Structural analysis of intrinsically disordered proteins: computer atomistic simulation

Intrinsically disordered proteins (IDPs) are biomolecules that do not have a definite 3D structure; their role in the biochemical network of a cell relates to their ability to switch rapidly among different secondary and tertiary structures. For this reason, applying a simulation computer program to their structural study turns out to be problematic, as their dynamical simulation cannot start from a known list of atomistic positions, as is the case for globular proteins that do crystallize and that one can analyse by X-ray spectroscopy to determine their structure. We have established a method to perform a computer simulation of these proteins, apt to gather statistically significant data on their transient structures. The only required input to start the procedure is the primary sequence of the disordered domains of the protein, and the 3D structure of the ordered domains, if any. For a fully disordered protein the method is as follows: (a) The first step is the creation of a multi-rod-like configuration of the molecule, derived from its primary sequence. This structure evolves dynamically in vacuo or in an implicit model of solvent, until its gyration radius - or any other measure of the overall configuration of the molecule - reaches the experimental average value; at this point, one may follow two different paths. (b1) If the study focuses on transient secondary structures of the molecule, one puts the structure obtained at the end of the first step in a box containing solvent molecules in explicit implementation, and a standard molecular dynamics simulation follows. (b2) If the study focuses on the tertiary structure of the molecule, a larger sampling of the phase space is required, with the molecule moving in very large and diverse regions of the phase space. To this end, the structure of the IDP is let evolve dynamically in an implicit solvent using metadynamics, an algorithm that keeps track of the regions of the phase space already sampled, and forces the system to wander in further regions of the phase space. (c) One can increase the accuracy of the statistical information gathered in both cases by fitting, where available, experimental data of the protein. In this step one extracts an ensemble of ’best’ conformers from the pool of all configurations produced in the simulated dynamics. One derives this ensemble by means of an ensemble optimization method, implementing a genetic algorithm. We have applied this procedure to the simulation of tau, one of the largest fully disordered proteins, which is involved in the development of Alzheimer’s disease and of other neurodegenerative diseases. We have combined the results of our simulation with small-angle X-ray scattering experimental data to extract from the dynamics an optimized ensemble of most probable conformers of tau. The method can be easily adapted to IDPs entailing ordered domains

Testing simplified protein models of the hPin1 WW domain

The WW domain of the human Pin1 protein for its simple topology and the large amount of experimental data is an ideal candidate to assess theoretical approaches to protein folding. The purpose of the present work is to compare the reliability of the chemically-based Sorenson/Head-Gordon (SHG) model and a standard native centric model in reproducing through molecular dynamics simulations some of the well known features of the folding transition of this small domain. Our results show that the G\={o} model correctly reproduces the cooperative, two-state, folding mechanism of the WW-domain, while the SHG model predicts a transition occurring in two stages: a collapse followed by a structural rearrangement. The lack of a cooperative folding in the SHG simulations appears to be related to the non-funnel shape of the energy landscape featuring a partitioning of the native valley in sub-basins corresponding to different chain chiralities. However the SHG approach remains more reliable in estimating the $\Phi$-values with respect to G\={o}-like description. This may suggest that the WW-domain folding process is stirred by energetic and topological factors as well, and it highlights the better suitability of chemically-based models in simulating mutations.Comment: RevTex4: 12 pages and 13 eps-figure file

Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes; sophisticated enhanced sampling methods have been proposed to generate these macromolecular transition paths. As such paths are curves in a high-dimensional space, they have been difficult to compare quantitatively, a prerequisite to, for instance, assess the quality of different sampling algorithms. The Path Similarity Analysis (PSA) approach alleviates these difficulties by utilizing the full information in 3N-dimensional trajectories in configuration space. PSA employs the Hausdorff or Fr\'echet path metrics---adopted from computational geometry---enabling us to quantify path (dis)similarity, while the new concept of a Hausdorff-pair map permits the extraction of atomic-scale determinants responsible for path differences. Combined with clustering techniques, PSA facilitates the comparison of many paths, including collections of transition ensembles. We use the closed-to-open transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for the assessment enhanced sampling algorithms---to examine multiple microsecond equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free form alongside transition ensembles from the MD-based dynamic importance sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for instance, that differences in DIMS-MD and FRODA paths were mediated by a set of conserved salt bridges whose charge-charge interactions are fully modeled in DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis methods relying on pre-defined collective variables, such as native contacts or geometric quantities, can be used synergistically with PSA, as well as the application of PSA to more complex systems such as membrane transporter proteins.Comment: 9 figures, 3 tables in the main manuscript; supplementary information includes 7 texts (S1 Text - S7 Text) and 11 figures (S1 Fig - S11 Fig) (also available from journal site