Proceedings of the National Academy of Sciences, 2008
Protein ␣-helices are ubiquitous secondary structural elements, seldom considered to be stable wi... more Protein ␣-helices are ubiquitous secondary structural elements, seldom considered to be stable without tertiary contacts. However, amino acid sequences in proteins that are based on alternating repeats of four glutamic acid (E) residues and four positively charged residues, a combination of arginine (R) and lysine (K), have been shown to form stable ␣-helices in a few proteins, in the absence of tertiary interactions. Here, we find that this ER/K motif is more prevalent than previously reported, being represented in proteins of diverse function from archaea to humans. By using molecular dynamics (MD) simulations, we characterize a dynamic pattern of side-chain interactions that extends along the backbone of ER/K ␣-helices. A simplified model predicts that side-chain interactions alone contribute substantial bending rigidity (0.5 pN/ nm) to ER/K ␣-helices. Results of small-angle x-ray scattering (SAXS) and single-molecule optical-trap analyses are consistent with the high bending rigidity predicted by our model. Thus, the ER/K ␣-helix is an isolated secondary structural element that can efficiently span long distances in proteins, making it a promising tool in designing synthetic proteins. We propose that the significant rigidity of the ER/K ␣-helix can help regulate protein function, as a force transducer between protein subdomains.
We present a systematic analysis of the aggregation number and shape of micelles formed by nine d... more We present a systematic analysis of the aggregation number and shape of micelles formed by nine detergents commonly used in the study of membrane proteins. Small-angle X-ray scattering measurements are reported for glucosides with 8 and 9 alkyl carbons (OG/NG), maltosides and phosphocholines with 10 and 12 alkyl carbons (DM/DDM and FC-10/FC-12), 1,2-dihexanoyl-sn-glycero-phosphocholine (DHPC), 1-palmitoyl-2-hydroxy-sn-glycero-3-[phospho-rac-(1-glycerol)] (LPPG), and 3-[(3-cholamidopropyl)dimethylammonio]-1-propane sulfonate (CHAPS).
Substantial evidence suggests that the aggregation of the presynaptic protein a-synuclein is a ke... more Substantial evidence suggests that the aggregation of the presynaptic protein a-synuclein is a key step in the etiology of Parkinson's disease (PD). Although the molecular mechanisms underlying a-synuclein aggregation remain unknown, oxidative stress has been implicated in the pathogenesis of PD. Here, we report the effects of tyrosine nitration on the propensity of human recombinant a-synuclein to fibrillate in vitro. The properties of nitrated a-synuclein were investigated using a variety of biophysical and biochemical techniques, which revealed that nitration led to formation of a partially folded conformation with increased secondary structure relative to the intrinsically disordered structure of the monomer, and to oligomerization at neutral pH. The degree of self-association was concentration-dependent, but at 1 mg/mL, nitrated a-synuclein was predominantly an octamer. At low pH, small-angle X-ray scattering data indicated that the nitrated protein was monomeric. a-Synuclein fibrillation at neutral pH was completely inhibited by nitrotyrosination and is attributed to the formation of stable soluble oligomers. The presence of heparin or metals did not overcome the inhibition; however, the inhibitory effect was eliminated at low pH. The addition of nitrated a-synuclein inhibited fibrillation of non-modified a-synuclein at neutral pH. Potential implications of these findings to the etiology of Parkinson's disease are discussed. D
Time-resolved small-angle X-ray scattering (SAXS) reports changes in the global conformation of m... more Time-resolved small-angle X-ray scattering (SAXS) reports changes in the global conformation of macromolecules and is thus a valuable probe of structural transitions like RNA folding. Time-resolved SAXS has been applied to study folding of the Tetrahymena ribozyme. This chapter describes the methods that enable acquisition and analysis of time-resolved SAXS data and insights into RNA folding gained from these studies.
