Fuzzy-oil-drop hydrophobic force field--a model to represent late-stage folding (in silico) of lysozyme

A model of hydrophobic collapse (in silico), which is generally considered to be the driving force for protein folding, is presented in this work. The model introduces the external field in the form of a fuzzy-oil-drop assumed to represent the environment. The drop is expressed in the form of a three-dimensional Gauss function. The usual probability value is assumed to represent the hydrophobicity distribution in the three-dimensional space of the virtual environment. The differences between this idealized hydrophobicity distribution and the one represented by the folded polypeptide chain is the parameter to be minimized in the structure optimization procedure. The size of fuzzy-oil-drop is critical for the folding process. A strong correlation between protein length and the dimension of the native and early-stage molecular form was found on the basis of single-domain proteins analysis. A previously presented early-stage folding (in silico) model was used to create the starting structure for the procedure of late-stage folding of lysozyme. The results of simulation were found to be promising, although additional improvements for the formation of beta-structure and disulfide bonds as well as the participation of natural ligand in folding process seem to be necessary.     

Limited conformational space for early-stage protein folding simulation

MOTIVATION: The problem of early-stage protein folding is critical for protein structure prediction. The model presented introduces a common definition of protein structures which may be treated as the possible in silico early-stage form of the polypeptide chain. Limitation of the conformational space to the ellipse path on the Ramachandran map was tested as a possible sub-space to represent the early-stage structure for simulation of protein folding. The proposed conformational sub-space was developed on the basis of the backbone conformation, with side-chain interactions excluded. RESULTS: The ellipse-path-limited conformation of BPTI was created using the criterion of shortest distance between Phi, Psi angles in native form of protein and the Phi, Psi angles belonging to the ellipse. No knots were observed in the structure created according to ellipse-path conformational sub-space. The energy minimization procedure applied to ellipse-path derived conformation directed structural changes toward the native form of the protein with SS-bonds system introduced to the procedure. AVAILABILITY: Program 'Ellipse' to create the ellipse-path derived structure available on request: myroterm@cyf-kr.edu.pl     

Fuzzy-Oil-Drop Hydrophobic Force Field—A Model to Represent Late-stage Folding (In Silico) of Lysozyme

Abstract

A model of hydrophobic collapse (in silico), which is generally considered to be the driving force for protein folding, is presented in this work. The model introduces the external field in the form of a fuzzy-oil-drop assumed to represent the environment. The drop is expressed in the form of a three-dimensional Gauss function. The usual probability value is assumed to represent the hydrophobicity distribution in the three-dimensional space of the virtual environment. The differences between this idealized hydrophobicity distribution and the one represented by the folded polypeptide chain is the parameter to be minimized in the structure optimization procedure. The size of fuzzy-oil-drop is critical for the folding process. A strong correlation between protein length and the dimension of the native and early-stage molecular form was found on the basis of single-domain proteins analysis. A previously presented early-stage folding (in silico) model was used to create the starting structure for the procedure of late-stage folding of lysozyme. The results of simulation were found to be promising, although additional improvements for the formation of β-structure and disulfide bonds as well as the participation of natural ligand in folding process seem to be necessary.     

Relationship between chain collapse and secondary structure formation in a partially folded protein

Chain collapse and secondary structure formation are frequently observed during the early stages of protein folding. Is the chain collapse brought about by interactions between secondary structure units or is it due to polymer behavior in a poor solvent (coil‐globule transition)? To answer this question, we measured small‐angle X‐ray scattering for a series of β‐lactoglobulin mutants under conditions in which they assume a partially folded state analogous to the folding intermediates. Mutants that were designed to disrupt the secondary structure units showed the gyration radii similar to that of the wild type protein, indicating that chain collapse is due to coil‐globule transitions. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 651–658, 2014.     

Localization of ligand binding site in proteins identified in silico

Knowledge-based models for protein folding assume that the early-stage structural form of a polypeptide is determined by the backbone conformation, followed by hydrophobic collapse. Side chain–side chain interactions, mostly of hydrophobic character, lead to the formation of the hydrophobic core, which seems to stabilize the structure of the protein in its natural environment. The fuzzy-oil-drop model is employed to represent the idealized hydrophobicity distribution in the protein molecule. Comparing it with the one empirically observed in the protein molecule reveals that they are not in agreement. It is shown in this study that the irregularity of hydrophobic distributions is aim-oriented. The character and strength of these irregularities in the organization of the hydrophobic core point to the specificity of a particular protein’s structure/function. When the location of these irregularities is determined versus the idealized fuzzy-oil-drop, function-related areas in the protein molecule can be identified. The presented model can also be used to identify ways in which protein–protein complexes can possibly be created. Active sites can be predicted for any protein structure according to the presented model with the free prediction server at . The implication based on the model presented in this work suggests the necessity of active presence of ligand during the protein folding process simulation. Figure Fuzzy-oil-drop model applied to identify the ligation site in lysozyme complexed with N-acetylglucosamine (PDB ID:1LMQ) in form of hydrophobicity deficiency (ΔH) profile and three-dimensional distribution of on protein surface     

