Fig 1.
Sketch of the Low-Order-Value-Optimization (LOVO) problem in structural alignment: The goal is to minimize a function which assumes the lowest value of a set {fi} of concurrent functions in the same domain.
For each correspondence between atoms, there exists a function fi that provides the quality measure of the alignment (the score) as function of rotations and translations of one of the structures. The minimization of the score is performed by iterating between minimizing the fi corresponding to the current correspondence between atoms (steps of type A), followed by obtaining the correspondence that minimizes the score for each rotation-translation (steps of type B). This procedure is guaranteed to converge with the appropriate choices of the methods used in steps A and B [7, 10, 11].
Fig 2.
Analysis of the mobility of two simulations of a Burkholderia cepacia lipase [14] in mixtures of water and sorbitol.
Different RMSD profiles are observed: (A) The standard RMSD of Simulation 1 (black) is much lower than the RMSD of Simulation 2 (red). (B) RMSD as a function of the fraction of the atoms considered in the alignment. These plots indicate that in Simulation 2 (red), there is a subset of about 25 to 30% of the atoms which are responsible for the greater overall RMSD observed in panel (A). (C) In both simulations, 70% of the atoms can be superposed to less than 1Å (RMSDL—dotted lines, black for Simulation 1, red for Simulation 2). The remaining 30% of the atoms behave differently in each simulation (RMSDH—solid lines, same colors). (D) and (E) Superposition of the frames and coloring of the 70% least mobile atoms (blue) and 30% most mobile atoms (red) provides the structural basis for the differential RMSDs. (F) Structures of Simulation 2 colored according to the RMSF of each residue relative to the initial structure after alignment. All these plots and figures can be obtained from the output of MDLovoFit.
Fig 3.
Analysis of the mobility of a simulation of the Ligand Binding Domain Thyroid Hormone Receptor-β, in which the structure diverges with time [19].
(A) The standard Cα RMSD indicates an unfolding process in a high temperature simulation (black). The RMSD of an equilibrium room-temperature simulation is also shown (red). (B) The alignment between the first and last conformations of the unfolding simulation with variable ϕ indicates that there is a persistent subset of about 30% of backbone atoms that can be aligned to 2Å. (C) The 30% least mobile atoms display structural deviations of about 2Å relative to the initial structure (RMSDL), while the remaining structure diverges (RMSDH). (D) Superposition of the unfolding simulation frames using standard Cα alignment. (E) Superposition using MDLovoFit for 30% of Cα atoms (blue) highlights the existence of a well preserved structural core. The 70% most mobile atoms are shown in red. (F) Structure colored according to the RMSF of each residue relative to the initial structure after alignment.