Protein Geometry and the Conformal Space

• Grant number: 25/19235-5
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: November 01, 2025
• End date: October 31, 2030
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Carlile Campos Lavor
• Grantee: Guilherme Philippi
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/08706-1 - Numerical optimization, AP.TEM

Abstract

The intersection of spheres plays a central role in the combinatorial model of the Molecular Distance Geometry Problem (MDGP), a classical formulation of the problem of determining molecular structures from exact distance data. However, when the distances provided by Nuclear Magnetic Resonance (NMR) experiments are represented as intervals, it becomes necessary to consider intersections of spherical shells, which are traditionally addressed through sampling techniques and interval arithmetic. In this project, we propose to investigate the use of Conformal Geometric Algebra as an alternative for describing spheres and spherical shells. This formulation enables the direct computation of spherical shell intersections without resorting to point sampling, integrating the combinatorial approach of the MDGP, based on search trees, with a representation that more naturally reflects the continuous characteristics of experimental data. The goal is to develop a theoretical and computational framework to handle interval distances with greater precision and efficiency. (AU)