Simon Olsson

Probabilistic Determination of Native State Ensembles of Proteins

The motions of biological macromolecules are tightly coupled to their functions. However, while the study of fast motions has become increasingly feasible in recent years, the study of slower, biologically important motions remains difficult. Here, we present a method to construct native state ensembles of proteins by the combination of physical force fields and experimental data through modern statistical methodology. As an example, we use NMR residual dipolar couplings to determine a native state ensemble of the extensively studied third immunoglobulin binding domain of protein G (GB3). The ensemble accurately describes both local and nonlocal backbone fluctuations as judged by its reproduction of complementary experimental data. While it is difficult to assess precise time-scales of the observed motions, our results suggest that it is possible to construct realistic conformational ensembles of biomolecules very efficiently. The approach may allow for a dramatic reduction in the computational as well as experimental resources needed to obtain accurate conformational ensembles of biological macromolecules in a statistically sound manner.

Inference of structure ensembles of flexible biomolecules from sparse, averaged data.

We present the theoretical foundations of a general principle to infer structure ensembles of flexible biomolecules from spatially and temporally averaged data obtained in biophysical experiments. The central idea is to compute the Kullback-Leibler optimal modification of a given prior distribution with respect to the experimental data and its uncertainty. This principle generalizes the successful inferential structure determination method and recently proposed maximum entropy methods. Tractability of the protocol is demonstrated through the analysis of simulated nuclear magnetic resonance spectroscopy data of a small peptide.

PHAISTOS: A framework for Markov chain Monte Carlo simulation and inference of protein structure.

We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force‐fields are available within the framework: PROFASI and OPLS‐AA/L, the latter including the generalized Born surface area solvent model. A flexible command‐line and configuration‐file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net. The software is implemented in C++ and has been tested on Linux and OSX platforms.

Combining experimental and simulation data of molecular processes via augmented Markov models

Significance Structural biology is moving toward a paradigm characterized by data from a broad range of sources sensitive to multiple timescales and length scales. However, a major open problem remains: to devise an inference method that optimally combines all of this information into models amenable to human analysis. In this work, we make a significant step toward achieving this goal. We introduce a statistically rigorous method to merge information from molecular simulations and experimental data into augmented Markov models (AMMs). AMMs are easy-to-analyze atomistic descriptions of biomolecular structure and exchange kinetics. We show how AMMs may provide accurate descriptions of molecular dynamics probed by NMR spin relaxation and thereby provide a unique way to integrate analysis of experimental with simulation data. Accurate mechanistic description of structural changes in biomolecules is an increasingly important topic in structural and chemical biology. Markov models have emerged as a powerful way to approximate the molecular kinetics of large biomolecules while keeping full structural resolution in a divide-and-conquer fashion. However, the accuracy of these models is limited by that of the force fields used to generate the underlying molecular dynamics (MD) simulation data. Whereas the quality of classical MD force fields has improved significantly in recent years, remaining errors in the Boltzmann weights are still on the order of a few kT, which may lead to significant discrepancies when comparing to experimentally measured rates or state populations. Here we take the view that simulations using a sufficiently good force-field sample conformations that are valid but have inaccurate weights, yet these weights may be made accurate by incorporating experimental data a posteriori. To do so, we propose augmented Markov models (AMMs), an approach that combines concepts from probability theory and information theory to consistently treat systematic force-field error and statistical errors in simulation and experiment. Our results demonstrate that AMMs can reconcile conflicting results for protein mechanisms obtained by different force fields and correct for a wide range of stationary and dynamical observables even when only equilibrium measurements are incorporated into the estimation process. This approach constitutes a unique avenue to combine experiment and computation into integrative models of biomolecular structure and dynamics.

Molecular Dynamics of Biomolecules through Direct Analysis of Dipolar Couplings.

Residual dipolar couplings (RDCs) are important probes in structural biology, but their analysis is often complicated by the determination of an alignment tensor or its associated assumptions. We here apply the maximum entropy principle to derive a tensor-free formalism which allows for direct, dynamic analysis of RDCs and holds the classic tensor formalism as a special case. Specifically, the framework enables us to robustly analyze data regardless of whether a clear separation of internal and overall dynamics is possible. Such a separation is often difficult in the core subjects of current structural biology, which include multidomain and intrinsically disordered proteins as well as nucleic acids. We demonstrate the method is tractable and self-consistent and generalizes to data sets comprised of observations from multiple different alignment conditions.

The Exact NOE as an Alternative in Ensemble Structure Determination.

