Topological features of rugged fitness landscapes in sequence space.

The factors that determine the tempo and mode of protein evolution continue to be a central question in molecular evolution. Traditionally, studies of protein evolution focused on the rates of amino acid substitutions. More recently, with the availability of sequence data and advanced experimental techniques, the focus of attention has shifted toward the study of evolutionary trajectories and the overall layout of protein fitness landscapes. In this review we describe the effect of epistasis on the topology of evolutionary pathways that are likely to be found in fitness landscapes and develop a simple theory to connect the number of maladapted genotypes to the topology of fitness landscapes with epistatic interactions. Finally, we review recent studies that have probed the extent of epistatic interactions and have begun to chart the fitness landscapes in protein sequence space.

Ensemble refinement of protein crystal structures: validation and application.

X-ray crystallography typically uses a single set of coordinates and B factors to describe macromolecular conformations. Refinement of multiple copies of the entire structure has been previously used in specific cases as an alternative means of representing structural flexibility. Here, we systematically validate this method by using simulated diffraction data, and we find that ensemble refinement produces better representations of the distributions of atomic positions in the simulated structures than single-conformer refinements. Comparison of principal components calculated from the refined ensembles and simulations shows that concerted motions are captured locally, but that correlations dissipate over long distances. Ensemble refinement is also used on 50 experimental structures of varying resolution and leads to decreases in R(free) values, implying that improvements in the representation of flexibility observed for the simulated structures may apply to real structures. These gains are essentially independent of resolution or data-to-parameter ratio, suggesting that even structures at moderate resolution can benefit from ensemble refinement.

Protein structural variation in computational models and crystallographic data.

Normal mode analysis offers an efficient way of modeling the conformational flexibility of protein structures. We use anisotropic displacement parameters from crystallography to test the quality of prediction of both the magnitude and directionality of conformational flexibility. Normal modes from four simple elastic network model potentials and from the CHARMM force field are calculated for a data set of 83 diverse, ultrahigh-resolution crystal structures. While all five potentials provide good predictions of the magnitude of flexibility, all-atom potentials have a clear edge at prediction of directionality, and the CHARMM potential has the highest prediction quality. The low-frequency modes from different potentials are similar, but those computed from the CHARMM potential show the greatest difference from the elastic network models. The comprehensive evaluation demonstrates the costs and benefits of using normal mode potentials of varying complexity.

Sampling of the native conformational ensemble of myoglobin via structures in different crystalline environments.

Proteins sample multiple conformational substates in their native environment, but the process of crystallization selects the conformers that allow for close packing. The population of conformers can be shifted by varying the environment through a range of crystallization conditions, often resulting in different space groups and changes in the packing arrangements. Three high resolution structures of myoglobin (Mb) in different crystal space groups are presented, including one in a new space group P6(1)22 and two structures in space groups P2(1)2(1)2(1) and P6. We compare coordinates and anisotropic displacement parameters (ADPs) from these three structures plus an existing structure in space group P2(1). While the overall changes are small, there is substantial variation in several external regions with varying patterns of crystal contacts across the space group packing arrangements. The structural ensemble containing four different crystal forms displays greater conformational variance (Calpha rmsd of 0.54-0.79 A) in comparison to a collection of four Mb structures with different ligands and mutations in the same crystal form (Calpha rmsd values of 0.28-0.37 A). The high resolution of the data enables comparison of both the magnitudes and directions of ADPs, which are found to be suppressed by crystal contacts. A composite dynamic profile of Mb structural variation from the four structures was compared with an independent structural ensemble developed from NMR refinement. Despite the limitations and biases of each method, the ADPs of the crystallographic ensemble closely match the positional variance from the solution NMR ensemble with linear correlation of 0.8. This suggests that crystal packing selects conformers representative of the solution ensemble, and several different crystal forms give a more complete view of the plasticity of a protein structure.

Structure and dynamics of gamma-SNAP: insight into flexibility of proteins from the SNAP family.

Soluble N-ethylmaleimide-sensitive factor attachment protein gamma (gamma-SNAP) is a member of an eukaryotic protein family involved in intracellular membrane trafficking. The X-ray structure of Brachydanio rerio gamma-SNAP was determined to 2.6 A and revealed an all-helical protein comprised of an extended twisted-sheet of helical hairpins with a helical-bundle domain on its carboxy-terminal end. Structural and conformational differences between multiple observed gamma-SNAP molecules and Sec17, a SNAP family protein from yeast, are analyzed. Conformational variation in gamma-SNAP molecules is matched with great precision by the two lowest frequency normal modes of the structure. Comparison of the lowest-frequency modes from gamma-SNAP and Sec17 indicated that the structures share preferred directions of flexibility, corresponding to bending and twisting of the twisted sheet motif. We discuss possible consequences related to the flexibility of the SNAP proteins for the mechanism of the 20S complex disassembly during the SNAP receptors recycling.

Structure and dynamics of UDP-glucose pyrophosphorylase from Arabidopsis thaliana with bound UDP-glucose and UTP.

The structure of the UDP-glucose pyrophosphorylase encoded by Arabidopsis thaliana gene At3g03250 has been solved to a nominal resolution of 1.86 Angstroms. In addition, the structure has been solved in the presence of the substrates/products UTP and UDP-glucose to nominal resolutions of 1.64 Angstroms and 1.85 Angstroms. The three structures revealed a catalytic domain similar to that of other nucleotidyl-glucose pyrophosphorylases with a carboxy-terminal beta-helix domain in a unique orientation. Conformational changes are observed between the native and substrate-bound complexes. The nucleotide-binding loop and the carboxy-terminal domain, including the suspected catalytically important Lys360, move in and out of the active site in a concerted fashion. TLS refinement was employed initially to model conformational heterogeneity in the UDP-glucose complex followed by the use of multiconformer refinement for the entire molecule. Normal mode analysis generated atomic displacement predictions in good agreement in magnitude and direction with the observed conformational changes and anisotropic displacement parameters generated by TLS refinement. The structures and the observed dynamic changes provide insight into the ordered mechanism of this enzyme and previously described oligomerization effects on catalytic activity.