Large RNAs can collapse into compact conformations well before the stable formation of the tertia... more Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved smallangle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.
We have used synchrotron radiation, together with stopped-¯ow and continuous-¯ow mixing technique... more We have used synchrotron radiation, together with stopped-¯ow and continuous-¯ow mixing techniques to monitor refolding of lysozyme at pH 5.2. From data measured at times which range from 14 ms to two seconds, we can monitor changes in the size, the shape and the pair distribution function of the polypeptide chain during the folding process. Comparison of the results with the properties of native and GdmClunfolded lysozyme shows that a major chain collapse occurs in the deadtime of mixing. During this process about 50 % of the change in radius of gyration between the unfolded protein and the native state occurs and the polypeptide chain adopts a globular shape. Time-resolved¯uorescence spectra of this collapsed state suggest that the hydrophobic sidechains are still highly solvent accessible. A subsequently formed intermediate with helical structure in the a-domain is nearly identical in size and shape with native lysozyme and has a solvent-inaccessible hydrophobic core. Despite its native-like properties, this intermediate is only slightly more stable (ÁG 0 À 4 kJ/mol) than the collapsed state and still much less stable than native lysozyme (ÁÁG 0 36 kJ/mol) at 20 C.
Using synchrotron radiation and the small-angle X-ray scattering technique we have measured the r... more Using synchrotron radiation and the small-angle X-ray scattering technique we have measured the radii of gyration of a series of alaninebased a-helix-forming peptides of the composition Ace-(AAKAA) n -GY-NH 2 , nZ2-7, in aqueous solvent at 10(G1) 8C. In contrast to other techniques typically used to study a-helices in isolation (such as nuclear magnetic resonance and circular dichroism), small-angle X-ray scattering reports on the global structure of a molecule and, as such, provides complementary information to these other, more sequence-local measuring techniques. The radii of gyration that we measure are, except for the 12-mer, lower than the radii of gyration of ideal a-helices or helices with frayed ends of the equivalent sequence-length. For example, the measured radius of gyration of the 37-mer is 14.2(G0.6) Å , which is to be compared with the radius of gyration of an ideal 37-mer a-helix of 17.6 Å . Attempts are made to analyze the origin of this discrepancy in terms of the analytical Zimm-Bragg-Nagai (ZBN) theory, as well as distributed computing explicit solvent molecular dynamics simulations using two variants of the AMBER force-field. The ZBN theory, which treats helices as cylinders connected by random walk segments, predicts markedly larger radii of gyration than those measured. This is true even when the persistence length of the random walk parts is taken to be extremely short (about one residue). Similarly, the molecular dynamics simulations, at the level of sampling available to us, give inaccurate values of the radii of gyration of the molecules (by overestimating them by around 25% for longer peptides) and/or their helical content. We conclude that even at the short sequences examined here (%37 amino acid residues), these a-helical peptides behave as fluctuating semi-broken rods rather than straight cylinders with frayed ends.
The non-linear problem of simulating the structural transition between two known forms of a macro... more The non-linear problem of simulating the structural transition between two known forms of a macromolecule still remains a challenge in structural biology. The problem is usually addressed in an approximate way using 'morphing' techniques, which are linear interpolations of either the Cartesian or the internal coordinates between the initial and end states, followed by energy minimization. Here we describe a web tool that implements a new method to calculate the most probable trajectory that is exact for harmonic potentials; as an illustration of the method, the classical Calpha-based Elastic Network Model (ENM) is used both for the initial and the final states but other variants of the ENM are also possible. The Langevin equation under this potential is solved analytically using the Onsager and Machlup action minimization formalism on each side of the transition, thus replacing the original non-linear problem by a pair of linear differential equations joined by a non-linear boundary matching condition. The crossover between the two multidimensional energy curves around each state is found numerically using an iterative approach, producing the most probable trajectory and fully characterizing the transition state and its energy. Jobs calculating such trajectories can be submitted on-line at: http:// lorentz.dynstr.pasteur.fr/joel/index.php.
