Fig. 4: Using TERP to explain VAMPnets for molecular dynamics simulations of alanine dipeptide in vacuum.

a Representative conformational states of alanine dipeptide labeled I, II, III. b, c Projected converged states are highlighted in three different colors as obtained by VAMPnets along (ϕ, ψ) dihedral angles. 713 different configurations are chosen for TERP. The first and second dominant features are highlighted using colored (⋆) in (b) and (c), respectively. d\({{{{\mathcal{U}}}}}^{\, j}\) vs. j, e\({{{{\mathcal{S}}}}}^{\, j}\) vs. j, fθ ^j vs. j, and gζ ^j vs. j plots for a specific black-box prediction with configuration ϕ = 0.084, ψ = 0.007, θ = 0.237, ω = 2.990 radians, showing optimal interpretation occurring at j = 2. h High-dimensional neighborhood data projected onto 1-d using LDA for improved similarity measure. Binarizing the class prediction probabilities of the neighborhood using a threshold of 0.5 results in explanation and not explanation classes, respectively. The LDA projection separates the two regimes of prediction probability, showing meaningful projection. Average similarity error, ΔΠ defined in Equation (9) per datapoint for i Euclidean, and j LDA-based similarity, respectively. Comparison between (i) and (j) shows minimal error for LDA-based similarity, specifically demonstrated for an input space constructed from the four dihedral angles plus one pure noise, four pure noise, and four correlated features with partial noise, respectively. The input space for no actual data and four pure noise features in (i) establishes a baseline, showing that the Euclidean similarity will include significant error even when one redundant feature is included. All the calculations were performed in 100 independent trials to appropriately examine the effects.