Creating protein models from electron-density maps using particle-filtering methods.

MOTIVATION: One bottleneck in high-throughput protein crystallography is interpreting an electron-density map, that is, fitting a molecular model to the 3D picture crystallography produces. Previously, we developed ACMI (Automatic Crystallographic Map Interpreter), an algorithm that uses a probabilistic model to infer an accurate protein backbone layout. Here, we use a sampling method known as particle filtering to produce a set of all-atom protein models. We use the output of ACMI to guide the particle filter's sampling, producing an accurate, physically feasible set of structures. RESULTS: We test our algorithm on 10 poor-quality experimental density maps. We show that particle filtering produces accurate all-atom models, resulting in fewer chains, lower sidechain RMS error and reduced R factor, compared to simply placing the best-matching sidechains on ACMI's trace. We show that our approach produces a more accurate model than three leading methods--Textal, Resolve and ARP/WARP--in terms of main chain completeness, sidechain identification and crystallographic R factor. AVAILABILITY: Source code and experimental density maps available at http://ftp.cs.wisc.edu/machine-learning/shavlik-group/programs/acmi/

Nonequilibrium dynamics simulations of nitric oxide release: comparative study of nitrophorin and myoglobin.

Nitrophorin 4 (NP4) is a heme protein that reversibly binds nitric oxide (NO), with release rates modulated by pH change. High-resolution structures of NP4 revealed that pH changes and NO binding induce a large conformational rearrangement in two loops that serve to protect the heme-bound NO molecule from solvent. We used extended (110 ns) molecular dynamics simulations of NP4 at pH 5 and pH 7, modeled by selective deprotonation of acidic groups. Conformational and dynamic changes were observed, consistent with those found in the crystal. Further, major solvent movement and NO escape were observed at pH 7, while the ligand remained in the heme binding pocket at pH 5. As a control, we also performed molecular dynamics (MD) simulations of sperm whale myoglobin, where NO migration into the interior cavities of the protein was observed, consistent with previous reports. We constructed a kinetic model of ligand escape to quantitatively relate the microscopic rate constants to the observed rates, and tested the predictions against the experimental data. The results suggest that release rates of diatomic molecules from heme proteins can be varied by several orders of magnitude through modest adjustments in geminate rebinding and gating behavior.

Structure of human J-type co-chaperone HscB reveals a tetracysteine metal-binding domain.

Iron-sulfur proteins play indispensable roles in a broad range of biochemical processes. The biogenesis of iron-sulfur proteins is a complex process that has become a subject of extensive research. The final step of iron-sulfur protein assembly involves transfer of an iron-sulfur cluster from a cluster-donor to a cluster-acceptor protein. This process is facilitated by a specialized chaperone system, which consists of a molecular chaperone from the Hsc70 family and a co-chaperone of the J-domain family. The 3.0 A crystal structure of a human mitochondrial J-type co-chaperone HscB revealed an L-shaped protein that resembles Escherichia coli HscB. The important difference between the two homologs is the presence of an auxiliary metal-binding domain at the N terminus of human HscB that coordinates a metal via the tetracysteine consensus motif CWXCX(9-13)FCXXCXXXQ. The domain is found in HscB homologs from animals and plants as well as in magnetotactic bacteria. The metal-binding site of the domain is structurally similar to that of rubredoxin and several zinc finger proteins containing rubredoxin-like knuckles. The normal mode analysis of HscB revealed that this L-shaped protein preferentially undergoes a scissors-like motion that correlates well with the conformational changes of human HscB observed in the crystals.

Optimization and evaluation of a coarse-grained model of protein motion using x-ray crystal data.

Simple coarse-grained models, such as the Gaussian network model, have been shown to capture some of the features of equilibrium protein dynamics. We extend this model by using atomic contacts to define residue interactions and introducing more than one interaction parameter between residues. We use B-factors from 98 ultra-high resolution (

Protein functional cycle viewed at atomic resolution: conformational change and mobility in nitrophorin 4 as a function of pH and NO binding.

The blood-sucking insect Rhodnius prolixus uses nitrophorin 4, a heme protein, to deliver nitric oxide (NO) to a victim, causing vasodilation and improved feeding. Binding of NO occurs at a ferric heme and is modulated by pH. NO binding at lower pH induces a large conformational change involving loops A-B and G-H that leads to distal pocket desolvation and protection of the nitrosyl heme complex. We have determined the crystal structures of Rhodnius nitrophorin 4 to ultrahigh resolution in four functional states: +/-NO at pH = 7.4 and +/-NO at pH = 5.6. The structure with NO at pH 7.4 (1.08 A) is newly determined while the other complexes have been modeled to resolutions much greater than previously reported (1.0-0.85 A). The ultrahigh resolution allowed us to resolve multiple conformers in binding-site loops, leading to a detailed description of the dynamics involved with storing NO in the insect salivary gland at low pH, and releasing NO in response to the increased pH of a victim's tissue. Strikingly, features for both the "open" and "closed" conformers exist under all conditions, suggesting that the flexible loops can transition with relative ease between conformational states. Yet, release of NO from rNP4 is much slower than found for other ferric heme proteins. The structures suggest that highly mobile loops can limit diffusion of diatomic molecules into and out of a protein cavity, a result with implications for the role of protein dynamics in function.