The concept of pair-wise forces. (A) Conventional MD uses the sum of all forces, , acting on a certain atom to derive the atomic motion. (B) In contrast, FDA works with pair-wise forces F
, which is the force calculated between each pair of atoms i, j during an MD simulation. (C) The total force F
atomic acting on an atom quickly decays to zero under equilibrium conditions. Observation of quickly decaying signals is not possible due to high equilibrium fluctuations. The plot shows only the x component of the xyz force vector for a single hydrogen bond O atom in the titin I27 domain . (D) In contrast, even in equilibrium, pair-wise forces will not average to zero. This allows to compare different (equilibrated) states of a system. The plot shows pair-wise forces between the O-H atoms for the same hydrogen bond as in Figure 1 C. (E) Approximations used to transform multi-body forces into a pair-wise representation. Only the force acting along the direction of atoms i, k for angles and i, l for dihedrals is considered. This is sufficient to detect even minor re-arrangements.