[Paper Review] Zepyros: A webserver to evaluate the shape complementarity of protein-protein interfaces

Mattia Miotto, Lorenzo Di Rienzo+3 more|arXiv (Cornell University)|Feb 10, 2024

Protein Structure and DynamicsBiochemistry, Genetics and Molecular Biology3 citations

TL;DR

Zepyros is a webserver that rapidly evaluates shape complementarity at protein-protein interfaces using Zernike polynomial decomposition of molecular surface patches. By computing Zernike distance between interacting surfaces and comparing it to random decoys, it quantifies complementarity with AUC up to 0.89, enabling fast, user-friendly assessment for drug design and protein engineering applications.

ABSTRACT

Shape complementarity of molecular surfaces at the interfaces is a well-known characteristic of protein-protein binding regions, and it is critical in influencing the stability of the complex. Measuring such complementarity is at the basis of methods for both the prediction of possible interactions and for the design/optimization of speficic ones. However, only a limited number of tools are currently available to efficiently and rapidly assess it. Here, we introduce Zepyros, a webserver for fast measuring of the shape complementarity between two molecular interfaces of a given protein-protein complex using structural information. Zepyros is implemented as a publicly available tool with a user-friendly interface. Our server can be found at the following link (all major browser supported): https://zepyros.bio-groups.com

Motivation & Objective

• To address the lack of efficient tools for assessing shape complementarity at protein-protein interfaces.
• To provide a fast, parameter-free method for quantifying local shape complementarity in protein complexes.
• To develop a user-friendly webserver that enables researchers without computational expertise to evaluate interface complementarity.
• To enable practical applications in protein interaction design, drug discovery, and stability analysis.
• To offer a reference framework comparing real interfaces with random decoys to assess significance.

Proposed method

• The method begins by identifying binding regions as residues with surface points within 3 Å of each other.
• Surface patches are rotated so their mean normal vectors align with the positive and negative z-axes, respectively.
• Each patch is projected onto a 2D plane within the unit circle, with pixel intensity weighted by distance from the cone origin.
• Projected maps are decomposed into Zernike polynomials using the formula $ f(r,\theta) = \sum_{n,m} c_n^m Z_n^m(r,\theta) $.
• Shape complementarity is measured as the Euclidean distance between the squared moduli of Zernike coefficients: $ D_z = \sqrt{\sum_{n,m} (|c_n^m| - |c_n^{m\prime}|)^2} $.
• The Zernike distance is compared against a distribution of distances from 100 random decoys on the target surface to assess significance.

Experimental results

Research questions

• RQ1 How accurately can Zernike polynomial decomposition quantify shape complementarity at protein-protein interfaces?
• RQ2 What is the optimal patch radius and expansion order for maximizing discrimination between real and random interfaces?
• RQ3 Can a parameter-free, fast method based on Zernike moments reliably distinguish biologically relevant interfaces from non-binding regions?
• RQ4 How does the Zernike distance distribution of real interfaces compare to that of random surface patches?
• RQ5 To what extent does shape complementarity correlate with complex stability, independent of electrostatic compatibility?

Key findings

• The method achieves an area under the ROC curve (AUC) of 0.80 for distinguishing binding from non-binding regions using a parameter-free approach.
• The highest AUC values (up to 0.89) are obtained with a patch radius of approximately 8 Å and an expansion order greater than 10.
• Zepyros computes results in under 3 minutes for average-sized proteins and under 5 minutes for larger complexes.
• The Zernike distance between real interface patches is significantly lower than that of random decoys, indicating higher shape complementarity in biologically relevant interfaces.
• The tool provides a reference distribution of Zernike distances from 100 random decoys, enabling statistical assessment of complementarity significance.
• The webserver supports PDB files up to 10 MB and is compatible with Chrome, Firefox, and Safari with JavaScript enabled.