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. We also 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. Further more, 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. Finally, our new framework is generalizablemore »
- Authors:
-
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Purdue Univ., West Lafayette, IN (United States). Dept. of Mathematics
- Publication Date:
- Research Org.:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1255409
- Report Number(s):
- PNNL-SA-110085
Journal ID: ISSN 1540-3459; KJ0401000
- Grant/Contract Number:
- AC05-76RL01830
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Multiscale Modeling & Simulation
- Additional Journal Information:
- Journal Volume: 13; Journal Issue: 4; Journal ID: ISSN 1540-3459
- Publisher:
- SIAM
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; uncertainty quantification; coarse graining; stochastic; biomolecular conformation fluctuation; polynomial chaos; compressive sensing method; model reduction
Citation Formats
Lei, Huan, Yang, Xiu, Zheng, Bin, Lin, Guang, and Baker, Nathan A. Constructing Surrogate Models of Complex Systems with Enhanced Sparsity: Quantifying the Influence of Conformational Uncertainty in Biomolecular Solvation. United States: N. p., 2015.
Web. doi:10.1137/140981587.
Lei, Huan, Yang, Xiu, Zheng, Bin, Lin, Guang, & Baker, Nathan A. Constructing Surrogate Models of Complex Systems with Enhanced Sparsity: Quantifying the Influence of Conformational Uncertainty in Biomolecular Solvation. United States. https://doi.org/10.1137/140981587
Lei, Huan, Yang, Xiu, Zheng, Bin, Lin, Guang, and Baker, Nathan A. Thu .
"Constructing Surrogate Models of Complex Systems with Enhanced Sparsity: Quantifying the Influence of Conformational Uncertainty in Biomolecular Solvation". United States. https://doi.org/10.1137/140981587. https://www.osti.gov/servlets/purl/1255409.
@article{osti_1255409,
title = {Constructing Surrogate Models of Complex Systems with Enhanced Sparsity: Quantifying the Influence of Conformational Uncertainty in Biomolecular Solvation},
author = {Lei, Huan and Yang, Xiu and Zheng, Bin and Lin, Guang and Baker, Nathan A.},
abstractNote = {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. We also 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. Further more, 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. Finally, our new framework is generalizable and can be used to investigate the uncertainty of a wide variety of target properties in biomolecular systems.},
doi = {10.1137/140981587},
journal = {Multiscale Modeling & Simulation},
number = 4,
volume = 13,
place = {United States},
year = {Thu Nov 05 00:00:00 EST 2015},
month = {Thu Nov 05 00:00:00 EST 2015}
}
Web of Science
Works referenced in this record:
Molecular Dynamics: Survey of Methods for Simulating the Activity of Proteins
journal, May 2006
- Adcock, Stewart A.; McCammon, J. Andrew
- Chemical Reviews, Vol. 106, Issue 5
Progress in the prediction of pKa values in proteins
journal, October 2011
- Alexov, Emil; Mehler, Ernest L.; Baker, Nathan
- Proteins: Structure, Function, and Bioinformatics, Vol. 79, Issue 12
Anisotropy of Fluctuation Dynamics of Proteins with an Elastic Network Model
journal, January 2001
- Atilgan, A. R.; Durell, S. R.; Jernigan, R. L.
- Biophysical Journal, Vol. 80, Issue 1
Biomolecular Applications of Poisson-Boltzmann Methods
book, January 2005
- Baker, Nathan A.
- Reviews in Computational Chemistry
Harmonic dynamics of proteins: normal modes and fluctuations in bovine pancreatic trypsin inhibitor.
journal, November 1983
- Brooks, B.; Karplus, M.
- Proceedings of the National Academy of Sciences, Vol. 80, Issue 21
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
journal, February 2009
- Bruckstein, Alfred M.; Donoho, David L.; Elad, Michael
- SIAM Review, Vol. 51, Issue 1, p. 34-81
The restricted isometry property and its implications for compressed sensing
journal, May 2008
- Candès, Emmanuel J.
- Comptes Rendus Mathematique, Vol. 346, Issue 9-10, p. 589-592
Decoding by Linear Programming
journal, December 2005
- Candes, E. J.; Tao, T.
- IEEE Transactions on Information Theory, Vol. 51, Issue 12
Solvent-accessible surfaces of proteins and nucleic acids
journal, August 1983
- Connolly, M.