The structure of C-terminal domain (CaD136, C-terminal residues 636 -771) of chicken gizzard cald... more The structure of C-terminal domain (CaD136, C-terminal residues 636 -771) of chicken gizzard caldesmon has been analyzed by a variety of physico-chemical methods. We are showing here that CaD136 does not have globular structure, has low secondary structure content, is essentially noncompact, as it follows from high R g and R S values, and is characterized by the absence of distinct heat absorption peaks, i.e. it belongs to the family of natively unfolded (or intrinsically unstructured) proteins. Surprisingly, effective binding of single calmodulin molecule (K d ؍ 1.4 ؎ 0.2 M) leads only to a very moderate folding of this protein and CaD136 remains substantially unfolded within its tight complex with calmodulin. The biological significance of these observations is discussed. Proteins 2003;53:855-862.
Proceedings of the National Academy of Sciences, 2002
We have used small angle x-ray scattering and computer simulations with a coarse-grained model to... more We have used small angle x-ray scattering and computer simulations with a coarse-grained model to provide a time-resolved picture of the global folding process of the Tetrahymena group I RNA over a time window of more than five orders of magnitude. A substantial phase of compaction is observed on the low millisecond timescale, and the overall compaction and global shape changes are largely complete within one second, earlier than any known tertiary contacts are formed. This finding indicates that the RNA forms a nonspecifically collapsed intermediate and then searches for its tertiary contacts within a highly restricted subset of conformational space. The collapsed intermediate early in folding of this RNA is grossly akin to molten globule intermediates in protein folding.
Proceedings of the National Academy of Sciences, 2008
Protein ␣-helices are ubiquitous secondary structural elements, seldom considered to be stable wi... more Protein ␣-helices are ubiquitous secondary structural elements, seldom considered to be stable without tertiary contacts. However, amino acid sequences in proteins that are based on alternating repeats of four glutamic acid (E) residues and four positively charged residues, a combination of arginine (R) and lysine (K), have been shown to form stable ␣-helices in a few proteins, in the absence of tertiary interactions. Here, we find that this ER/K motif is more prevalent than previously reported, being represented in proteins of diverse function from archaea to humans. By using molecular dynamics (MD) simulations, we characterize a dynamic pattern of side-chain interactions that extends along the backbone of ER/K ␣-helices. A simplified model predicts that side-chain interactions alone contribute substantial bending rigidity (0.5 pN/ nm) to ER/K ␣-helices. Results of small-angle x-ray scattering (SAXS) and single-molecule optical-trap analyses are consistent with the high bending rigidity predicted by our model. Thus, the ER/K ␣-helix is an isolated secondary structural element that can efficiently span long distances in proteins, making it a promising tool in designing synthetic proteins. We propose that the significant rigidity of the ER/K ␣-helix can help regulate protein function, as a force transducer between protein subdomains.
Proceedings of the National Academy of Sciences, 2004
Spectroscopic studies have identified a number of proteins that appear to retain significant resi... more Spectroscopic studies have identified a number of proteins that appear to retain significant residual structure under even strongly denaturing conditions. Intrinsic viscosity, hydrodynamic radii, and small-angle x-ray scattering studies, in contrast, indicate that the dimensions of most chemically denatured proteins scale with polypeptide length by means of the power-law relationship expected for random-coil behavior. Here we further explore this discrepancy by expanding the length range of characterized denatured-state radii of gyration (R G) and by reexamining proteins that reportedly do not fit the expected dimensional scaling. We find that only 2 of 28 crosslink-free, prosthetic-group-free, chemically denatured polypeptides deviate significantly from a powerlaw relationship with polymer length. The R G of the remaining 26 polypeptides, which range from 16 to 549 residues, are well fitted (r 2 ؍ 0.988) by a power-law relationship with a best-fit exponent, 0.598 ؎ 0.028, coinciding closely with the 0.588 predicted for an excluded volume random coil. Therefore, it appears that the mean dimensions of the large majority of chemically denatured proteins are effectively indistinguishable from the mean dimensions of a random-coil ensemble.
