MinActionPath2: path generation between different conformations of large macromolecular assemblies by action minimization.

Recent progress in solving macromolecular structures and assemblies by cryogenic electron microscopy techniques enables sampling of their conformations in different states that are relevant to their biological function. Knowing the transition path between these conformations would provide new avenues for drug discovery. While the experimental study of transition paths is intrinsically difficult, in-silico methods can be used to generate an initial guess for those paths. The Elastic Network Model (ENM), along with a coarse-grained representation (CG) of the structures are among the most popular models to explore such possible paths. Here we propose an update to our software platform MinActionPath that generates non-linear transition paths based on ENM and CG models, using action minimization to solve the equations of motion. The new website enables the study of large structures such as ribosomes or entire virus envelopes. It provides direct visualization of the trajectories along with quantitative analyses of their behaviors at http://dynstr.pasteur.fr/servers/minactionpath/minactionpath2_submission.

Molecular basis for proofreading by the unique exonuclease domain of Family-D DNA polymerases.

Replicative DNA polymerases duplicate entire genomes at high fidelity. This feature is shared among the three domains of life and is facilitated by their dual polymerase and exonuclease activities. Family D replicative DNA polymerases (PolD), found exclusively in Archaea, contain an unusual RNA polymerase-like catalytic core, and a unique Mre11-like proofreading active site. Here, we present cryo-EM structures of PolD trapped in a proofreading mode, revealing an unanticipated correction mechanism that extends the repertoire of protein domains known to be involved in DNA proofreading. Based on our experimental structures, mutants of PolD were designed and their contribution to mismatch bypass and exonuclease kinetics was determined. This study sheds light on the convergent evolution of structurally distinct families of DNA polymerases, and the domain acquisition and exchange mechanism that occurred during the evolution of the replisome in the three domains of life.

Analyzing the Geometry and Dynamics of Viral Structures: A Review of Computational Approaches Based on Alpha Shape Theory, Normal Mode Analysis, and Poisson-Boltzmann Theories.

The current SARS-CoV-2 pandemic highlights our fragility when we are exposed to emergent viruses either directly or through zoonotic diseases. Fortunately, our knowledge of the biology of those viruses is improving. In particular, we have more and more structural information on virions, i.e., the infective form of a virus that includes its genomic material and surrounding protective capsid, and on their gene products. It is important to have methods that enable the analyses of structural information on such large macromolecular systems. We review some of those methods in this paper. We focus on understanding the geometry of virions and viral structural proteins, their dynamics, and their energetics, with the ambition that this understanding can help design antiviral agents. We discuss those methods in light of the specificities of those structures, mainly that they are huge. We focus on three of our own methods based on the alpha shape theory for computing geometry, normal mode analyses to study dynamics, and modified Poisson-Boltzmann theories to study the organization of ions and co-solvent and solvent molecules around biomacromolecules. The corresponding software has computing times that are compatible with the use of regular desktop computers. We show examples of their applications on some outer shells and structural proteins of the West Nile Virus.

DNA-binding mechanism and evolution of replication protein A.

Replication Protein A (RPA) is a heterotrimeric single stranded DNA-binding protein with essential roles in DNA replication, recombination and repair. Little is known about the structure of RPA in Archaea, the third domain of life. By using an integrative structural, biochemical and biophysical approach, we extensively characterize RPA from Pyrococcus abyssi in the presence and absence of DNA. The obtained X-ray and cryo-EM structures reveal that the trimerization core and interactions promoting RPA clustering on ssDNA are shared between archaea and eukaryotes. However, we also identified a helical domain named AROD (Acidic Rpa1 OB-binding Domain), and showed that, in Archaea, RPA forms an unanticipated tetrameric supercomplex in the absence of DNA. The four RPA molecules clustered within the tetramer could efficiently coat and protect stretches of ssDNA created by the advancing replisome. Finally, our results provide insights into the evolution of this primordial replication factor in eukaryotes.

Reclassification of family A DNA polymerases reveals novel functional subfamilies and distinctive structural features.

Family A DNA polymerases (PolAs) form an important and well-studied class of extant polymerases participating in DNA replication and repair. Nonetheless, despite the characterization of multiple subfamilies in independent, dedicated works, their comprehensive classification thus far is missing. We therefore re-examine all presently available PolA sequences, converting their pairwise similarities into positions in Euclidean space, separating them into 19 major clusters. While 11 of them correspond to known subfamilies, eight had not been characterized before. For every group, we compile their general characteristics, examine their phylogenetic relationships and perform conservation analysis in the essential sequence motifs. While most subfamilies are linked to a particular domain of life (including phages), one subfamily appears in Bacteria, Archaea and Eukaryota. We also show that two new bacterial subfamilies contain functional enzymes. We use AlphaFold2 to generate high-confidence prediction models for all clusters lacking an experimentally determined structure. We identify new, conserved features involving structural alterations, ordered insertions and an apparent structural incorporation of a uracil-DNA glycosylase (UDG) domain. Finally, genetic and structural analyses of a subset of T7-like phages indicate a splitting of the 3'-5' exo and pol domains into two separate genes, observed in PolAs for the first time.

