Perez-Salas, U. A. ; Rangan, P. ; Krueger, S. ; Briber, R. M. ; Thirumalai, D. ; Woodson, S. A. Compaction of a bacterial group I ribozyme coincides with the assembly of core helices. Biochemistry 43, 1746-53.Abstract
Counterions are critical to the self-assembly of RNA tertiary structure because they neutralize the large electrostatic forces which oppose the folding process. Changes in the size and shape of the Azoarcus group I ribozyme as a function of Mg(2+) and Na(+) concentration were followed by small angle neutron scattering. In low salt buffer, the RNA was expanded, with an average radius of gyration (R(g)) of 53 +/- 1 A. A highly cooperative transition to a compact form (R(g) = 31.5 +/- 0.5 A) was observed between 1.6 and 1.7 mM MgCl(2). The collapse transition, which is unusually sharp in Mg(2+), has the characteristics of a first-order phase transition. Partial digestion with ribonuclease T1 under identical conditions showed that this transition correlated with the assembly of double helices in the ribozyme core. Fivefold higher Mg(2+) concentrations were required for self-splicing, indicating that compaction occurs before native tertiary interactions are fully stabilized. No further decrease in R(g) was observed between 1.7 and 20 mM MgCl(2), indicating that the intermediates have the same dimensions as the native ribozyme, within the uncertainty of the data (+/-1 A). A more gradual transition to a final R(g) of approximately 33.5 A was observed between 0.45 and 2 M NaCl. This confirms the expectation that monovalent ions not only are less efficient in charge neutralization but also contract the RNA less efficiently than multivalent ions.
Buchete, N. - V. ; Straub, J. E. ; Thirumalai, D. Orientational potentials extracted from protein structures improve native fold recognition. Protein Sci 13, 862-74.Abstract
We develop coarse-grained, distance- and orientation-dependent statistical potentials from the growing protein structural databases. For protein structural classes (alpha, beta, and alpha/beta), a substantial number of backbone-backbone and backbone-side-chain contacts stabilize the native folds. By taking into account the importance of backbone interactions with a virtual backbone interaction center as the 21st anisotropic site, we construct a 21 x 21 interaction scheme. The new potentials are studied using spherical harmonics analysis (SHA) and a smooth, continuous version is constructed using spherical harmonic synthesis (SHS). Our approach has the following advantages: (1) The smooth, continuous form of the resulting potentials is more realistic and presents significant advantages for computational simulations, and (2) with SHS, the potential values can be computed efficiently for arbitrary coordinates, requiring only the knowledge of a few spherical harmonic coefficients. The performance of the new orientation-dependent potentials was tested using a standard database of decoy structures. The results show that the ability of the new orientation-dependent potentials to recognize native protein folds from a set of decoy structures is strongly enhanced by the inclusion of anisotropic backbone interaction centers. The anisotropic potentials can be used to develop realistic coarse-grained simulations of proteins, with direct applications to protein design, folding, and aggregation.
Klimov, D. K. ; Straub, J. E. ; Thirumalai, D. Aqueous urea solution destabilizes Abeta(16-22) oligomers. Proc Natl Acad Sci U S A 101, 14760-5.Abstract
We use long multiple trajectories generated by molecular dynamics simulations to probe the stability of oligomers of Abeta(16-22) (KLVFFAE) peptides in aqueous urea solution. High concentration of urea promotes the formation of beta-strand structures in Abeta(16-22) monomers, whereas in water they adopt largely compact random coil structures. The tripeptide system, which forms stable antiparallel beta-sheet structure in water, is destabilized in urea solution. The enhancement of beta-strand content in the monomers and the disruption of oligomeric structure occur largely by direct interaction of urea with the peptide backbone. Our simulations suggest that the oligomer unbinding dynamics is determined by two opposing effects, namely, by the increased propensity of monomers to form beta-strands and the rapid disruption of the oligomers. The qualitative conclusions are affirmed by using two urea models. Because the proposed destabilization mechanism depends largely on hydrogen bond formation between urea and the peptide backbone, we predict that high urea concentration will destabilize oligomers of other amyloidogenic peptides as well.