Molecular basis of cooperativity in protein folding IV. Core: A general cooperative folding model

The cooperative nature of the protein folding process is independent of the characteristic fold and the specific secondary structure attributes of a globular protein. A general folding/unfolding model should, therefore, be based upon structural features that transcend the peculiarities of α-helices, β-sheets, and other structural motifs found in proteins. The studies presented in this paper suggest that a single structural characteristic common to all globular proteins is essential for cooperative folding. The formation of a partly folded state from the native state results in the exposure to solvent of two distinct regions: (1) the portions of the protein that are unfolded; and (2) the “complementary surfaces,” located in the regions of the protein that remain folded. The cooperative character of the folding/unfolding transition is determined largely by the energetics of exposing complementary surface regions to the solvent. By definition, complementary regions are present only in partly folded states; they are absent from the native and unfolded states. An unfavorable free energy lowers the probability of partly folded states and increases the cooperativity of the transition. In this paper we present a mathematical formulation of this behavior and develop a general cooperative folding/unfolding model, termed the “complementary region” (CORE) model. This model successfully reproduces the main properties of folding/unfolding transitions without limiting the number of partly folded states accessible to the protein, thereby permitting a systematic examination of the structural and solvent conditions under which intermediates become populated. It is shown that the CORE model predicts two-state folding/unfolding behavior, even though the two-state character is not assumed in the model. © 1993 Wiley-Liss, Inc.     

Water dynamics clue to key residues in protein folding

A computational method independent of experimental protein structure information is proposed to recognize key residues in protein folding, from the study of hydration water dynamics. Based on all-atom molecular dynamics simulation, two key residues are recognized with distinct water dynamical behavior in a folding process of the Trp-cage protein. The identified key residues are shown to play an essential role in both 3D structure and hydrophobic-induced collapse. With observations on hydration water dynamics around key residues, a dynamical pathway of folding can be interpreted.     

Formation of a native-like subdomain in a partially folded intermediate of bovine pancreatic trypsin inhibitor.

In the folding of bovine pancreatic trypsin inhibitor (BPTI), the single-disulfide intermediate [30-51] plays a key role. We have investigated a recombinant analog of [30-51] using a 2-dimensional nuclear magnetic resonance (2D-NMR). This recombinant analog, named [30-51]Ala, contains a disulfide bond between Cys-30 and Cys-51, but contains alanine in place of the other cysteines in BPTI to prevent the formation of other intermediates. By 2D-NMR, [30-51]Ala consists of 2 regions-one folded and one predominantly unfolded. The folded region resembles a previously characterized peptide model of [30-51], named P alpha P beta, that contains a native-like subdomain with tertiary packing. The unfolded region includes the first 14 N-terminal residues of [30-51] and is as unfolded as an isolated peptide containing these residues. Using protein dissection, we demonstrate that the folded and unfolded regions of [30-51]Ala are structurally independent. The partially folded structure of [30-51]Ala explains many of the properties of authentic [30-51] in the folding pathway of BPTI. Moreover, direct structural characterization of [30-51]Ala has revealed that a crucial step in the folding pathway of BPTI coincides with the formation of a native-like subdomain, supporting models for protein folding that emphasize the formation of cooperatively folded subdomains.     

