Rational optimization of peptides and TCR sequences requires the determination of the binding free energy component associated with each side chain involved in the interaction between the TCR and the p-MHC complex. We have developed or adapted several free energy calculation methods to address this question, including an MMGB-SA approach and alchemical free energy calculations using thermodynamical integration. These methods are now used to optimize several TCR sequences that have been shown to play an important role in a patient’s immune responses. They will be used for adoptive transfer therapies. Similarly, tumour-specific peptides optimized with these techniques will be used for vaccination trials.
Most force fields are distance-dependent, making the most convenient expression for these Cartesian coordinates. Yet the comparatively rigid nature of bonds which occur between specific atoms, and in essence, defines what is meant by the designation molecule , make an internal coordinate system the most logical representation. In some fields the IC representation (bond length, angle between bonds, and twist angle of the bond as shown in the figure) is termed the Z-matrix or torsion angle representation. Unfortunately, continuous motions in Cartesian space often require discontinuous angular branches in internal coordinates, making it relatively hard to work with force fields in the internal coordinate representation, and conversely a simple displacement of an atom in Cartesian space may not be a straight line trajectory due to the prohibitions of the interconnected bonds. Thus, it is very common for computational optimizing programs to flip back and forth between representations during their iterations. This can dominate the calculation time of the potential itself and in long chain molecules introduce cumulative numerical inaccuracy. While all conversion algorithms produce mathematically identical results, they differ in speed and numerical accuracy.  Currently, the fastest and most accurate torsion to Cartesian conversion is the Natural Extension Reference Frame (NERF) method.