Simulating the Entropic Collapse of Coarse-Grained Chromosomes

Depletion forces play a role in the compaction and decompaction of chromosomal material in simple cells, but it has remained debatable whether they are sufficient to account for chromosomal collapse. We present coarse-grained molecular dynamics simulations, which reveal that depletion-induced attraction is sufficient to cause the collapse of a flexible chain of large structural monomers immersed in a bath of smaller depletants. These simulations use an explicit coarse-grained computational model that treats both the supercoiled DNA structural monomers and the smaller protein crowding agents as combinatorial, truncated Lennard-Jones spheres. By presenting a simple theoretical model, we quantitatively cast the action of depletants on supercoiled bacterial DNA as an effective solvent quality. The rapid collapse of the simulated flexible chromosome at the predicted volume fraction of depletants is a continuous phase transition. Additional physical effects to such simple chromosome models, such as enthalpic interactions between structural monomers or chain rigidity, are required if the collapse is to be a first-order phase transition.     

Folding of a small helical protein using hydrogen bonds and hydrophobicity forces

A reduced protein model with five to six atoms per amino acid and five amino acid types is developed and tested on a three-helix-bundle protein, a 46-amino acid fragment from staphylococcal protein A. The model does not rely on the widely used Go approximation, which ignores non-native interactions. We find that the collapse transition is considerably more abrupt for the protein A sequence than for random sequences with the same composition. The chain collapse is found to be at least as fast as helix formation. Energy minimization restricted to the thermodynamically favored topology gives a structure that has a root-mean-square deviation of 1.8 A from the native structure. The sequence-dependent part of our potential is pairwise additive. Our calculations suggest that fine-tuning this potential by parameter optimization is of limited use.     

Protein folding and chain collapse

It is currently assumed that the folded structure of a globular protein is controlled in a highly deterministic way by its amino acid sequence. We show here that a very different although not necessarily contrasting viewpoint can be adopted. From statistical treatment of x-ray results, we suggest that the folding pattern essentially follows the collapse to be expected on statistical-mechanical grounds for an ideal chain effectively experiencing self-attraction and comprising identical units, whose conformational properties are obtained as an average over the actual amino acid units. The local details of folding of each protein, obviously dictated byits amino acid sequence, can be regarded as statistical fluctuations. We consider 31 globular fragments belonging to 21 different water-soluble, nonmembrane proteins. By the theory of chain collapse proposed by two of us [G. Allegra and F. Ganazzoli (1985) J. Chem. Phys. 83 , 397], all the average intramolecular distances may be obtained. Accordingly, first an average plot of the mean-square distances between kth neighboring amino acid units is constructed, starting from the observed crystallographic coordinates. Then the plot is basically reproduced with a wormlike chain model undergoing collapse as a result of intramolecular attractive forces. Agreement is especially good for short amino acid sequences (k ? 30), in which case the statistical sampling is more accurate, enabling us to determine the model parameters. The resulting mean-square radius of gyration is also in good agreement with the experimental average, whereas the unperturbed characteristic ratio is roughly consistent with results from conformational calculations by W. L. Mattice [(1977) Macromolecules 10 , 516], based on the rotational isomeric state approach.     

Electrostatic contributions drive the interaction between Staphylococcus aureus protein Efb-C and its complement target C3d

The C3-inhibitory domain of Staphylococcus aureus extracellular fibrinogen-binding protein (Efb-C) defines a novel three-helix bundle motif that regulates complement activation. Previous crystallographic studies of Efb-C bound to its cognate subdomain of human C3 (C3d) identified Arg-131 and Asn-138 of Efb-C as key residues for its activity. In order to characterize more completely the physical and chemical driving forces behind this important interaction, we employed in this study a combination of structural, biophysical, and computational methods to analyze the interaction of C3d with Efb-C and the single-point mutants R131A and N138A. Our results show that while these mutations do not drastically affect the structure of the Efb-C/C3d recognition complex, they have significant adverse effects on both the thermodynamic and kinetic profiles of the resulting complexes. We also characterized other key interactions along the Efb-C/C3d binding interface and found an intricate network of salt bridges and hydrogen bonds that anchor Efb-C to C3d, resulting in its potent complement inhibitory properties.     