Counterion atmospheres condensed onto charged biopolymers strongly affect their physical properti... more Counterion atmospheres condensed onto charged biopolymers strongly affect their physical properties and biological functions, but have been difficult to quantify experimentally. Here, monovalent and divalent counterion atmospheres around DNA double helices in solution are probed using small-angle x-ray scattering techniques. Modulation of the ion scattering factors by anomalous (resonant) x-ray scattering and by interchanging ion identities yields direct measurements of the scattering signal due to the spatial correlation of surrounding ions to the DNA. The quality of the data permit, for the first time, quantitative tests of extended counterion distributions calculated from atomic-scale models of biologically relevant molecules.
Small Angle X-ray Scattering (SAXS) techniques are becoming more and more useful for structural b... more Small Angle X-ray Scattering (SAXS) techniques are becoming more and more useful for structural biologists and biochemists, thanks to better access to dedicated synchrotron beamlines, better detectors and the relative easiness of sample preparation. The ability to compute the theoretical SAXS profile of a given structural model, and to compare this profile with the measured scattering intensity, yields crucial structural informations about the macromolecule under study and/or its complexes in solution. An important contribution to the profile, besides the macromolecule itself and its solvent-excluded volume, is the excess density due to the hydration layer. AquaSAXS takes advantage of recently developed methods, such as AquaSol, that give the equilibrium solvent density map around macromolecules, to compute an accurate SAXS/WAXS profile of a given structure and to compare it to the experimental one. Here, we describe the interface architecture and capabilities of the AquaSAXS web server
Membrane proteins impose enormous challenges to cellular protein homeostasis during their posttra... more Membrane proteins impose enormous challenges to cellular protein homeostasis during their posttranslational targeting, and require chaperones to keep them soluble and translocation-competent.
We recently used computational protein design to create an extremely stable, globular protein, To... more We recently used computational protein design to create an extremely stable, globular protein, Top7, with a sequence and fold not observed previously in nature. Since Top7 was created in the absence of genetic selection, it provides a rare opportunity to investigate aspects of the cellular protein production and surveillance machinery that are subject to natural selection. Here we show that a portion of the Top7 protein corresponding to the final 49 C-terminal residues is efficiently mis-translated and accumulates at high levels in Escherichia coli. We used circular dichroism, sizeexclusion chromatography, small-angle X-ray scattering, analytical ultracentrifugation, and NMR spectroscopy to show that the resulting C-terminal fragment (CFr) protein adopts a compact, extremely stable, homo-dimeric structure. Based on the solution structure, we engineered an even more stable variant of CFr by disulfide-induced covalent circularisation that should be an excellent platform for design of novel functions. The accumulation of high levels of CFr exposes the high error rate of the protein translation machinery. The rarity of correspondingly stable fragments in natural proteins coupled with the observation that high quality ribosome binding sites are found to occur within E. coli protein-coding regions significantly less often than expected by random chance implies a stringent evolutionary pressure against protein sub-fragments that can independently fold into stable structures. The symmetric self-association between two identical mis-translated CFr sub-domains to generate an extremely stable structure parallels a mechanism for natural protein-fold evolution by modular recombination of protein sub-structures. a The first four rows correspond to the 1000th, 1500th, 2000th, and 2500th best-scoring E. coli upstream ribosome binding sites, respectively. The last three rows correspond to the alternative translation initiation sites within Top7 ), as they appear in 5′ to 3′ order. The Shine-Dalgarno sequence is shown in upper case and the start codon in bold.
Large RNAs can collapse into compact conformations well before the stable formation of the tertia... more Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved smallangle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.
