Using an appropriate first order derivative approach, develop a solution to discover the lowest potential energy for ONE (1) of the residue L-lysine atoms utilizing a 3D function. Propose an alternative algorithm to solve this problem with clear explanation supported by mathematical functions. The coordinates extracted from the RSCS Protein Data Bank website are given in FIGURE 1.

1aki - Notepad File Edit Format View Help SCALE3 0.000000 0.000000 0.032769 0.00000 ATOM 1 N LYS A 1 5.365 2.342 -3.980 1.00 22.28 ATOM 2 CA LYS A 1 5.892 1.073 -3.427 1.00 21.12 ATOM 3 LYS A 1 4.741 2.264 -3.844 1.00 16.85 ATOM 4 0 LYS A 1 3.945 2.813 -3.081 1.00 18.94 ATOM 5 CB LYS A 1 6.872 2.435 -3.306 1.00 20.78 N C 1aki - Notepad File Edit Format View Help SCALE3 0.000000 0.000000 0.032769 0.00000 ATOM 1 N LYS A 1 5.365 2.342 -3.980 1.00 22.28 ATOM 2 CA LYS A 1 5.892 1.073 -3.427 1.00 21.12 ATOM 3 LYS A 1 4.741 2.264 -3.844 1.00 16.85 ATOM 4 0 LYS A 1 3.945 2.813 -3.081 1.00 18.94 ATOM 5 CB LYS A 1 6.872 2.435 -3.306 1.00 20.78 N C