Yammp: Development of a molecular mechanics program using the modular programming method

YUP.SCX: coaxing atomic models into medium resolution electron density maps

The structures of large macromolecular complexes in different functional states can be determined by cryo-electron microscopy, which yields electron density maps of low to intermediate resolutions. The maps can be combined with high-resolution atomic structures of components of the complex, to produce a model for the complex that is more accurate than the formal resolution of the map. To this end, methods have been developed to dock atomic models into density maps rigidly or flexibly, and to refine a docked model so as to optimize the fit of the atomic model into the map. We have developed a new refinement method called YUP.SCX. The electron density map is converted into a component of the potential energy function to which terms for stereochemical restraints and volume exclusion are added. The potential energy function is then minimized (using simulated annealing) to yield a stereochemically-restrained atomic structure that fits into the electron density map optimally. We used this procedure to construct an atomic model of the 70S ribosome in the pre-accommodation state. Although some atoms are displaced by as much as 33A, they divide themselves into nearly rigid fragments along natural boundaries with smooth transitions between the fragments.

A corkscrew model for dynamin constriction

Numerous vesiculation processes throughout the eukaryotic cell are dependent on the protein dynamin, a large GTPase that constricts lipid bilayers. We have combined X-ray crystallography and cryo-electron microscopy (cryo-EM) data to generate a coherent model of dynamin-mediated membrane constriction. GTPase and pleckstrin homology domains of dynamin were fit to cryo-EM structures of human dynamin helices bound to lipid in nonconstricted and constricted states. Proteolysis and immunogold labeling experiments confirm the topology of dynamin domains predicted from the helical arrays. Based on the fitting, an observed twisting motion of the GTPase, middle, and GTPase effector domains coincides with conformational changes determined by cryo-EM. We propose a corkscrew model for dynamin constriction based on these motions and predict regions of sequence important for dynamin function as potential targets for future mutagenic and structural studies.

DNA organization and thermodynamics during viral packing

An elastic DNA molecular mechanics model is used to compare DNA structures and packing thermodynamics in two bacteriophage systems, T7 and phi29. A discrete packing protocol allows for multiple molecular dynamics simulations of the entire packing event. In T7, the DNA is coaxially spooled around the cylindrical core protein, whereas the phi29 system, which lacks a core protein, organizes the DNA concentrically, but not coaxially. Two-dimensional projections of the packed structures from T7 simulations are consistent with cryo-electron micrographs of T7 phage DNA. The functional form of the force required to package the phi29 DNA is similar to forces determined experimentally, although the total free energy change is only 40% of the experimental value. Since electrostatics are not included in the simulations, this suggests that electrostatic repulsions are responsible for approximately 60% of the free energy required for packaging. The entropic penalty from DNA confinement has not been computed in previous studies, but it is often assumed to make a negligible contribution to the total work done in packing the DNA. Conformational entropy can be measured in our approach, and it accounts for 70-80% of the total work done in packing the elastic model DNA in both phages. For phi29, this corresponds to an entropic penalty of approximately 35% of the total work observed experimentally.

Evaluating and learning from RNA pseudotorsional space: quantitative validation of a reduced representation for RNA structure