Proceedings of the National Academy of Sciences, 2008
Protein ␣-helices are ubiquitous secondary structural elements, seldom considered to be stable wi... more Protein ␣-helices are ubiquitous secondary structural elements, seldom considered to be stable without tertiary contacts. However, amino acid sequences in proteins that are based on alternating repeats of four glutamic acid (E) residues and four positively charged residues, a combination of arginine (R) and lysine (K), have been shown to form stable ␣-helices in a few proteins, in the absence of tertiary interactions. Here, we find that this ER/K motif is more prevalent than previously reported, being represented in proteins of diverse function from archaea to humans. By using molecular dynamics (MD) simulations, we characterize a dynamic pattern of side-chain interactions that extends along the backbone of ER/K ␣-helices. A simplified model predicts that side-chain interactions alone contribute substantial bending rigidity (0.5 pN/ nm) to ER/K ␣-helices. Results of small-angle x-ray scattering (SAXS) and single-molecule optical-trap analyses are consistent with the high bending rigidity predicted by our model. Thus, the ER/K ␣-helix is an isolated secondary structural element that can efficiently span long distances in proteins, making it a promising tool in designing synthetic proteins. We propose that the significant rigidity of the ER/K ␣-helix can help regulate protein function, as a force transducer between protein subdomains.
We present a systematic analysis of the aggregation number and shape of micelles formed by nine d... more We present a systematic analysis of the aggregation number and shape of micelles formed by nine detergents commonly used in the study of membrane proteins. Small-angle X-ray scattering measurements are reported for glucosides with 8 and 9 alkyl carbons (OG/NG), maltosides and phosphocholines with 10 and 12 alkyl carbons (DM/DDM and FC-10/FC-12), 1,2-dihexanoyl-sn-glycero-phosphocholine (DHPC), 1-palmitoyl-2-hydroxy-sn-glycero-3-[phospho-rac-(1-glycerol)] (LPPG), and 3-[(3-cholamidopropyl)dimethylammonio]-1-propane sulfonate (CHAPS).
Substantial evidence suggests that the aggregation of the presynaptic protein a-synuclein is a ke... more Substantial evidence suggests that the aggregation of the presynaptic protein a-synuclein is a key step in the etiology of Parkinson's disease (PD). Although the molecular mechanisms underlying a-synuclein aggregation remain unknown, oxidative stress has been implicated in the pathogenesis of PD. Here, we report the effects of tyrosine nitration on the propensity of human recombinant a-synuclein to fibrillate in vitro. The properties of nitrated a-synuclein were investigated using a variety of biophysical and biochemical techniques, which revealed that nitration led to formation of a partially folded conformation with increased secondary structure relative to the intrinsically disordered structure of the monomer, and to oligomerization at neutral pH. The degree of self-association was concentration-dependent, but at 1 mg/mL, nitrated a-synuclein was predominantly an octamer. At low pH, small-angle X-ray scattering data indicated that the nitrated protein was monomeric. a-Synuclein fibrillation at neutral pH was completely inhibited by nitrotyrosination and is attributed to the formation of stable soluble oligomers. The presence of heparin or metals did not overcome the inhibition; however, the inhibitory effect was eliminated at low pH. The addition of nitrated a-synuclein inhibited fibrillation of non-modified a-synuclein at neutral pH. Potential implications of these findings to the etiology of Parkinson's disease are discussed. D
Time-resolved small-angle X-ray scattering (SAXS) reports changes in the global conformation of m... more Time-resolved small-angle X-ray scattering (SAXS) reports changes in the global conformation of macromolecules and is thus a valuable probe of structural transitions like RNA folding. Time-resolved SAXS has been applied to study folding of the Tetrahymena ribozyme. This chapter describes the methods that enable acquisition and analysis of time-resolved SAXS data and insights into RNA folding gained from these studies.
Large RNAs can collapse into compact conformations well before the stable formation of the tertia... more Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved smallangle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.
