Effect of Weakly Interacting Cosolutes on Lysozyme Conformations

Exposure of a protein to cosolutes, like denaturants, changes its folding equilibrium. To determine the ensemble of protein conformations at equilibrium, in the presence of weakly interacting cosolutes, we present a two-stage analysis of solution X-ray scattering data. In the first stage, Guinier analysis and Kratky plot revealed information about the compactness and flexibility of the protein. In the second stage, elastic network contact model and coarse-grained normal mode analysis were used to generate an ensemble of conformations. The scattering curves of the conformations were computed and fitted to the measured scattering curves to get insights into the dominating folding states at equilibrium. Urea and guanidine hydrochloride (GuHCl) behaved as preferentially included weakly interacting cosolutes and induced denaturation of hen egg-white lysozyme, which served as our test case. The computed models adequately fit the data and gave ensembles of conformations that were consistent with our measurements. The analysis suggests that in the presence of urea, lysozyme retained its compactness and assumed molten globule characteristics, whereas in the presence of GuHCl lysozyme adopted random coiled conformations. Interestingly, no equilibrium intermediate states were observed in both urea and GuHCl

Effect of Calcium Ions and Disulfide Bonds on Swelling of Virus Particles

Multivalent ions affect the structure and organization of virus nanoparticles. Wild-type simian virus 40 (wt SV40) is a nonenveloped virus belonging to the polyomavirus family, whose external diameter is 48.4 nm. Calcium ions and disulfide bonds are involved in the stabilization of its capsid and are playing a role in its assembly and disassembly pathways. Using solution small-angle X-ray scattering (SAXS), we found that the volume of wt SV40 swelled by about 17% when both of its calcium ions were chelated by ethylene glycol-bis(2-aminoethylether)-N,N,N′,N′-tetraacetic acid and its disulfide bonds were reduced by dithiothreitol. By applying osmotic stress, the swelling could be reversed. DNA-containing virus-like particles behaved in a similar way. The results provide insight into the structural role of calcium ions and disulfide bonds in holding the capsid proteins in compact conformation

Effect of Calcium Ions and Disulfide Bonds on Swelling of Virus Particles

Multivalent ions affect the structure and organization of virus nanoparticles. Wild-type simian virus 40 (wt SV40) is a nonenveloped virus belonging to the polyomavirus family, whose external diameter is 48.4 nm. Calcium ions and disulfide bonds are involved in the stabilization of its capsid and are playing a role in its assembly and disassembly pathways. Using solution small-angle X-ray scattering (SAXS), we found that the volume of wt SV40 swelled by about 17% when both of its calcium ions were chelated by ethylene glycol-bis(2-aminoethylether)-N,N,N′,N′-tetraacetic acid and its disulfide bonds were reduced by dithiothreitol. By applying osmotic stress, the swelling could be reversed. DNA-containing virus-like particles behaved in a similar way. The results provide insight into the structural role of calcium ions and disulfide bonds in holding the capsid proteins in compact conformation

Assembly Reactions of Hepatitis B Capsid Protein into Capsid Nanoparticles Follow a Narrow Path through a Complex Reaction Landscape

For many viruses, capsids (biological nanoparticles) assemble to protect genetic material and dissociate to release their cargo. To understand these contradictory properties, we analyzed capsid assembly for hepatitis B virus; an endemic pathogen with an icosahedral, 120-homodimer capsid. We used solution X-ray scattering to examine trapped and equilibrated assembly reactions. To fit experimental results, we generated a library of distinct intermediates, selected by umbrella sampling of Monte Carlo simulations. The number of possible capsid intermediates is immense, ∼1030, yet assembly reactions are rapid and completed with high fidelity. If the huge number of possible intermediates were actually present, maximum entropy analysis shows that assembly reactions would be blocked by an entropic barrier, resulting in incomplete nanoparticles. When an energetic term was applied to select the stable species that dominated the reaction mixture, we found only a few hundred intermediates, mapping out a narrow path through the immense reaction landscape. This is a solution to a viral application of the Levinthal paradox. With the correct energetic term, the match between predicted intermediates and scattering data was striking. The grand canonical free energy landscape for assembly, calibrated by our experimental results, supports a detailed analysis of this complex reaction. There is a narrow range of energies that supports on-path assembly. If association energy is too weak or too strong, progressively more intermediates will be entropically blocked, spilling into paths leading to dissociation or trapped incomplete nanoparticles, respectively. These results are relevant to many viruses and provide a basis for simplifying assembly models and identifying new targets for antiviral intervention. They provide a basis for understanding and designing biological and abiological self-assembly reactions

