Radius of gyration is indicator of compactness of protein structure

Search and study of the general principles that govern kinetics and thermodynamics of protein folding generate a new insight into the factors controlling this process. Statistical analysis of radii of gyration for 3769 protein structures from four general structural classes (all-alpha, all-beta, alpha/beta, alpha + beta) demonstrates that each class of proteins has its own class-specific radius of gyration, which determines compactness of protein structures: alpha-proteins have the largest radius of gyration. This indicates that they are less tightly packed than beta- and alpha + beta-proteins. Finally, alpha/beta-proteins are the most tightly packed proteins with the least radius of gyration. It should be underlined that radius of gyration normalized on the radius of gyration of ball with the same volume, is independent of the length in comparison with such parameters as compactness and number of contacts per residue.     

Radius of gyration as an indicator of protein structure compactness

Identification and study of the main principles underlying the kinetics and thermodynamics of protein folding generate a new insight into the factors that control this process. Statistical analysis of the radius of gyration for 3769 protein domains of four major classes (α, β, α/β, and α + β) showed that each class has a characteristic radius of gyration that determines the protein structure compactness. For instance, α proteins have the highest radius of gyration throughout the protein size range considered, suggesting a less tight packing as compared with β-and (α + β)-proteins. The lowest radius of gyration and, accordingly, the tightest packing are characteristic of α/β-proteins. The protein radius of gyration normalized by the radius of gyration of a ball with the same volume is independent of the protein size, in contrast to compactness and the number of contacts per residue.     

Growth process and interfacial process considered in connection with specific surface area

Analytical expressions for the radius of gyration and maximum dimension of compound bodies formed from simple geometric elements are derived. Using principles of symmetry and of commonly observed features of globular protein structures, it is shown how a priori reasonable tertiary and quaternary structures can be distinguished. The formulae, which are simple to apply, permit a rapid comparison of relatively complex shapes, so reducing the amount of computation necessary for a detailed analysis of small angle scattering data. In conjunction with other biophysical data, the morphological parameters derived from scattering curves can be used to generate quite complex biologically reasonable models of protein structures.     

Protein unfolded states populated at high and ambient pressure are similarly compact

The relationship between the dimensions of pressure-unfolded states of proteins compared with those at ambient pressure is controversial; resolving this issue is related directly to the mechanisms of pressure denaturation. Moreover, a significant pressure dependence of the compactness of unfolded states would complicate the interpretation of folding parameters from pressure perturbation and make comparison to those obtained using alternative perturbation approaches difficult. Here, we determined the compactness of the pressure-unfolded state of a small, cooperatively folding model protein, CTL9-I98A, as a function of temperature. This protein undergoes both thermal unfolding and cold denaturation, and the temperature dependence of the compactness at atmospheric pressure is known. High-pressure small angle x-ray scattering studies, yielding the radius of gyration and high-pressure diffusion ordered spectroscopy NMR experiments, yielding the hydrodynamic radius were carried out as a function of temperature at 250 MPa, a pressure at which the protein is unfolded. The radius of gyration values obtained at any given temperature at 250 MPa were similar to those reported previously at ambient pressure, and the trends with temperature are similar as well, although the pressure-unfolded state appears to undergo more pronounced expansion at high temperature than the unfolded state at atmospheric pressure. At 250 MPa, the compaction of the unfolded chain was maximal between 25 and 30°C, and the chain expanded upon both cooling and heating. These results reveal that the pressure-unfolded state of this protein is very similar to that observed at ambient pressure, demonstrating that pressure perturbation represents a powerful approach for observing the unfolded states of proteins under otherwise near-native conditions.     

Microsecond hydrophobic collapse in the folding of Escherichia coli dihydrofolate reductase, an alpha/beta-type protein

Using small-angle X-ray scattering combined with a continuous-flow mixing device, we monitored the microsecond compaction dynamics in the folding of Escherichia coli dihydrofolate reductase, an alpha/beta-type protein. A significant collapse of the radius of gyration from 30 A to 23.2 A occurs within 300 micros after the initiation of refolding by a urea dilution jump. The subsequent folding after the major chain collapse occurs on a considerably longer time-scale. The protein folding trajectories constructed by comparing the development of the compactness and the secondary structure suggest that the specific hydrophobic collapse model rather than the framework model better explains the experimental observations. The folding trajectory of this alpha/beta-type protein is located between those of alpha-helical and beta-sheet proteins, suggesting that native structure determines the folding landscape.     

