An antisymmetric neural network to predict free energy changes in protein variants

Abstract

Abstract The prediction of free energy changes upon protein residue variations is an important application in biophysics and biomedicine. Several methods have been developed to address this problem so far, including physical-based and machine learning models. However, most of the current computational tools, especially data-driven approaches, fail to incorporate the antisymmetric basic thermodynamic principle: a variation from wild-type to a mutated form of the protein structure ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>W</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">→</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) and its reverse process ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">→</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>W</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) must have opposite values of the free energy difference: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msub> <mml:mi>G</mml:mi> <mml:mrow> <mml:mi>W</mml:mi> <mml:mi>M</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msub> <mml:mi>G</mml:mi> <mml:mrow> <mml:mi>M</mml:mi> <mml:mi>W</mml:mi> </mml:mrow> </mml:msub> </mml:math> . Here, we build a deep neural network system that, by construction, satisfies the antisymmetric properties. We show that the new method (ACDC-NN) achieved comparable or better performance with respect to other state-of-the-art approaches on both direct and reverse variations, making this method suitable for scoring new protein variants preserving the antisymmetry. The code is available at: https://github.com/compbiomed-unito/acdc-nn .