Figure 1.

Schematic restraint vector r, an instantaneous path-increment $dL$ and the corresponding angle $\Xi$, which re-weights the adaptive bias coordinate towards an experimental distance information $d_{12}$ between a pair of amino-acids 1 and 2. In this article, we present a method for the coupling of experimental distance restraints along distances between 2 atoms ($d_{12}$) and multiple path-dependent biasing increments $\nabla H\left(B\right)$. We define a novel restrained biasing Hamiltonian $\nabla H{\left(B\right)}_R$ as the overlapping fraction of the path-dependent bias in the dynamical trajectory space with the experimental distance vector. We re-evaluate the un-biased Hamiltonian $H\left(A\right)$ using a renormalization technique, which leads to an accelerating hybrid Hamiltonian $H\left(C\right)$.