Computational Structural Biology (CSB) is the scientific domain
concerned with the development of algorithms and software to
understand and predict the structure and function of biological
macromolecules.
This research field is inherently multi-disciplinary.
On the experimental side, biology and medicine provide the objects
studied, while biophysics and bioinformatics supply experimental data, which are of two
main kinds. On the one hand, genome sequencing projects give supply
protein sequences, and ~200 millions of sequences have been archived in UniProtKB/TrEMBL – which collects the protein sequences yielded
by genome sequencing projects. On the other hand, structure
determination experiments (notably X-ray crystallography, nuclear magnetic resonance, and
cryo-electron microscopy) give access to geometric models of molecules
– atomic coordinates.
Alas, only ~150,000 structures have been solved and deposited in
the Protein Data Bank (PDB), a number to be compared against the
UniProtKB/TrEMBL. With one
structure for ~1000 sequences, we hardly know anything about
biological functions at the atomic/structural level.
Complementing experiments, physical chemistry/chemical physics supply
the required models (energies, thermodynamics, etc). More
specifically, let us recall that proteins with lock-and-key metaphor
for interacting molecules, Biology is based on the interactions stable
conformations make with each other. Turning these intuitive notions
into quantitative ones requires delving into statistical physics, as
macroscopic properties are average properties computed over ensembles
of conformations.
Developing effective algorithms to perform accurate simulations is
especially challenging for two main reasons. The first one is the high
dimension of conformational spaces – see tour
de force rarely achieved 45.

The first challenge, sequence-to-structure prediction, aims to
infer the possible structure(s) of a protein from its amino acid
sequence. While recent progress has been made
recently using in particular deep learning techniques
44, the models obtained so far are
static and coarse-grained.

The second one is protein function prediction. Given a protein
with known structure, i.e., 3D coordinates, the goal is to predict the
partners of this protein, in terms of stability and
specificity. This understanding is fundamental to biology and
medicine, as illustrated by the example of the SARS-CoV-2 virus
responsible of the Covid19 pandemic. To infect a host, the virus first
fuses its envelope with the membrane of a target cell, and then
injects its genetic material into that cell. Fusion is achieved by a
so-called class I fusion protein, also found in other viruses
(influenza, SARS-CoV-1, HIV, etc). The fusion process is a highly
dynamic process involving large amplitude conformational changes of
the molecules. It is poorly understood, which hinders our ability to
design therapeutics to block it.

Finally, the third one, large assembly reconstruction,
aims at solving (coarse-grain) structures of molecular machines involving
tens or even hundreds of subunits. This research vein was promoted
about 15 years back by the work on the nuclear pore complex
32. It is often referred to as reconstruction by
data integration, as it necessitates to combine coarse-grain models
(notably from cryo-electron microscopy (cryo-EM) and native mass
spectrometry) with atomic models of subunits obtained from X ray
crystallography.
Fitting the latter into the former requires exploring
the conformation space of subunits, whence the importance of protein
dynamics.

As an illustration of these three challenges, consider
the problem of designing proteins blocking the entry of SARS-CoV-2 into our cells
(Fig. 1).
The first challenge is illustrated by the problem of predicting the
structure of a blocker protein from its sequence of amino-acids – a tractable
problem here since the mini proteins used only comprise of the order
of 50 amino-acids (Fig. 1(A), 35).
The second challenge is illustrated by the calculation of the binding
modes and the binding affinity of the designed proteins for the RBD of
SARS-CoV-2 (Fig. 1(B)).
Finally, the last challenge
is illustrated by the problem of solving structures of the virus
with a cell, to understand how many spikes are involved in the fusion
mechanism leading to infection.
In 35, the promising designs suggested by modeling
have been assessed by an array of wet lab experiments (affinity
measurements, circular dichroism for thermal stability assessment,
structure resolution by cryo-EM).
The hyperstable minibinders identified provide starting points
for SARS-CoV-2 therapeutics 35.
We note in passing that this is truly remarkable work, yet, the
designed proteins stem from a template (the bottom helix from
ACE2), and are rather small.