Topological constraints strongly affect chromatin reconstitution in silico

The fundamental building block of chromatin, and of chromosomes, is the nucleosome, a composite material made up from DNA wrapped around a histone octamer. In this study we provide the first computer simulations of chromatin self-assembly, starting from DNA and histone proteins, and use these to understand the constraints which are imposed by the topology of DNA molecules on the creation of a polynucleosome chain. We take inspiration from the in vitro chromatin reconstitution protocols which are used in many experimental studies. Our simulations indicate that during self-assembly, nucleosomes can fall into a number of topological traps (or local folding defects), and this may eventually lead to the formation of disordered structures, characterised by nucleosome clustering. Remarkably though, by introducing the action of topological enzymes such as type I and II topoisomerase, most of these defects can be avoided and the result is an ordered 10-nm chromatin fibre. These findings provide new insight into the biophysics of chromatin formation, both in the context of reconstitution in vitro and in terms of the topological constraints which must be overcome during de novo nucleosome formation in vivo, e.g. following DNA replication or repair.     

Kinetic analysis of the pre-equilibrium steps in the self-assembly of RecA protein from Escherichia coli

Total intensity light scattering is employed to investigate the self-assembly kinetics of RecA protein. Reaction conditions are employed where the kinetics of self-assembly are slow enough to yield reliable scattered intensity measurements over the range of scattering angles from 40 to 130 degrees as a function of time. From these measurements the time-dependent behavior of the weight average molecular weight, Mr, and radius of gyration, RG, of the associating protein species as a function of [MgCl2], [NaCl], [RecA], and pH was determined. The temperature dependence of RecA self-assembly was also investigated and allowed an evaluation of the activation thermodynamic parameters of association. Results reveal RecA self-assembly is bi-phasic under all conditions examined. The first phase, referred to as "filamentation" is second-order in [RecA] and occurs via a quasi linear condensation scheme with an Arrhenius activation energy of 88.6 kcal/mol. Filamentation assembly involves the uptake of one proton, one MgCl2, the release of five to six NaCls, and is driven by the release of approximately 70 water molecules. The evaluated activation parameters of the first kinetic phase are consistent with the proposition that linear self-assembly of RecA protein into ordered filaments is entropically driven. The second kinetic phase, referred to as "bundling" is greater than second-order in both [RecA] and [MgCl2], is considerably slower that filamentation assembly, and is apparently initiated by 2nd order collisions of linear filaments.     

In silico chaperonin-like cycle helps folding of proteins for structure prediction

Currently, one of the most serious problems in protein-folding simulations for de novo structure prediction is conformational sampling of medium-to-large proteins. In vivo, folding of these proteins is mediated by molecular chaperones. Inspired by the functions of chaperonins, we designed a simple chaperonin-like simulation protocol within the framework of the standard fragment assembly method: in our protocol, the strength of the hydrophobic interaction is periodically modulated to help the protein escape from misfolded structures. We tested this protocol for 38 proteins and found that, using a certain defined criterion of success, our method could successfully predict the native structures of 14 targets, whereas only those of 10 targets were successfully predicted using the standard protocol. In particular, for non-α-helical proteins, our method yielded significantly better predictions than the standard approach. This chaperonin-inspired protocol that enhanced de novo structure prediction using folding simulations may, in turn, provide new insights into the working principles underlying the chaperonin system.     

Tissue-specific expression of mouse alpha-amylase genes

Ribosomal protein S4 isolated from the small (30 S) subunits of Escherichia coli ribosomes has been studied by a complex of physical methods such as sedimentation, ultraviolet absorption and circular dichroism spectroscopy, proton magnetic resonance spectroscopy, scanning microcalorimetry and neutron scattering. It has been shown that protein S4 exists in solution in a monomeric form. It is characterized by a high content of secondary structure including both α-helices (43%) and β-form (about 30%). The protein S4 molecules possess a well-developed tertiary structure which melts in a co-operative manner. The compactness of the molecules has been found to be very high (radius of gyration, $\text{R}{}_{\mathrm{<mtext>g</mtext>}}\text{= 18 ± 2}\text{A}\text{?}$), corresponding to that of standard compact globular proteins. The compactness of protein S4 does not change as a result of its interaction with the specifically binding 13 S fragment of the ribosomal 16 8 RNA; this suggests that serious conformational changes in protein S4 upon 30 S subunit assembly are unlikely and that the protein is compact within the ribosome.     

