Fig. 1
From: Learning dynamical information from static protein and sequencing data
Inference scheme for estimating transition networks and mean first passage times (MFPTs). We apply the protocol to test data generated from a Gaussian Mixture Model (GMM; Supplementary Methods). a Inputs are the instantaneously measured data, sampled here from a ten-dimensional GMM with five Gaussians, plotted in the first three principal components (PCs); colors denote the Gaussian that a point was sampled from. b Top: a GMM is fit to the samples to construct the empirical probability distribution, which is then converted to the energy landscape using Eq. (1). Background color indicates the projection of the empirical energy landscape onto the first two PCs. Minimum-energy paths (MEPs, gray lines) between minima 1–5 on the landscape are calculated using the NEB algorithm (Supplementary Methods). Bottom: disconnectivity graph illustrating minima on the energy landscape (circles) and saddle points between them (squares). c A Markov state model (MSM) is constructed with transition rates given by Eq. (2) and solved to predict the MFPTs between discrete states (top right; Methods). MFPTs predicted by the MSM agree with direct estimates from Brownian dynamics simulations in the inferred energy landscape (top left; Supplementary Methods). MFPTs calculated in a reduced four-dimensional space using the scaling given in Eq. (3) recover the MFPTs accurately (bottom left). Without the appropriate scaling, the predicted MFPTs are inaccurate (bottom right).