To present challenges in structural modeling, let us recall the following ingredients
(Fig. 2). First, a molecular model with d.o.f.).
Second, recall that the potential energy landscape (PEL) is the
mapping CHARMM, AMBER, MARTINI, etc. Such PE belong to the realm of molecular mechanics,
and implement atomic or coarse-grain models. They may embark a solvent
model, either explicit or implicit. Their definition requires a
significant number of parameters (up to

These PE are usually considered good enough to study non covalent interactions – our focus, even tough they do not cover the modification of chemical bonds. In any case, we take such a function for granted 1.

The PEL codes all structural, thermodynamic, and kinetic properties, which can be obtained by averaging
properties of
conformations over so-called thermodynamic ensembles.
The structure of a macromolecular system requires the
characterization of active conformations and important intermediates
in functional pathways involving significant basins.
In assigning occupation probabilities to these conformations by
integrating Boltzmann's distribution, one treats thermodynamics.
Finally, transitions between the states,
modeled, say, by a master equation (a continuous-time Markov process),
correspond to kinetics.
Classical simulation methods based on molecular dynamics (MD)
and Monte Carlo sampling (MC) are developed in the lineage of the
seminal work by the 2013 recipients of the Nobel prize in chemistry
(Karplus, Levitt, Warshel), which was awarded “for the
development of multiscale models for complex chemical systems”.
However, except for highly specialized cases where massive
calculations have been used 45, neither MD nor MC
give access to the aforementioned time scales. In fact, the main
limitation of such methods is that they treat structural,
thermodynamic and kinetic aspects at once
39. The absence of specific
insights on these three complementary pieces of the puzzle makes it
impossible to optimize simulation methods, and results in general in
the inability to obtain converged simulations on biologically relevant
time-scales.

The hardness of structural modeling owes to three intertwined reasons.

First, PELs of biomolecules usually exhibit a number of critical
points exponential in the dimension 33; fortunately, they
enjoy a multi-scale structure 36.
Intuitively, the significant local minima/basins are those which are
deep or isolated/wide, two notions which are mathematically
qualified by the concepts of persistence and prominence.
Mathematically, problems are plagued with the curse of dimensionality and measure concentration phenomena.
Second, biomolecular processes are inherently multi-scale, with motions spanning
i.e., observables, are
average properties computed over ensembles of conformations, which calls
for a multi-scale statistical treatment both of thermodynamics and kinetics.

A natural and critical question naturally concerns the validation of models proposed in structural bioinformatics. For all three types of questions of interest (structures, thermodynamics, kinetics), there exist experiments to which the models must be confronted – when the experiments can be conducted.

For structures, the models proposed can readily be compared against
experimental results stemming from X ray crystallography, NMR, or cryo
electron microscopy. For thermodynamics, which we illustrate here
with binding affinities, predictions can be compared against
measurements provided by calorimetry or surface plasmon resonance.
Lastly, kinetic predictions can also be assessed by various experiments
such as binding affinity measurements (for the prediction of

Our research program ambition to develop a comprehensive set of novel concepts and algorithms to study protein dynamics, based on the modular framework of PEL.

As noticed while discussing Protein dynamics: core CS -
maths challenges, the integrated nature of simulation methods such
as MD or MC is such that these methods do not in general give access to
biologically relevant time scales.
The framework of energy landscapes
46, 43 (Fig. 2) is
much more modular, yet, large biomolecular systems remain out of
reach.

To make a definitive step towards solving the prediction of protein
dynamics, we will serialize the discovery and the exploitation of a
PEL 4, 13, 3.
Ideas and concepts from computational geometry/geometric motion
planning, machine learning, probabilistic algorithms, and numerical
probability will be used to develop two classes of probabilistic
algorithms.
The first deals with algorithms to discover/sketch PELs, i.e., enumerate
all significant (persistent or prominent) local minima and their
connections across saddles, a difficult task since the number of all
local minima/critical points is generally exponential in the
dimension. To this end, we will develop a hierarchical data structure
coding PELs as well as multi-scale proposals to explore molecular
conformations. (NB: in Monte Carlo methods, a proposal generates a new
conformation from an existing one.)
The second focuses on methods to exploit/sample PELs, i.e., compute
so-called densities of states, from which all thermodynamic quantities
are given by standard
relations 3442. This is a
hard problem akin to high-dimensional numerical integration. To solve
this problem, we will develop a learning based strategy for the
Wang-Landau algorithm 41–an adaptive Monte Carlo
Markov Chain (MCMC) algorithm, as well as a generalization of
multi-phase Monte Carlo methods for convex/polytope volume
calculations 40, 38, for non
convex strata of PELs.