Quantitatively describing RNA structure and conformational elements remains a formidable problem. Seven standard torsion angles and the sugar pucker are necessary to characterize the conformation of an RNA nucleotide completely. Progress has been made toward understanding the discrete nature of RNA structure, but classifying simple and ubiquitous structural elements such as helices and motifs remains a difficult task. One approach for describing RNA structure in a simple, mathematically consistent, and computationally accessible manner involves the invocation of two pseudotorsions, eta (C4'(n-1), P(n), C4'(n), P(n+1)) and theta (P(n), C4'(n), P(n+1), C4'(n+1)), which can be used to describe RNA conformation in much the same way that varphi and psi are used to describe backbone configuration of proteins. Here, we conduct an exploration and statistical evaluation of pseudotorsional space and of the Ramachandran-like eta-theta plot. We show that, through the rigorous quantitative analysis of the eta-theta plot, the pseudotorsional descriptors eta and theta, together with sugar pucker, are sufficient to describe RNA backbone conformation fully in most cases. These descriptors are also shown to contain considerable information about nucleotide base conformation, revealing a previously uncharacterized interplay between backbone and base orientation. A window function analysis is used to discern statistically relevant regions of density in the eta-theta scatter plot and then nucleotides in colocalized clusters in the eta-theta plane are shown to have similar 3-D structures through RMSD analysis of the RNA structural constituents. We find that major clusters in the eta-theta plot are few, underscoring the discrete nature of RNA backbone conformation. Like the Ramachandran plot, the eta-theta plot is a valuable system for conceptualizing biomolecular conformation, it is a useful tool for analyzing RNA tertiary structures, and it is a vital component of new approaches for solving the 3-D structures of large RNA molecules and RNA assemblies.

A structural model for the large subunit of the mammalian mitochondrial ribosome

Protein translation is essential for all forms of life and is conducted by a macromolecular complex, the ribosome. Evolutionary changes in protein and RNA sequences can affect the 3D organization of structural features in ribosomes in different species. The most dramatic changes occur in animal mitochondria, whose genomes have been reduced and altered significantly. The RNA component of the mitochondrial ribosome (mitoribosome) is reduced in size, with a compensatory increase in protein content. Until recently, it was unclear how these changes affect the 3D structure of the mitoribosome. Here, we present a structural model of the large subunit of the mammalian mitoribosome developed by combining molecular modeling techniques with cryo-electron microscopic data at 12.1A resolution. The model contains 93% of the mitochondrial rRNA sequence and 16 mitochondrial ribosomal proteins in the large subunit of the mitoribosome. Despite the smaller mitochondrial rRNA, the spatial positions of RNA domains known to be involved directly in protein synthesis are essentially the same as in bacterial and archaeal ribosomes. However, the dramatic reduction in rRNA content necessitates evolution of unique structural features to maintain connectivity between RNA domains. The smaller rRNA sequence also limits the likelihood of tRNA binding at the E-site of the mitoribosome, and correlates with the reduced size of D-loops and T-loops in some animal mitochondrial tRNAs, suggesting co-evolution of mitochondrial rRNA and tRNA structures.

Packaging double-helical DNA into viral capsids

DNA packaging in bacteriophage P4 has been examined using a molecular mechanics model with a reduced representation containing one pseudoatom per turn of the double helix. The model is a discretized version of an elastic continuum model. The DNA is inserted piecewise into the model capsid, with the structure being reoptimized after each piece is inserted. Various optimization protocols were investigated, and it was found that molecular dynamics at a very low temperature (0.3 K) produces the optimal packaged structure. This structure is a concentric spool, rather than the coaxial spool that has been commonly accepted for so many years. This geometry, which was originally suggested by Hall and Schellman in 1982 (Biopolymers Vol. 21, pp. 2011-2031), produces a lower overall elastic energy than coaxial spooling.

Ca2+-induced conformational transition in the inhibitory and regulatory regions of cardiac troponin I

Cardiac muscle activation is initiated by the binding of Ca(2+) to the single N-domain regulatory site of cardiac muscle troponin C (cTnC). Ca(2+) binding causes structural changes between cTnC and two critical regions of cardiac muscle troponin I (cTnI): the regulatory region (cTnI-R, residues 150-165) and the inhibitory region (cTnI-I, residues130-149). These changes are associated with a decreased cTnI affinity for actin and a heightened affinity for cTnC. Using Förster resonance energy transfer, we have measured three intra-cTnI distances in the deactivated (Mg(2+)-saturated) and Ca(2+)-activated (Ca(2+)-saturated) states in reconstituted binary (cTnC-cTnI) and ternary (cTnC-cTnI-cTnT) troponin complexes. Distance A (spanning cTnI-R) was unaltered by Ca(2+). Distances B (spanning both cTnI-R and cTnI-I) and C (from a residue flanking cTnI-I to a residue in the center of cTnI-R) exhibited Ca(2+)-induced increases of >8 A. These results compliment our previous determination of the distance between residues flanking cTnI-I alone. Together, the data suggest that Ca(2+) activation causes residues within cTnI-I to switch from a beta-turn/coil to an extended quasi-alpha-helical conformation as the actin-contacts are broken, whereas cTnI-R remains alpha-helical in both Mg(2+)- and Ca(2+)-saturated states. We have used the data to construct a structural model of the cTnI inhibitory and regulatory regions in the Mg(2+)- and Ca(2+)-saturated states.