Buchete, N. - V. ; Straub, J. E. ; Thirumalai, D. Continuous anisotropic representation of coarse-grained potentials for proteins by spherical harmonics synthesis. J Mol Graph Model 22, 441-50.Abstract
A new method is presented for extracting statistical potentials dependent on the relative side chain and backbone orientations in proteins. Coarse-grained, anisotropic potentials are constructed for short-, medium-, and long-range interactions using the Boltzmann method and a database of non-homologous protein structures. The new orientation-dependent potentials are analyzed using a spherical harmonics decomposition method with real eigenfunctions. This method permits a more realistic, continuous angular representation of the coarse-grained potentials. Results of tests for discriminating the native protein conformations from large sets of decoy proteins, show that the new continuous distance- and orientation-dependent potentials present significantly improved performance. Novel graphical representations are developed and used to depict the orientational dependence of the interaction potentials. These new continuous anisotropic statistical potentials could be instrumental in developing new computational methods for structure prediction, threading and coarse-grained simulations.
Buchete, N. - V. ; Straub, J. E. ; Thirumalai, D. Development of novel statistical potentials for protein fold recognition. Curr Opin Struct Biol 14, 225-32.Abstract
The need to perform large-scale studies of protein fold recognition, structure prediction and protein-protein interactions has led to novel developments of residue-level minimal models of proteins. A minimum requirement for useful protein force-fields is that they be successful in the recognition of native conformations. The balance between the level of detail in describing the specific interactions within proteins and the accuracy obtained using minimal protein models is the focus of many current protein studies. Recent results suggest that the introduction of explicit orientation dependence in a coarse-grained, residue-level model improves the ability of inter-residue potentials to recognize the native state. New statistical and optimization computational algorithms can be used to obtain accurate residue-dependent potentials for use in protein fold recognition and, more importantly, structure prediction.
Li, M. S. ; Klimov, D. K. ; Thirumalai, D. Finite size effects on thermal denaturation of globular proteins. Phys Rev Lett 93, 268107.Abstract
Finite size effects on the cooperative thermal denaturation of proteins are considered. A dimensionless measure of cooperativity, Omegac, scales as Nzeta, where N is the number of amino acids. Surprisingly, we find that zeta is universal with zeta=1+gamma, where the exponent gamma characterizes the divergence of the susceptibility for a self-avoiding walk. Our lattice model simulations and experimental data are consistent with the theory. Our finding rationalizes the marginal stability of proteins and substantiates the earlier predictions that the efficient folding of two-state proteins requires TF approximately Ttheta, where Ttheta and TF are the collapse and folding transition temperatures, respectively.
Koculi, E. ; Lee, N. - K. ; Thirumalai, D. ; Woodson, S. A. Folding of the Tetrahymena ribozyme by polyamines: importance of counterion valence and size. J Mol Biol 341, 27-36.Abstract
Polyamines are abundant metabolites that directly influence gene expression. Although the role of polyamines in DNA condensation is well known, their role in RNA folding is less understood. Non-denaturing gel electrophoresis was used to monitor the equilibrium folding transitions of the Tetrahymena ribozyme in the presence of polyamines. All of the polyamines tested induce near-native structures that readily convert to the native conformation in Mg(2+). The stability of the folded structure increases with the charge of the polyamine and decreases with the size of the polyamine. When the counterion excluded volume becomes large, the transition to the native state does not go to completion even under favorable folding conditions. Brownian dynamics simulations of a model polyelectrolyte suggest that the kinetics of counterion-mediated collapse and the dimensions of the collapsed RNA chains depend on the structure of the counterion. The results are consistent with delocalized condensation of polyamines around the RNA. However, the effective charge of the counterions is lowered by their excluded volume. The stability of the folded RNA is enhanced when the spacing between amino groups matches the distance between adjacent phosphate groups. These results show how changes in intracellular polyamine concentrations could alter RNA folding pathways.