As discussed in the previous Section, the study of PEL and protein dynamics raises difficult algorithmic / mathematical questions. As an illustration, one may consider our recent work on the comparison of high dimensional distribution 6, statistical tests / two-sample tests 7, 10, the comparison of clustering 8, the complexity study of graph inference problems for low-resolution reconstruction of assemblies 9, the analysis of partition (or clustering) stability in large networks, the complexity of the representation of simplicial complexes 2. Making progress on such questions is fundamental to advance the state-of-the art on protein dynamics.

We will continue to work on such questions, motivated by CSB / theoretical biophysics, both in the continuous (geometric) and discrete settings. The developments will be based on a combination of ideas and concepts from computational geometry, machine learning (notably on non linear dimensionality reduction, the reconstruction of cell complexes, and sampling methods), graph algorithms, probabilistic algorithms, optimization, numerical probability, and also biophysics.

While our main ambition is to advance the algorithmic foundations
of molecular simulation, a major challenge will be to ensure that the
theoretical and algorithmic developments will change the fate of
applications, as illustrated by our case studies.
To foster such a symbiotic relationship between theory, algorithms and
simulation, we will pursue high quality software development and
integration within the SBL, and will also take the appropriate
measures for the software to be widely adopted.

Software development for structural bioinformatics is especially
challenging, combining advanced geometric, numerical and combinatorial
algorithms, with complex biophysical models for PEL and related
thermodynamic/kinetic properties. Specific features of the proteins
studied must also be accommodated.
About 50 years after the development of force fields and simulation
methods (see the 2013 Nobel prize in chemistry), the software implementing
such methods has a profound impact on molecular science at large.
One can indeed cite packages such as
CHARMM,
AMBER,
gromacs,
gmin,
MODELLER,
Rosetta,
VMD,
PyMol, ....
On the other hand, these packages are goal oriented, each tackling a
(small set of) specific goal(s). In fact, no real modular software
design and integration has taken place.
As a result, despite the high quality software packages available,
inter-operability between algorithmic building blocks has remained
very limited.

Predicting the dynamics of large molecular systems
requires the integration of advanced algorithmic building blocks /
complex software components.
To achieve a sufficient level of integration, we undertook the
development of the Structural Bioinformatics Library (SBL,
SB) 5,
a generic C++/python cross-platform library providing software to solve complex
problems in structural bioinformatics.
For end-users, the SBL provides ready to use, state-of-the-art
applications to model macro-molecules and their complexes at various
resolutions, and also to store results in perennial and easy to use data
formats (SBL Applications).
For developers, the SBL provides a broad C++/python toolbox with
modular design (SBL Doc).
This hybrid status targeting both end-users and developers stems from
an advanced software design involving four software components, namely
applications, core algorithms, biophysical models, and modules
(SBL Modules).
This modular design makes it possible to optimize robustness and the
performance of individual components, which can then be assembled
within a goal oriented application.

Our methods will be validated on various systems for which flexibility operates at various scales. Example such systems are antibody-antigen complexes, (viral) polymerases, (membrane) transporters.

Even very complex biomolecular systems are deterministic in prescribed
conditions (temperature, pH, etc), demonstrating that despite their
high dimensionality, all d.o.f. are not at play at the same time. This
insight suggests three classes of systems of particular interest.
The first class consists of systems defined from (essentially) rigid blocks
whose relative positions change thanks to conformational changes of
linkers; a Newton cradle provides an interesting way to envision such
as system. We have recently worked on one such system, a membrane
proteins involve in antibiotic resistance (AcrB, see
14).
The second class consists of cases where relative positions of subdomains do
not significantly change, yet, their intrinsic dynamics are
significantly altered. A classical illustration is provided by
antibodies, whose binding affinity owes to dynamics localized in six
specific loops 11, 12.
The third class, consisting of composite cases, will greatly benefit
from insights on the first two classes. As an example, we may
consider the spikes of the SARS-CoV-2 virus, whose function (performing
infection) involves both large amplitude conformational changes and
subtle dynamics of the so-called receptor binding domain. We have
started to investigate this system, in collaboration with B. Delmas
(INRAe) 15.

