The scientific discovery process is very often based on cycles of measurement, classification, and generalisation. It is easy to argue that this is especially true in the biological sciences. The proteins that exist today represent the molecular product of some three billion years of evolution. Therefore, comparing protein sequences and structures is important for understanding their functional and evolutionary relationships , . There is now overwhelming evidence that all living organisms and many biological processes share a common ancestry in the tree of life. Historically, much of bioinformatics research has focused on developing mathematical and statistical algorithms to process, analyse, annotate, and compare protein and DNA sequences because such sequences represent the primary form of information in biological systems. However, there is growing evidence that structure-based methods can help to predict networks of protein-protein interactions (PPIs) with greater accuracy than those which do not use structural evidence , . Therefore, developing techniques which can mine knowledge of protein structures and their interactions is an important way to enhance our knowledge of biology .

Concerning protein structure classification, we aim to explore novel classification paradigms to circumvent the problems encountered with existing hierarchical classifications of protein folds and domains. In particular it will be interesting to set up fuzzy clustering methods taking advantage of our previous work on gene functional classification , but instead using Kpax domain-domain similarity matrices. A non-trivial issue with fuzzy clustering is how to handle similarity rather than mathematical distance matrices, and how to find the optimal number of clusters, especially when using a non-Euclidean similarity measure. We will adapt the algorithms and the calculation of quality indices to the Kpax similarity measure. More fundamentally, it will be necessary to integrate this classification step in the more general process leading from data to knowledge called Knowledge Discovery in Databases (KDD) .

Another example where domain knowledge can be useful is during result interpretation: several sources of knowledge have to be used to explicitly characterise each cluster and to help decide its validity. Thus, it will be useful to be able to express data models, patterns, and rules in a common formalism using a defined vocabulary for concepts and relationships. Existing approaches such as the Molecular Interaction (MI) format  developed by the Human Genome Organization (HUGO) mostly address the experimental wet lab aspects leading to data production and curation  . A different point of view is represented in the Interaction Network Ontology (INO), a community-driven ontology that aims to standardise and integrate data on interaction networks and to support computer-assisted reasoning  . However, this ontology does not integrate basic 3D concepts and structural relationships. Therefore, extending such formalisms and symbolic relationships will be beneficial, if not essential, when classifying the 3D shapes of proteins at the domain family level.

Domain family classification is also relevant for studying domain-domain interactions (DDI). Our previous work on Knowledge-Based Docking (KBDOCK, , will be updated and extended using newly published DDIs. Methods for inferring new DDIs from existing protein-protein interactions (PPIs) will be developped. Efforts should be made for validating such inferred DDIs so that they can be used to enrich DDI classification and predict new PPIs.

In parallel, we also intend to design algorithms for leveraging information embedded in biological knowledge graphs (also known as complex networks). Knowledge graphs mostly represent PPIs, integrated with various properties attached to proteins, such as pathways, drug binding or relation with diseases. Setting up similarity measures for proteins in a knowledge graph is a difficult challenge. Our objective is to extract useful knowledge from such graphs in order to better understand and highlight the role of multi-component assemblies in various types of cell or organisms. Ultimately, knowledge graphs can be used to model and simulate the functioning of such molecular machinery in the context of the living cell, under physiological or pathological conditions.

Knowledge of the functional properties of proteins can shed considerable light on how they might interact. However, huge numbers of protein sequences in public databases such as UniProt/TrEMBL lack any functional annotation, and the functional annotation of such sequences is a highly challenging problem. We are developing graph-based and machine learning techniques to annotate automatically the available unannotated sequences with functional properties such as EC numbers and Gene Ontology (GO) terms (note that these terms are organized hierarchically allowing generalization/specialization reasoning). The idea is to transfer annotations from expert-reviewed sequences present in the UniProt/SwissProt database (about 560 thousands entries) to unreviewed sequences present in the UniProt/TrEMBL database (about 80% of 180 millions entries). For this, we have to learn from the UniProt/SwissProt database how to compute the similarity of proteins sharing identical or similar functional annotations. Various similarity measures can be tested using cross-validation approches in the UniProt/SwissProt database. For instance, we can use primary sequence or domain signature similarities. More complex similarities can be computed with graph-embedding techniques.