DNA bending by bHLH charge variants

We wish to understand the role of electrostatics in DNA stiffness and bending. The DNA charge collapse model suggests that mutual electrostatic repulsions between neighboring phosphates significantly contribute to DNA stiffness. According to this model, placement of fixed charges near the negatively charged DNA surface should induce bending through asymmetric reduction or enhancement of these inter-phosphate repulsive forces. We have reported previously that charged variants of the elongated basic-leucine zipper (bZIP) domain of Gcn4p bend DNA in a manner consistent with this charge collapse model. To extend this result to a more globular protein, we present an investigation of the dimeric basic-helix–loop–helix (bHLH) domain of Pho4p. The 62 amino acid bHLH domain has been modified to position charged amino acid residues near one face of the DNA double helix. As observed for bZIP charge variants, DNA bending toward appended cations (away from the protein:DNA interface) is observed. However, unlike bZIP proteins, DNA is not bent away from bHLH anionic charges. This finding can be explained by the structure of the more globular bHLH domain which, in contrast to bZIP proteins, makes extensive DNA contacts along the binding face.     

How, when and why proteins collapse: the relation to folding

Unfolded proteins under strongly denaturing conditions are highly expanded. However, when the conditions are more close to native, an unfolded protein may collapse to a compact globular structure distinct from the folded state. This transition is akin to the coil-globule transition of homopolymers. Single-molecule FRET experiments have been particularly conducive in revealing the collapsed state under conditions of coexistence with the folded state. The collapse can be even more readily observed in natively unfolded proteins. Time-resolved studies, using FRET and small-angle scattering, have shown that the collapse transition is a very fast event, probably occurring on the submicrosecond time scale. The forces driving collapse are likely to involve both hydrophobic and backbone interactions. The loss of configurational entropy during collapse makes the unfolded state less stable compared to the folded state, thus facilitating folding.     

Simulating the minimum core for hydrophobic collapse in globular proteins.

To investigate the nature of hydrophobic collapse considered to be the driving force in protein folding, we have simulated aqueous solutions of two model hydrophobic solutes, methane and isobutylene. Using a novel methodology for determining contacts, we can precisely follow hydrophobic aggregation as it proceeds through three stages: dispersed, transition, and collapsed. Theoretical modeling of the cluster formation observed by simulation indicates that this aggregation is cooperative and that the simulations favor the formation of a single cluster midway through the transition stage. This defines a minimum solute hydrophobic core volume. We compare this with protein hydrophobic core volumes determined from solved crystal structures. Our analysis shows that the solute core volume roughly estimates the minimum core size required for independent hydrophobic stabilization of a protein and defines a limiting concentration of nonpolar residues that can cause hydrophobic collapse. These results suggest that the physical forces driving aggregation of hydrophobic molecules in water is indeed responsible for protein folding.     

Characterization of the folding kinetics of a three-helix bundle protein via a minimalist Langevin model.

We use a simple off-lattice Langevin model of protein folding to characterize the folding and unfolding of a fast-folding, 46 residue three-helix bundle. Under conditions at which the C-terminal helix is 30 % stable, we observe a clear three-state folding mechanism. In the on-pathway intermediate state, the middle and C-terminal helices are folded and in contact with each other, while the N-terminal region remains disordered. Nevertheless, under these conditions this intermediate is thermodynamically unstable relative to its unfolded state. The first and highest folding barrier corresponds to the organization of the hinge between the middle and C-terminal helices. A subsequent major barrier corresponds to the organization of the hinge between the middle and N-terminal helices. Hyperstabilizing the hinge regions leads to twice the folding rate that is obtained from hyperstabilizing the helices, even though much fewer contacts are involved in hinge hyperstabilization than in helix hyperstabilization. Unfolding follows single-exponential kinetics, even at temperatures only slightly above the folding transition temperature.     

