Configurational Entropy of Folded Proteins and its Importance for Intrinsically Disordered Proteins

Many pairwise additive force fields are in active use for intrinsically disordered proteins (IDPs) and regions (IDRs), some of which modify energetic terms to improve description of IDPs/IDRs, but are largely in disagreement with solution experiments for the disordered states. We have evaluated representative pairwise and many-body protein and water force fields against experimental data on representative IDPs and IDRs, a peptide that undergoes a disorder-to-order transition, and for seven globular proteins ranging in size from 130-266 amino acids. We find that force fields with the largest statistical fluctuations consistent with the radius of gyration and universal Lindemann values for folded states simultaneously better describe IDPs and IDRs and disorder to order transitions. Hence the crux of what a force field should exhibit to well describe IDRs/IDPs is not just the balance between protein and water energetics, but the balance between energetic effects and configurational entropy of folded states of globular proteins

Understanding Structure and Kinetics of Aβ Monomer and Fibril Ensembles Using Molecular Simulations

My doctoral research involves the characterization of the structure, kinetics, and function of amyloid-β (Aβ) proteins by computational means via atomistic and coarse-grained molecular dynamics simulations. Aβ has critical clinical relevance as one of the key hallmarks of Alzheimer’s disease pathology. My research has four primary foci. The first of these is studying the properties of the Aβ monomer, an intrinsically disordered protein (IDP), using all-atom simulations. Using a combination of two enhanced sampling techniques - replica-exchange molecular dynamics simulations (REMD) and temperature cool walking (TCW), I have shown that the addition of paramagnetic tags in paramagnetic relaxation enhancement (PRE) experiments of IDPs, perturbs the structural ensembles of the Aβ monomer with an increase in structural order, and the PRE experimental observables are thus not a true representation of the unmodified monomers in solution. Very few experimental techniques can provide residue-specific structural information about IDPs because of their disordered nature, and my work provides valuable insights into the usefulness of commonly used PRE experiments in the IDP field. IDP structural ensembles are usually generated using REMD simulations with fixed charge protein models. Most computationally generated IDP ensembles using physics-based models are more ordered and compact than expected. The current focus is mostly on improving or modifying parameters in fixed charge force fields to generate more accurate conformational ensembles for IDPs. By comparing different sampling techniques and fixed charge force fields (with and without IDP-specific parameter modification) for the Aβ42 and Aβ43 peptide, I show that the sampling method used to generate the ensemble is equally important as the “correct” force field. The IDP ensembles generated using TCW have better convergence and experimental agreement than the REMD-ensemble for same amount of sampling. Thus, TCW is a better sampling alternative to REMD simulations.Fixed charge force fields used in IDP simulations are parameterized on folded protein data, and thus predict overly structured and globular configurations for IDPs, which are usually more disordered and solvent exposed compared to folded proteins. Consequently, it is important that the molecular interactions are modeled as accurately as possible during IDP simulations. In chapter 4, using the cationic 24-residue Histatin 5 peptide as a test system, I show that the computationally generated ensemble using the polarizable AMOEBA force field is more consistent with experimental radius of gyration and secondary structure data. Thus, the many-body polarization effect that is ignored in fixed charge force field is important for simulating IDP systems across a range of solvent-exposed to folded states, capturing the true breadth of structural biology. The last major emphasis of this dissertation research, is investigating of kinetic elongation mechanisms of amyloid fibril (aggregates of Aβ monomer) using an in-house coarse-grained protein model. In chapter 5, I studied the mechanism of amyloid fibrils elongation via binding of monomers from solution, and demonstrated that the monomer structure only influences the kinetics, but not the overall binding mechanism. This result provides a fundamental understanding of growth of amyloid fibrils

Understanding Structure and Kinetics of Aβ Monomer and Fibril Ensembles Using Molecular Simulations

