Electrostatics analysis

Analysis of the electrostatic environment of both the wild type MAO-A and the R45W variant was done using our own computational model, described in detail in our previous studies^22,23. For this analysis we treated the reacting moiety (SRO and the truncated flavin cofactor, lumiflavin—abbrev. LFN) with the quantum treatment at the M06-2X/6–31 + G(d,p) level, while the rest of the solvated enzyme was represented only with point charges. This kind of representation ensures that the only interaction between the reacting moiety and its environment comes from Coulombic forces. Therefore, by performing quantum computations in the presence as well as in the absence of the point charges, we can evaluate the influence of the electrostatic environment on several parameters we consider to be important for catalysis (namely the energy barrier between the state of reactants and the transition state, charge transfer between serotonin and the truncated flavin cofactor, the dipole moment, and the energy gap between the two reacting molecular orbitals i.e., the HOMO–LUMO gap). For this approach we require ‘snapshots’ (i.e., characteristic structures) of our system in the state of reactants (R) and in the transition state (TS), as those are the two states relevant for evaluating catalysis. For the R45W variant, these snapshots were acquired from the above-described MD simulation, while for the wild type they were obtained from the simulation described in Ref.⁴⁵. For each simulation, we extracted 100 snapshots for both R and TS, giving us 400 in total. For all snapshots the energy and the electronic structure of our system were computed in the presence and in the absence of 13,193 point charges corresponding to the surrounding protein and water molecules. The electronic structure was analyzed using the Natural Bond Orbital v. 3.1 method⁵⁹. Analysis of the HOMO–LUMO gap was done by separately treating SRO and LFN in the same point charge surroundings. The HOMO of SRO was taken directly from the quantum computation, while the LUMO of LFN was approximated as the negative of the electronic affinity. All quantum computations were performed using the Gaussian09 program package⁶⁰.

Additionally, the electric field (ε→) at the midpoint between the C of SRO and the N of LFN was evaluated for all snapshots, by using the following fundamental expression:

where ϵ0 is the free space permittivity constant, qi is the charge of the i-th atom, ri is the distance of the i-th atom from the point of interest (i.e., the midpoint between the C of SRO and the N of LFN), and ri→ is the vector connecting the i-th atom and the point of interest. The dot product of the electric field vector and the dipole moment vector yields the free energy of the electrostatic interaction between the reacting moiety and the surrounding enzyme (Gelec). The difference in this value between R and TS gives the barrier change due to the (de)stabilizing interaction between the dipole moment and electric field vectors:

Note that the negative sign in the above expression comes from the opposite orientation definitions for the electric field and the dipole moment vectors—their parallel alignment results in stabilization (negative Gelec), while their antiparallel alignment results in destabilization (positive Gelec). When the electric field is given in MV/cm and the dipole moment in Debyes, the above expression needs to be multiplied by a factor of 0.048 to give the result in kcal/mol. This approach also allows us to analyze ΔGelec‡ in terms of contributions of individual amino acid residues.