The structure-function paradigm is increasingly replaced by the structure-dynamics-function paradigm. All protein activity is steered by the interplay between enthalpy and entropy. Conformational dynamics serves as a proxy of conformational entropy. Therefore, it is essential to study not only the average conformation but also the spatial sampling of a protein on all timescales. To this purpose, we have established a protocol for determining multiple-state ensembles of proteins based on exact nuclear Overhauser effects (eNOEs). We have recently extended our previously reported eNOE data set for the protein GB3 by a very large set of backbone and side-chain residual dipolar couplings and three-bond J couplings. Here, we demonstrate that at least four structural states are required to represent the complete data set by dissecting the contributions to the CYANA target function, which quantifies restraint violations in structure calculation. We present a four-state ensemble of GB3, which largely preserves the characteristics obtained from eNOEs only. Due to the abundance of the input data, the ensemble and χ(1) angles in particular are well suited for cross-validation of the input data and comparison to x-ray structures. Principal component analysis is used to automatically identify and validate relevant states of the ensembles. Overall, our findings suggest that eNOEs are a valuable alternative to traditional NMR probes in spatial elucidation of proteins.

Generative probabilistic models extend the scope of inferential structure determination

Conventional methods for protein structure determination from NMR data rely on the ad hoc combination of physical forcefields and experimental data, along with heuristic determination of free parameters such as weight of experimental data relative to a physical forcefield. Recently, a theoretically rigorous approach was developed which treats structure determination as a problem of Bayesian inference. In this case, the forcefields are brought in as a prior distribution in the form of a Boltzmann factor. Due to high computational cost, the approach has been only sparsely applied in practice. Here, we demonstrate that the use of generative probabilistic models instead of physical forcefields in the Bayesian formalism is not only conceptually attractive, but also improves precision and efficiency. Our results open new vistas for the use of sophisticated probabilistic models of biomolecular structure in structure determination from experimental data.

Complementarity and congruence between exact NOEs and traditional NMR probes for spatial decoding of protein dynamics.

The study of the spatial sampling of biomolecules is essential to understanding the structure-dynamics-function relationship. We have established a protocol for the determination of multiple-state ensembles based on exact measurements of the nuclear Overhauser effect (eNOE). The protocol is practical since it does not require any additional data, while all other NMR data sets must be supplemented by NOE restraints. The question arises as to how much structural and dynamics information is shared between the eNOEs and other NMR probes. We compile one of the largest and most diverse NMR data sets of a protein to date consisting of eNOEs, RDCs and J couplings for GB3. We show that the eNOEs improve the back-prediction of RDCs and J couplings, either upon use of more than one state, or in comparison to conventional NOEs. Our findings indicate that the eNOE data is self-consistent, consistent with other data, and that the structural representation with multiple states is warranted.

The Dynamic Basis for Signal Propagation in Human Pin1-WW

Allostery is the structural manifestation of information transduction in biomolecules. Its hallmark is conformational change induced by perturbations at a distal site. An increasing body of evidence demonstrates the presence of allostery in very flexible and even disordered proteins, encouraging a thermodynamic description of this phenomenon. Still, resolving such processes at atomic resolution is difficult. Here we establish a protocol to determine atomistic thermodynamic models of such systems using high-resolution solution state nuclear magnetic resonance data and extensive molecular simulations. Using this methodology, we study information transduction in the WW domain of a key cell-cycle regulator Pin1. Pin1 binds promiscuously to phospho-Ser/Thr-Pro motifs, however, disparate structural and dynamic responses have been reported upon binding different ligands. Our model consists of two topologically distinct states whose relative population may be specifically skewed by an incoming ligand. This model provides a canonical basis for the understanding of multi-functionality in Pin1.

Compiled data set of exact NOE distance limits, residual dipolar couplings and scalar couplings for the protein GB3.

We compiled an NMR data set consisting of exact nuclear Overhauser enhancement (eNOE) distance limits, residual dipolar couplings (RDCs) and scalar (J) couplings for GB3, which forms one of the largest and most diverse data set for structural characterization of a protein to date. All data have small experimental errors, which are carefully estimated. We use the data in the research article Vogeli et al., 2015, Complementarity and congruence between exact NOEs and traditional NMR probes for spatial decoding of protein dynamics, J. Struct. Biol., 191, 3, 306–317, doi:10.1016/j.jsb.2015.07.008 [1] for cross-validation in multiple-state structural ensemble calculation. We advocate this set to be an ideal test case for molecular dynamics simulations and structure calculations.