SES: memory requirements.

<p>Comparison of the peak memory needed to build and triangulate the SES for NanoShaper, EDTSurf, and MSMS.</p

SES: MSMS false positive identification of a cavity.

<p>In this figure, a schematic illustration of how the MSMS algorithm can confuse an accessible region with an internal cavity during the SES construction. The probe can roll both inside and outside. In MSMS, this task is performed in two separate steps. If self-intersections occur at the entrance(s) of a given region, they may lead to the depicted situation and to the incorrect detection of a cavity.</p

SES and Skin surface: build-up time comparison in seconds (NS stands for NanoShaper and Adj. for adjusted for different architecture performance).

<p>Timings for NS have been measured at a resolution that is not accurate below the second, while reported timings for the other approaches have been taken from the respective publications.</p

Skin surface: mesh quality.

<p>Comparison of the mesh of the Skin surface obtained by our algorithm (up) and CGAL (down) with a small detail highlighted.</p

Skin surface: performance.

<p>Execution times and memory usage are reported in the upper and lower panels, respectively. The scale for each molecule was set accordingly to that assigned by EDTSurf <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059744#pone.0059744-Xu1" target="_blank">[18]</a>.</p

Detail of the volume of the cavities obtained by NanoShaper on FAAH.

<p>Detail of the volume of the cavities obtained by NanoShaper on FAAH.</p

Cavity detection.

<p>Cavity detection for NanoShaper-built Gaussian, Skin, and SES.</p

Surfacing Steps.

<p>On the left are the steps involved in the surfacing pipeline. On the right are the corresponding outcomes. 1) The surface is computed or externally loaded, 2) the surface is ray-cast, 3) cavities are detected and possibly removed, 4) the surface is triangulated.</p

A general and Robust Ray-Casting-Based Algorithm for Triangulating Surfaces at the Nanoscale

<div><p>We present a general, robust, and efficient ray-casting-based approach to triangulating complex manifold surfaces arising in the nano-bioscience field. This feature is inserted in a more extended framework that: i) builds the molecular surface of nanometric systems according to several existing definitions, ii) can import external meshes, iii) performs accurate surface area estimation, iv) performs volume estimation, cavity detection, and conditional volume filling, and v) can color the points of a grid according to their locations with respect to the given surface. We implemented our methods in the publicly available NanoShaper software suite (<a href="http://www.electrostaticszone.eu" target="_blank">www.electrostaticszone.eu</a>). Robustness is achieved using the CGAL library and an <i>ad hoc</i> ray-casting technique. Our approach can deal with any manifold surface (including nonmolecular ones). Those explicitly treated here are the Connolly-Richards (SES), the Skin, and the Gaussian surfaces. Test results indicate that it is robust to rotation, scale, and atom displacement. This last aspect is evidenced by cavity detection of the highly symmetric structure of fullerene, which fails when attempted by MSMS and has problems in EDTSurf. In terms of timings, NanoShaper builds the Skin surface three times faster than the single threaded version in Lindow et al. on a 100,000 atoms protein and triangulates it at least ten times more rapidly than the Kruithof algorithm. NanoShaper was integrated with the DelPhi Poisson-Boltzmann equation solver. Its SES grid coloring outperformed the DelPhi counterpart. To test the viability of our method on large systems, we chose one of the biggest molecular structures in the Protein Data Bank, namely the 1VSZ entry, which corresponds to the human adenovirus (180,000 atoms after Hydrogen addition). We were able to triangulate the corresponding SES and Skin surfaces (6.2 and 7.0 million triangles, respectively, at a scale of 2 grids per Å) on a middle-range workstation.</p></div

Volume estimation for the FAAH protein.

<p>Estimated volume of the FAAH protein at varying grid resolutions and different molecular surface definitions. The upper panel represents a detailed comparison of the SES. Results show that NanoShaper SES after cavity removal is approximately equal to the main component generated by MSMS. In the lower panel for the Skin, we used a value of s = , for the Gaussian a value of B = , and for the SES a probe radius of Å.</p