Nonequilibrium Self-Assembly Time Forecasting by the Stochastic Landscape Method

Abstract

Many biological systems rely on the ability to self-assemble target structures from different molecular building blocks using nonequilibrium drives, stemming, for example, from chemical potential gradients. The complex interactions between the different components give rise to a rugged energy landscape with a plethora of local minima on the dynamic pathway to the target assembly. Exploring a toy physical model of multicomponents nonequilibrium self-assembly, we demonstrate that a segmented description of the system dynamics can be used to provide predictions of the first assembly times. We show that for a wide range of values of the nonequilibrium drive, a log-normal distribution emerges for the first assembly time statistics. Based on data segmentation by a Bayesian estimator of abrupt changes (BEAST), we further present a general data-based algorithmic scheme, namely, the stochastic landscape method (SLM), for assembly time predictions. We demonstrate that this scheme can be implemented for the first assembly time forecast during a nonequilibrium self-assembly process, with improved prediction power compared to a naïve guess based on the mean remaining time to the first assembly. Our results can be used to establish a general quantitative framework for nonequilibrium systems and to improve control protocols of nonequilibrium self-assembly processes.

A Stochastic Landscape Approach for Protein Folding State Classification

“…The Stochastic Landscape Classification (SLC) is an empirical approach to detect and classify protein states along a CV trajectory. 57 The key idea is to segment the trajectory data using the BEAST algorithm and exploit the statistical information on the segments as input for the unsupervised classification of the protein states. Unlike the Stochastic Landscape Method, developed for self-assembly inference, 57 the proposed technique does not rely on learning from previous data.…”

“… 57 The key idea is to segment the trajectory data using the BEAST algorithm and exploit the statistical information on the segments as input for the unsupervised classification of the protein states. Unlike the Stochastic Landscape Method, developed for self-assembly inference, 57 the proposed technique does not rely on learning from previous data. A prerequisite is that the protein visits each relevant metastable state along the path a few times.…”

“…The third step involves directly applying the BEAST algorithm to the data, considering only trend changes, so the CV trajectory is divided into segments. Fourth, we focus on extracting stochastic coordinates 57 from each segment of the data, including the mean, standard deviation (STD), and average trend. To ensure comparability across different segments, we standardize these coordinates by subtracting the mean value of each coordinate from all corresponding coordinates and then dividing the result by the standard deviation.…”

“…As a result, it becomes feasible to automatically find trajectory segments assosiated with a metastable state by detecting trend changes. This approach has been recently demonstrated for predicting self-assembly times in a toy physical model of interacting particles under nonequilibrium conditions …”

“…This approach has been recently demonstrated for predicting self-assembly times in a toy physical model of interacting particles under nonequilibrium conditions. 57 …”