Attenuating dependence on structural data in computing protein energy landscapes.

BACKGROUND: Nearly all cellular processes involve proteins structurally rearranging to accommodate molecular partners. The energy landscape underscores the inherent nature of proteins as dynamic molecules interconverting between structures with varying energies. In principle, reconstructing a protein's energy landscape holds the key to characterizing the structural dynamics and its regulation of protein function. In practice, the disparate spatio-temporal scales spanned by the slow dynamics challenge both wet and dry laboratories. However, the growing number of deposited structures for proteins central to human biology presents an opportunity to infer the relevant dynamics via exploitation of the information encoded in such structures about equilibrium dynamics. RESULTS: Recent computational efforts using extrinsic modes of motion as variables have successfully reconstructed detailed energy landscapes of several medium-size proteins. Here we investigate the extent to which one can reconstruct the energy landscape of a protein in the absence of sufficient, wet-laboratory structural data. We do so by integrating intrinsic modes of motion extracted off a single structure in a stochastic optimization framework that supports the plug-and-play of different variable selection strategies. We demonstrate that, while knowledge of more wet-laboratory structures yields better-reconstructed landscapes, precious information can be obtained even when only one structural model is available. CONCLUSIONS: The presented work shows that it is possible to reconstruct the energy landscape of a protein with reasonable detail and accuracy even when the structural information about the protein is limited to one structure. By attenuating the dependence on structural data of methods designed to compute protein energy landscapes, the work opens up interesting venues of research on structure-based inference of dynamics. Of particular interest are directions of research that will extend such inference to proteins with no experimentally-characterized structures.

From mutations to mechanisms and dysfunction via computation and mining of protein energy landscapes.

BACKGROUND: The protein energy landscape underscores the inherent nature of proteins as dynamic molecules interconverting between structures with varying energies. Reconstructing a protein's energy landscape holds the key to characterizing a protein's equilibrium conformational dynamics and its relationship to function. Many pathogenic mutations in protein sequences alter the equilibrium dynamics that regulates molecular interactions and thus protein function. In principle, reconstructing energy landscapes of a protein's healthy and diseased variants is a central step to understanding how mutations impact dynamics, biological mechanisms, and function. RESULTS: Recent computational advances are yielding detailed, sample-based representations of protein energy landscapes. In this paper, we propose and describe two novel methods that leverage computed, sample-based representations of landscapes to reconstruct them and extract from them informative local structures that reveal the underlying organization of an energy landscape. Such structures constitute landscape features that, as we demonstrate here, can be utilized to detect alterations of landscapes upon mutation. CONCLUSIONS: The proposed methods detect altered protein energy landscape features in response to sequence mutations. By doing so, the methods allow formulating hypotheses on the impact of mutations on specific biological activities of a protein. This work demonstrates that the availability of energy landscapes of healthy and diseased variants of a protein opens up new avenues to harness the quantitative information embedded in landscapes to summarize mechanisms via which mutations alter protein dynamics to percolate to dysfunction.

Structure-Guided Protein Transition Modeling with a Probabilistic Roadmap Algorithm.

Proteins are macromolecules in perpetual motion, switching between structural states to modulate their function. A detailed characterization of the precise yet complex relationship between protein structure, dynamics, and function requires elucidating transitions between functionally-relevant states. Doing so challenges both wet and dry laboratories, as protein dynamics involves disparate temporal scales. In this paper, we present a novel, sampling-based algorithm to compute transition paths. The algorithm exploits two main ideas. First, it leverages known structures to initialize its search and define a reduced conformation space for rapid sampling. This is key to address the insufficient sampling issue suffered by sampling-based algorithms. Second, the algorithm embeds samples in a nearest-neighbor graph where transition paths can be efficiently computed via queries. The algorithm adapts the probabilistic roadmap framework that is popular in robot motion planning. In addition to efficiently computing lowest-cost paths between any given structures, the algorithm allows investigating hypotheses regarding the order of experimentally-known structures in a transition event. This novel contribution is likely to open up new venues of research. Detailed analysis is presented on multiple-basin proteins of relevance to human disease. Multiscaling and the AMBER ff14SB force field are used to obtain energetically-credible paths at atomistic detail.