Atomic force microscopy studies of the adhesive properties of DPPC vesicles containing β-carotene

A role of carotenoids as modulators of physical properties of model and biological membranes has been already postulated. However, there is a lack of information on the influence of these pigments on interactions between the lipids which form such membranes. This paper applies atomic force microscopy (AFM) in to study the effects of β-carotene on the adhesion properties of DPPC multilamellar liposomes. This allowed us to gain, for the first time, a direct insight into the interactions between the components in model systems on a molecular level. We observe that the adhesive forces in DPPC multilamellar liposomes containing 1mol% of β-carotene decrease exponentially with increasing temperature, and that at about 37°C they diminish. In the case of pure liposomes the decline in adhesion is of a different nature and the adhesive forces disappear at 34°C. The adhesive forces are about 5 times higher at 31°C in the presence of β-carotene than in its absence. However, measurements using differential scanning calorimetry (DSC) showed a shift of the lamellar-to-undulled-lamellar phase transition toward lower temperatures by about 0.8 ± 0.2°C in a system containing β-carotene. The enthalpy changes (ΔH) of this transition are similar for both systems. For the main transition, gel-to-liquid crystalline, the peak is shifted by about 0.5 ± 0.1°C, and ΔH decreases by about 30% in liposomes treated with β-carotene in comparison to pure liposomes. Our results suggest increased cooperation between liposome components in a system with enriched β-carotene, which cause a change in phase transition temperatures. Moreover, these interactions are very sensitive to temperature.     

Topological examination of the bacteriophage lambda S holin by EPR spectroscopy

The S protein from bacteriophage lambda is a three-helix transmembrane protein produced by the prophage which accumulates in the host membrane during late gene expression. It is responsible for the first step in lysing the host cell at the end of the viral life cycle by multimerizing together to form large pores which permeabilize the host membrane to allow the escape of virions. Several previous studies have established a model for the assembly of holin into functional holes and the manner in which they pack together, but it is still not fully understood how the very rapid transition from monomer or dimer to multimeric pore occurs with such precise timing once the requisite threshold is reached. Here, site-directed spin labeling with a nitroxide label at introduced cysteine residues is used to corroborate existing topological data from a crosslinking study of the multimerized holin by EPR spectroscopy. CW-EPR spectral lineshape analysis and power saturation data are consistent with a three-helix topology with an unstructured C-terminal domain, as well as at least one interface on transmembrane domain 1 which is exposed to the lumen of the hole, and a highly constrained steric environment suggestive of a tight helical packing interface at transmembrane domain 2.     

Phi-analysis of the folding of the B domain of protein A using multiple optical probes

We examined the co-operativity of ultra-fast folding of a protein and whether the Phi-value analysis of its transition state depended on the location of the optical probe. We incorporated in turn a tryptophan residue into each of the three helices of the B domain of Protein A. Each Trp mutant of the three-helix bundle protein was used as a pseudo-wild-type parent for Phi-analysis in which the intrinsic Trp fluorescence probed the formation of each helix during the transition state. Apart from local effects in the immediate vicinity of the probe, the three separate sets of Phi-values were in excellent agreement, demonstrating the overall co-operativity of folding and the robustness of the Phi-analysis. The transition state of folding of Protein A contains the second helix being well formed with many stabilizing tertiary hydrophobic interactions. In contrast, the first and the third helices are more poorly structured in the transition state. The mechanism of folding thus involves the concurrent formation of secondary and tertiary interactions, and is towards the nucleation-condensation extreme in the nucleation-condensation-framework continuum of mechanism, with helix 2 being the nucleus. We provide an error analysis of Phi-values derived purely from the kinetics of two-state chevron plots.     