In ABS, we will investigate systems in these three tiers, in collaboration with expert collaborators, to hopefully open new perspectives in biology and medicine. Along the way, we will also collaborate on selected questions at the interface between CSB and systems biology, as it is now clear that the structural level and the systems level (pathways of interacting molecules) can benefit from one another.

The main application domain is Computational Structural Biology, as
underlined in the Research Program.

A tenet of ABS is to carefully analyse the performances of the algorithms designed–either formally or experimentally, so as to avoid massive calculations. Therefore, the footprint of our research activities has remained limited.

The scientific agenda of ABS is geared towards a fine understanding of
complex phenomena at the atomic/molecular level. While the current
focus is rather fundamental, as explained in Research program,
an overarching goal for the current period (i.e. 12 years) is to make
significant contributions to important problems in biology and
medicine.

In Decembre 2022, Côme Le Breton has joined ABS as engineer in charge of the Structural Bioinformatics Library. This is a critical addition which will help the project-team streamline the distribution of the library, help new users, evolve the code basis (C++, python), and integrate new packages.

A main achievement has been
the completion of the PhD thesis of Timothee O'Donnell,
entitled A kinematic view of protein loop flexibility, with applications to conformational exploration 29.
As detailed in the Results section, the thesis indeed proposes novel
sampling algorithms to explore the conformational space of flexible
proteins. These non supervised approaches are in sharp contrast with a
number of ongoing works based on deep learning techniques exploiting
static databases of protein structures.
See also 37.

Finally, TerraNumerica@Sophia has been inaugurated on June 11th, 2022. Terra Numerica is an ambitious scientific popularisation project and its main goal is to develop a "Dedicated Digital space" in the south of France, (in the spirit of the "Cité des Sciences" or "Palais de la découverte" in Paris).

Flexible loops are paramount to protein functions, with action modes ranging from localized dynamics contributing to the free energy of the system, to large amplitude conformational changes accounting for the repositioning whole secondary structure elements or protein domains. However, generating diverse and low energy loops remains a difficult problem.

This work 24 introduces a novel paradigm to sample loop conformations, in
the spirit of the Hit-and-Run (HAR) Markov chain Monte Carlo
technique. The algorithm uses a decomposition of the loop into
tripeptides, and a novel characterization of necessary conditions for
Tripeptide Loop Closure to admit solutions. Denoting

Designing movesets providing high quality protein conformations
remains a hard problem, especially when it comes to deform a long
protein backbone segment, and a key building block to do so is the
so-called tripeptide loop closure (TLC) 21. Consider a tripeptide whose
first and last bonds (

In this work 23, we relax the previous constraints, allowing the last
bond (

Computing the volume of a polytope in high dimensions is
computationally challenging but has wide
applications 18. Current state-of-the-art
algorithms to compute such volumes rely on efficient sampling of a
Gaussian distribution restricted to the polytope, using, e.g.,
Hamiltonian Monte Carlo. In this work
27, we present a new sampling strategy
that uses a Piecewise Deterministic Markov Process. Like Hamiltonian
Monte Carlo, this new method involves simulating trajectories of a
non-reversible process and inherits similar good mixing
properties. However, importantly, the process can be simulated more
easily due to its piecewise linear trajectories — and this leads to a
reduction of the computational cost by a factor of the dimension of
the space. Our experiments indicate that our method is numerically
robust and is one order of magnitude faster (or better) than existing
methods using Hamiltonian Monte Carlo. On a single core processor, we
report computational time of a few minutes up to dimension 500.

In 19, we analyze a generalization of the
minimum connectivity inference problem (MCI) that models the
computation of low-resolution structures of macro-molecular
assemblies, based on data obtained by native mass spectrometry. The
generalization studied in this work, allows us to consider more
refined constraints for the characterization of low resolution models
of large assemblies, such as degree constraints (e.g., a protein has a
limited number of other proteins in contact).