This work is in progress with Bishnu Sarker's PhD project and a first approach called GrAPFI (Graph-based Automatic Protein Function Inference) was presented at conferences in 2018 , .

At the molecular level, each PPI is embodied by a physical 3D protein-protein interface. Therefore, if the 3D structures of a pair of interacting proteins are known, it should in principle be possible for a docking algorithm to use this knowledge to predict the structure of the complex. However, modeling protein flexibility accurately during docking is very computationally expensive. This is due to the very large number of internal degrees of freedom in each protein, associated with twisting motions around covalent bonds. Therefore, it is highly impractical to use detailed force-field or geometric representations in a brute-force docking search. Instead, most protein docking algorithms use fast heuristic methods to perform an initial rigid-body search in order to locate a relatively small number of candidate binding orientations, and these are then refined using a more expensive interaction potential or force-field model, which might also include flexible refinement using molecular dynamics (MD), for example.

In our Hex protein docking program , the shape of a protein molecule is represented using polar Fourier series expansions of the form

where $\sigma \left(\underline{x}\right)$ is a 3D shape-density function, $a_{nlm}$ are the expansion coefficients, $R_{nl}\left(r\right)$ are orthonormal Gauss-Laguerre polynomials and $y_{lm}(\theta ,\phi )$ are the real spherical harmonics. The electrostatic potential, $\phi \left(\underline{x}\right)$, and charge density, $\rho \left(\underline{x}\right)$, of a protein may be represented using similar expansions. Such representations allow the in vacuo electrostatic interaction energy between two proteins, A and B, to be calculated as

This equation demonstrates using the notion of overlap between 3D scalar quantities to give a physics-based scoring function. If the aim is to find the configuration that gives the most favourable interaction energy, then it is necessary to perform a six-dimensional search in the space of available rotational and translational degrees of freedom. By re-writing the polar Fourier expansions using complex spherical harmonics, we showed previously that fast Fourier transform (FFT) techniques may be used to accelerate the search in up to five of the six degrees of freedom . Furthermore, we also showed that such calculations may be accelerated dramatically on modern graphics processor units , . Consequently, we are continuing to explore new ways to exploit the polar Fourier approach.

Although protein-protein docking algorithms are improving , , it still remains challenging to produce a high resolution 3D model of a protein complex using ab initio techniques. This is mainly due to the problem of structural flexibility described above. However, with the aid of even just one simple constraint on the docking search space, the quality of docking predictions can improve considerably , . In particular, many protein complexes involve symmetric arrangements of one or more sub-units, and the presence of symmetry may be exploited to reduce the search space considerably , , . For example, using our operator notation (in which $\widehat{R}$ and $\widehat{T}$ represent 3D rotation and translation operators, respectively), we have developed an algorithm which can generate and score candidate docking orientations for monomers that assemble into cyclic ($C_n$) multimers using 3D integrals of the form

where the identical monomers A and B are initially placed at the origin, and ${\omega }_n=2\pi /n$ is the rotation about the principal $n$-fold symmetry axis. This example shows that complexes with cyclic symmetry have just 4 rigid body degrees of freedom (DOFs), compared to $6(n-1)$ DOFs for non-symmetrical $n$-mers. We have generalised these ideas in order to model protein complexes that crystallise into any of the naturally occurring point group symmetries ($C_n$, $D_n$, $T$, $O$, $I$). This approach was published in 2016 , and was subsequently applied to several symmetrical complexes from the “CAPRI” blind docking experiment . Although we currently use shape-based FFT correlations, the symmetry operator technique may equally be used to build and refine candidate solutions using a more accurate coarse-grained (CG) force-field scoring function.