Breaking non-native hydrophobic clusters is the rate-limiting step in the folding of an alanine-based peptide

The formation mechanism of an alanine-based peptide has been studied by all-atom molecular dynamics simulations with a recently developed all-atom point-charge force field and the Generalize Born continuum solvent model at an effective salt concentration of 0.2M. Thirty-two simulations were conducted. Each simulation was performed for 100 ns. A surprisingly complex folding process was observed. The development of the helical content can be divided into three phases with time constants of 0.06-0.08, 1.4-2.3, and 12-13 ns, respectively. Helices initiate extreme rapidly in the first phase similar to that estimated from explicit solvent simulations. Hydrophobic collapse also takes place in this phase. A folding intermediate state develops in the second phase and is unfolded to allow the peptide to reach the transition state in the third phase. The folding intermediate states are characterized by the two-turn short helices and the transition states are helix-turn-helix motifs-both of which are stabilized by hydrophobic clusters. The equilibrium helical content, calculated by both the main-chain Phi-Psi torsion angles and the main-chain hydrogen bonds, is 64-66%, which is in remarkable agreement with experiments. After corrected for the solvent viscosity effect, an extrapolated folding time of 16-20 ns is obtained that is in qualitative agreement with experiments. Contrary to the prevailing opinion, neither initiation nor growth of the helix is the rate-limiting step. Instead, the rate-limiting step for this peptide is breaking the non-native hydrophobic clusters in order to reach the transition state. The implication to the folding mechanisms of proteins is also discussed.     

Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

Ab initio folding simulation of the Trp-cage mini-protein approaches NMR resolution

Here, we report a 100 ns molecular dynamics simulation of the folding process of a recently designed autonomous-folding mini-protein designated as tc5b with a new AMBER force field parameter set developed based on condensed-phase quantum mechanical calculations and a Generalized Born continuum solvent model. Starting from its fully extended conformation, our simulation has produced a final structure resembling that of NMR native structure to within 1A main-chain root mean square deviation. Remarkably, the simulated structure stayed in the native state for most part of the simulation after it reached the state. Of greater significance is that our simulation has not only reached the correct main-chain conformation, but also a very high degree of accuracy in side-chain packing conformation. This feat has traditionally been a challenge for ab initio simulation studies. In addition to characterization of the trajectory, comparison of our results to experimental data is also presented. Analysis of the trajectory suggests that the rate-limiting step of folding of this mini-protein is the packing of the Trp side-chain.     

Molecular dynamics simulations of hydrophobic collapse of ubiquitin.

Nine nonnative conformations of ubiquitin, generated during two different thermal denaturation trajectories, were simulated under nearly native conditions (62 degrees C). The simulations included all protein and solvent atoms explicitly, and simulation times ranged from 1-2.4 ns. The starting structures had alpha-carbon root-mean-square deviations (RMSDs) from the crystal structure of 4-12 A and radii of gyration as high as 1.3 times that of the native state. In all but one case, the protein collapsed when the temperature was lowered and sampled conformations as compact as those reached in a control simulation beginning from the crystal structure. In contrast, the protein did not collapse when simulated in a 60% methanol:water mixture. The behavior of the protein depended on the starting structure: during simulation of the most native-like starting structures (<5 A RMSD to the crystal structure) the RMSD decreased, the number of native hydrogen bonds increased, and the secondary and tertiary structure increased. Intermediate starting structures (5-10 A RMSD) collapsed to the radius of gyration of the control simulation, hydrophobic residues were preferentially buried, and the protein acquired some native contacts. However, the protein did not refold. The least native starting structures (10-12 A RMSD) did not collapse as completely as the more native-like structures; instead, they experienced large fluctuations in radius of gyration and went through cycles of expansion and collapse, with improved burial of hydrophobic residues in successive collapsed states.     

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.     

GENFOLD: a genetic algorithm for folding protein structures using NMR restraints.

We report the development and validation of the program GENFOLD, a genetic algorithm that calculates protein structures using restraints obtained from NMR, such as distances derived from nuclear Overhauser effects, and dihedral angles derived from coupling constants. The program has been tested on three proteins: the POU domain (a small three-helix DNA-binding protein), bovine pancreatic trypsin inhibitor (BPTI), and the starch-binding domain from Aspergillus niger glucoamylase I, a 108-residue beta-sheet protein. Structures were calculated for each protein using published NMR restraints. In addition, structures were calculated for BPTI using artificial restraints generated from a high-resolution crystal structure. In all cases the fittest calculated structures were close to the target structure, and could be refined to structures indistinguishable from the target structures by means of a low-temperature simulated annealing refinement. The effectiveness of the program is similar to that of distance geometry and simulated annealing methods, and it is capable of using a very wide range of restraints as input. It can thus be readily extended to the calculation of structures of large proteins, for which few NOE restraints may be available.     

Structural heterogeneity of the various forms of apomyoglobin: implications for protein folding.