We have used synchrotron radiation, together with stopped-¯ow and continuous-¯ow mixing technique... more We have used synchrotron radiation, together with stopped-¯ow and continuous-¯ow mixing techniques to monitor refolding of lysozyme at pH 5.2. From data measured at times which range from 14 ms to two seconds, we can monitor changes in the size, the shape and the pair distribution function of the polypeptide chain during the folding process. Comparison of the results with the properties of native and GdmClunfolded lysozyme shows that a major chain collapse occurs in the deadtime of mixing. During this process about 50 % of the change in radius of gyration between the unfolded protein and the native state occurs and the polypeptide chain adopts a globular shape. Time-resolved¯uorescence spectra of this collapsed state suggest that the hydrophobic sidechains are still highly solvent accessible. A subsequently formed intermediate with helical structure in the a-domain is nearly identical in size and shape with native lysozyme and has a solvent-inaccessible hydrophobic core. Despite its native-like properties, this intermediate is only slightly more stable (ÁG 0 À 4 kJ/mol) than the collapsed state and still much less stable than native lysozyme (ÁÁG 0 36 kJ/mol) at 20 C.
Using synchrotron radiation and the small-angle X-ray scattering technique we have measured the r... more Using synchrotron radiation and the small-angle X-ray scattering technique we have measured the radii of gyration of a series of alaninebased a-helix-forming peptides of the composition Ace-(AAKAA) n -GY-NH 2 , nZ2-7, in aqueous solvent at 10(G1) 8C. In contrast to other techniques typically used to study a-helices in isolation (such as nuclear magnetic resonance and circular dichroism), small-angle X-ray scattering reports on the global structure of a molecule and, as such, provides complementary information to these other, more sequence-local measuring techniques. The radii of gyration that we measure are, except for the 12-mer, lower than the radii of gyration of ideal a-helices or helices with frayed ends of the equivalent sequence-length. For example, the measured radius of gyration of the 37-mer is 14.2(G0.6) Å , which is to be compared with the radius of gyration of an ideal 37-mer a-helix of 17.6 Å . Attempts are made to analyze the origin of this discrepancy in terms of the analytical Zimm-Bragg-Nagai (ZBN) theory, as well as distributed computing explicit solvent molecular dynamics simulations using two variants of the AMBER force-field. The ZBN theory, which treats helices as cylinders connected by random walk segments, predicts markedly larger radii of gyration than those measured. This is true even when the persistence length of the random walk parts is taken to be extremely short (about one residue). Similarly, the molecular dynamics simulations, at the level of sampling available to us, give inaccurate values of the radii of gyration of the molecules (by overestimating them by around 25% for longer peptides) and/or their helical content. We conclude that even at the short sequences examined here (%37 amino acid residues), these a-helical peptides behave as fluctuating semi-broken rods rather than straight cylinders with frayed ends.
The non-linear problem of simulating the structural transition between two known forms of a macro... more The non-linear problem of simulating the structural transition between two known forms of a macromolecule still remains a challenge in structural biology. The problem is usually addressed in an approximate way using 'morphing' techniques, which are linear interpolations of either the Cartesian or the internal coordinates between the initial and end states, followed by energy minimization. Here we describe a web tool that implements a new method to calculate the most probable trajectory that is exact for harmonic potentials; as an illustration of the method, the classical Calpha-based Elastic Network Model (ENM) is used both for the initial and the final states but other variants of the ENM are also possible. The Langevin equation under this potential is solved analytically using the Onsager and Machlup action minimization formalism on each side of the transition, thus replacing the original non-linear problem by a pair of linear differential equations joined by a non-linear boundary matching condition. The crossover between the two multidimensional energy curves around each state is found numerically using an iterative approach, producing the most probable trajectory and fully characterizing the transition state and its energy. Jobs calculating such trajectories can be submitted on-line at: http:// lorentz.dynstr.pasteur.fr/joel/index.php.