Investigation of viral DNA packaging using molecular mechanics models

A simple molecular mechanics model has been used to investigate optimal spool-like packing conformations of double-stranded DNA molecules in viral capsids with icosahedral symmetry. The model represents an elastic segmented chain by using one pseudoatom for each ten basepairs (roughly one turn of the DNA double helix). Force constants for the various terms in the energy function were chosen to approximate known physical properties, and a radial restraint was used to confine the DNA into a sphere with a volume corresponding to that of a typical bacteriophage capsid. When the DNA fills 90% of the spherical volume, optimal packaging is obtained for coaxially spooled models, but this result does not hold when the void volume is larger. When only 60% of the spherical volume is filled with DNA, the lowest energy structure has two layers, with a coiled core packed at an angle to an outer coaxially spooled shell. This relieves bending strain associated with tight curvature near the poles in a model with 100% coaxial spooling. Interestingly, the supercoiling density of these models is very similar to typical values observed in plasmids in bacterial cells. Potential applications of the methodology are also discussed.

Constrained global optimization for estimating molecular structure from atomic distances

Finding optimal three-dimensional molecular configurations based on a limited amount of experimental and/or theoretical data requires efficient nonlinear optimization algorithms. Optimization methods must be able to find atomic configurations that are close to the absolute, or global, minimum error and also satisfy known physical constraints such as minimum separation distances between atoms (based on van der Waals interactions). The most difficult obstacles in these types of problems are that 1) using a limited amount of input data leads to many possible local optima and 2) introducing physical constraints, such as minimum separation distances, helps to limit the search space but often makes convergence to a global minimum more difficult. We introduce a constrained global optimization algorithm that is robust and efficient in yielding near-optimal three-dimensional configurations that are guaranteed to satisfy known separation constraints. The algorithm uses an atom-based approach that reduces the dimensionality and allows for tractable enforcement of constraints while maintaining good global convergence properties. We evaluate the new optimization algorithm using synthetic data from the yeast phenylalanine tRNA and several proteins, all with known crystal structure taken from the Protein Data Bank. We compare the results to commonly applied optimization methods, such as distance geometry, simulated annealing, continuation, and smoothing. We show that compared to other optimization approaches, our algorithm is able combine sparse input data with physical constraints in an efficient manner to yield structures with lower root mean squared deviation.

Structural studies of the tRNA domain of tmRNA

tmRNA is a small, stable prokaryotic RNA. It rescues ribosomes that have become stalled during the translation of mRNA fragments lacking stop codons, or during periods of tRNA scarcity. It derives its name from the presence of two separate domains, one that functions as a tRNA, and another that serves as an mRNA. We have carried out modeling and transient electric birefringence studies to determine the angle between the acceptor stem and anticodon stem of the tRNA domain of Eschericia coli tmRNA. The results of the modeling studies yielded an interstem angle of 110 degrees, in agreement with the lower end of the range of angles (111 degrees -137 degrees ) determined experimentally for various solution conditions. The range of experimental angles is greater than the angles observed for any of the tRNA crystal structures, in line with the presence of a shortened D stem. The secondary structure of the tRNA domain is conserved for all known tmRNA sequences, so we propose that the angle is also conserved. These results also suggest that the region of tmRNA between P2a and P2b may interact with the decoding site of the ribosome.