My doctoral research involves the characterization of the structure, kinetics, and function of amyloid-β (Aβ) proteins by computational means via atomistic and coarse-grained molecular dynamics simulations. Aβ has critical clinical relevance as one of the key hallmarks of Alzheimer’s disease pathology. My research has four primary foci. The first of these is studying the properties of the Aβ monomer, an intrinsically disordered protein (IDP), using all-atom simulations. Using a combination of two enhanced sampling techniques - replica-exchange molecular dynamics simulations (REMD) and temperature cool walking (TCW), I have shown that the addition of paramagnetic tags in paramagnetic relaxation enhancement (PRE) experiments of IDPs, perturbs the structural ensembles of the Aβ monomer with an increase in structural order, and the PRE experimental observables are thus not a true representation of the unmodified monomers in solution. Very few experimental techniques can provide residue-specific structural information about IDPs because of their disordered nature, and my work provides valuable insights into the usefulness of commonly used PRE experiments in the IDP field. IDP structural ensembles are usually generated using REMD simulations with fixed charge protein models. Most computationally generated IDP ensembles using physics-based models are more ordered and compact than expected. The current focus is mostly on improving or modifying parameters in fixed charge force fields to generate more accurate conformational ensembles for IDPs. By comparing different sampling techniques and fixed charge force fields (with and without IDP-specific parameter modification) for the Aβ42 and Aβ43 peptide, I show that the sampling method used to generate the ensemble is equally important as the “correct” force field. The IDP ensembles generated using TCW have better convergence and experimental agreement than the REMD-ensemble for same amount of sampling. Thus, TCW is a better sampling alternative to REMD simulations.Fixed charge force fields used in IDP simulations are parameterized on folded protein data, and thus predict overly structured and globular configurations for IDPs, which are usually more disordered and solvent exposed compared to folded proteins. Consequently, it is important that the molecular interactions are modeled as accurately as possible during IDP simulations. In chapter 4, using the cationic 24-residue Histatin 5 peptide as a test system, I show that the computationally generated ensemble using the polarizable AMOEBA force field is more consistent with experimental radius of gyration and secondary structure data. Thus, the many-body polarization effect that is ignored in fixed charge force field is important for simulating IDP systems across a range of solvent-exposed to folded states, capturing the true breadth of structural biology. The last major emphasis of this dissertation research, is investigating of kinetic elongation mechanisms of amyloid fibril (aggregates of Aβ monomer) using an in-house coarse-grained protein model. In chapter 5, I studied the mechanism of amyloid fibrils elongation via binding of monomers from solution, and demonstrated that the monomer structure only influences the kinetics, but not the overall binding mechanism. This result provides a fundamental understanding of growth of amyloid fibrils

D3R Grand Challenge 4: Ligand Similarity and MM-GBSA-Based Pose Prediction and Affinity Ranking for BACE-1 Inhibitors

The Drug Design Data Resource (D3R) Grand Challenges present an opportunity to assess, in the context of a blind predictive challenge, the accuracy and the limits of tools and methodologies designed to help guide pharmaceutical drug discovery projects. Here, we report the results of our participation in the D3R Grand Challenge 4, which focused on predicting the binding poses and affinity ranking for compounds targeting the beta-amyloid precursor protein (BACE-1). Our ligand similarity-based protocol using HYBRID (OpenEye Scientific Software) successfully identified poses close to the native binding mode for most of the ligands with less than 2 A RMSD accuracy. Furthermore, we compared the performance of our HYBRID-based approach to that of AutoDock Vina and Dock 6 and found that HYBRID performed better here for pose prediction. We also conducted end-point free energy estimates on protein-ligand complexes using molecular mechanics combined with generalized Born surface area method (MM-GBSA). We found that the binding affinity ranking based on MM-GBSA scores have poor correlation with the experimental values. Finally, the main lessons from our participation in D3R Grand Challenge 4 suggest that: i) the generation of the macrocycles conformers is a key step for successful pose prediction, ii) the protonation states of the BACE-1 binding site should be treated carefully, iii) the MM-GBSA method could not discriminate well between different predicted binding poses, and iv) the MM-GBSA method does not perform well at predicting protein-ligand binding affinities here

The combined force field-sampling problem in simulations of disordered amyloid-β peptides