The structure of C-terminal domain (CaD136, C-terminal residues 636 -771) of chicken gizzard cald... more The structure of C-terminal domain (CaD136, C-terminal residues 636 -771) of chicken gizzard caldesmon has been analyzed by a variety of physico-chemical methods. We are showing here that CaD136 does not have globular structure, has low secondary structure content, is essentially noncompact, as it follows from high R g and R S values, and is characterized by the absence of distinct heat absorption peaks, i.e. it belongs to the family of natively unfolded (or intrinsically unstructured) proteins. Surprisingly, effective binding of single calmodulin molecule (K d ؍ 1.4 ؎ 0.2 M) leads only to a very moderate folding of this protein and CaD136 remains substantially unfolded within its tight complex with calmodulin. The biological significance of these observations is discussed. Proteins 2003;53:855-862.
Proceedings of the National Academy of Sciences, 2002
We have used small angle x-ray scattering and computer simulations with a coarse-grained model to... more We have used small angle x-ray scattering and computer simulations with a coarse-grained model to provide a time-resolved picture of the global folding process of the Tetrahymena group I RNA over a time window of more than five orders of magnitude. A substantial phase of compaction is observed on the low millisecond timescale, and the overall compaction and global shape changes are largely complete within one second, earlier than any known tertiary contacts are formed. This finding indicates that the RNA forms a nonspecifically collapsed intermediate and then searches for its tertiary contacts within a highly restricted subset of conformational space. The collapsed intermediate early in folding of this RNA is grossly akin to molten globule intermediates in protein folding.
Proceedings of the National Academy of Sciences, 2008
Protein ␣-helices are ubiquitous secondary structural elements, seldom considered to be stable wi... more Protein ␣-helices are ubiquitous secondary structural elements, seldom considered to be stable without tertiary contacts. However, amino acid sequences in proteins that are based on alternating repeats of four glutamic acid (E) residues and four positively charged residues, a combination of arginine (R) and lysine (K), have been shown to form stable ␣-helices in a few proteins, in the absence of tertiary interactions. Here, we find that this ER/K motif is more prevalent than previously reported, being represented in proteins of diverse function from archaea to humans. By using molecular dynamics (MD) simulations, we characterize a dynamic pattern of side-chain interactions that extends along the backbone of ER/K ␣-helices. A simplified model predicts that side-chain interactions alone contribute substantial bending rigidity (0.5 pN/ nm) to ER/K ␣-helices. Results of small-angle x-ray scattering (SAXS) and single-molecule optical-trap analyses are consistent with the high bending rigidity predicted by our model. Thus, the ER/K ␣-helix is an isolated secondary structural element that can efficiently span long distances in proteins, making it a promising tool in designing synthetic proteins. We propose that the significant rigidity of the ER/K ␣-helix can help regulate protein function, as a force transducer between protein subdomains.
Proceedings of the National Academy of Sciences, 2004
Spectroscopic studies have identified a number of proteins that appear to retain significant resi... more Spectroscopic studies have identified a number of proteins that appear to retain significant residual structure under even strongly denaturing conditions. Intrinsic viscosity, hydrodynamic radii, and small-angle x-ray scattering studies, in contrast, indicate that the dimensions of most chemically denatured proteins scale with polypeptide length by means of the power-law relationship expected for random-coil behavior. Here we further explore this discrepancy by expanding the length range of characterized denatured-state radii of gyration (R G) and by reexamining proteins that reportedly do not fit the expected dimensional scaling. We find that only 2 of 28 crosslink-free, prosthetic-group-free, chemically denatured polypeptides deviate significantly from a powerlaw relationship with polymer length. The R G of the remaining 26 polypeptides, which range from 16 to 549 residues, are well fitted (r 2 ؍ 0.988) by a power-law relationship with a best-fit exponent, 0.598 ؎ 0.028, coinciding closely with the 0.588 predicted for an excluded volume random coil. Therefore, it appears that the mean dimensions of the large majority of chemically denatured proteins are effectively indistinguishable from the mean dimensions of a random-coil ensemble.