Three-dimensional placement of the conserved 530 loop of 16 S rRNA and of its neighboring components in the 30 S subunit

Nucleotides 518-533 form a loop in ribosomal 30 S subunits that is almost universally conserved. Both biochemical and genetic evidence clearly implicate the 530 loop in ribosomal function, with respect both to the accuracy control mechanism and to tRNA binding. Here, building on earlier work, we identify proteins and nucleotides (or limited sequences) site-specifically photolabeled by radioactive photolabile oligoDNA probes targeted toward the 530 loop of 30 S subunits. The probes we employ are complementary to 16 S rRNA nucleotides 517-527, and have aryl azides attached to nucleotides complementary to nucleotides 518, 522, and 525-527, positioning the photogenerated nitrene a maximum of 19-26 A from the complemented rRNA base. The crosslinks obtained are used as constraints to revise an earlier model of 30 S structure, using the YAMMP molecular modeling package, and to place the 530 loop region within that structure.

Exploring three-dimensional structures of the HIV-1 RNA/tRNALys3 initiation complex

Human immunodeficiency virus type 1 (HIV-1) uses host tRNA as a primer for reverse transcription of its viral RNA. The 3' terminal 18 nucleotides of human tRNALys3 are complementary to the primer binding site on the viral RNA. A secondary structure model for the HIV-1 RNA/tRNALys3 initiation complex has been proposed that includes additional base-pairing between the tRNA and the HIV-1 RNA beyond the 18 nucleotides of the primer binding site. Included in these interactions is base-pairing between the anticodon of tRNALys3 and an A-rich loop in the HIV-1 secondary structure. The tRNA and HIV-1 RNA are significantly unfolded from their native structures in order to form the initiation complex proposed in this model. We have found several problems with the proposed secondary structure in our efforts to build a three-dimensional model that is compatible with it. The additional interactions between the tRNA and viral RNA cause the structure to be topologically knotted. This poses a problem for folding of the initiation complex and transcription by reverse transcriptase. We have also not been able to build any all-atom models based on known RNA structures that follow the secondary structure model in the extended tRNA/HIV-1 RNA complex. Finally, beyond the primer binding site interaction, subsequent biochemical and genetic studies have given further insight into the structure of the initiation complex. These results call into question some of the extended HIV-1 RNA/tRNA interactions that have been proposed.

To knot or not to knot? Examination of 16S ribosomal RNA models

The presence of topological knots in large RNA structures is highly unlikely given that 1) no RNA structures determined thus far contain topological knots, 2) secondary structure maps for most RNA molecules are knot free, 3) there are no known RNA topoisomerases, and 4) it is difficult to imagine how knots could be formed specifically and uniquely during transcription. Since native RNA structures probably lack topological knots, models of these RNA molecules should be free of knots as well. Therefore, we have examined four existing models for the 30S ribosomal subunit to determine if any of the three domains of the 16S rRNA molecule is knotted. We found that all but one model had at least one knotted domain. We conclude that models of large RNA molecules should be examined for knotting before publication.

A molecular builder for carbohydrates: application to polysaccharides and complex carbohydrates

A new procedure (POLYS) for producing three-dimensional structures of polysaccharides and complex carbohydrates is described. This employs a builder concept combining a database of monosaccharide structures with a database containing information on populations of independent neighboring glycosidic linkages in disaccharide fragments. The computer program is written in C, and it can cope with both the complexity and the diversity of carbohydrates and the unique topological features arising from multiple branching. A simple ASCII syntax was developed for describing the primary structures in accordance with IUPAC nomenclature. The translation of the primary structure is made through the combined use of a lexical analyzer and a command interpreter. In this way the program can be considered as a compiler of primary structures of carbohydrates. However, it also generates secondary and tertiary structures in the form of Cartesian coordinates in formats used by most molecular mechanics programs and packages. In our laboratory POLYS was exhaustively tested on standard homopolysaccharide systems such as cellulose and mannan and found to work very well. We now report the ease of use and the efficiency of the molecular builder in applications to more complex carbohydrate systems. These include the structural exploration of a pentaantennary oligosaccharide having 135 residues, the complex family of pectic polysaccharides including the organization and distribution of side chains (arabinan, arabinogalactan, and galactan) on the rhamnogalacturonan backbone.