Molecular dynamics simulations of intrinsically disordered proteins (IDPs) can provide high resolution structural ensembles if the force field is accurate enough and if the simulation sufficiently samples the conformational space of the IDP with the correct weighting of sub-populations. Here, we investigate the combined force field-sampling problem by testing a standard force field as well as newer fixed charge force fields, the latter specifically motivated for better description of unfolded states and IDPs, and comparing them with a standard temperature replica exchange (TREx) protocol and a non-equilibrium Temperature Cool Walking (TCW) sampling algorithm. The force field and sampling combinations are used to characterize the structural ensembles of the amyloid-beta peptides Aβ42 and Aβ43, which both should be random coils as shown recently by experimental nuclear magnetic resonance (NMR) and 2D Förster resonance energy transfer (FRET) experiments. The results illustrate the key importance of the sampling algorithm: while the standard force field using TREx is in poor agreement with the NMR J-coupling and nuclear Overhauser effect and 2D FRET data, when using the TCW method, the standard and optimized protein-water force field combinations are in very good agreement with the same experimental data since the TCW sampling method produces qualitatively different ensembles than TREx. We also discuss the relative merit of the 2D FRET data when validating structural ensembles using the different force fields and sampling protocols investigated in this work for small IDPs such as the Aβ42 and Aβ43 peptides

Mechanism of Nucleation and Growth of Aβ40 Fibrils from All-Atom and Coarse-Grained Simulations.

In this work, we characterize the nucleation and elongation mechanisms of the "diseased" polymorph of the amyloid-β 40 (Aβ40) fibril using an off-lattice coarse-grained (CG) protein model. After determining the nucleation size and subsequent stable protofibrillar structure from the CG model, validated with all-atom simulations, we consider the "lock and dock" and "activated monomer" fibril elongation mechanisms for the protofibril by statistical additions of a monomer drawn from four different ensembles of the free Aβ40 peptide to grow the fibril. Our CG model shows that the dominant mechanism for fibril elongation is the lock and dock mechanism across all monomer ensembles, even when the monomer is in the activated form. Although our CG model finds no thermodynamic difference between the two fibril elongation mechanisms, the activated monomer is found to be kinetically faster by a factor of 2 for the "locking" step compared with all other structured or unstructured monomer ensembles

Effect of a Paramagnetic Spin Label on the Intrinsically Disordered Peptide Ensemble of Amyloid-β.

Paramagnetic relaxation enhancement is an NMR technique that has yielded important insight into the structure of folded proteins, although the perturbation introduced by the large spin probe might be thought to diminish its usefulness when applied to characterizing the structural ensembles of intrinsically disordered proteins (IDPs). We compare the computationally generated structural ensembles of the IDP amyloid-β42 (Aβ42) to an alternative sequence in which a nitroxide spin label attached to cysteine has been introduced at its N-terminus. Based on this internally consistent computational comparison, we find that the spin label does not perturb the signature population of the β-hairpin formed by residues 16-21 and 29-36 that is dominant in the Aβ42 reference ensemble. However, the presence of the tag induces a strong population shift in a subset of the original Aβ42 structural sub-populations, including a sevenfold enhancement of the β-hairpin formed by residues 27-31 and 33-38. Through back-calculation of NMR observables from the computational structural ensembles, we show that the structural differences between the labeled and unlabeled peptide would be evident in local residual dipolar couplings, and possibly differences in homonuclear 1H-1H nuclear Overhauser effects (NOEs) and heteronuclear 1H-15N NOEs if the paramagnetic contribution to the longitudinal relaxation does not suppress the NOE intensities in the real experiment. This work shows that molecular simulation provides a complementary approach to resolving the potential structural perturbations introduced by reporter tags that can aid in the interpretation of paramagnetic relaxation enhancement, double electron-electron resonance, and fluorescence resonance energy transfer experiments applied to IDPs

Comparing generalized ensemble methods for sampling of systems with many degrees of freedom.

We compare two standard replica exchange methods using temperature and dielectric constant as the scaling variables for independent replicas against two new corresponding enhanced sampling methods based on non-equilibrium statistical cooling (temperature) or descreening (dielectric). We test the four methods on a rough 1D potential as well as for alanine dipeptide in water, for which their relatively small phase space allows for the ability to define quantitative convergence metrics. We show that both dielectric methods are inferior to the temperature enhanced sampling methods, and in turn show that temperature cool walking (TCW) systematically outperforms the standard temperature replica exchange (TREx) method. We extend our comparisons of the TCW and TREx methods to the 5 residue met-enkephalin peptide, in which we evaluate the Kullback-Leibler divergence metric to show that the rate of convergence between two independent trajectories is faster for TCW compared to TREx. Finally we apply the temperature methods to the 42 residue amyloid-β peptide in which we find non-negligible differences in the disordered ensemble using TCW compared to the standard TREx. All four methods have been made available as software through the OpenMM Omnia software consortium (http://www.omnia.md/)