(10)-helix, and beta-hairpin structures, among which there are no energy barriers at 300 K, were embedded in the ensemble of the random-coil conformations. Two types of beta-hairpin with different beta-turn regions were observed in Q(300K). The two beta-hairpin structures may have different mechanisms for the beta-hairpin formation. The current study proposes a scheme that the random state of this peptide consists of both ordered and disordered conformations. In contrast, the energy landscape obtained from the parm94 force field was funnel like, in which the peptide formed the helical conformation at room temperature and random coil at high temperature.     

Dual energy landscape: the functional state of the β-barrel outer membrane protein G molds its unfolding energy landscape

We applied dynamic single-molecule force spectroscopy to quantify the parameters (free energy of activation and distance of the transition state from the folded state) characterizing the energy barriers in the unfolding energy landscape of the outer membrane protein G (OmpG) from Escherichia coli. The pH-dependent functional switching of OmpG directs the protein along different regions on the unfolding energy landscape. The two functional states of OmpG take the same unfolding pathway during the sequential unfolding of β-hairpins I-IV. After the initial unfolding events, the unfolding pathways diverge. In the open state, the unfolding of β-hairpin V in one step precedes the unfolding of β-hairpin VI. In the closed state, β-hairpin V and β-strand S11 with a part of extracellular loop L6 unfold cooperatively, and subsequently β-strand S12 unfolds with the remaining loop L6. These two unfolding pathways in the open and closed states join again in the last unfolding step of β-hairpin VII. Also, the conformational change from the open to the closed state witnesses a rigidified extracellular gating loop L6. Thus, a change in the conformational state of OmpG not only bifurcates its unfolding pathways but also tunes its mechanical properties for optimum function.     

Conformation of a group 2 late embryogenesis abundant protein from soybean. Evidence of poly (L-proline)-type II structure

Late embryogenesis abundant (LEA) proteins are members of a large group of hydrophilic, glycine-rich proteins found in plants, algae, fungi, and bacteria known collectively as hydrophilins that are preferentially expressed in response to dehydration or hyperosmotic stress. Group 2 LEA (dehydrins or responsive to abscisic acid) proteins are postulated to stabilize macromolecules against damage by freezing, dehydration, ionic, or osmotic stress. However, the structural and physicochemical properties of group 2 LEA proteins that account for such functions remain unknown. We have analyzed the structural properties of a recombinant form of a soybean (Glycine max) group 2 LEA (rGmDHN1). Differential scanning calorimetry of purified rGmDHN1 demonstrated that the protein does not display a cooperative unfolding transition upon heating. Ultraviolet absorption and circular dichroism spectroscopy revealed that the protein is in a largely hydrated and unstructured conformation in solution. However, ultraviolet absorption and circular dichroism measurements collected at different temperatures showed that the protein exists in equilibrium between two extended conformational states: unordered and left-handed extended helical or poly (L-proline)-type II structures. It is estimated that 27% of the residues of rGmDHN1 adopt or poly (L-proline)-type II-like helical conformation at 12 degrees C. The content of extended helix gradually decreases to 15% as the temperature is increased to 80 degrees C. Studies of the conformation of the protein in solution in the presence of liposomes, trifluoroethanol, and sodium dodecyl sulfate indicated that rGmDHN1 has a very low intrinsic ability to adopt alpha-helical structure and to interact with phospholipid bilayers through amphipathic alpha-helices. The ability of the protein to remain in a highly extended conformation at low temperatures could constitute the basis of the functional role of GmDHN1 in the prevention of freezing, desiccation, ionic, or osmotic stress-related damage to macromolecular structures.     

Detection of local structures in reduced unfolded bovine pancreatic trypsin inhibitor.

The structure of BPTI and reduced BPTI in concentrated guanidinium HCl (GUHCl) in the presence of glycerol has been probed by measurements of dynamic nonradiative excitation energy transfer between probes attached to its amino groups. Interprobe distance distributions were obtained from analysis of donor fluorescence decay curves and used to characterize local structures in unordered states of the protein. Site specifically fluorescently labeled BPTI derivatives (1-n)BPTI (n = 15, 20, 41, 46) were used, each carrying a 2-methoxy-naphthyl-1-methylenyl group (MNA) at the N-terminal amino group of arg1 and 7-(dimethylamino)-coumarin-4-yl-acetyl residue (DA-coum) at one of its epsilon-NH2 groups of the lysine side chains. Analysis of donor fluorescence decay kinetics gave the interprobe distance distributions in the native and denatured states. The N-terminal-segment, residues 1-15, is in an extended conformation (with an average interprobe distance of 34 +/- 2 A) in the native state. Upon unfolding by reduction with DTT or beta-mercapto ethanol in 6 M GUHCl/glycerol mixture, the conformation of this segment relaxed to a state characterized by a reduced average interprobe distance and a larger width of the distances distribution. The average distance between residues 1 and 26, i.e., between the N-terminus and the turn of the twisted beta sheet element (residues 18-35), increased upon unfolding. At -30 degrees C in the above solvent, the distribution between these two sites was probably composed of two conformational subpopulations. About 45 +/- 20% of the molecules were characterized by a short interprobe distance (like the native state) representing a compact conformation, and 55 +/- 20% of the molecules showed large interprobe distances representing an expanded (unfolded) conformation. Thus local structures seem to exist in reduced denatured BPTI even under denaturing conditions in 6 M GUHCl/glycerol mixtures. Some of those structures are unstable in guanidinium isothiocyanate (GUSCN). The method introduced here is suitable for probing local structures and very long range interactions in unfolded proteins and for search for folding initiation sites (FISs) and early folding intermediates.     

Interpretation of protein folding psi values

The structural characterization of transition states is essential for understanding the mechanism of protein folding. Analyzing the effect of mutations on protein stability and folding kinetics in phi-value analysis is commonly used to gain information about the presence of side-chain interactions in transition states. Recently, specific binding of ligands to engineered binding sites was applied to monitor the formation of local structures in transition states (psi analysis). A surprising result from psi analysis was the presence of parallel folding pathways in all reported studies and a major discrepancy between phi and psi values measured in the same protein. Here, we show that psi values cannot be analyzed in the same way as other rate-equilibrium free energy relationships due to the involvement of bimolecular reactions that may have different dissociation constants for the native, unfolded and transition state. As a consequence, psi values reflect the relative binding energy (kappa) of the transition state only for the extreme values of kappa=0 or kappa=1. In all other cases, non-linear rate-equilibrium free-energy relationships (Leffler plots) are observed. This apparently indicates the presence of parallel folding pathways even if folding occurs over a single homogeneous transition state. Consequently, the results from Leffler plots do not yield information about the structural properties of the transition state. This explains the lack of agreement between results from psi analysis and other methods used to characterize protein folding transition states. We further show that the same considerations apply for the analysis of the effect of pH on protein folding.     

Understanding the structural characteristics of compstatin by conformational space annealing

The structural characteristics of the 13-residue compstatin molecule are investigated using the conformational space annealing (CSA) method with CHARMM force field and the GBSA continuum solvent model. In order to sample conformations in the energy range of the minimized NMR structures, we have used the stopping criterion to the CSA search when a conformation whose energy is less than -490 kcal/mol is found. With this stopping criterion, a great variety of conformations are generated around experimentally known structures. Twenty independent CSA runs starting from random states find 1000 representative conformations in the energy landscape of the compstatin, which are classified into thirty-one structural families. The majority of the conformations (94.4%) are in the coil state. Other conformers containing a 3(10)-helix, a pi-helix, a beta-hairpin, and an alpha-helix are also found.