iMapD: intrinsic Map Dynamics exploration for uncharted effective free energy landscapes

TL;DR

The paper introduces iMapD, a geometry-based approach that couples atomistic/molecular dynamics with diffusion-map manifold learning to uncover and exploit low-dimensional, smooth regions of the effective free energy surface. By iteratively extending the identified manifold outward (predictor step) and reinitializing simulations with lifted ambient configurations (corrector step), iMapD accelerates exploration without imposing biases on the dynamics. Applied to alanine dipeptide and the Mga2 transmembrane dimer, the method discovers new metastable states and slow pathways with substantial computational savings (on the order of 10^3× for simple systems and ≥10^3× for more challenging, long-timescale transitions). This computer-assisted epiphany in slow-variable discovery enables efficient mapping of coarse-grained FES and rapid identification of slow coordinates, with potential integration into established MD platforms for automated enhanced sampling. The results demonstrate substantial practical impact for exploring biomolecular landscapes that are inaccessible to conventional long-timescale MD.

Abstract

We describe and implement iMapD, a computer-assisted approach for accelerating the exploration of uncharted effective Free Energy Surfaces (FES), and more generally for the extraction of coarse-grained, macroscopic information from atomistic or stochastic (here Molecular Dynamics, MD) simulations. The approach functionally links the MD simulator with nonlinear manifold learning techniques. The added value comes from biasing the simulator towards new, unexplored phase space regions by exploiting the smoothness of the (gradually, as the exploration progresses) revealed intrinsic low-dimensional geometry of the FES.

Figures (6)

• Figure 1: Pictorial illustration of the iMapD exploration procedure with one-dimensional (left panel) and two-dimensional (right panel) effective FES. In the top left inset, a good collective coordinate (s) is already available - the collective coordinates in the main panels are not a priori known. See full description in the text.
• Figure 2: Left panel: A long initial trajectory trapped in two nearby metastable wells is shown in the corresponding two-dimensional DMAP projection (a three-dimension DMAP space embedding is also reported in the inset on the right-hand side). Boundary points are identified (red circles) and extended outward (green stars). Local PCA suffices to lift to ambient space (see below). Middle panel: Short simulation runs are performed from previously extended boundary points. New configurations are generated and displayed (blue dots) in a two-dimensional (and in a three-dimensional) DMAP reduced space. Right panel: After two steps, two new potential wells are reached by some of the simulation frames. The "starting" portion of the FES geometry accessed by the initial simulations is marked in yellow - the rest has been revealed through exploration.
• Figure 3: The discovery process of the above Figure is redisplayed here as a Ramachandran plot. Two steps are sufficient to reveal two initially unknown metastable configurations of the molecule. At each step, before outward extension of the boundary, we also performed global PCA filtering of the data noise where $98\%$ of the variance was retained (see Materials and Methods below).
• Figure 4: Enhanced exploration of Mga2 dimer configurations represented on the free energy surface as a function of the first two global diffusion map coordinates, DC. (A) Configurations sampled from ten 100 ns long unbiased simulations initiated from a single configuration (black squares). Final configurations of 100 ns long unbiased simulations initialized from the first set of 16 newly projected structures (blue circles). (B) Final configurations of 100 ns long unbiased simulations started from the second set of 16 newly projected structures. (C) Configurations from the initial ten unbiased simulations that were extended and are here tracked up to 2 $\mathrm{\mu s}$, (D) from 2 to 3 $\mathrm{\mu s}$ (black squares), and from from 3 to 4 $\mathrm{\mu s}$ (magenta squares). The free energy surface was previously extracted from a 2.52 ms long equilibrium simulation.
• Figure 5: (Upper panel) Enhanced exploration represented in $u, v$ space. Angles were calculated on configurations sampled from cumulative trajectories simulated during the successive exploration phases and represented as blue squares. The free energy surface as a function of $u, v$ was extracted from a 2.52 ms long equilibrium simulation. (Lower panel) Distance separating the two TMH monitored during all the exploration phases. Insets show different representative structures of the dimer, with the reference residue W10 shown in yellow, and a schematic definition of $u$ and $v$.