VeRNAl: Mining RNA Structures for Fuzzy Base Pairing Network Motifs

RNA 3D motifs are recurrent substructures, modelled as networks of base pair interactions, which are crucial for understanding structure-function relationships. The task of automatically identifying such motifs is computationally hard, and remains a key challenge in the field of RNA structural biology and network analysis. State of the art methods solve special cases of the motif problem by constraining the structural variability in occurrences of a motif, and narrowing the substructure search space. Here, we relax these constraints by posing the motif finding problem as a graph representation learning and clustering task. This framing takes advantage of the continuous nature of graph representations to model the flexibility and variability of RNA motifs in an efficient manner. We propose a set of node similarity functions, clustering methods, and motif construction algorithms to recover flexible RNA motifs. Our tool, VeRNAl can be easily customized by users to desired levels of motif flexibility, abundance and size. We show that VeRNAl is able to retrieve and expand known classes of motifs, as well as to propose novel motifs

Overview of the MCMC PCA algorithm.

<p>A: Initialization of the algorithm involves three steps. The proteins are modeled as spheres (1) and randomly placed on a grid (2). This random placement constitutes as the initial conformation sampled. A score is calculated for this initial complex (3). B: At the beginning of each iteration, three protein is chosen at random (with repetition) to be translated by up to 4 nm in a random direction in x, y and z. The arrow indicates a move chosen by the algorithm. C: We accept the new complex according to the Metropolis-Hasting sampling method.</p

Exploration of the Dynamic Properties of Protein Complexes Predicted from Spatially Constrained Protein-Protein Interaction Networks

<div><p>Protein complexes are not static, but rather highly dynamic with subunits that undergo 1-dimensional diffusion with respect to each other. Interactions within protein complexes are modulated through regulatory inputs that alter interactions and introduce new components and deplete existing components through exchange. While it is clear that the structure and function of any given protein complex is coupled to its dynamical properties, it remains a challenge to predict the possible conformations that complexes can adopt. Protein-fragment Complementation Assays detect physical interactions between protein pairs constrained to ≤8 nm from each other in living cells. This method has been used to build networks composed of 1000s of pair-wise interactions. Significantly, these networks contain a wealth of dynamic information, as the assay is fully reversible and the proteins are expressed in their natural context. In this study, we describe a method that extracts this valuable information in the form of predicted conformations, allowing the user to explore the conformational landscape, to search for structures that correlate with an activity state, and estimate the abundance of conformations in the living cell. The generator is based on a Markov Chain Monte Carlo simulation that uses the interaction dataset as input and is constrained by the physical resolution of the assay. We applied this method to an 18-member protein complex composed of the seven core proteins of the budding yeast Arp2/3 complex and 11 associated regulators and effector proteins. We generated 20,480 output structures and identified conformational states using principle component analysis. We interrogated the conformation landscape and found evidence of symmetry breaking, a mixture of likely active and inactive conformational states and dynamic exchange of the core protein Arc15 between core and regulatory components. Our method provides a novel tool for prediction and visualization of the hidden dynamics within protein interaction networks.</p></div

A: The experimental DHFR-<i>pca</i> interaction network.

<p>Arp3 was not included in the Tassarov <i>et al.</i> analysis and DHFR-<i>pca</i> edges are not available. Edges for Arp3 are based in predictions from the Arp2/3 structure (blue) and protein interaction data from BIOGRID (pink). B: Principal Component Analysis (PCA) was performed on the set of all conformations to project each conformation on to the two first principal components. Two clusters are formed: major (top) and minor (bottom). C: Biplot for the PCA. The biplot creates a visual representation of the contribution of each variable to the first two principal components. The length and direction of each line associated to each variable indicates its importance in the separation of the data. The PCA landscape indicates the presence of 5 different sub-regions. D: PCA scores were grouped in to a 2D histogram with sub-regions indicated. In parenthesis: number of conformations in sub-region.</p

Visual representation of 3-dimensional complex conformations within cluster 1 (A) and cluster 2 (B).

<p>Distributions of Myo5, Las17 and Rvs161/7 show the most striking conformational changes across the two clusters. Green: Myo5, Dark blue: Las17, Red: Rvs161/167Blue-grey: Core+7; composed of the seven core proteins of the Arp2/3 complex and adaptor proteins Sla1/2, Lsb3, End3, Gly1, Sec4 and the expression product of YNR065C. Symmetry breaking within the extended complex suggests branching versus scission complexes. C: Contact frequency is used to quantitatively assess functional domains and spatial relationships amongst components, typically using a resolution of 20 nm. D: Contact frequency demonstrates symmetry breaking of Myo5 and Rvs161/167, and a Myo5 bias in the distribution of Las17.</p

Arc15 bridges Arp2/3 core proteins and accessory proteins/regulators.

<p>A: Arc15 interacts with several accessory proteins (Las17, Myo5, Sla2 and Rvs161) and Arp2, but not other core proteins. B: Distance/edge matrix for core proteins. C: Arc15 exhibits “outward” directed diffusion towards Myo5 or Rvs161. D: Direct diffusion towards core proteins is correlated with a bias to Las17.</p

Comparison of structural and <i>pca</i> binary interactions in the Arp2/3 complex ([37], [38]).

1<p>1K8K. Note that the last crystallizable residue was used, which may not represent the actual position of the C-terminal as the last residue was not present in the structure. ²From Tassarov et al. 2008.</p

Proteins experience directed diffusion throughout a single MCMC simulation as a consequence of the set of attractors and repressors.

<p>A: The axis along the path of directed motion is expected to have the highest variance. Using the covariance matrix from the fitted Gaussian for the Protein of Interest (POI), the eigenvector (EV) with the largest absolute eigenvalue (EV1) forms the axis along which diffusion is occurring. B: Diffusion is occurring either in the direction of the EV or in the opposite direction. The long tail of the distribution determines the direction of diffusion, which can be calculated from the skew of the distribution. C: Activation of the Arp2/3 complex by Las17. Arp2 and Arp3 move towards each other, and Las17 moves towards (and binds) to Arp2 and Arp3. Sub-region 1 contains conformations that are consistent with Arp2/3 activation. D: Visualization of sub-region 1 Arp2, Arp3 and Las17 conformations. E: Visualization of Arp2, Arp3 and Las17 conformations in sub-regions 2-5. F: Directed diffusion amongst Arp2, Arp3 and Las17. Arrow length represents diffusiveness (EV1) relative to the center of mass (COM; circles) of the distribution of conformations for each protein. Numerical value is the skew, or direction of diffusion. Higher values correspond to increasing bias. In sub-region 1, Arp2 and Arp2 move towards each other and Las17 moves towards Arp2 and Arp3.</p