Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape

Abstract

The size and shape of macromolecules such as proteins and nucleic acids play an important role in their functions. Prior efforts to quantify these properties have been based on various discretization or tessellation procedures involving analytical or numerical computations. In this article, we present an analytically exact method for computing the metric properties of macromolecules based on the alpha shape theory. This method uses the duality between alpha complex and the weighted Voronoi decomposition of a molecule. We describe the intuitive ideas and concepts behind the alpha shape theory and the algorithm for computing areas and volumes of macromolecules. We apply our method to compute areas and volumes of a number of protein systems. We also discuss several difficulties commonly encountered in molecular shape computations and outline methods to overcome these problems.

Insights into an Original Pocket-Ligand Pair Classification: A Promising Tool for Ligand Profile Prediction

“…Concerning the pocket space, we observe that small pockets tend to be more polar and to bind small and polar ligands, as previously observed [25], [27], [31]–[33]. These descriptors are in agreement with a PCA model developed in [28], which indicates that size and shape descriptors are the most important properties followed by polarity and charge.…”

Insights into an Original Pocket-Ligand Pair Classification: A Promising Tool for Ligand Profile Prediction

“…Concerning the pocket space, we observe that small pockets tend to be more polar and to bind small and polar ligands, as previously observed [25], [27], [31]–[33]. These descriptors are in agreement with a PCA model developed in [28], which indicates that size and shape descriptors are the most important properties followed by polarity and charge.…”

Dynamic void distribution in myoglobin and five mutants

“…We compute the average surface area from the snapshots taken from the simulation trajectory. SACA finds the average surface area of MB to be 16,550 ± 414 Å 2 and the result agrees favorably well with the surface area computed by a widely used method32. Using a similar procedure to SACA we also compute the protein volume.…”

Protein Structure Inspired Drug Discovery

“…[20] Statistical methods incorporate random surface alignments, global surface volume overlap Tanimoto coefficient, and lead to the generation of a composite SurfaceScreen Score. [20,[25][26][27][28] Fig 1 . Schema for identification and characterization of 3D protein structures with the potential to bind therapeutically active small molecules.…”

“…We next sought to identify small molecule ligands that have the potential to interact with identified pockets using our computational pipeline for docking and scoring (Fig 3). [19][20][21][23][24][25][26] Docking simulations were against a library of 60 million compounds optimized for use in this pipeline and represent a subset of the ZINC compound library. [58] The library was first filtered for properties that have been associated with oral FDA approved small molecule therapeutics, inclusive of molecular weight between 160-480 g/mol and total polar surface area <140 square Angstroms (i.e., <5 and <10 hydrogen-bond donors and acceptors, respectfully).…”

Insights into an Original Pocket-Ligand Pair Classification: A Promising Tool for Ligand Profile Prediction

“…Concerning the pocket space, we observe that small pockets tend to be more polar and to bind small and polar ligands, as previously observed [25], [27], [31]–[33]. These descriptors are in agreement with a PCA model developed in [28], which indicates that size and shape descriptors are the most important properties followed by polarity and charge.…”

Dynamic void distribution in myoglobin and five mutants

“…We compute the average surface area from the snapshots taken from the simulation trajectory. SACA finds the average surface area of MB to be 16,550 ± 414 Å 2 and the result agrees favorably well with the surface area computed by a widely used method32. Using a similar procedure to SACA we also compute the protein volume.…”

Protein Structure Inspired Drug Discovery

“…[20] Statistical methods incorporate random surface alignments, global surface volume overlap Tanimoto coefficient, and lead to the generation of a composite SurfaceScreen Score. [20,[25][26][27][28] Fig 1 . Schema for identification and characterization of 3D protein structures with the potential to bind therapeutically active small molecules.…”

“…We next sought to identify small molecule ligands that have the potential to interact with identified pockets using our computational pipeline for docking and scoring (Fig 3). [19][20][21][23][24][25][26] Docking simulations were against a library of 60 million compounds optimized for use in this pipeline and represent a subset of the ZINC compound library. [58] The library was first filtered for properties that have been associated with oral FDA approved small molecule therapeutics, inclusive of molecular weight between 160-480 g/mol and total polar surface area <140 square Angstroms (i.e., <5 and <10 hydrogen-bond donors and acceptors, respectfully).…”

Insights into an Original Pocket-Ligand Pair Classification: A Promising Tool for Ligand Profile Prediction

“…Concerning the pocket space, we observe that small pockets tend to be more polar and to bind small and polar ligands, as previously observed [25], [27], [31]–[33]. These descriptors are in agreement with a PCA model developed in [28], which indicates that size and shape descriptors are the most important properties followed by polarity and charge.…”

Dynamic void distribution in myoglobin and five mutants

“…We compute the average surface area from the snapshots taken from the simulation trajectory. SACA finds the average surface area of MB to be 16,550 ± 414 Å 2 and the result agrees favorably well with the surface area computed by a widely used method32. Using a similar procedure to SACA we also compute the protein volume.…”

Protein Structure Inspired Drug Discovery

“…[20] Statistical methods incorporate random surface alignments, global surface volume overlap Tanimoto coefficient, and lead to the generation of a composite SurfaceScreen Score. [20,[25][26][27][28] Fig 1 . Schema for identification and characterization of 3D protein structures with the potential to bind therapeutically active small molecules.…”

“…We next sought to identify small molecule ligands that have the potential to interact with identified pockets using our computational pipeline for docking and scoring (Fig 3). [19][20][21][23][24][25][26] Docking simulations were against a library of 60 million compounds optimized for use in this pipeline and represent a subset of the ZINC compound library. [58] The library was first filtered for properties that have been associated with oral FDA approved small molecule therapeutics, inclusive of molecular weight between 160-480 g/mol and total polar surface area <140 square Angstroms (i.e., <5 and <10 hydrogen-bond donors and acceptors, respectfully).…”