- Science, Vol. 221, Issue 4612
Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces
journal, January 2014
- Constantine, Paul G.; Dow, Eric; Wang, Qiqi
- SIAM Journal on Scientific Computing, Vol. 36, Issue 4
Stable recovery of sparse overcomplete representations in the presence of noise
journal, January 2006
- Donoho, D. L.; Elad, M.; Temlyakov, V. N.
- IEEE Transactions on Information Theory, Vol. 52, Issue 1
A non-adapted sparse approximation of PDEs with stochastic inputs
journal, April 2011
- Doostan, Alireza; Owhadi, Houman
- Journal of Computational Physics, Vol. 230, Issue 8
Biomolecular Simulation: A Computational Microscope for Molecular Biology
journal, June 2012
- Dror, Ron O.; Dirks, Robert M.; Grossman, J. P.
- Annual Review of Biophysics, Vol. 41, Issue 1
Multi-element probabilistic collocation method in high dimensions
journal, March 2010
- Foo, Jasmine; Karniadakis, George Em
- Journal of Computational Physics, Vol. 229, Issue 5
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
journal, November 2008
- Foo, Jasmine; Wan, Xiaoliang; Karniadakis, George Em
- Journal of Computational Physics, Vol. 227, Issue 22
Sparse grid collocation schemes for stochastic natural convection problems
journal, July 2007
- Ganapathysubramanian, Baskar; Zabaras, Nicholas
- Journal of Computational Physics, Vol. 225, Issue 1
Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight
journal, July 1996
- Genz, Alan; Keister, B. D.
- Journal of Computational and Applied Mathematics, Vol. 71, Issue 2
Dynamics of a small globular protein in terms of low-frequency vibrational modes.
journal, June 1983
- Go, N.; Noguti, T.; Nishikawa, T.
- Proceedings of the National Academy of Sciences, Vol. 80, Issue 12
The Split Bregman Method for L1-Regularized Problems
journal, January 2009
- Goldstein, Tom; Osher, Stanley
- SIAM Journal on Imaging Sciences, Vol. 2, Issue 2
Gaussian Dynamics of Folded Proteins
journal, October 1997
- Haliloglu, Turkan; Bahar, Ivet; Erman, Burak
- Physical Review Letters, Vol. 79, Issue 16
Influence of Grid Spacing in Poisson–Boltzmann Equation Binding Energy Estimation
journal, July 2013
- Harris, Robert C.; Boschitsch, Alexander H.; Fenley, Marcia O.
- Journal of Chemical Theory and Computation, Vol. 9, Issue 8
The interpretation of protein structures: Estimation of static accessibility
journal, February 1971
- Lee, B.; Richards, F. M.
- Journal of Molecular Biology, Vol. 55, Issue 3
Finding Deterministic Solution From Underdetermined Equation: Large-Scale Performance Variability Modeling of Analog/RF Circuits
journal, November 2010
- Li, Xin
- IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 29, Issue 11
An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
journal, May 2009
- Ma, Xiang; Zabaras, Nicholas
- Journal of Computational Physics, Vol. 228, Issue 8
An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations
journal, May 2010
- Ma, Xiang; Zabaras, Nicholas
- Journal of Computational Physics, Vol. 229, Issue 10
Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation
journal, January 2012
- Narayan, Akil; Xiu, Dongbin
- SIAM Journal on Scientific Computing, Vol. 34, Issue 3
Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation
journal, January 2013
- Narayan, Akil; Xiu, Dongbin
- SIAM Journal on Scientific Computing, Vol. 35, Issue 5
An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
journal, January 2008
- Nobile, F.; Tempone, R.; Webster, C. G.
- SIAM Journal on Numerical Analysis, Vol. 46, Issue 5
Sparse Legendre expansions via <mml:math altimg="si12.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-minimization
journal, May 2012
- Rauhut, Holger; Ward, Rachel
- Journal of Approximation Theory, Vol. 164, Issue 5
Biomolecular electrostatics and solvation: a computational perspective
journal, November 2012
- Ren, Pengyu; Chun, Jaehun; Thomas, Dennis G.
- Quarterly Reviews of Biophysics, Vol. 45, Issue 4
Solvent accessible surface area and excluded volume in proteins
journal, September 1984
- Richmond, Timothy J.
