Predictions of protein chemical shifts and protein slow motions

Nuclear magnetic resonance spectroscopy (NMR) is one of the most powerful biophysical techniques for studying biomacromolecules. The advances of NMR techniques are often facilitated by the development of computational methods for the purpose of data interpretation and analyses. In this way, more information is extracted from the experimental measurements and complementary descriptions are given to details elusive to NMR probes, so that the structural and dynamical behavior of the biomolecule can be adequately described. Hence the two major goals of this thesis are: (i) To calculate chemical shift anisotropy (CSA) accurately and to understand how CSA is influenced by the local environment. (ii) To predict and characterize important metastable conformations of proteins probed in NMR relaxation experiments.;The first aspect is covered by three chapters (Chapter 2--4), where CSA calculations using QM and QM/MM models are described and compared. First, we used a small fragment (NMA3) model to determine the effect of vibrational motion on the magnitude and orientation of CSAs. Next, we applied the same model to predict chemical shift tensors and achieve qualitative agreement with experimental measurements for the GB1 protein. Later we showed that a more expanded AF-QM/MM (automated fragment quantum mechanical/molecular mechanical) model is able to provide better quantitative predictions to chemical shift tensors via an appropriate representation of environmental effects. Our study is expected to compensate for the lack of direct experimental measurements of CSAs, and help uncover the rich structural information hidden in CSA data.;The second aspect is covered by four chapters (Chapter 5--8), where we used the loop motion of triosephosphate isomerase (TIM) as our primary model to study protein conformational changes. To corroborate the "population shift" theory, conventional MD simulations was first performed to show that metastable states of TIM can be induced and stabilized. Then adaptively biased molecular dynamics (ABMD) simulations were used to predict and characterize the metastable conformations for monomeric TIM. In order to characterize the free energy landscape of this loop motion accurately and efficiently, an iterative approach combining ABMD and umbrella sampling was developed. Subsequently, this approach was applied to understand why TIM is only active as a dimer from energy and dynamics perspectives. Futhermore, we extended the ABMD method so that the metastable states of proteins can be predicted from their essential motions. The details of the methods used to predict and characterize protein minor conformations are described, providing insights into the energy and dynamics programmed in protein functions.