Structural analysis of homologous repeated domains in alpha-actinin and spectrin

The amino acid sequences of chick and slime mould alpha-actinin each contain four repeats of approximately 122 residues. These repeats are homologous to the 18-22 repeats, each of approximately 106 residues, found in the alpha and beta subunits of spectrin and fodrin, and to the multiple repeats of approximately 110 residues found in the Duchenne muscular dystrophy protein (dystrophin). The repeats correspond to the elongated rod-like portion of these molecules. We present a multiple sequence alignment of 21 repeats from this superfamily (8 alpha-actinin and 13 spectrin/fodrin), based on optimal pairwise alignments, from which a characteristic consensus pattern of amino acid types is deduced. Trp 46 is invariant in all but one repeat, and physicochemical classes of amino acids are conserved at 25 other positions. Secondary structure prediction on both the alpha-actinin and spectrin repeats taken together with the distribution of proline residues in the sequences, strongly suggest that each repeated domain consists of a four-helix structure. Our predictions differ significantly from previous three-helix models based on analyses of fewer sequences. To determine possible interdomain regions, sites of limited proteolysis of the native chick alpha-actinin dimer were determined and located in the amino acid sequence. The majority of these sites were in corresponding positions in different repeats within a segment predicted as a long helix. We propose a model, consistent with the overall dimensions of the rod-like portions of the molecules, in which these long, probably interrupted helices, link adjacent domains.     

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

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

Folding thermodynamics of model four-strand antiparallel beta-sheet proteins.

The thermodynamic properties for three different types of off-lattice four-strand antiparallel beta-strand protein models interacting via a hybrid Go-type potential have been investigated. Discontinuous molecular dynamic simulations have been performed for different sizes of the bias gap g, an artificial measure of a model protein's preference for its native state. The thermodynamic transition temperatures are obtained by calculating the squared radius of gyration R(g)(2), the root-mean-squared pair separation fluctuation Delta(B), the specific heat C(v), the internal energy of the system E, and the Lindemann disorder parameter Delta(L). Despite these models' simplicity, they exhibit a complex set of protein transitions, consistent with those observed in experimental studies on real proteins. Starting from high temperature, these transitions include a collapse transition, a disordered-to-ordered globule transition, a folding transition, and a liquid-to-solid transition. The high temperature transitions, i.e., the collapse transition and the disordered-to-ordered globule transition, exist for all three beta-strand proteins, although the native-state geometry of the three model proteins is different. However the low temperature transitions, i.e., the folding transition and the liquid-to-solid transition, strongly depend on the native-state geometry of the model proteins and the size of the bias gap.     

A dynamic model for the structure of acyl carrier protein in solution

The determination of solution structures of proteins using two-dimensional NMR data is commonly based on the assumption that the structure can be represented by a single rigid conformer. We present here a procedure whereby this assumption can be relaxed and illustrate its application to acyl carrier protein from Escherichia coli, a small negatively charged protein with no internal disulfide bonds. The methodology rests on a model having two distinct conformers in dynamic equilibrium. Use of this two-state model results in a dramatic improvement in fit to cross-relaxation-derived distance constraints and a substantial lowering of molecular mechanics energies for individual conformers of acyl carrier protein. The two-state model retains the three-helix motif previously identified on the basis of a one-state structure, but substantial motion of loop regions and the C-terminal peptide, as well as partial disruption of the second helix, is suggested to occur. Support for the existence of these motions can be found in amide exchange rate and spin relaxation time data.     

Role of amino acid insertions on intermolecular forces between arginine peptide condensed DNA helices: implications for protamine-DNA packaging in sperm

In spermatogenesis, chromatin histones are replaced by arginine-rich protamines to densely compact DNA in sperm heads. Tight packaging is considered necessary to protect the DNA from damage. To better understand the nature of the forces condensing protamine-DNA assemblies and their dependence on amino acid content, the effect of neutral and negatively charged amino acids on DNA-DNA intermolecular forces was studied using model peptides containing six arginines. We have previously observed that the neutral amino acids in salmon protamine decrease the net attraction between protamine-DNA helices compared with the equivalent homo-arginine peptide. Using osmotic stress coupled with x-ray scattering, we have investigated the component attractive and repulsive forces that determine the net attraction and equilibrium interhelical distance as a function of the chemistry, position, and number of the amino acid inserted. Neutral amino acids inserted into hexa-arginine increase the short range repulsion while only slightly affecting longer range attraction. The amino acid content alone of salmon protamine is enough to rationalize the forces that package DNA in sperm heads. Inserting a negatively charged amino acid into hexa-arginine dramatically weakens the net attraction. Both of these observations have biological implications for protamine-DNA packaging in sperm heads.     