- Journal of Molecular Biology, Vol. 178, Issue 1
Uncertainty Quantification in MD Simulations. Part I: Forward Propagation
journal, January 2012
- Rizzi, F.; Najm, H. N.; Debusschere, B. J.
- Multiscale Modeling & Simulation, Vol. 10, Issue 4
Uncertainty Quantification in MD Simulations. Part II: Bayesian Inference of Force-Field Parameters
journal, January 2012
- Rizzi, F.; Najm, H. N.; Debusschere, B. J.
- Multiscale Modeling & Simulation, Vol. 10, Issue 4
Implicit solvent models
journal, April 1999
- Roux, Benoı̂t; Simonson, Thomas
- Biophysical Chemistry, Vol. 78, Issue 1-2
Environment and exposure to solvent of protein atoms. Lysozyme and insulin
journal, September 1973
- Shrake, A.; Rupley, J. A.
- Journal of Molecular Biology, Vol. 79, Issue 2
Conformational change of proteins arising from normal mode calculations
journal, January 2001
- Tama, F.; Sanejouand, Y. -H.
- Protein Engineering, Design and Selection, Vol. 14, Issue 1
Basis adaptation in homogeneous chaos spaces
journal, February 2014
- Tipireddy, Ramakrishna; Ghanem, Roger
- Journal of Computational Physics, Vol. 259
Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis
journal, August 1996
- Tirion, Monique M.
- Physical Review Letters, Vol. 77, Issue 9
Probing the Pareto Frontier for Basis Pursuit Solutions
journal, January 2009
- van den Berg, Ewout; Friedlander, Michael P.
- SIAM Journal on Scientific Computing, Vol. 31, Issue 2
Structure of bovine pancreatic trypsin inhibitor
journal, December 1984
- Wlodawer, Alexander; Walter, Jochen; Huber, Robert
- Journal of Molecular Biology, Vol. 180, Issue 2
High-Order Collocation Methods for Differential Equations with Random Inputs
journal, January 2005
- Xiu, Dongbin; Hesthaven, Jan S.
- SIAM Journal on Scientific Computing, Vol. 27, Issue 3
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
journal, January 2002
- Xiu, Dongbin; Karniadakis, George Em
- SIAM Journal on Scientific Computing, Vol. 24, Issue 2
STOCHASTIC COLLOCATION ALGORITHMS USING l1-MINIMIZATION
journal, January 2012
- Yan, Liang; Guo, Ling; Xiu, Dongbin
- International Journal for Uncertainty Quantification, Vol. 2, Issue 3
Adaptive ANOVA decomposition of stochastic incompressible and compressible flows
journal, February 2012
- Yang, Xiu; Choi, Minseok; Lin, Guang
- Journal of Computational Physics, Vol. 231, Issue 4
Reweighted minimization method for stochastic elliptic differential equations
journal, September 2013
- Yang, Xiu; Karniadakis, George Em
- Journal of Computational Physics, Vol. 248
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
journal, January 2008
- Yin, Wotao; Osher, Stanley; Goldfarb, Donald
- SIAM Journal on Imaging Sciences, Vol. 1, Issue 1
Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions
journal, January 2012
- Zhang, Zhongqiang; Choi, Minseok; Karniadakis, George Em
- SIAM Journal on Scientific Computing, Vol. 34, Issue 2
A Recursive Sparse Grid Collocation Method for Differential Equations with White Noise
journal, January 2014
- Zhang, Z.; Tretyakov, M. V.; Rozovskii, B.
- SIAM Journal on Scientific Computing, Vol. 36, Issue 4
Works referencing / citing this record:
A comparative study of coarse-graining methods for polymeric fluids: Mori-Zwanzig vs. iterative Boltzmann inversion vs. stochastic parametric optimization
journal, July 2016
- Li, Zhen; Bian, Xin; Yang, Xiu
- The Journal of Chemical Physics, Vol. 145, Issue 4
Calibration of reduced-order model for a coupled Burgers equations based on PC-EnKF
journal, January 2018
- Wang, Yuepeng; Cheng, Yue; Zhang, Zongyuan
- Mathematical Modelling of Natural Phenomena, Vol. 13, Issue 2
Probabilistic surrogate models for uncertainty analysis: Dimension reduction‐based polynomial chaos expansion
journal, November 2019
- Son, Jeongeun; Du, Yuncheng
- International Journal for Numerical Methods in Engineering, Vol. 121, Issue 6