Cryo-electron microscopy (cryo-EM) is rapidly emerging as a powerful tool for protein structure determination at high resolution. Here we report the structure of a complex between Escherichia coli β-galactosidase and the cell-permeant inhibitor phenylethyl β-D-thiogalactopyranoside (PETG), determined by cryo-EM at an average resolution of ~2.2 angstroms (Å). Besides the PETG ligand, we identified densities in the map for ~800 water molecules and for magnesium and sodium ions. Although it is likely that continued advances in detector technology may further enhance resolution, our findings demonstrate that preparation of specimens of adequate quality and intrinsic protein flexibility, rather than imaging or image-processing technologies, now represent the major bottlenecks to routinely achieving resolutions close to 2 Å using single-particle cryo-EM.

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This work presents an accurate and efficient approach to the calculation of long-range interactions for molecular modeling and simulation. This method defines a local region for each particle and describes the remaining region as images of the local region statistically distributed in an isotropic and periodic way, which we call isotropic periodic images. Different from lattice sum methods that sum over discrete lattice images generated by periodic boundary conditions, this method sums over the isotropic periodic images to calculate long-range interactions, and is referred to as the isotropic periodic sum (IPS) method. The IPS method is not a lattice sum method and eliminates the need for a reciprocal space sum. Several analytic solutions of IPS for commonly used potentials are presented. It is demonstrated that the IPS method produces results very similar to that of Ewald summation, but with three major advantages, (1) it eliminates unwanted symmetry artifacts raised from periodic boundary conditions, (2) it can be applied to potentials of any functional form and to fully and partially homogenous systems as well as finite systems, and (3) it is more computationally efficient and can be easily parallelized for multiprocessor computers. Therefore, this method provides a general approach to an efficient calculation of long-range interactions for various kinds of molecular systems.

Electron cryo-microscopy of`single particles' is a powerful method to determine the three-dimensional (3D) architectures of complex cellular assemblies. The pyruvate dehydrogenase multi-enzyme complex couples the activity of three component enzymes (E1, E2 and E3) in the oxidative decarboxylation of pyruvate to generate acetyl-CoA, linking glycolysis and the tricarboxylic acid cycle. We report here a 3D model for an 11 MDa, icosahedral pyruvate dehydrogenase sub-complex, obtained by combining a 28 A Ê structure derived from electron cryo-microscopy with previously determined atomic coordinates of the individual E1 and E2 components. A key feature is that the E1 molecules are located on the periphery of the assembly in an orientation that allows each of the 60 mobile lipoyl domains tethered to the inner E2 core to access multiple E1 and E2 active sites from inside the icosahedral complex. This unexpected architecture provides a highly ef®cient mechanism for active site coupling and catalytic rate enhancement by the motion of the lipoyl domains in the restricted annular region between the inner core and outer shell of the complex. Keywords: electron microscopy/molecular machine/ pyruvate dehydrogenase/single particle analysis/threedimensional reconstruction IntroductionMulti-enzyme complexes in the 2-oxo acid dehydrogenase family of multi-functional enzymes catalyse multi-step oxidative decarboxylations that furnish several of the cornerstones of energy metabolism in many cell types (Reed and Hackert, 1990;Perham 1991Perham , 2000. They are crucial to the glycolytic pathway, the tricarboxylic acid cycle and the metabolism of branched-chain amino acids. Their dysfunction leads to several well recognized metabolic disorders, among them lactic acidosis, maple syrup urine disease and primary biliary cirrhosis (Patel and Harris, 1995;Yeaman et al., 2000;Nellis and Danner, 2001). They have been the subject of intense investigation and have achieved the status of a paradigm in the study of multi-step catalysis. Nevertheless, while an impressive understanding of the structures and activities of their individual component enzymes has been obtained, no overall detailed architecture has been established that permits a properly integrated picture of their mode of action.Like the pyruvate dehydrogenase (PDH) complexes of eukaryotes and of other Gram-positive bacteria, the Bacillus stearothermophilus PDH complex (Figure 1) is assembled around a core of 60 dihydrolipoyl acetyltransferase (E2) chains arranged with icosahedral symmetry (Reed and Hackert, 1990;Perham, 1991). Each E2 chain consists of three domains: (i) an N-terminal 9 kDa lipoyl domain (Dardel et al., 1993), which visits the active sites of the pyruvate decarboxylase (E1) component and then those of E2 and dihydrolipoyl dehydrogenase (E3); (ii) a 4 kDa peripheral subunit-binding domain to which E1 and E3 bind tightly and mutually exclusively (Dardel et al., 1993;Kalia et al., 1993;Lessard and Perham, 1995;Lessard et al., 1996); and (iii) a C-terminal 28 kDa catalyt...

