Modeling motions in proteins at the molecular level. Theoretical and methodological approaches in an experimental perspective

Dynamical aspects have a central role in the biological function of proteins. Each motional process has a characteristic time scale, amplitude and energy range. Proteins in particular display a broad range of characteristic motions, from very fast and localized, such as atomic fluctuations, to motions that occours on the scale of the whole molecule, such as folding transitions. Futhermore, dynamical events occourring at long time scales are actually coupled to faster motions, and they can be seen as rare events, the origin of which is found on the microdynamics of rotation around chemical bonds. Electron and nuclear magnetic spectroscopies are sensible to molecular motions at different time scales, making them very powerful tools in the study of molecular dynamics. Nevertheless the dynamical information contained in the experimental data is hidden and theorethical methodologies of interpretation are needed. In this work, we present different theoretical approaches which allow to better describe the stochastic descriptions of flexible macromolecules in solution. State-of-the-art approaches to dynamic models are first reviewed, aimed at the interpretation of magnetic resonance relaxation experiments. Next, the main focus is on i) the comparison between information content of the experiment and prediction capability of the model, using a Bayesian Markov-Chain Monte Carlo approach ii) defining a way to identify subgroups of atoms, the dynamics of which can be treated independently from the others iii) a new model of description of flexible macromolecules via projection operators, which allows to tune the description of the system to the preferred level of description in relation to the spectroscopic observable of interest

Modeling motions in proteins at the molecular level. Theoretical and methodological approaches in an experimental perspective

Dynamical aspects have a central role in the biological function of proteins. Each motional process has a characteristic time scale, amplitude and energy range. Proteins in particular display a broad range of characteristic motions, from very fast and localized, such as atomic fluctuations, to motions that occours on the scale of the whole molecule, such as folding transitions. Futhermore, dynamical events occourring at long time scales are actually coupled to faster motions, and they can be seen as rare events, the origin of which is found on the microdynamics of rotation around chemical bonds. Electron and nuclear magnetic spectroscopies are sensible to molecular motions at different time scales, making them very powerful tools in the study of molecular dynamics. Nevertheless the dynamical information contained in the experimental data is hidden and theorethical methodologies of interpretation are needed. In this work, we present different theoretical approaches which allow to better describe the stochastic descriptions of flexible macromolecules in solution. State-of-the-art approaches to dynamic models are first reviewed, aimed at the interpretation of magnetic resonance relaxation experiments. Next, the main focus is on i) the comparison between information content of the experiment and prediction capability of the model, using a Bayesian Markov-Chain Monte Carlo approach ii) defining a way to identify subgroups of atoms, the dynamics of which can be treated independently from the others iii) a new model of description of flexible macromolecules via projection operators, which allows to tune the description of the system to the preferred level of description in relation to the spectroscopic observable of interest.Aspetti dinamici hanno un ruolo centrale nella funzione biologica delle proteine. Ad ogni processo dinamico, sono associati un tempo, ampiezza ed energia caratteristici del moto. In particolare, le proteine presentano una vasta distribuzione dinamica, da moti rapidi e localizzati, come fluttuazioni atomiche, a processi che coinvolgono l’intera molecola, come le transizioni di folding. Inoltre, i processi che avvengono a scale temporali lente, sono accoppiati a moti piú rapidi, i primi possono essere quindi visti come eventi rari, la cui origine risiede nella microdinamica di rotazione attorno ai legami chimici. Le risonanze magnetiche, sia elettroniche che nucleari, sono estremamente sensibili ai moti molecolari a diverse scale temporali, rendendo di fatto tali tecniche, strumenti fondamentali per lo studio di aspetti dinamici. Tuttavia, l’informazione dinamica contenuta negli esperimenti è nascosta, per cui sono necessari modelli teorici interpretativi. In questo lavoro, vengono presentati diversi approcci teorici con lo scopo di migliorare la descrizione stocastica della dinamica di macromolecole flessibili in soluzione. Nella prima parte sono quindi descritte ed applicate metodologie teoriche avanzate ai fini dell’interpretazione di esperimenti di risonanza magnetica. Successivamente, l’attenzione viene posta i) sul confronto tra la quantità di informazione contenuta in un esperimento e le capacità predittive di un determinato modello teorico interpretativo, basato sulla combinazione di simulazioni Monte Carlo di catene Markoviane ed il teorema di Bayes, ii) sulla definizione di una metodica identificativa di sottogruppi di atomi la cui dinamica puó essere trattata in maniera indipendente rispetto agli altri, basata su metodi di clustering dinamico ottenuti da simulazioni di dinamica molecolare, iii) sulla descrizione di una nuova modellistica descrittiva di macromolecole flessibili attraverso tecniche di operatori proiettivi; tale metodologia permette di adattare la descrizione del sistemaal livello di dettaglio oppertuno, in funzione dell’osservabile spettroscopica d’interesse

Decomposition of proteins into dynamic units from atomic cross-correlation functions

n this article, we present a clustering method of atoms in proteins based on the analysis of the correlation times of interatomic distance correlation functions computed from MD simulations. The goal is to provide a coarse-grained description of the protein in terms of fewer elements that can be treated as dynamically independent subunits. Importantly, this domain decomposition method does not take into account structural properties of the protein. Instead, the clustering of protein residues in terms of networks of dynamically correlated domains is defined on the basis of the effective correlation times of the pair distance correlation functions. For these properties, our method stands as a complementary analysis to the customary protein decomposition in terms of quasi-rigid, structure-based domains. Results obtained for a prototypal protein structure illustrate the approach proposed

Integrated Computational Approach to the Electron Paramagnetic Resonance Characterization of Rigid 310-Helical Peptides with TOAC Nitroxide Spin Labels

We address the interpretation, via an integrated computational approach, of the experimental continuous-wave electron paramagnetic resonance (cw-EPR) spectra of a complete set of conformationally highly restricted, stable 310-helical peptides from hexa- to nonamers, each bis-labeled with nitroxide radical-containing TOAC (4-amino-1-oxyl-2,2,6,6-tetramethylpiperidine-4-carboxylic acid) residues. The usefulness of TOAC for this type of analysis has been shown already to be due to its cyclic piperidine side chain, which is rigidly connected to the peptide backbone \u3b1-carbon. The TOAC \u3b1-amino acids are separated by two, three, four, and five intervening residues. This set of compounds has allowed us to modulate both the radical\ub7\ub7\ub7radical distance and the relative orientation parameters. To further validate our conclusion, a comparative analysis has been carried out on three singly TOAC-labeled peptides of similar main-chain length

Integrated Computational Approach to the Electron Paramagnetic Resonance Characterization of Rigid 3₁₀-Helical Peptides with TOAC Nitroxide Spin Labels

We address the interpretation, via an integrated computational approach, of the experimental continuous-wave electron paramagnetic resonance (cw-EPR) spectra of a complete set of conformationally highly restricted, stable 3₁₀-helical peptides from hexa- to nonamers, each bis-labeled with nitroxide radical-containing TOAC (4-amino-1-oxyl-2,2,6,6-tetramethylpiperidine-4-carboxylic acid) residues. The usefulness of TOAC for this type of analysis has been shown already to be due to its cyclic piperidine side chain, which is rigidly connected to the peptide backbone α-carbon. The TOAC α-amino acids are separated by two, three, four, and five intervening residues. This set of compounds has allowed us to modulate both the radical···radical distance and the relative orientation parameters. To further validate our conclusion, a comparative analysis has been carried out on three singly TOAC-labeled peptides of similar main-chain length