Dima, R. I. ; Thirumalai, D. Probing the instabilities in the dynamics of helical fragments from mouse PrPC. Proc Natl Acad Sci U S A 101, 15335-40.Abstract
The first step in the formation of the protease resistant form (PrPSc) of prion proteins involves a conformational transition of the monomeric cellular form of PrPC to a more stable aggregation prone state PrPC*. A search of PDBselect and Escherichia coli and yeast genomes shows that the exact pattern of charges in helix 1 (H1) is rare. Among the 23 fragments in PDBselect with the pattern of charges that match H1, 83% are helical. Mapping of the rarely found (in E. coli and yeast genomes) hydrophobicity patterns in helix 2 (H2) to known secondary structures suggests that the PrPC-->PrPC* transition must be accompanied by alterations in conformations in second half of H2. We probe the dynamical instability in H1 and in the combined fragments of H2 and helix 3 (H3) from mPrPC (H2+H3), with intact disulfide bond, using all atom molecular dynamics (MD) simulations totaling 680 ns. In accord with recent experiments, we found that H1 is helical, whereas the double mutant H1[D147A-R151A] is less stable, implying that H1 is stabilized by the (i,i + 4) charged residues. The stability of H1 suggests that it is unlikely to be involved in the PrPC-->PrPC* transition. MD simulations of H2+H3 shows that the second half of H2 (residues 184-194) and parts of H3 (residues 200-204 and 215-223) undergo a transition from alpha-helical conformation to a beta and/or random coil state. Simulations using two force fields (optimized potentials for liquid simulations and CHARMM) give qualitatively similar results. We use the MD results to propose tentative structures for the PrPC* state.
Dima, R. I. ; Thirumalai, D. Proteins associated with diseases show enhanced sequence correlation between charged residues. Bioinformatics 20, 2345-54.Abstract
MOTIVATION: Function of proteins or a network of interacting proteins often involves communication between residues that are well separated in sequence. The classic example is the participation of distant residues in allosteric regulation. Bioinformatic and structural analysis methods have been introduced to infer residues that are correlated. Recently, increasing attention has been paid to obtain the sequence properties that determine the tendency of disease-related proteins (Abeta peptides, prion proteins, transthyretin, etc.) to aggregate and form fibrils. Motivated in part by the need to identify sequence characteristics that indicate a tendency to aggregate, we introduce a general method that probes covariations in charged residues along the sequence in a given protein family. The method, which involves computing the sequence correlation entropy (SCE) using the quenched probability P(sk)(i,j) of finding a residue pair at a given sequence separation, sk, allows us to classify protein families in terms of their SCE. Our general approach may be a useful way in obtaining evolutionary covariations of amino acid residues on a genome wide level. RESULTS: We use a combination of SCE and clustering based on the principle component analysis to classify the protein families. From an analysis of 839 families, covering approximately 500,000 sequences, we find that proteins with relatively low values of SCE are predominantly associated with various diseases. In several families, residues that give rise to peaks in P(sk)(i,j) are clustered in the three-dimensional structure. For the class of proteins with low SCE values, there are significant numbers of mixed charged-hydrophobic (CH) and charged-polar (CP) runs. Our findings suggest that the low values of SCE and the presence of (CH) and/or (CP) may be indicative of disease association or tendency to aggregate. Our results led to the hypothesis that functions of proteins with similar SCE values may be linked. The hypothesis is validated with a few anecdotal examples. The present results also lead to the prediction that the overall charge correlations in proteins affect the kinetics of amyloid formation--a feature that is common to all proteins implicated in neurodegenerative diseases.
Lee, N. - K. ; Thirumalai, D. Pulling-speed-dependent force-extension profiles for semiflexible chains. Biophys J 86, 2641-9.Abstract
We present theory and simulations to describe nonequilibrium stretching of semiflexible chains that serve as models of DNA molecules. Using a self-consistent dynamical variational approach, we calculate the force-extension curves for worm-like chains as a function of the pulling speed, v(0). Due to nonequilibrium effects the stretching force, which increases with v(0), shows nonmonotonic variations as the persistence length increases. To complement the theoretical calculations we also present Langevin simulation results for extensible worm-like chain models for the dynamics of stretching. The theoretical force-extension predictions compare well with the simulation results. The simulations show that, at high enough pulling speeds, the propagation of tension along the chain conformations transverse to the applied force occurs by the Brochard-Wyart's stem-flower mechanism. The predicted nonequilibrium effects can only be observed in double-stranded DNA at large ( approximately 100 microm/s) pulling speeds.