The advent of direct electron detectors has enabled the routine use of single-particle cryo-electron microscopy (EM) approaches to determine structures of a variety of protein complexes at near-atomic resolution. Here, we report the development of methods to account for local variations in defocus and beam-induced drift, and the implementation of a data-driven dose compensation scheme that significantly improves the extraction of high-resolution information recorded during exposure of the specimen to the electron beam. These advances enable determination of a cryo-EM density map for β-galactosidase bound to the inhibitor phenylethyl β-D-thiogalactopyranoside where the ordered regions are resolved at a level of detail seen in X-ray maps at ∼ 1.5 Å resolution. Using this density map in conjunction with constrained molecular dynamics simulations provides a measure of the local flexibility of the non-covalently bound inhibitor and offers further opportunities for structure-guided inhibitor design.

Conformational searching is a basic approach in theoretical and computational chemistry, and molecular dynamics [MD] simulation is a powerful computational tool to study structural, thermodynamic, and kinetic properties of molecular systems. In this paper, we report a new MD simulation method with the primary goal of improving dramatically the conformational searching efficiency in an MD simulation in order to study slow events in physics, chemistry, and biology. This new MD simulation method was based upon a new equation of motion in which a guiding force was introduced, in addition to the instantaneous force, to accelerate the systematic motion. This guiding force may be calculated as a time average of the instantaneous force from the trajectory obtained from the very same MD simulation. Bonded substructures were defined for molecular systems in order to enhance effectively both the inter-and intramolecular systematic motions. The improvement of the overall conformational searching efficiency and the possible alterations of ensemble properties and the conformational distribution of the system were investigated through comparative simulations of two peptide systems, an alanine dipeptide and a 16-residue synthetic peptide, both in vacuum and in explicit water. We demonstrated that the self-guided MD simulation method improved conformational searching efficiency but did not significantly alter the ensemble average properties and the conformational distributions of the systems. The successful helix-folding simulations of the 16-residue synthetic peptide both in vacuum and in explicit water clearly showed that the self-guided MD simulations achieved a dramatic enhancement in the conformational searching efficiency and showed an extraordinary ability to overcome energy barriers, as compared to the conventional MD simulations. Our results suggest that this new MD simulation method may be used as a powerful tool to study many important yet slow events or processes in physics, chemistry, and biology.

Molecular dynamics (MD) simulations of heptane/vapor, hexadecane/vapor, water/vapor, hexadecane/water, and dipalmitoylphosphatidylcholine (DPPC) bilayers and monolayers are analyzed to determine the accuracy of treating long-range interactions in interfaces with the isotropic periodic sum (IPS) method. The method and cutoff (rc) dependences of surface tensions, density profiles, water dipole orientation, and electrostatic potential profiles are used as metrics. The water/vapor, heptane/vapor, and hexadecane/vapor interfaces are accurately and efficiently calculated with 2D IPS (rc=10 A). It is demonstrated that 3D IPS is not practical for any of the interfacial systems studied. However, the hybrid method PME/IPS [Particle Mesh Ewald for electrostatics and 3D IPS for Lennard-Jones (LJ) interactions] provides an efficient way to include both types of long-range forces in simulations of large liquid/vacuum and all liquid/liquid interfaces, including lipid monolayers and bilayers. A previously published pressure-based long-range LJ correction yields results similar to those of PME/IPS for liquid/liquid interfaces. The contributions to surface tension of LJ terms arising from interactions beyond 10 A range from 13 dyn/cm for the hexadecane/vapor interface to approximately 3 dyn/cm for hexadecane/water and DPPC bilayers and monolayers. Surface tensions of alkane/vapor, hexadecane/water, and DPPC monolayers based on the CHARMM lipid force fields agree very well with experiment, whereas surface tensions of the TIP3P and TIP4P-Ew water models underestimate experiment by 16 and 11 dyn/cm, respectively. Dipole potential drops (DeltaPsi) are less sensitive to long-range LJ interactions than surface tensions. However, DeltaPsi for the DPPC bilayer (845+/-3 mV proceeding from water to lipid) and water (547+/-2 mV for TIP4P-Ew and 521+/-3 mV for TIP3P) overestimate experiment by factors of 3 and 5, respectively, and represent expected deficiencies in nonpolarizable force fields.

Isotropic periodic sum ͑IPS͒ is a method for the calculation of long-range interactions in molecular simulation based on the homogeneity of simulation systems. Three IPS models, 3D IPS, 2D IPS, and 1D IPS have been developed for three common types of homogeneous systems. Based on the fact that 3D IPS can well describe the long-range interactions of a heterogeneous system if a local region larger than the homogeneity scale is used, this work presents a method based on 3D IPS to calculate long-range interactions for all kinds of simulation systems, including homogeneous, heterogeneous, and finite systems. Unlike the original 3D IPS method that uses a local region defined by the cutoff distance, this method uses a local region larger than that defined by the cutoff distance to reach the homogeneity scale. To efficiently calculate interactions within such a large local region, this method split long-range interactions into two parts, a cutoff part and a long-range part. The cutoff part is calculated by summing over atom pairs within a cutoff range ͑about 10 Å͒, and the long-range part is calculated using the discrete fast Fourier transform ͑DFFT͒ technique. This method is applied to electrostatic and van der Waals interactions for both periodic and non-periodic systems. Example simulations demonstrate that this method can accurately and efficiently calculate long-range interactions for molecular simulation.