The Exploration of Protein Electrostatics Through NMR Chemical Shift Perturbations

Understanding the relationship between protein structure and function is paramount to gaining insight into important biological mechanisms. In this context, pH often plays a significant role. The organization of charge within a protein prepares it to form intra-/inter-molecular interactions as the environmental pH changes. Studying the pKa values of titratable groups in a protein allows us to understand its electrostatic network. Computational pKa values are influenced by a microscopic environment and are often compared to macroscopic pKa values derived from NMR experiments. In this work we aim to understand the impact of pH on NMR chemical shift perturbations such that we can bridge the gap between computational and experimental observables. Peptide model systems have historically been used in NMR spectroscopy to detangle the many contributions which compose the observable NMR chemical shift. Utilizing molecular dynamics simulations, we sampled the conformational preferences of model tripeptides each containing one of the four titratable groups (aspartic acid, glutamic acid, histidine or lysine) in either a protonated or deprotonated state. The conformational ensembles obtained during the simulations were then used to compute pH-dependent NMR chemical shift perturbations for each nucleus in the tripeptides. The perturbations agree well with experimental findings and elucidate the relationship between charge and chemical shift. Furthermore, these results allow for better interpretation of NMR spectra and the possible integration of pH in chemical shift prediction paradigms. Although random coil chemical shifts serve as the basis for chemical shift prediction and interpretation, the complexity of the protein environment can produce drastically different behaviors. In the second study, we investigate the ability to utilize peptide derived chemical shift perturbations along with through-space electrostatic and conformational effects to compute pH-dependent NMR chemical shifts of the dynamic ensembles produced by constant pH molecular dynamics (CpHMD). Hen egg white lysozyme (HEWL) is an appropriate benchmark protein to probe the efficacy of a new protocol which fortifies the microscopic pKa values from simulation with macroscopic influences. The inclusion of the pH-dependent chemical shift contribution improved the results from the empirical chemical shift predictor for both 15N and 1H atoms and added dimensionality to the CpHMD simulations informing pH-dependent conformational fluctuations in HEWL. The newly derived macroscopic pKa values from simulation were directly compared to the experimental pKa values. Lastly, hisactophilin, a highly charged protein, is studied in order to identify critical residues that trigger the pH-dependent switching behavior of a post-translational modification. Hisactophilin has an N-terminal myristoyl group which is buried inside the beta-trefoil cavity in pH values greater than 7.5. However, at pH values lower than 6.5, the myristoyl group is accessible and may incorporate itself into an external lipid membrane. The small pH range where this switching behavior occurs likely corresponds with the protonation event of one or a few titratable residues. Implicit and explicit solvent CpHMD simulations allow us to explore the residues involved in the pH-dependent mechanism and formulate conclusions about charge redistribution.PHDBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163051/1/eartikis_1.pd

Bernoulli selecting processes in actuarial decisions

Bernoulli selecting processes are generally considered as valuable analytical tools for making decisions in many disciplines of particular theoretical and practical importance. The present paper concentrates on the formulation, investigation and actuarial applications of a stochastic model describing a Bernoulli selecting process. It is shown that the formulated stochastic model can substantially support the applicability of such a selecting process for making insurance decisions incorporating significant elements of proactivity.peer-reviewe