Crystallization, Reentrant Melting, and Resolubilization of Virus Nanoparticles

Crystallization is a fundamental and ubiquitous process that is well understood in the case of atoms or small molecules, but its outcome is still hard to predict in the case of nanoparticles or macromolecular complexes. Controlling the organization of virus nanoparticles into a variety of 3D supramolecular architectures is often done by multivalent ions and is of great interest for biomedical applications such as drug or gene delivery and biosensing, as well as for bionanomaterials and catalysis. In this paper, we show that slow dialysis, over several hours, of wild-type Simian Virus 40 (wt SV40) nanoparticle solution against salt solutions containing MgCl₂, with or without added NaCl, results in wt SV40 nanoparticles arranged in a body cubic center crystal structure with <i>Im</i>3<i>m</i> space group, as a thermodynamic product, in coexistence with soluble wt SV40 nanoparticles. The nanoparticle crystals formed above a critical MgCl₂ concentrations. Reentrant melting and resolubilization of the virus nanoparticles took place when the MgCl₂ concentrations passed a second threshold. Using synchrotron solution X-ray scattering we determined the structures and the mass fraction of the soluble and crystal phases as a function of MgCl₂ and NaCl concentrations. A thermodynamic model, which balances the chemical potentials of the Mg²⁺ ions in each of the possible states, explains our observations. The model reveals the mechanism of both the crystallization and the reentrant melting and resolubilization and shows that counterion entropy is the main driving force for both processes

D+: Software for High-Resolution Hierarchical Modeling of Solution X-Ray Scattering from Complex Structures

In this paper, we present our new computer program, D+, which uses the reciprocal-grid (RG) algorithm to efficiently compute X-ray scattering curves from solutions of complex structures at high-resolution. Structures are defined in hierarchical trees in which subunits can be represented by geometric or atomic models. Repeating subunits can be docked into their assembly symmetries, describing their locations and orientations in space. The scattering amplitude of the entire structure can be calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the RGs of the larger structures, and by repeating this process for all the leaves and nodes of the tree. For very large structures, a Hybrid method can be used to avoid numerical artifacts. In the Hybrid method, only grids of smaller subunits are summed and used as subunits in a direct computation of the scattering amplitude. D+ can accurately analyze both small- and wide-angle solution X-ray scattering data. We present how D+ applies the RG algorithm, accounts for rotations and translations of subunits, processes atomic models, accounts for the contribution of the solvent as well as the solvation layer of complex structures in a scalable manner, writes and accesses RGs, interpolates between grid points, computes numerical integrals, enables the use of scripts to define complicated structures, applies fitting algorithms, accounts for several coexisting uncorrelated populations, and accelerates computations using GPUs. D+ may also account for different X-ray energies to analyze anomalous solution X-ray scattering data. An accessory tool that can identify repeating subunits in a protein data bank (PDB) file of a complex structure is provided. The tool can compute the orientation and translation of repeating subunits needed for exploiting the advantages of the RG algorithm in D+. In addition, a python wrapper is also available, enabling more advanced computations and integration of D+ with other computational tools. Finally, we present a large number of tests and compare the results of D+ with other programs when possible and demonstrate the use of D+ to analyze solution scattering data from dynamic microtubule structures with different protofilament number. D+ and its source code are freely available (https://scholars.huji.ac.il/uriraviv/software/d-software) for academic users and developers

Reciprocal Grids: A Hierarchical Algorithm for Computing Solution X‑ray Scattering Curves from Supramolecular Complexes at High Resolution

In many biochemical processes large biomolecular assemblies play important roles. X-ray scattering is a label-free bulk method that can probe the structure of large self-assembled complexes in solution. As we demonstrate in this paper, solution X-ray scattering can measure complex supramolecular assemblies at high sensitivity and resolution. At high resolution, however, data analysis of larger complexes is computationally demanding. We present an efficient method to compute the scattering curves from complex structures over a wide range of scattering angles. In our computational method, structures are defined as hierarchical trees in which repeating subunits are docked into their assembly symmetries, describing the manner subunits repeat in the structure (in other words, the locations and orientations of the repeating subunits). The amplitude of the assembly is calculated by computing the amplitudes of the basic subunits on 3<i>D</i> reciprocal-space grids, moving up in the hierarchy, calculating the grids of larger structures, and repeating this process for all the leaves and nodes of the tree. For very large structures, we developed a hybrid method that sums grids of smaller subunits in order to avoid numerical artifacts. We developed protocols for obtaining high-resolution solution X-ray scattering data from taxol-free microtubules at a wide range of scattering angles. We then validated our method by adequately modeling these high-resolution data. The higher speed and accuracy of our method, over existing methods, is demonstrated for smaller structures: short microtubule and tobacco mosaic virus. Our algorithm may be integrated into various structure prediction computational tools, simulations, and theoretical models, and provide means for testing their predicted structural model, by calculating the expected X-ray scattering curve and comparing with experimental data

Effect of Temperature on the Interactions between Dipolar Membranes

It is well-known that phospholipids in aqueous environment self-assemble into lamellar structures with a repeat distance governed by the interactions between them. Yet, the understanding of these interactions is incomplete. In this paper, we study the effect of temperature on the interlamellar interactions between dipolar membranes. Using solution small-angle X-ray scattering (SAXS), we measured the repeat distance between 1,2-dilauroyl-<i>sn</i>-glycero-3-phosphocholine (DLPC) bilayers at different temperatures and osmotic stresses. We found that when no pressure is applied the lamellar repeat distance, <i>D</i>, decreases and then increases with increasing temperature. As the osmotic stress increases, <i>D</i> decreases with temperature and then increases to a limited extent, until at sufficiently high pressure <i>D</i> decreases with temperature in all the examined range. We then reconstructed experimentally the equation of state and fit it with a modified interaction model that takes into account the temperature dependence of the fluctuation term. Finally, we showed how the thickness of DLPC membranes decreases with temperature