Verification of correctness for multipole electrostatic gradients.

<p><b>A.</b> Analytical gradients were calculated for every torsional degree of freedom in a test set of proteins (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0195578#sec002" target="_blank">Methods</a>) without incorporating reference atoms to address the frame rotation problem. In addition, a numerical approximation to the gradient was calculated by evaluating the electrostatic energy for conformations in which each degree of freedom was perturbed by +/- 1.0x10^-3 degrees, in turn. <b>B.</b> The same data is shown for the restricted range of -5 to 5 kcal-mol^-1-deg^-1, within which ~77% of the data points fall. <b>C., D.</b> Similar data to panels A and B are shown, with the difference that the analytical gradients now include the reference atom treatment to account for frame rotation. <b>E., F.</b> Similar data to panels C and D, in which the dipole and quadrupole parameters for the two atom types that suffer from the split frame problem have been artificially zeroed out.</p

Evaluating SASA derivatives from intersectional information.

<p>Expressions for the derivative of SASA of a molecule with respect to its torsional degrees of freedom can be deduced from the arcs that define the intersections of spherical overlaps, without differentiating the full expression for each atomic SASA. <b>A.</b> An atom is shown rendered as a grey sphere with a patch buried by a neighboring atom colored in white. The unit vector <b><i>e</i></b> shows the direction from the atom under consideration to the neighboring atom responsible for the overlap. The first contribution to the SASA derivative comes from motions that change the distance between two atoms. In the absence of other atoms, the rotation of the neighboring atom about the atom of interest serves only to relocate the buried patch without changing the SASA. <b>B.</b> The change in the size of the buried patch due to another atom with respect to interatomic separation can be determined by applying the law of cosines to the intersectional geometry for the spheres. <b>C.</b> When multiple patches overlap, the surface of the sphere that is occluded is described by a set of arcs. In this case, there are two arcs. One arc goes clockwise from <b><i>v</i></b>_<b>1</b> to <b><i>v</i></b>_<b>2</b>, and a second arc completes the cycle clockwise from <b><i>v</i></b>_<b>2</b> to <b><i>v</i></b>_<b>1</b>. The contribution to the change in SASA due to altered distance to a neighboring atom is modified relative to the two atom case in that only a fraction of the buried patch is independent of other atoms. In this example, the change in patch size with respect to interatomic separation in panel A is scaled by . In addition, a second contribution to the SASA derivative results from distance-preserving rotations of intersecting atoms about the atom under consideration. Infinitesimal rotations perpendicular to the line between the points that define each arc (<b><i>v</i></b>_<b>1</b> and <b><i>v</i></b>_<b>2</b> in panel C) sweep out an infinitesimal slice of surface area (shown as a grey box).</p

The frame rotation problem.

<p>Rotation about a torsion bond (for example, the bond colored green in the figure) changes the distances between atoms upstream and downstream of the bond. It also causes a rotation of the coordinate frame centered on the atom at the downstream end of the bond (atom 2 in the figure). This frame rotation results in a change in the dipole (denoted by the orange lobes) and quadrupole moments for the atom in the global frame. Thus, the energetic interaction between atoms 1 and 2 has a derivative with respect to the torsion angle even though the distance between the atoms remains constant.</p

Multipole energy term derivatives for Gō framework in vector form.

<p>Multipole energy term derivatives for Gō framework in vector form.</p

The split coordinate frame problem.

<p><b>A.</b> Cycles in molecular topology complicate a tree-based description of molecular topology. Proline residues contain a cycle, as the side chain emanating from the <i>C</i>_<i>α</i> atom forms a closed ring, reentering the main chain at the N atom. Because of the requirement for ring closure, the torsion values (indicated by gray arrows) are not independent. <b>B.</b> The strategy for handling cycles in the Rosetta program is to create an artificial break in the ring, restoring a tree-like topology. The requirement for closure is enforced with the introduction of a ‘virtual’ N atom (denoted by the hollow typeface). Supplemental constraints are added to the energy potential to ensure that the virtual atom overlays its real atom counterpart. <b>C.</b> Interaction between ring breakage and local coordinate definitions complicate gradient calculation. A coordinate system is defined for each atom to properly orient its dipole and quadrupole moments in the global frame. This local frame is defined for each atom in terms of its bonded neighbors. For the N atom of proline, the z-axis is defined to lie along its bond with the <i>C</i>_<i>α</i> atom, and the x-axis lies in the plane formed by the z-axis and the direction towards the <i>C</i>_<i>δ</i> atom. When the bond between the N and <i>C</i>_<i>δ</i> atoms is artificially broken to reestablish a tree-like topology, rotations such as that about the torsion indicated by the star can lead to alteration of the local coordinate frame at the N atom (the two configurations of the <i>C</i>_<i>δ</i> atom give rise to the two local coordinate frames shown inside the proline ring). This change in local frame effects the interactions between the N atom and every other atom in the molecule, resulting in an energy gradient between atoms that are on the same side of a rotatable bond. Strong constraints to enforce the overlap between the ‘real’ and ‘virtual’ copies of the N atom can minimize the value of this gradient. However, this effect represents a violation of the original assumption of Noguti and Gō that energy potentials depend only on interatomic distances [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0195578#pone.0195578.ref031" target="_blank">31</a>].</p

Examples of re-usable features and widgets shared across ROSIE servers.

<p>(<b>a</b>) Global job queue page, which can be filtered by specific application (e.g., docking). (<b>b</b>) Self-registration (not required). (<b>c</b>) Coordinate file uploader using Protein Databank format, (<b>d</b>) Automatic visualization of uploaded coordinate file, (<b>e</b>) Score vs. root mean squared deviation plotting widget, (<b>f</b>) Automatic rendering of final models, which can be customized by developer for specific applications (in this case, RNA <i>de novo</i> modeling).</p

Public Rosetta servers available prior to current work, in chronological order of development.

<p>Public Rosetta servers available prior to current work, in chronological order of development.</p

Files required for app implementation and their role.

<p>Files required for app implementation and their role.</p

Schematic of ROSIE (Rosetta Online Server that Includes Everyone), which permits a number of front-ends for job submission by users, a number of servers (stored in a unified database), and a number of backends to allow expansion of computational resources.

<p>Schematic of ROSIE (Rosetta Online Server that Includes Everyone), which permits a number of front-ends for job submission by users, a number of servers (stored in a unified database), and a number of backends to allow expansion of computational resources.</p