Cecilia Clementi

Interplay Among Tertiary Contacts, Secondary Structure Formation and Side-chain Packing in the Protein Folding Mechanism: All-atom Representation Study of Protein L

Experimental and theoretical results suggest that, since proteins are energetically minimally frustrated, the native fold, or topology, plays a primary role in determining the structure of the transition state ensemble and on-pathway intermediate states in protein folding. Although the central role of native state topology in determining the folding mechanism is thought to be a quite general result-at least for small two-state folding proteins-there are remarkable exceptions. Recent experimental findings have shown that topology alone cannot always determine the folding mechanism, and demonstrated that the balance between topology and energetics is very delicate. This balance seems to be particularly critical in proteins with a highly symmetrical native structure, such as proteins L and G, which have similar native structure topology but fold by different mechanisms. Simplified, C(alpha)-atom only protein models have shown not be sufficient to differentiate these mechanisms. An all-atom Gō model provides a valuable intermediate model between structurally simplified protein representations and all-atom protein simulations with explicit/implicit solvent descriptions. We present here a detailed study of an all-atom Gō-like representation of protein L, in close comparison with the experimental results and with the results obtained from a simple C(alpha)-atom representation of the same protein. We also perform simulations for protein G, where we obtain a folding mechanism in which the protein symmetry is broken exactly in the opposite way to protein L as has been observed experimentally. A detailed analysis for protein L also shows that the role of specific residues is correctly and quantitatively reproduced by the all-atom Gō model over almost the entire protein.

The effects of nonnative interactions on protein folding rates: theory and simulation.

Proteins are minimally frustrated polymers. However, for realistic protein models, nonnative interactions must be taken into account. In this paper, we analyze the effect of nonnative interactions on the folding rate and on the folding free energy barrier. We present an analytic theory to account for the modification on the free energy landscape upon introduction of nonnative contacts, added as a perturbation to the strong native interactions driving folding. Our theory predicts a rate‐enhancement regime at fixed temperature, under the introduction of weak, nonnative interactions. We have thoroughly tested this theoretical prediction with simulations of a coarse‐grained protein model, by using an off‐lattice Cαmodel of the src‐SH3 domain. The strong agreement between results from simulations and theory confirm the nontrivial result that a relatively small amount of nonnative interaction energy can actually assist the folding to the native structure.

Determination of reaction coordinates via locally scaled diffusion map.

We present a multiscale method for the determination of collective reaction coordinates for macromolecular dynamics based on two recently developed mathematical techniques: diffusion map and the determination of local intrinsic dimensionality of large datasets. Our method accounts for the local variation of molecular configuration space, and the resulting global coordinates are correlated with the time scales of the molecular motion. To illustrate the approach, we present results for two model systems: all-atom alanine dipeptide and coarse-grained src homology 3 protein domain. We provide clear physical interpretation for the emerging coordinates and use them to calculate transition rates. The technique is general enough to be applied to any system for which a Boltzmann-sampled set of molecular configurations is available.

Adaptive resolution simulation of liquid water

Water plays a central role in biological systems and processes, and is equally relevant in a large range of industrial and technological applications. Being the most important natural solvent, its presence uniquely influences biological function as well as technical processes. Because of their importance, aqueous solutions are among the most experimentally and theoretically studied systems. However, many questions still remain open. Both experiments and theoretical models are usually restricted to specific cases. In particular all-atom simulations of biomolecules and materials in water are computationally very expensive and often not possible, mainly due to the computational effort to obtain water–water interactions in regions not relevant for the problem under consideration. In this paper we present a coarse-grained model that can reproduce the behaviour of liquid water at a standard temperature and pressure remarkably well. The model is then used in a multiscale simulation of liquid water, where a spatially adaptive molecular resolution procedure allows one to change from a coarse-grained to an all-atom representation on-the-fly. We show that this approach leads to the correct description of essential thermodynamic and structural properties of liquid water. Our adaptive multiscale scheme allows for significantly greater extensive simulations than existing approaches by taking explicit water into account only in the regions where the atomistic details are physically relevant.

From coarse-grain to all-atom: Toward multiscale analysis of protein landscapes

Multiscale methods are becoming increasingly promising as a way to characterize the dynamics of large protein systems on biologically relevant time‐scales. The underlying assumption in multiscale simulations is that it is possible to move reliably between different resolutions. We present a method that efficiently generates realistic all‐atom protein structures starting from the Cα atom positions, as obtained for instance from extensive coarse‐grain simulations. The method, a reconstruction algorithm for coarse‐grain structures (RACOGS), is validated by reconstructing ensembles of coarse‐grain structures obtained during folding simulations of the proteins src‐SH3 and S6. The results show that RACOGS consistently produces low energy, all‐atom structures. A comparison of the free energy landscapes calculated using the coarse‐grain structures versus the all‐atom structures shows good correspondence and little distortion in the protein folding landscape. Proteins 2007.