Theoretical investigation of the photoinitiated folding of HP-36

A computational model was developed to examine the phototriggered folding of a caged protein, a protein modified with an organic photolabile cross-linker. Molecular dynamics simulations of the modified 36-residue fragment of subdomain B of chicken villin head piece with a photolabile linker were performed, starting from both the caged and the uncaged structures. Construction of a free-energy landscape, based on principal components as well as on radius of gyration versus root-mean-square deviation, and circular dichroism calculations were employed to characterize folding behavior and structures. The folded structures observed in the molecular dynamics trajectories were found to be similar to that of the wild-type protein, in agreement with the published experimental results. The free-energy landscapes of the modified and wild-type proteins have similar topology, suggesting common thermodynamic/kinetic behavior. The existence of small differences in the free-energy surface of the modified protein from that of the native protein, however, indicates subtle differences in the folding behavior.     

Non‐native α‐helix formation is not necessary for folding of lipocalin: Comparison of burst‐phase folding between tear lipocalin and β‐lactoglobulin

Tear lipocalin and β‐lactoglobulin are members of the lipocalin superfamily. They have similar tertiary structures but unusually low overall sequence similarity. Non‐native helical structures are formed during the early stage of β‐lactoglobulin folding. To address whether the non‐native helix formation is found in the folding of other lipocalin superfamily proteins, the folding kinetics of a tear lipocalin variant were investigated by stopped‐flow methods measuring the time‐dependent changes in circular dichroism (CD) spectrum and small‐angle X‐ray scattering (SAXS). CD spectrum showed that extensive secondary structures are not formed during a burst‐phase (within a measurement dead time). The SAXS data showed that the radius of gyration becomes much smaller than in the unfolded state during the burst‐phase, indicating that the molecule is collapsed during an early stage of folding. Therefore, non‐native helix formation is not general for folding of all lipocalin family members. The non‐native helix content in the burst‐phase folding appears to depend on helical propensities of the amino acid sequence. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Metal Ion Dependence of Cooperative Collapse Transitions in RNA

Positively charged counterions drive RNA molecules into compact configurations that lead to their biologically active structures. To understand how the valence and size of the cations influences the collapse transition in RNA, small-angle X-ray scattering was used to follow the decrease in the radius of gyration (R_g) of the Azoarcus and Tetrahymena ribozymes in different cations. Small, multivalent cations induced the collapse of both ribozymes more efficiently than did monovalent ions. Thus, the cooperativity of the collapse transition depends on the counterion charge density. Singular value decomposition of the scattering curves showed that folding of the smaller and more thermostable Azoarcus ribozyme is well described by two components, whereas collapse of the larger Tetrahymena ribozyme involves at least one intermediate. The ion-dependent persistence length, extracted from the distance distribution of the scattering vectors, shows that the Azoarcus ribozyme is less flexible at the midpoint of transition in low-charge-density ions than in high-charge-density ions. We conclude that the formation of sequence-specific tertiary interactions in the Azoarcus ribozyme overlaps with neutralization of the phosphate charge, while tertiary folding of the Tetrahymena ribozyme requires additional counterions. Thus, the stability of the RNA structure determines its sensitivity to the valence and size of the counterions.     

Small-angle X-ray scattering studies of the structure of nucleosome core histone complexes in solution

The nucleosome core histone complex in solution at 2 M NaCl and pH 7 has a radius of gyration R_s, of 3.48 nm and a maximum dimension, L, of 12 nm. Its shape is disc-like with a mean thickness of 3 nm. The radius of gyration determined by us is of the same value as the radius of gyration of the complex in intact core particles (Braddock) et al., Biopolymers 1981, 20, 327). Thus, we conclude that the basic histone tails of the protein complex project about 2 nm from its central part.     

Small angle X-ray scattering of dimeric yeast hexokinase in solution.

Small angle x-ray scattering measurements on dimeric yeast hexokinase B at pH 5.5 in acetate buffer yield a radius of gyration of 31.28 +/- 0.23 angstrom. This measured value is comparable to the radius of gyration of 31.5 angstrom calculated from the refined coordinates of the dimer in the BII crystal form. The hexokinase dimer found in the BI crystal form has a radius of gyration of 42 angstrom calculated from the atomic coordinates. Thus, the measured radius of gyration is consistent with the BII dimer being the predominant species in solution and rules out the existence of the BI dimer as a major species under these conditions.     

The ferritin superfamily: Supramolecular templates for materials synthesis

Members of the ferritin superfamily are multi-subunit cage-like proteins with a hollow interior cavity. These proteins possess three distinct surfaces, i.e. interior and exterior surfaces of the cages and interface between subunits. The interior cavity provides a unique reaction environment in which the interior reaction is separated from the external environment. In biology the cavity is utilized for sequestration of irons and biomineralization as a mechanism to render Fe inert and sequester it from the external environment. Material scientists have been inspired by this system and exploited a range of ferritin superfamily proteins as supramolecular templates to encapsulate nanoparticles and/or as well-defined building blocks for fabrication of higher order assembly. Besides the interior cavity, the exterior surface of the protein cages can be modified without altering the interior characteristics. This allows us to deliver the protein cages to a targeted tissue in vivo or to achieve controlled assembly on a solid substrate to fabricate higher order structures. Furthermore, the interface between subunits is utilized for manipulating chimeric self-assembly of the protein cages and in the generation of symmetry-broken Janus particles. Utilizing these ideas, the ferritin superfamily has been exploited for development of a broad range of materials with applications from biomedicine to electronics.     

