A stochastic roadmap method to model protein structural transitions

Adaptive Stochastic Optimization to Improve Protein Conformation Sampling

We have long known that characterizing protein structures structure is key to understanding protein function. Computational approaches have largely addressed a narrow formulation of the problem, seeking to compute one native structure from an amino-acid sequence. Now AlphaFold2 is shown to be able to reveal a high-quality native structure for many proteins. However, researchers over the years have argued for broadening our view to account for the multiplicity of native structures. We now know that many protein molecules switch between different structures to regulate interactions with molecular partners in the cell. Elucidating such structures de novo is exceptionally difficult, as it requires exploration of possibly a very large structure space in search of competing, near-optimal structures. Here we report on a novel stochastic optimization method capable of revealing very different structures for a given protein from knowledge of its amino-acid sequence. The method leverages evolutionary search techniques and adapts its exploration of the search space to balance between exploration and exploitation in the presence of a computational budget. In addition to demonstrating the utility of this method for identifying multiple native structures, we additionally provide a benchmark dataset for researchers to continue work on this problem.

Collision-free poisson motion planning in ultra high-dimensional molecular conformation spaces

The function of protein, RNA, and DNA is modulated by fast, dynamic exchanges between three-dimensional conformations. Conformational sampling of biomolecules with exact and nullspace inverse kinematics, using rotatable bonds as revolute joints and noncovalent interactions as holonomic constraints, can accurately characterize these native ensembles. However, sampling biomolecules remains challenging owing to their ultra-high dimensional configuration spaces, and the requirement to avoid (self-) collisions, which results in low acceptance rates. Here, we present two novel mechanisms to overcome these limitations. First, we introduce temporary constraints between near-colliding links. The resulting constraint varieties instantaneously redirect the search for collision-free conformations, and couple motions between distant parts of the linkage. Second, we adapt a randomized Poisson-disk motion planner, which prevents local oversampling and widens the search, to ultra-high dimensions. Tests on several model systems show that the sampling acceptance rate can increase from 16% to 70%, and that the conformational coverage in loop modeling measured as average closeness to existing loop conformations doubled. Correlated protein motions identified with our algorithm agree with those from MD simulations. © 2018 Wiley Periodicals, Inc.

Computing energy landscape maps and structural excursions of proteins

BACKGROUND

Structural excursions of a protein at equilibrium are key to biomolecular recognition and function modulation. Protein modeling research is driven by the need to aid wet laboratories in characterizing equilibrium protein dynamics. In principle, structural excursions of a protein can be directly observed via simulation of its dynamics, but the disparate temporal scales involved in such excursions make this approach computationally impractical. On the other hand, an informative representation of the structure space available to a protein at equilibrium can be obtained efficiently via stochastic optimization, but this approach does not directly yield information on equilibrium dynamics.

METHODS

We present here a novel methodology that first builds a multi-dimensional map of the energy landscape that underlies the structure space of a given protein and then queries the computed map for energetically-feasible excursions between structures of interest. An evolutionary algorithm builds such maps with a practical computational budget. Graphical techniques analyze a computed multi-dimensional map and expose interesting features of an energy landscape, such as basins and barriers. A path searching algorithm then queries a nearest-neighbor graph representation of a computed map for energetically-feasible basin-to-basin excursions.

RESULTS

Evaluation is conducted on intrinsically-dynamic proteins of importance in human biology and disease. Visual statistical analysis of the maps of energy landscapes computed by the proposed methodology reveals features already captured in the wet laboratory, as well as new features indicative of interesting, unknown thermodynamically-stable and semi-stable regions of the equilibrium structure space. Comparison of maps and structural excursions computed by the proposed methodology on sequence variants of a protein sheds light on the role of equilibrium structure and dynamics in the sequence-function relationship.

CONCLUSIONS

Applications show that the proposed methodology is effective at locating basins in complex energy landscapes and computing basin-basin excursions of a protein with a practical computational budget. While the actual temporal scales spanned by a structural excursion cannot be directly obtained due to the foregoing of simulation of dynamics, hypotheses can be formulated regarding the impact of sequence mutations on protein function. These hypotheses are valuable in instigating further research in wet laboratories.