Discovering Mountain Passes via Torchlight: Methods for the Definition of Reaction Coordinates and Pathways in Complex Macromolecular Reactions

The long-timescale dynamics of macromolecular systems can be oftentimes viewed as a reaction connecting metastable states of the system. In the past decade, various approaches have been developed to discover the collective motions associated with this dynamics. The corresponding collective variables are used in many applications, e.g., to understand the reaction mechanism, to quantify the systems free energy landscape, to enhance the sampling of the reaction path, and to determine the reaction rate. In this review we focus on a number of key developments in this field, providing an overview of several methods along with their relative regimes of applicability.

AWSEM-MD: protein structure prediction using coarse-grained physical potentials and bioinformatically based local structure biasing.

The associative memory, water mediated, structure and energy model (AWSEM) is a coarse-grained protein force field. AWSEM contains physically motivated terms, such as hydrogen bonding, as well as a bioinformatically based local structure biasing term, which efficiently takes into account many-body effects that are modulated by the local sequence. When combined with appropriate local or global alignments to choose memories, AWSEM can be used to perform de novo protein structure prediction. Herein we present structure prediction results for a particular choice of local sequence alignment method based on short residue sequences called fragments. We demonstrate the models structure prediction capabilities for three levels of global homology between the target sequence and those proteins used for local structure biasing, all of which assume that the structure of the target sequence is not known. When there are no homologues in the database of structures used for local structure biasing, AWSEM calculations produce structural predictions that are somewhat improved compared with prior works using related approaches. The inclusion of a small number of structures from homologous sequences improves structure prediction only marginally, but when the fragment search is restricted to only homologous sequences, AWSEM can perform high resolution structure prediction and can be used for kinetics and dynamics studies.

Multiscale characterization of protein conformational ensembles

We propose a multiscale exploration method to characterize the conformational space populated by a protein at equilibrium. The method efficiently obtains a large set of equilibrium conformations in two stages: first exploring the entire space at a coarse‐grained level of detail, then narrowing a refined exploration to selected low‐energy regions. The coarse‐grained exploration periodically adds all‐atom detail to selected conformations to ensure that the search leads to regions which maintain low energies in all‐atom detail. The second stage reconstructs selected low‐energy coarse‐grained conformations in all‐atom detail. A low‐dimensional energy landscape associated with all‐atom conformations allows focusing the exploration to energy minima and their conformational ensembles. The lowest energy ensembles are enriched with additional all‐atom conformations through further multiscale exploration. The lowest energy ensembles obtained from the application of the method to three different proteins correctly capture the known functional states of the considered systems. Proteins 2009.

Modeling diffusive dynamics in adaptive resolution simulation of liquid water

We present a dual-resolution molecular dynamics (MD) simulation of liquid water employing a recently introduced Adaptive Resolution Scheme (AdResS). The spatially adaptive molecular resolution procedure allows for changing from a coarse-grained to an all-atom representation and vice versa on-the-fly. In order to find the most appropriate coarse-grained water model to be employed with AdResS, we first study the accuracy of different coarse-grained water models in reproducing the structural properties of the all-atom system. Typically, coarse-grained molecular models have a higher diffusion constant than the corresponding all-atom models due to the reduction in degrees of freedom (DOFs) upon coarse-graining that eliminates the fluctuating forces associated with those integrated-out molecular DOFs. Here, we introduce the methodology to obtain the same diffusional dynamics across different resolutions. We show that this approach leads to the correct description of the here relevant structural, thermodynamical, and dynamical properties, i.e., radial distribution functions, pressure, temperature, and diffusion, of liquid water at ambient conditions.

Modeling protein conformational ensembles: From missing loops to equilibrium fluctuations

Characterizing protein flexibility is an important goal for understanding the physical–chemical principles governing biological function. This paper presents a Fragment Ensemble Method to capture the mobility of a protein fragment such as a missing loop and its extension into a Protein Ensemble Method to characterize the mobility of an entire protein at equilibrium. The underlying approach in both methods is to combine a geometric exploration of conformational space with a statistical mechanics formulation to generate an ensemble of physical conformations on which thermodynamic quantities can be measured as ensemble averages. The Fragment Ensemble Method is validated by applying it to characterize loop mobility in both instances of strongly stable and disordered loop fragments. In each instance, fluctuations measured over generated ensembles are consistent with data from experiment and simulation. The Protein Ensemble Method captures the mobility of an entire protein by generating and combining ensembles of conformations for consecutive overlapping fragments defined over the protein sequence. This method is validated by applying it to characterize flexibility in ubiquitin and protein G. Thermodynamic quantities measured over the ensembles generated for both proteins are fully consistent with available experimental data. On these proteins, the method recovers nontrivial data such as order parameters, residual dipolar couplings, and scalar couplings. Results presented in this work suggest that the proposed methods can provide insight into the interplay between protein flexibility and function. Proteins 2006.