Structural test of the parameterized-backbone method for protein design

Designing new protein folds requires a method for simultaneously optimizing the conformation of the backbone and the side-chains. One approach to this problem is the use of a parameterized backbone, which allows the systematic exploration of families of structures. We report the crystal structure of RH3, a right-handed, three-helix coiled coil that was designed using a parameterized backbone and detailed modeling of core packing. This crystal structure was determined using another rationally designed feature, a metal-binding site that permitted experimental phasing of the X-ray data. RH3 adopted the intended fold, which has not been observed previously in biological proteins. Unanticipated structural asymmetry in the trimer was a principal source of variation within the RH3 structure. The sequence of RH3 differs from that of a previously characterized right-handed tetramer, RH4, at only one position in each 11 amino acid sequence repeat. This close similarity indicates that the design method is sensitive to the core packing interactions that specify the protein structure. Comparison of the structures of RH3 and RH4 indicates that both steric overlap and cavity formation provide strong driving forces for oligomer specificity.     

The N-terminal domains of syntaxin 7 and vti1b form three-helix bundles that differ in their ability to regulate SNARE complex assembly

The SNAREs syntaxin 7, syntaxin 8, vti1b, and endobrevin/VAMP8 function in the fusion of late endosomes. Although the core complex formed by these SNAREs is very similar to the neuronal SNARE complex, it differs from the neuronal complex in that three of the four SNAREs contain extended N-terminal regions of unknown structure and function. Here we show that the N-terminal regions of syntaxin 7, syntaxin 8, and vti1b contain well folded alpha-helical domains. Multidimensional NMR spectroscopy revealed that in syntaxin 7 and vti1b, the domains form three-helix bundles resembling those of syntaxin 1, Sso1p, and Vam3p. The three-helix bundle domain of vti1b is the first of its kind identified in a SNARE outside the syntaxin family. Only syntaxin 7 adopts a closed conformation, whereas in vti1b and syntaxin 8, the N-terminal domains do not interact with the adjacent SNARE motifs. Accordingly, the rate of SNARE complex assembly is retarded about 7-fold when syntaxin 7 contains its N-terminal domain, whereas the N-terminal domains of vti1b and syntaxin 8 have no influence on assembly kinetics. We conclude that three-helix bundles represent a common fold for SNARE N-terminal domains, not restricted to the syntaxin family. However, they differ in their ability to adopt closed conformations and thus to regulate the assembly of SNARE complexes.     

Contact stress distributions on the femoral head of the emu (Dromaius novaehollandiae)

Osteonecrosis of the femoral head remains a challenging orthopaedic problem. The disease frequently progresses to femoral head collapse, leading to debilitating osteoarthritis in the affected hip(s). Since a major goal of pre-collapse interventions is to forestall the need for hip arthroplasty, it is important that any animal models used to develop or study such interventions also have a natural history of progression to femoral head collapse. The emu (Dromaius novaehollandiae), a large flightless bird native to Australia, consistently progresses to femoral head collapse when osteonecrosis is experimentally induced cryogenically. Full biomechanical characterization of the demands this animal places on its hip is an important consideration in future usage of this model. This study reports in vitro measurement of the contact stress distributions on the emu femoral head during stance phase of the gait cycle, using Fuji pressure-sensitive film. Applied hip loadings were based upon ground reaction forces and hip flexion angles recorded in vivo. The contact stress data showed reasonable homology with the human hip, both in terms of stress magnitude and sites of habitual loading on the femoral head.