Cluster Interface / Interface Similarity
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# Cluster Interface / Interface Similarity

## Some Other Insights

### PatchBag

#### Introduction

Previous Works

Several algorithms were developed to identify surface similarities, independent of the overall protein folds. These algorithms represent the surface shapes in various ways, such as

• Alpha Shapes and Delaunay Triangulations
• Three-Dimensional Zernike Descriptors (3DZD)
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• or an unordered collection of the three-dimensional (3D) coordinates of the surface atoms
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• Some of these algorithms were implemented for a fast 3D comparison of protein surfaces
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In addition, algorithms were developed dedicatedly to compare interfaces - the functional part of the surface. The available interface-comparison and interface clustering algorithms are usually limited to specific interface types, such as

Other methods based on local structural surface comparison have been employed for

• pocket comparison
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• and interface prediction, for instance,
• predicting protein-protein interacting residues
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• or finding ligand binding sites
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What PatchBag Has Fulfilled

Here, we present a novel geometry-based approach, named PatchBag, for characterizing and comparing protein surfaces or sub-surfaces (interface) in an accurate and highly efficient manner.

• In contrast to other interface-comparison tools, Patchbag is applicable for comparing interfaces of any type, as it does not require any information from the specific partner of the protein of interest.
• PatchBag represents protein surfaces or interfaces as vectors that count the number of appearances of various geometrical types of small surface units, defined as surface patches.
• This is known as the bag-of-words approach (BOW), where the surface is described as an unordered collection of local features.
• The advantage of using BOWs is that it is magnitudes faster to compare vectors than to compare the original objects.
• Indeed, the BOW approach is extensively used in large search systems such as web search engines.
• BOW algorithms were also used in the context of protein study, as for example in SVM-Fold to detect protein sequence homology, in FragBag to rapidly retrieve protein structures from the Protein Data Bank (PDB), and to discriminate native structures from structure prediction decoys.
• In PatchBag, we define local surface patches by the coordinates of the C-alpha atom of an exposed residue and their nearest C-alpha atoms that are not consecutive along the protein chain.

#### Calculating protein surfaces or interface similarities using PatchBag

Given a library L < patch_size, library_size > , we characterize a protein surface or subsurface P by its PatchBag vector of library_size entries; the vector represents the number of times each library-patch best approximates a surface patch in P. We calculate the similarity between two protein surfaces by the cosine distance of their corresponding PatchBag vectors – see equation (2). We refer to 1 - the cosine angle between two PatchBag vectors as “PatchBag distance”.

\begin{aligned} \text{PatchBag\_Distance}(P_{1},P_{2})=1-\frac{P_{1}P_{2}^{T}}{\sqrt{P_{1}P_{1}^{T}}\sqrt{P_{2}P_{2}^{T}}},\, (2) \end{aligned}

### InterComp

iAlign was developed (Gao and Skolnick, 2010a). It is a protein–protein interface comparison method based on an extension of the Kabsch algorithm (Kabsch, 1976), also used in TM-align, that will optionally allow for sequence-order independent comparisons for interfaces. However, it utilizes a definition of protein interface, where the interfacial residues are collected across both the protein chains involved in the interaction. This means that the mutual position of the patches of interfacial residues must be known before any comparison can be performed against a template. Thus, iAlign can only be used if the complete interface is known, e.g. for comparing known interfaces, and not for searching for interfacial residues on a monomer structure.

## Reference

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