Substrate Dipole Moment Calculations

Cartesian coordinates with orthogonal axes, a, c, and d, originating at the C2 atom of each substrate, matrix A = [a, c, and d], were determined from models of TPI and TPI-ribosome complexes bound with DHAP and GAP. Two vectors, C2C4 and C2C1, originating from carbon C2 and terminating at carbons, C4 and C1, respectively, were normalized into unit column vector coordinate files, a and b, with orthogonal axes a, c, and d (Table S5); c and d were determined from the cross products: c = a × b and d = a × c. The Cartesian coordinates were transformed into Q-Chem coordinates with orthogonal axes a”, b”, c”, and d”, matrix B = [a”, c”, d”] originating at the C2” atom (Table S6), and input into the Q-Chem server.³⁰a” and b” are the unit column vectors of C2”C4” and C2”C1”, respectively, and c” and d” were determined from the cross products: c” = a” × b” and d” = a” × c”. A total charge of −2 were assigned to each substrate to calculate the dipole moment, μ”, and the Q-Chem server,³⁰ accessed through the IQmol molecular viewer, was used with default settings to calculate the magnitude, in Debyes, D, and orientation of the molecular dipole moments, μ”, at the center of mass of each substrate. Orthogonal vectors in matrix A (Cartesian) and matrix B (Q-Chem) were used to generate rotational matrix M and convert μ” to μ in Cartesian coordinates using the matrix operation M = A × B^–1. This operation calculates the rotational matrix, M, needed to interconvert matrices A and B. Finally, the dipole moment in its original coordinates, μ, was obtained through the equation, μ = M × μ”. All calculations and matrix operations were performed in MATLAB version R2020b.