Constructing Surrogate Models of Complex Systems with Enhanced Sparsity: Quantifying the Influence of Conformational Uncertainty in Biomolecular Solvation

Abstract

Biomolecules exhibit conformational fluctuations near equilibrium states, inducing uncertainty in various biological properties in a dynamic way. We have developed a general method to quantify the uncertainty of target properties induced by conformational fluctuations. Using a generalized polynomial chaos (gPC) expansion, we construct a surrogate model of the target property with respect to varying conformational states. To alleviate the high-dimensionality of the corresponding stochastic space, we propose a method to increase the sparsity of the gPC expansion by defining a set of conformational “active space” random variables. With the increased sparsity, we employ the compressive sensing method to accurately construct the surrogate model. We demonstrate the performance of the surrogate model by evaluating fluctuation-induced uncertainty in solvent-accessible surface area for the bovine trypsin inhibitor protein system and show that the new approach offers more accurate statistical information than standard Monte Carlo approaches. Furthermore, the constructed surrogate model also enables us to directly evaluate the target property under various conformational states, yielding a more accurate response surface than standard sparse grid collocation methods. In particular, the new method provides higher accuracy in high-dimensional systems, such as biomolecules, where sparse grid performance is limited by the accuracy of the computed quantity of interest. Our new framework is generalizable and can be used to investigate the uncertainty of a wide variety of target properties in biomolecular systems.

A bi-fidelity surrogate modeling approach for uncertainty propagation in three-dimensional hemodynamic simulations

“…As an alternative, data-fit surrogate models aim to build an empirical approximation of the full-order model using supervised learning from the full-fidelity simulation data (i.e., training data) at selected collocation points in the parameter space, which is thus nonintrusive to the code. There are many different ways to construct a data-fit approximation, including Gaussian process (GP) [51,52], radial basis [53], neural networks [54][55][56], and polynomial chaos expansion (PCE) [57][58][59][60], among others. Data-fit surrogate models are preferable in hemodynamics modeling due to their non-intrusive nature and several prior studies have begun to emerge in the past a few years.…”

Rank adaptive tensor recovery based model reduction for partial differential equations with high-dimensional random inputs

“…To alleviate the difficulty, modifications of these methods have been actively introduced by exploiting certain properties of the underlying problem. For example, sparse (generalized) polynomial chaos (gPC) expansions [6,7,8,9,10,11] are developed through using the sparsity in spectral approximations. Moreover, the stochastic collocation method [3,12,4] is reformulated as a tensor style quadrature problem in [13], which shows that the corresponding collocation coefficients can be efficiently computed through tensor recovery techniques.…”

Probabilistic surrogate models for uncertainty analysis: Dimension reduction‐based polynomial chaos expansion

“…The SG projection minimizes the error resulting from truncation used in gPC expansions and converts the original stochastic model into a set of coupled deterministic models. The new‐coupled deterministic models are often termed as surrogate models that approximate the statistical information of the original stochastic system . Since the surrogate model is used to describe the original system, the existing computer program has to be modified, which is the main reason the SG‐based gPC is called as intrusive method.…”

“…The new-coupled deterministic models are often termed as surrogate models that approximate the statistical information of the original stochastic system. 12 Since the surrogate model is used to describe the original system, the existing computer program has to be modified, which is the main reason the SG-based gPC is called as intrusive method. It is important to note that each model in the resulting coupled deterministic system (or surrogate models) describes the dynamics of gPC coefficients of a model response, which can be solved numerically.…”