Stan, G. ; Thirumalai, D. ; Lorimer, G. H. ; Brooks, B. R. Annealing function of GroEL: structural and bioinformatic analysis. Biophys Chem 100, 453-67.Abstract
The Escherichia coli chaperonin system, GroEL-GroES, facilitates folding of substrate proteins (SPs) that are otherwise destined to aggregate. The iterative annealing mechanism suggests that the allostery-driven GroEL transitions leading to changes in the microenvironment of the SP constitutes the annealing action of chaperonins. To describe the molecular basis for the changes in the nature of SP-GroEL interactions we use the crystal structures of GroEL (T state), GroEL-ATP (R state) and the GroEL-GroES-(ADP)(7) (R" state) complex to determine the residue-specific changes in the accessible surface area and the number of tertiary contacts as a result of the T-->R-->R" transitions. We find large changes in the accessible area in many residues in the apical domain, but relatively smaller changes are associated with residues in the equatorial domain. In the course of the T-->R transition the microenvironment of the SP changes which suggests that GroEL is an annealing machine even without GroES. This is reflected in the exposure of Glu386 which loses six contacts in the T-->R transition. We also evaluate the conservation of residues that participate in the various chaperonin functions. Multiple sequence alignments and chemical sequence entropy calculations reveal that, to a large extent, only the chemical identities and not the residues themselves important for the nominal functions (peptide binding, nucleotide binding, GroES and substrate protein release) are strongly conserved. Using chemical sequence entropy, which is computed by classifying aminoacids into four types (hydrophobic, polar, positively charged and negatively charged) we make several new predictions that are relevant for peptide binding and annealing function of GroEL. We identify a number of conserved peptide binding sites in the apical domain which coincide with those found in the 1.7 A crystal structure of 'mini-chaperone' complexed with the N-terminal tag. Correlated mutations in the HSP60 family, that might control allostery in GroEL, are also strongly conserved. Most importantly, we find that charged solvent-exposed residues in the T state (Lys 226, Glu 252 and Asp 253) are strongly conserved. This leads to the prediction that mutating these residues, that control the annealing function of the SP, can decrease the efficacy of the chaperonin function.
Thirumalai, D. ; Klimov, D. K. ; Lorimer, G. H. Caging helps proteins fold. Proc Natl Acad Sci U S A 100, 11195-7. caging-helps-proteins-fold.pdf
Hyeon, C. ; Thirumalai, D. Can energy landscape roughness of proteins and RNA be measured by using mechanical unfolding experiments?. Proc Natl Acad Sci U S A 100, 10249-53.Abstract
By considering temperature effects on the mechanical unfolding rates of proteins and RNA, whose energy landscape is rugged, the question posed in the title is answered in the affirmative. Adopting a theory by Zwanzig [Zwanzig, R. (1988) Proc. Natl. Acad. Sci. USA 85, 2029-2030], we show that, because of roughness characterized by an energy scale epsilon, the unfolding rate at constant force is retarded. Similarly, in nonequilibrium experiments done at constant loading rates, the most probable unfolding force increases because of energy landscape roughness. The effects are dramatic at low temperatures. Our analysis suggests that, by using temperature as a variable in mechanical unfolding experiments of proteins and RNA, the ruggedness energy scale epsilon, can be directly measured.
Klimov, D. K. ; Thirumalai, D. Dissecting the assembly of Abeta16-22 amyloid peptides into antiparallel beta sheets. Structure 11, 295-307.Abstract
Multiple long molecular dynamics simulations are used to probe the oligomerization mechanism of Abeta(16-22) (KLVFFAE) peptides. The peptides, in the monomeric form, adopt either compact random-coil or extended beta strand-like structures. The assembly of the low-energy oligomers, in which the peptides form antiparallel beta sheets, occurs by multiple pathways with the formation of an obligatory alpha-helical intermediate. This observation and the experimental results on fibrillogenesis of Abeta(1-40) and Abeta(1-42) peptides suggest that the assembly mechanism (random coil --> alpha helix --> beta strand) is universal for this class of peptides. In Abeta(16-22) oligomers both interpeptide hydrophobic and electrostatic interactions are critical in the formation of the antiparallel beta sheet structure. Mutations of either hydrophobic or charged residues destabilize the oligomer, which implies that the 16-22 fragments of Arctic (E22G), Dutch (E22Q), and Italian (E22K) mutants are unlikely to form ordered fibrils.