Counterion atmospheres condensed onto charged biopolymers strongly affect their physical properti... more Counterion atmospheres condensed onto charged biopolymers strongly affect their physical properties and biological functions, but have been difficult to quantify experimentally. Here, monovalent and divalent counterion atmospheres around DNA double helices in solution are probed using small-angle x-ray scattering techniques. Modulation of the ion scattering factors by anomalous (resonant) x-ray scattering and by interchanging ion identities yields direct measurements of the scattering signal due to the spatial correlation of surrounding ions to the DNA. The quality of the data permit, for the first time, quantitative tests of extended counterion distributions calculated from atomic-scale models of biologically relevant molecules.
Small Angle X-ray Scattering (SAXS) techniques are becoming more and more useful for structural b... more Small Angle X-ray Scattering (SAXS) techniques are becoming more and more useful for structural biologists and biochemists, thanks to better access to dedicated synchrotron beamlines, better detectors and the relative easiness of sample preparation. The ability to compute the theoretical SAXS profile of a given structural model, and to compare this profile with the measured scattering intensity, yields crucial structural informations about the macromolecule under study and/or its complexes in solution. An important contribution to the profile, besides the macromolecule itself and its solvent-excluded volume, is the excess density due to the hydration layer. AquaSAXS takes advantage of recently developed methods, such as AquaSol, that give the equilibrium solvent density map around macromolecules, to compute an accurate SAXS/WAXS profile of a given structure and to compare it to the experimental one. Here, we describe the interface architecture and capabilities of the AquaSAXS web server
Membrane proteins impose enormous challenges to cellular protein homeostasis during their posttra... more Membrane proteins impose enormous challenges to cellular protein homeostasis during their posttranslational targeting, and require chaperones to keep them soluble and translocation-competent.
We recently used computational protein design to create an extremely stable, globular protein, To... more We recently used computational protein design to create an extremely stable, globular protein, Top7, with a sequence and fold not observed previously in nature. Since Top7 was created in the absence of genetic selection, it provides a rare opportunity to investigate aspects of the cellular protein production and surveillance machinery that are subject to natural selection. Here we show that a portion of the Top7 protein corresponding to the final 49 C-terminal residues is efficiently mis-translated and accumulates at high levels in Escherichia coli. We used circular dichroism, sizeexclusion chromatography, small-angle X-ray scattering, analytical ultracentrifugation, and NMR spectroscopy to show that the resulting C-terminal fragment (CFr) protein adopts a compact, extremely stable, homo-dimeric structure. Based on the solution structure, we engineered an even more stable variant of CFr by disulfide-induced covalent circularisation that should be an excellent platform for design of novel functions. The accumulation of high levels of CFr exposes the high error rate of the protein translation machinery. The rarity of correspondingly stable fragments in natural proteins coupled with the observation that high quality ribosome binding sites are found to occur within E. coli protein-coding regions significantly less often than expected by random chance implies a stringent evolutionary pressure against protein sub-fragments that can independently fold into stable structures. The symmetric self-association between two identical mis-translated CFr sub-domains to generate an extremely stable structure parallels a mechanism for natural protein-fold evolution by modular recombination of protein sub-structures. a The first four rows correspond to the 1000th, 1500th, 2000th, and 2500th best-scoring E. coli upstream ribosome binding sites, respectively. The last three rows correspond to the alternative translation initiation sites within Top7 ), as they appear in 5′ to 3′ order. The Shine-Dalgarno sequence is shown in upper case and the start codon in bold.
Large RNAs can collapse into compact conformations well before the stable formation of the tertia... more Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved smallangle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.
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Papers by Sebastian Doniach