  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. Our new framework is generalizable and can be used to
investigate the uncertainty of a wide variety of target properties in
biomolecular systems.