More precisely, let

Given a graph

In 30, we first establish the complexity dichotomies (polynomial vs NP-complete) for Conflict Coloring and its variants. We provide some experiments in which we build instances of Conflict Coloring associated to Voronoi diagram in the plane, and we then analyse the existences of a solution related to parameters used in our experimental setup.

Prioritizing genes for their role in drug sensitivity, is an important
step in understanding drugs mechanisms of action and discovering new
molecular targets for co-treatment.
In this work 25, we formalize this problem by
considering two sets of genes Genetrank, a method to prioritize the genes in

Genetrank uses asymmetric random walks with
restarts, absorbing states, and a suitable renormalization scheme.
Using novel so-called saturation indices, we show that the conjunction
of absorbing states and renormalization yields an exploration of the
PPIN which is much more progressive than that afforded by random walks
with restarts only.
Using MINT as underlying network, we apply Genetrank to a
predictive gene signature of cancer cells sensitivity to
tumor-necrosis-factor-related apoptosis-inducing ligand (TRAIL),
performed in single-cells. Our ranking provides biological insights
on drug sensitivity and a gene set considerably enriched in genes
regulating TRAIL pharmacodynamics when compared to the most
significant differentially expressed genes obtained from a statistical
analysis framework alone. We also introduce gene expression
radars, a visualization tool to assess all pairwise interactions at
a glance.

Genetrank is made available in
the Structural Bioinformatics Library
(Genetrank). It
should prove useful for mining gene sets in conjunction with a
signaling pathway, whenever other approaches yield relatively large
sets of genes.

Among the peculiar characteristics shared by membrane proteins,
evolutionary divergence of their sequences and low compositional
complexity of their hydrophobic regions are important obstacles often
preventing their correct alignment with traditional algorithms.
The AlignMe method and the corresponding AlignMe webserver
have been improving throughout the last decade by integrating ever
more information sources on top of a generalized version of the classical
Needleman-Wunsch algorithm. Yet, user-guided information (e.g., coming from
individual and point-wise experimental setups) were still excluded from
the AlignMe input types.

In this work 26 we release a new version of the AlignMe webserver that allows the user to bias the resulting sequence alignment with an arbitrary number of forced couplings called anchors, yet still retaining the global optimization given by the extended Needleman-Wunsch algorithm.

Other technical advancements include the possibility of submitting job batches and the visualization of the alignment characteristics on any user-provided structure.

Chloroplast fructose-1,6-bisphosphate aldolase (FBA) is an enzyme taking
part in the Calvin-Benson cycle, responsible for fixing carbon dioxide into
organic triosephosphates. In the unicellular green alga Chlamydomonas
reinhardtii (Cr), FBA has four paralogs: the chloroplast FBA and other
three cytoplasmic enzymes that are not connected with photosynthesis and
whose functions have been extensively studied. This work 20
describes the newly obtained crystal structure of plastidial FBA from
C. reinhardtii.

The functional annotation of this molecule has been confirmed using ProfileView, a novel algorithm for protein function prediction based on hidden Markov models able to discriminate functional patterns without needing input multiple sequence alignments. For the first time, we applied ProfileView for discriminating the function of paralgous sequences, which are much more similar in sequence identity than the average similarity between any two protein sequences chosen at random from a same family.

ProfileView has also been able to highlight structural feature that are key differences between FBA paralogs. This has paved the way for a more generic study of paralog functional annotation with ProfileView.

Residue coevolution signals provide most of the information for even the most advanced, AI-based approaches to protein structure prediction. This work 22 presents iBISAnalyzer, a new freely available web server that implements iBIS2, an iterative version of the Blocks in Sequence (BIS) algorithm for finding groups of coevolving residues.

For the first time the user can visualize, compare and inspect clusters of coevolving residues by mapping them onto sequences, alignments or structures of choice, greatly simplifying downstream analysis steps. A rich and interactive graphic interface facilitates the biological interpretation of the results.

Frédéric Cazals participated to the following program committees:

PhD thesis:

Frédéric Cazals participated to the following committees:

Frédéric Cazals authored the following article L’intelligence artificielle au défi du design de protéines : des prouesses et limites d’AlphaFold.

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