Many approaches have been proposed in the literature to take into account protein flexibility during docking. The most thorough methods rely on expensive atomistic simulations using MD. However, much of a MD trajectory is unlikely to be relevant to a docking encounter unless it is constrained to explore a putative protein-protein interface. Consequently, MD is normally only used to refine a small number of candidate rigid body docking poses. A much faster, but more approximate method is to use "coarse-grained" (CG) normal mode analysis (NMA) techniques to reduce the number of flexible degrees of freedom to just one or a handful of the most significant vibrational modes , , , . In our experience, docking ensembles of NMA conformations does not give much improvement over basic FFT-based soft docking , and it is very computationally expensive to use side-chain repacking to refine candidate soft docking poses .

In the last few years, CG force-field models have become increasingly popular in the MD community because they allow very large biomolecular systems to be simulated using conventional MD programs . Typically, a CG force-field representation replaces the atoms in each amino acid with from 2 to 4 “pseudo-atoms”, and it assigns each pseudo-atom a small number of parameters to represent its chemo-physical properties. By directly attacking the quadratic nature of pair-wise energy functions, coarse-graining can speed up MD simulations by up to three orders of magnitude. Nonetheless, such CG models can still produce useful models of very large multi-component assemblies . Furthermore, this kind of CG model effectively integrates out many of the internal DOFs to leave a smoother but still physically realistic energy surface . We are currently developing a CG scoring function for fast protein-protein docking and multi-component assembly. This work is part of the PhD project of Maria-Elisa Ruiz-Echartea , . Beyond this PhD project, the CG scoring function will be exploited in all our docing projects, especially for RNA-Protein docking (see below).

We also want to develop related approaches for integrative structure modeling using cryo-electron microscopy (cryo-EM). Thanks to recent developments in cryo-EM instruments and technologies, it is now feasible to capture low resolution images of very large macromolecular machines. However, while such developments offer the intriguing prospect of being able to trap biological systems in unprecedented levels of detail, there will also come with an increasing need to analyse, annotate, and interpret the enormous volumes of data that will soon flow from the latest instruments. In particular, a new challenge that is emerging is how to fit previously solved high resolution protein structures into low resolution cryo-EM density maps. However, the problem here is that large molecular machines will have multiple sub-components, some of which will be unknown, and many of which will fit each part of the map almost equally well. Thus, the general problem of building high resolution 3D models from cryo-EM data is like building a complex 3D jigsaw puzzle in which several pieces may be unknown or missing, and none of which will fit perfectly. We wish to proceed firstly by putting more emphasis on the single-body terms in the scoring function , and secondly by using fast CG representations and knowledge-based distance restraints to prune large regions of the search space. This work has made some progress during the PhD project of Maria Elisa Ruiz Echartea but still requires further efforts.

As well as playing an essential role in the translation of DNA into proteins, RNA molecules carry out many other essential biological functions in cells, often through their interactions with proteins. A critical challenge in modelling such interactions computationally is that the RNA is often highly flexible, especially in single-stranded (ssRNA) regions of its structure. These flexible regions are often very important because it is through their flexibility that the RNA can adjust its 3D conformation in order to bind to a protein surface. However, conventional protein-protein docking algorithms generally assume that the 3D structures to be docked are rigid, and so are not suitable for modeling protein-RNA interactions. There is therefore much interest in developing protein-RNA docking algorithms which can take RNA flexibility into account. This research topic has been initiated with the recruitement of Isaure Chauvot de Beauchêne in 2016 and is becoming a major activity in the team. A novel flexible docking algorithm is currently under development in the team. It first docks small fragments of ssRNA (typically three nucleotides at a time) onto a protein surface, and then combinatorially reassembles those fragments in order to recover a contiguous ssRNA structure on the protein surface , .

As the correctness of the initial docking of the fragments settles an upper limit to the correctness of the full model, we are now focusing on improving that step. A key component of our docking tool is the energy function of the protein - fragment interactions, that is used both to drive the sampling (positioning of the fragments) by minimization and to discriminate the correct final positions from decoys (i.e. false positives). We are developing a new knowledge-based energy function that will be learnt by machine-learning methods from public structural data on ssRNA-protein complexes.

In the future, we will improve the combinatorial algorithm used for reassembling the docked fragments using experimental constraints and machine-learning approaches.