Temperature-induced denaturation transitions of different structural forms of apomyoglobin were studied monitoring intrinsic tryptophan fluorescence. It was found that the tryptophans are effectively screened from solvent both in native and acid forms throughout most of the temperature range tested. Thus, the tryptophans' surrounding do not show a considerable change in structure where major protein conformational transitions have been found in apomyoglobin using other techniques. At high temperatures and under strong destabilizing conditions, the tryptophans' fluorescence parameters show sigmoidal thermal denaturation. These results, combined with previous studies, show that the structure of this protein is heterogeneous, including native-like (tightly packed) and molten globule-like substructures that exhibit conformation (denaturation) transitions under different conditions of pH and temperature (and denaturants). The results suggest that the folding of this protein proceeds via two "nucleation" events whereby native-like contacts are formed. One of these events, which involves AGH "core" formation, appears to occur very early in the folding process, even before significant hydrophobic collapse in the rest of the protein molecule. From the current studies and other results, a rather detailed picture of the folding of myoglobin is presented, on the level of specific structures and their thermodynamical properties as well as formation kinetics.     

Exploring protein native states and large-scale conformational changes with a modified generalized born model

Implicit solvation models provide, for many applications, a reasonably accurate and computationally effective way to describe the electrostatics of aqueous solvation. Here, a popular analytical Generalized Born (GB) solvation model is modified to improve its accuracy in calculating the solvent polarization part of free energy changes in large-scale conformational transitions, such as protein folding. In contrast to an earlier GB model (implemented in the AMBER-6 program), the improved version does not overstabilize the native structures relative to the finite-difference Poisson-Boltzmann continuum treatment. In addition to improving the energy balance between folded and unfolded conformers, the algorithm (available in the AMBER-7 and NAB molecular modeling packages) is shown to perform well in more than 50 ns of native-state molecular dynamics (MD) simulations of thioredoxin, protein-A, and ubiquitin, as well as in a simulation of Barnase/Barstar complex formation. For thioredoxin, various combinations of input parameters have been explored, such as the underlying gas-phase force fields and the atomic radii. The best performance is achieved with a previously proposed modification to the torsional potential in the Amber ff99 force field, which yields stable native trajectories for all of the tested proteins, with backbone root-mean-square deviations from the native structures being approximately 1.5 A after 6 ns of simulation time. The structure of Barnase/Barstar complex is regenerated, starting from an unbound state, to within 1.9 A relative to the crystal structure of the complex.     

Thermal unfolding molecular dynamics simulation of Escherichia coli dihydrofolate reductase: thermal stability of protein domains and unfolding pathway

Temperature induced unfolding of Escherichia coli dihydrofolate reductase was carried out by using molecular dynamic simulations. The simulations show that the unfolding generally involves an initial end-to-end collapse of the adenine binding domain into partially extended loops, followed by a gradual breakdown of the remaining beta sheet core structure. The core, which consists of beta strands 5-7, was observed to be the most resistant to thermal unfolding. This region, which is made up of part of the N terminus domain and part of the large domain of the E. coli dihydrofolate reductase, may constitute the nucleation site for protein folding and may be important for the eventual formation of both domains. The unfolding of different domains at different stages of the unfolding process suggests that protein domains vary in stability and that the rate at which they unfold can affect the overall outcome of the unfolding pathway. This observation is compared with the recently proposed hierarchical folding model. Finally, the results of the simulation were found to be consistent with a previous experimental study (Frieden, Proc Natl Acad Sci USA 1990;87:4413-4416) which showed that the folding process of E. coli dihydrofolate reductase involves sequential formation of the substrate binding sites.     

RNA tertiary interactions mediate native collapse of a bacterial group I ribozyme

Large RNAs collapse into compact intermediates in the presence of counterions before folding to the native state. We previously found that collapse of a bacterial group I ribozyme correlates with the formation of helices within the ribozyme core, but occurs at Mg2+ concentrations too low to support stable tertiary structure and catalytic activity. Here, using small-angle X-ray scattering, we show that Mg2+-induced collapse is a cooperative folding transition that can be fit by a two-state model. The Mg2+ dependence of collapse is similar to the Mg2+ dependence of helix assembly measured by partial ribonuclease T1 digestion and of an unfolding transition measured by UV hypochromicity. The correspondence between multiple probes of RNA structure further supports a two-state model. A mutation that disrupts tertiary contacts between the L9 tetraloop and its helical receptor destabilized the compact state by 0.8 kcal/mol, while mutations in the central triplex were less destabilizing. These results show that native tertiary interactions stabilize the compact folding intermediates under conditions in which the RNA backbone remains accessible to solvent.