New results
Modeling the dynamics of proteins
Simpler protein domain identification using spectral clustering
The decomposition of a biomolecular complex into domains is an important step to investigate biological functions and ease structure determination. A successful approach to do so is the SPECTRUS algorithm, which provides a segmentation based on spectral clustering applied to a graph coding inter-atomic fluctuations derived from an elastic network model.
We present 20, which makes three straightforward and useful additions to SPECTRUS. For single structures, we show that high quality partitionings can be obtained from a graph Laplacian derived from pairwise interactions–without normal modes. For sets of homologous structures, we introduce a Multiple Sequence Alignment mode, exploiting both the sequence based information (MSA) and the geometric information embodied in experimental structures. Finally, we propose to analyze the clusters/domains delivered using the so-called D-Family matching algorithm, which establishes a correspondence between domains yielded by two decompositions, and can be used to handle fragmentation issues.
Our domains compare favorably to those of the original SPECTRUS, and those of the deep learning based method Chainsaw. Using two complex cases, we show in particular that is the only method handling complex conformational changes involving several sub-domains. Finally, a comparison of and Chainsaw on the manually curated domain classification ECOD as a reference shows that high quality domains are obtained without using any evolutionary related piece of information.
is provided in the Structural Bioinformatics Library, see SBL and Spectral domain explorer.
Algorithmic foundations
A mini-review of clustering algorithms and their theoretical properties, with applications to molecular science
Clustering is a fundamental task, in particular to analyze potential and free energy landscapes in molecular science. In this survey 19, I review the key properties of three remarkable clustering algorithms (k-means ++, persistence-based clustering, and spectral clustering) with a double perspective. The first one is the specification of the main mathematical and algorithmic properties of the algorithms; the second one is the relevance of these methods for structural, thermodynamic, and kinetic analysis. Doing so provides a unique opportunity to mention important connexions between optimization, graph theory, geometry, and theoretical biophysics.
Improved seeding strategies for k-means and Gaussian mixture fitting with Expectation-Maximization
k-means clustering and Gaussian Mixture model fitting are fundamental tasks in data analysis and statistical modeling. Practically, both algorithms follow a general iterative pattern, relying on (randomized) seeding techniques.
We revisit the previous seeding methods and formalize their key ingredients (metric used for seed sampling, number of seed candidates, metric used for seed selection). This analysis results in casting most of the previous methods into a coherent framework and, most importantly, yields novel families of initialization methods. Incidentally, these novel methods exploit a lookahead principle–conditioning the seed selection to an enhanced coherence with the final metric used to assess the algorithm, and a multipass strategy–using at least two selection passes to tame down the effect of randomization.
Experiments show a consistent constant factor improvement over classical contenders in terms of the final metric (sum of square error (SSE) for k-means, log-likelihood for Expectation-Maximization applied to Gaussian mixture model fitting), at the same cost. Roughly speaking, our improvement with respect to the greedy smart seeding of k-means++ matches that yielded by this greedy smart seeding with respect to the classical randomized smart seeding.
Remark. Due to the double blind review process of machine learning conferences, the tech report will be made public early 2025.
Subspace-Embedded Spherical Clusters: a novel cluster model for compact clusters of arbitrary dimension
Subspace clustering aims at selecting a small number of original coordinates (features) so that clusters are clearly identified in those subspaces. Subspace techniques rely on parametric cluster models including affine, spherical, Gaussian cluster models–to name a few. To go beyond fully dimensional spherical cluster models and affine clusters of arbitrary dimension, we introduce Subspace-embedded spherical clusters (SESC), a novel cluster model for compact clusters of arbitrary intrinsic dimension. The well posed nature of such clusters is established via the study of an optimization problem relying on an arrangement of hyper-spheres. This arrangement is used to exhibit a piecewise smooth strictly convex function, amenable to non smooth optimization.
We illustrate the merits of the SESC model via comparisons against projection medians and the distance to the measure, and for clustering.
Remark. Due to the double blind review process of machine learning conferences, the tech report will be made public early 2025.
Applications in structural bioinformatics and beyond
AlphaFold predictions on whole genomes at a glance
The 2024 Nobel prize in chemistry was awarded to David Baker (Univ. of Washington) for computational protein design, and to Demis Hassabis and John Jumper (Google DeepMind, London, UK), for protein structure prediction. The DeepMind software, called AlphaFold, plays a crucial role to help biologists understand protein functions. We designed novel statistical analysis to assess predictions 21.
For model organisms, AlphaFold predictions show that 30% to 40% of amino acids have a (very) low pLDDT (predicted local distance difference test) confidence score. This observation, combined with the method’s high complexity, commands to investigate difficult cases, the link with IDPs (intrinsically disordered proteins) or IDRs (intrinsically disordered regions), and potential hallucinations. We do so via four contributions. First, we provide a multiscale characterization of stretches with coherent 2D arity map, which simultaneously performs dimensionality reduction and clustering, effectively summarizing all structural elements across all predictions. Third, using the database of domains ECOD , we study potential biases in AlphaFold predictions at the sequence and structural levels, identifying a specific region of the arity map populated with low quality 3D domains. Finally, with a focus on proteins with intrinsically disordered regions (IDRs), using DisProt and AIUPred, we identify specific regions of the arity map characterized by false positive and false negatives in terms of IDRs.
Summarizing, the arity map sheds light on the accuracy of AlphaFold predictions, both in terms of 3D domains and IDRs.
EncoMPASS: a database for the analysis of membrane protein structures, and symmetries
Membrane proteins (MPs) constitute about 30% of the proteome of each organisms, but they represent only 2% of the entries in the Protein Data Bank (PDB), as their three-dimensional structure is difficult to determine experimentally. Membrane protein structures differ from the rest of the proteome in two respects: 1) despite the great variety of functions performed, their structures are very similar, thus making structural classification more challenging and 2) although symmetric regions are common throughout the whole proteome, in MPs they are often essential for their functional mechanism.
Among the databases collecting and organizing experimental structures of MPs, EncoMPASS is the only one relating the structure and internal symmetry of experimentally determined membrane protein complexes. In this new publication 18, the pipeline and founding criteria for building the database are described along with a complete analysis of the available data. The quality and consistency checks regularly performed on EncoMPASS make it a high quality resource for membrane protein structure algorithms.
Detecting orphan proteins in a nematode’s genome
Protein classified in the same family are called homologs and are thought to share a common ancestor from which they have evolved. Proteins that cannot at present be classified in any known family are called orphan proteins, and their existence can be attributed to either the current limitations in protein classification (we talk then of distant homologs) or to genuinely novel proteins (de novo proteins). Determining whether a protein is orphan – or, even more, a distant homolog or a de novo – is particularly challenging due to the uncertainties and intricateness of homolog detection. In the poster 23 presented at JOBIM2024 by E. Seçkin, we show a new pipeline for determining orphan proteins, and its application to the genomes of the Meloidogyne genus of nematodes. This work is a fundamental step in preparation to the first ever algorithm for characterizing the structure of orphan proteins.