Tobi, D. ; Elber, R. ; Thirumalai, D. The dominant interaction between peptide and urea is electrostatic in nature: a molecular dynamics simulation study. Biopolymers 68, 359-69.Abstract
The conformational equilibrium of a blocked valine peptide in water and aqueous urea solution is studied using molecular dynamics simulations. Pair correlation functions indicate enhanced concentration of urea near the peptide. Stronger hydrogen bonding of urea-peptide compared to water-peptide is observed with preference for helical conformation. The potential of mean force, computed using umbrella sampling, shows only small differences between urea and water solvation that are difficult to quantify. The changes in solvent structure around the peptide are explained by favorable electrostatic interactions (hydrogen bonds) of urea with the peptide backbone. There is no evidence for significant changes in hydrophobic interactions in the two conformations of the peptide in urea solution. Our simulations suggest that urea denatures proteins by preferentially forming hydrogen bonds to the peptide backbone, reducing the barrier for exposing protein residues to the solvent, and reaching the unfolded state.
Thirumalai, D. ; Klimov, D. K. ; Dima, R. I. Emerging ideas on the molecular basis of protein and peptide aggregation. Curr Opin Struct Biol 13, 146-59.Abstract
Several neurodegenerative diseases are associated with the unfolding and subsequent fibrillization of proteins. Although neither the assembly mechanism nor the atomic structures of the amyloid fibrils are known, recent experimental and computational studies suggest that a few general principles that govern protein aggregation may exist. Analysis of the results of several important recent studies has led to a set of tentative ideas concerning the oligomerization of proteins and peptides. General rules have been described that may be useful in predicting regions of known proteins (prions and transthyretin) that are susceptible to fluctuations, which give rise to structures that can aggregate by the nucleation-growth mechanism. Despite large variations in the sequence-dependent polymerization kinetics of several structurally unrelated proteins, there appear to be only a few plausible scenarios for protein and peptide aggregation.
Mountain, R. D. ; Thirumalai, D. Molecular dynamics simulations of end-to-end contact formation in hydrocarbon chains in water and aqueous urea solution. J Am Chem Soc 125, 1950-7.Abstract
We probe the urea-denaturation mechanism using molecular dynamics simulations of an elementary "folding" event, namely, the formation of end-to-end contact in the linear hydrocarbon chain (HC) CH(3)(CH(2))(18)CH(3). Electrostatic effects are examined using a model HC in which one end of the chain is positively charged (+0.2e) and the other contains a negative charge (-0.2e). For these systems multiple transitions between "folded" (conformations in which the chain ends are in contact) and "unfolded" (end-to-end contact is broken) can be observed during 4 ns molecular dynamics simulations. In water and 6 M aqueous urea solution HC and the charged HC fluctuate between collapsed globular conformations and a set of expanded structures. The collapsed conformation adopted by the HC in water is slightly destablized in 6 M urea. In contrast, the end-to-end contact is disrupted in the charged HC only in aqueous urea solution. Despite the presence of a large hydrophobic patch, on length scales on the order of approximately 8-10 A "denaturation" (transition to the expanded unfolded state) occurs by a direct interaction of urea with charges on the chain ends. The contiguous patch of hydrophobic moieties leads to "mild dewetting", which becomes more pronounced in the charged HC in 6 M aqueous urea solution. Our simulations establish that the urea denaturation mechanism is most likely electrostatic in origin.
Massi, F. ; Klimov, D. ; Thirumalai, D. ; Straub, J. E. Charge states rather than propensity for beta-structure determine enhanced fibrillogenesis in wild-type Alzheimer's beta-amyloid peptide compared to E22Q Dutch mutant. Protein Sci 11, 1639-47.Abstract
The activity of the Alzheimer's amyloid beta-peptide is a sensitive function of the peptide's sequence. Increased fibril elongation rate of the E22Q Dutch mutant of the Alzheimer's amyloid beta-peptide relative to that of the wild-type peptide has been observed. The increased activity has been attributed to a larger propensity for the formation of beta structure in the monomeric E22Q mutant peptide in solution relative to the WT peptide. That hypothesis is tested using four nanosecond timescale simulations of the WT and Dutch mutant forms of the Abeta(10-35)-peptide in aqueous solution. The simulation results indicate that the propensity for formation of beta-structure is no greater in the E22Q mutant peptide than in the WT peptide. A significant measure of "flickering" of helical structure in the central hydrophobic cluster region of both the WT and mutant peptides is observed. The simulation results argue against the hypothesis that the Dutch mutation leads to a higher probability of formation of beta-structure in the monomeric peptide in aqueous solution. We propose that the greater stability of the solvated WT peptide relative to the E22Q mutant peptide leads to decreased fibril elongation rate in the former. Stability difference is due to the differing charge state of the two peptides. The other proposal leads to the prediction that the fibril elongation rates for the WT and the mutant E22Q should be similar under acid conditions.