Sample-Based Models of Protein Energy Landscapes and Slow Structural Rearrangements.

Proteins often undergo slow structural rearrangements that involve several angstroms and surpass the nanosecond timescale. These spatiotemporal scales challenge physics-based simulations and open the way to sample-based models of structural dynamics. This article improves an understanding of current capabilities and limitations of sample-based models of dynamics. Borrowing from widely used concepts in evolutionary computation, this article introduces two conflicting aspects of sampling capability and quantifies them via statistical (and graphical) analysis tools. This allows not only conducting a principled comparison of different sample-based algorithms but also understanding which algorithmic ingredients to use as knobs via which to control sampling and, in turn, the accuracy and detail of modeled structural rearrangements. We demonstrate the latter by proposing two powerful variants of a recently published sample-based algorithm. We believe that this work will advance the adoption of sample-based models as reliable tools for modeling slow protein structural rearrangements.

Fast and reliable analysis of molecular motion using proximity relations and dimensionality reduction.

The analysis of molecular motion starting from extensive sampling of molecular configurations remains an important and challenging task in computational biology. Existing methods require a significant amount of time to extract the most relevant motion information from such data sets. In this work, we provide a practical tool for molecular motion analysis. The proposed method builds upon the recent ScIMAP (Scalable Isomap) method, which, by using proximity relations and dimensionality reduction, has been shown to reliably extract from simulation data a few parameters that capture the main, linear and/or nonlinear, modes of motion of a molecular system. The results we present in the context of protein folding reveal that the proposed method characterizes the folding process essentially as well as ScIMAP. At the same time, by projecting the simulation data and computing proximity relations in a low-dimensional Euclidean space, it renders such analysis computationally practical. In many instances, the proposed method reduces the computational cost from several CPU months to just a few CPU hours, making it possible to analyze extensive simulation data in a matter of a few hours using only a single processor. These results establish the proposed method as a reliable and practical tool for analyzing motions of considerably large molecular systems and proteins with complex folding mechanisms.

Motion generation of robotic surgical tasks: learning from expert demonstrations.

Robotic surgical assistants offer the possibility of automating portions of a task that are time consuming and tedious in order to reduce the cognitive workload of a surgeon. This paper proposes using programming by demonstration to build generative models and generate smooth trajectories that capture the underlying structure of the motion data recorded from expert demonstrations. Specifically, motion data from Intuitive Surgical's da Vinci Surgical System of a panel of expert surgeons performing three surgical tasks are recorded. The trials are decomposed into subtasks or surgemes, which are then temporally aligned through dynamic time warping. Next, a Gaussian Mixture Model (GMM) encodes the experts' underlying motion structure. Gaussian Mixture Regression (GMR) is then used to extract a smooth reference trajectory to reproduce a trajectory of the task. The approach is evaluated through an automated skill assessment measurement. Results suggest that this paper presents a means to (i) extract important features of the task, (ii) create a metric to evaluate robot imitative performance (iii) generate smoother trajectories for reproduction of three common medical tasks.

Distributed Computation of the knn Graph for Large High-Dimensional Point Sets.

High-dimensional problems arising from robot motion planning, biology, data mining, and geographic information systems often require the computation of k nearest neighbor (knn) graphs. The knn graph of a data set is obtained by connecting each point to its k closest points. As the research in the above-mentioned fields progressively addresses problems of unprecedented complexity, the demand for computing knn graphs based on arbitrary distance metrics and large high-dimensional data sets increases, exceeding resources available to a single machine. In this work we efficiently distribute the computation of knn graphs for clusters of processors with message passing. Extensions to our distributed framework include the computation of graphs based on other proximity queries, such as approximate knn or range queries. Our experiments show nearly linear speedup with over one hundred processors and indicate that similar speedup can be obtained with several hundred processors.