On the Structural Diversity and Individuality of Polymorphic Amyloid Protein Assemblies

The prediction of highly ordered three-dimensional structures of amyloid protein fibrils from the amino acid sequences of their monomeric self-assembly precursors constitutes a challenging and unresolved aspect of the classical protein folding problem. Because of the polymorphic nature of amyloid assembly whereby polypeptide chains of identical amino acid sequences under identical conditions are capable of self-assembly into a spectrum of different fibril structures, the prediction of amyloid structures from an amino acid sequence requires a detailed and holistic understanding of its assembly free energy landscape. The full extent of the structure space accessible to the cross-β molecular architecture of amyloid must also be resolved. Here, we review the current understanding of the diversity and the individuality of amyloid structures, and how the polymorphic landscape of amyloid links to biology and disease phenotypes. We present a comprehensive review of structural models of amyloid fibrils derived by cryo-EM, ssNMR and AFM to date, and discuss the challenges ahead for resolving the structural basis and the biological consequences of polymorphic amyloid assemblies.     

Self-assembling Shell Proteins PduA and PduJ have Essential and Redundant Roles in Bacterial Microcompartment Assembly

Protein self-assembly is a common and essential biological phenomenon, and bacterial microcompartments present a promising model system to study this process. Bacterial microcompartments are large, protein-based organelles which natively carry out processes important for carbon fixation in cyanobacteria and the survival of enteric bacteria. These structures are increasingly popular with biological engineers due to their potential utility as nanobioreactors or drug delivery vehicles. However, the limited understanding of the assembly mechanism of these bacterial microcompartments hinders efforts to repurpose them for non-native functions. Here, we comprehensively investigate proteins involved in the assembly of the 1,2-propanediol utilization bacterial microcompartment from Salmonella enterica serovar Typhimurium LT2, one of the most widely studied microcompartment systems. We first demonstrate that two shell proteins, PduA and PduJ, have a high propensity for self-assembly upon overexpression, and we provide a novel method for self-assembly quantification. Using genomic knock-outs and knock-ins, we systematically show that these two proteins play an essential and redundant role in bacterial microcompartment assembly that cannot be compensated by other shell proteins. At least one of the two proteins PduA and PduJ must be present for the bacterial microcompartment shell to assemble. We also demonstrate that assembly-deficient variants of these proteins are unable to rescue microcompartment formation, highlighting the importance of this assembly property. Our work provides insight into the assembly mechanism of these bacterial organelles and will aid downstream engineering efforts.     

The Effect of Chemical Chaperones on the Assembly and Stability of HIV-1 Capsid Protein

Chemical chaperones are small organic molecules which accumulate in a broad range of organisms in various tissues under different stress conditions and assist in the maintenance of a correct proteostasis under denaturating environments. The effect of chemical chaperones on protein folding and aggregation has been extensively studied and is generally considered to be mediated through non-specific interactions. However, the precise mechanism of action remains elusive. Protein self-assembly is a key event in both native and pathological states, ranging from microtubules and actin filaments formation to toxic amyloids appearance in degenerative disorders, such as Alzheimer''s and Parkinson''s diseases. Another pathological event, in which protein assembly cascade is a fundamental process, is the formation of virus particles. In the late stage of the virus life cycle, capsid proteins self-assemble into highly-ordered cores, which encapsulate the viral genome, consequently protect genome integrity and mediate infectivity. In this study, we examined the effect of different groups of chemical chaperones on viral capsid assembly in vitro, focusing on HIV-1 capsid protein as a system model. We found that while polyols and sugars markedly inhibited capsid assembly, methylamines dramatically enhanced the assembly rate. Moreover, chemical chaperones that inhibited capsid core formation, also stabilized capsid structure under thermal denaturation. Correspondingly, trimethylamine N-oxide, which facilitated formation of high-order assemblies, clearly destabilized capsid structure under similar conditions. In contrast to the prevailing hypothesis suggesting that chemical chaperones affect proteins through preferential exclusion, the observed dual effects imply that different chaperones modify capsid assembly and stability through different mechanisms. Furthermore, our results indicate a correlation between the folding state of capsid to its tendency to assemble into highly-ordered structures.