Dima, R. I. ; Thirumalai, D. Exploring protein aggregation and self-propagation using lattice models: phase diagram and kinetics. Protein Sci 11, 1036-49.Abstract
Many seemingly unrelated neurodegenerative disorders, such as amyloid and prion diseases, are associated with propagating fibrils whose structures are dramatically different from the native states of the corresponding monomers. This observation, along with the experimental demonstration that any protein can aggregate to form either fibrils or amorphous structures (inclusion bodies) under appropriate external conditions, suggest that there must be general principles that govern aggregation mechanisms. To probe generic aspects of prion-like behavior we use the model of Harrison, Chan, Prusiner, and Cohen. In this model, aggregation of a structure, that is conformationally distinct from the native state of the monomer, occurs by three parallel routes. Kinetic partitioning, which leads to parallel assembly pathways, occurs early in the aggregation process. In all pathways transient unfolding precedes polymerization and self-propagation. Chain polymerization is consistent with templated assembly, with the dimer being the minimal nucleus. The kinetic effciency of R(n-1) + G --> R(n) (R is the aggregation prone state and G is either U, the unfolded state, or N, the native state of the monomer) is increased when polymerization occurs in the presence of a "seed" (a dimer). These results support the seeded nucleated-polymerization model of fibril formation in amyloid peptides. To probe generic aspects of aggregation in two-state proteins, we use lattice models with side chains. The phase diagram in the (T,C) plane (T is the temperature and C is the polypeptide concentration) reveals a bewildering array of "phases" or structures. Explicit computations for dimers show that there are at least six phases including ordered structures and amorphous aggregates. In the ordered region of the phase diagram there are three distinct structures. We find ordered dimers (OD) in which each monomer is in the folded state and the interaction between the monomers occurs via a well-defined interface. In the domain-swapped structures a certain fraction of intrachain contacts are replaced by interchain contacts. In the parallel dimers the interface is stabilized by favorable intermolecular hydrophobic interactions. The kinetics of folding to OD shows that aggregation proceeds directly from U in a dynamically cooperative manner without populating partially structured intermediates. These results support the experimental observation that ordered aggregation in the two-state folders U1A and CI2 takes place from U. The contrasting aggregation processes in the two models suggest that there are several distinct mechanisms for polymerization that depend not only on the polypeptide sequence but also on external conditions (such as C, T, pH, and salt concentration).
Klimov, D. K. ; Newfield, D. ; Thirumalai, D. Simulations of beta-hairpin folding confined to spherical pores using distributed computing. Proc Natl Acad Sci U S A 99, 8019-24.Abstract
We report the thermodynamics and kinetics of an off-lattice Go model beta-hairpin from Ig-binding protein confined to an inert spherical pore. Confinement enhances the stability of the hairpin due to the decrease in the entropy of the unfolded state. Compared with their values in the bulk, the rates of hairpin formation increase in the spherical pore. Surprisingly, the dependence of the rates on the pore radius, R(s), is nonmonotonic. The rates reach a maximum at R(s)/R(g,N)(b) approximately equal to 1.5, where R(g,N)(b) is the radius of gyration of the folded beta-hairpin in the bulk. The denatured state ensemble of the encapsulated beta-hairpin is highly structured even at substantially elevated temperatures. Remarkably, a profound effect of confinement is evident even when the beta-hairpin occupies less than a 10th of the sphere volume. Our calculations show that the emergence of substantial structure in the denatured state of proteins in inert pores is a consequence of confinement. In contrast, the structure of the bulk denatured state ensemble depends dramatically on the extent of denaturation.