Molecular modeling of closed circular DNA thermodynamic ensembles

Many modeling studies of supercoiled DNA are based on equilibrium structures from theoretical calculations or energy minimization. Since closed circular DNAs are flexible, it is possible that errors are introduced by calculating properties from a single minimum energy structure, rather than from a complete thermodynamic ensemble. We have investigated this question using molecular dynamics simulations on a low resolution molecular mechanics model in which each base pair is represented by three points (a plane). This allows the inclusion of sequence-dependent variations of tip, inclination, and twist. Three kinds of sequences were tested: (1) homogeneous DNA, in which all base pairs have the helicoidal parameters of an ideal, average B-DNA; (2) random sequence DNA; and (3) curved DNA. We examined the rate of convergence of various structural parameters. Convergence for most of these is slowest for homogeneous sequences, more rapid for random sequences, and most rapid for curved sequences. The most slowly converging parameter is the antipodes profile. In a plasmid with N base pairs (bp), the antipodes distance is the distance dij from base pair i to base pair j halfway around the plasmid, j = i + N/2. The antipodes profile at time tau is a plot of dij over the range i = 1, N/2. In a homogeneous plasmid, convergence requires that the antipodes profile averaged over time must be flat. Even in the small plasmids examined here, the average properties of the ensembles were found to differ from those of static equilibrium structures. These effects will be even more dramatic for larger plasmids. Further, average and dynamic properties are affected by both plasmid size and sequence.

Molecular dynamics simulations of small DNA plasmids: effects of sequence and supercoiling on intramolecular motions

Small (600 base pair) DNA plasmids were modeled with a simplified representation (3DNA) and the intramolecular motions were studied using molecular mechanics and molecular dynamics techniques. The model is detailed enough to incorporate sequence effects. At the same time, it is simple enough to allow long molecular dynamics simulations. The simulations revealed that large-scale slithering occurs in a homogeneous sequence. In a heterogeneous sequence, containing numerous small intrinsic curves, the centers of the curves are preferentially positioned at the tips of loops. With more curves than loop tips (two in unbranched supercoiled DNA), the heterogeneous sequence plasmid slithers short distances to reposition other curves into the loop tips. However, the DNA is immobilized most of the time, with the loop tips positioned over a few favored curve centers. Branching or looping also appears in the heterogeneous sequence as a new method of repositioning the loop tips. Instead of a smooth progression of increasing writhing with increasing linking difference, theoretical studies have predicted that there is a threshold between unwrithed and writhed DNA at a linking difference between one and two. This has previously been observed in simulations of static structures and is demonstrated here for dynamic homogeneous closed DNA. Such an abrupt transition is not found in the heterogeneous sequence in both the static and dynamic cases.

Modeling the structure of the ribosome

Considering the size and complexity of the ribosome and the growing body of data from a wide range of experiments on ribosomal structure, it is becoming increasingly important to develop tools that facilitate the development of reliable models for the ribosome. We use a combination of manual and computer-based approaches for building and refining models of the ribosome and other RNA-protein complexes. Our methods are aimed at determining the range of models compatible with the data, making quantitative statements about the positional uncertainties (resolution) of different regions, identifying conflicts in the data, establishing which regions of the ribosome need further experimental exploration, and, where possible, predicting the outcome of future experiments. Our previous low-resolution model for the small subunit of the Escherichia coli ribosome is briefly reviewed, along with progress on atomic resolution modeling of the mRNA-tRNA complex and its interaction with the decoding site of the 16S RNA.