Structural dynamics and determinants of 2-aminoadenine specificity in DNA polymerase DpoZ of vibriophage ϕVC8.

All genetic information in cellular life is stored in DNA copolymers composed of four basic building blocks (ATGC-DNA). In contrast, a group of bacteriophages belonging to families Siphoviridae and Podoviridae has abandoned the usage of one of them, adenine (A), replacing it with 2-aminoadenine (Z). The resulting ZTGC-DNA is more stable than its ATGC-DNA counterpart, owing to the additional hydrogen bond present in the 2-aminoadenine:thymine (Z:T) base pair, while the additional amino group also confers resistance to the host endonucleases. Recently, two classes of replicative proteins found in ZTGC-DNA-containing phages were characterized and one of them, DpoZ from DNA polymerase A (PolA) family, was shown to possess significant Z-vs-A specificity. Here, we present the crystallographic structure of the apo form of DpoZ of vibriophage ϕVC8, composed of the 3'-5' exonuclease and polymerase domains. We captured the enzyme in two conformations that involve the tip of the thumb subdomain and the exonuclease domain. We highlight insertions and mutations characteristic of ϕVC8 DpoZ and its close homologues. Through mutagenesis and functional assays we suggest that the preference of ϕVC8 DpoZ towards Z relies on a polymerase backtracking process, more efficient when the nascent base pair is A:T than when it is Z:T.

Extracting Dynamical Correlations and Identifying Key Residues for Allosteric Communication in Proteins by correlationplus.

Extracting dynamical pairwise correlations and identifying key residues from large molecular dynamics trajectories or normal-mode analysis of coarse-grained models are important for explaining various processes like ligand binding, mutational effects, and long-distance interactions. Efficient and flexible tools to perform this task can provide new insights about residues involved in allosteric regulation and protein function. In addition, combining and comparing dynamical coupling information with sequence coevolution data can help to understand better protein function. To this aim, we developed a Python package called correlationplus to calculate, visualize, and analyze pairwise correlations. In this way, the package aids to identify key residues and interactions in proteins. The source code of correlationplus is available under LGPL version 3 at https://github.com/tekpinar/correlationplus. The current version of the package (0.2.0) can be installed with common installation methods like conda or pip in addition to source code installation. Moreover, docker images are also available for usage of the code without installation.

Characterization of a triad of genes in cyanophage S-2L sufficient to replace adenine by 2-aminoadenine in bacterial DNA.

Cyanophage S-2L is known to profoundly alter the biophysical properties of its DNA by replacing all adenines (A) with 2-aminoadenines (Z), which still pair with thymines but with a triple hydrogen bond. It was recently demonstrated that a homologue of adenylosuccinate synthetase (PurZ) and a dATP triphosphohydrolase (DatZ) are two important pieces of the metabolism of 2-aminoadenine, participating in the synthesis of ZTGC-DNA. Here, we determine that S-2L PurZ can use either dATP or ATP as a source of energy, thereby also depleting the pool of nucleotides in dATP. Furthermore, we identify a conserved gene (mazZ) located between purZ and datZ genes in S-2L and related phage genomes. We show that it encodes a (d)GTP-specific diphosphohydrolase, thereby providing the substrate of PurZ in the 2-aminoadenine synthesis pathway. High-resolution crystal structures of S-2L PurZ and MazZ with their respective substrates provide a rationale for their specificities. The Z-cluster made of these three genes - datZ, mazZ and purZ - was expressed in E. coli, resulting in a successful incorporation of 2-aminoadenine in the bacterial chromosomal and plasmidic DNA. This work opens the possibility to study synthetic organisms containing ZTGC-DNA.

Parameterizing elastic network models to capture the dynamics of proteins.

Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

Simultaneous Identification of Multiple Binding Sites in Proteins: A Statistical Mechanics Approach.

We present an extension of the Poisson-Boltzmann model in which the solute of interest is immersed in an assembly of self-orienting Langevin water dipoles, anions, cations, and hydrophobic molecules, all of variable densities. Interactions between charges are controlled by electrostatics, while hydrophobic interactions are modeled with a Yukawa potential. We impose steric constraints by assuming that the system is represented on a cubic lattice. We also assume incompressibility; i.e., all sites of the lattice are occupied. This model, which we refer to as the Hydrophobic Dipolar Poisson-Boltzmann Langevin (HDPBL) model, leads to a system of two equations whose solutions give the water dipole, salt, and hydrophobic molecule densities, all of them in the presence of the others in a self-consistent way. We use those to study the organization of the ions, cosolvent, and solvent molecules around proteins. In particular, peaks of densities are expected to reveal, simultaneously, the presence of compatible binding sites of different kinds on a protein. We have tested and validated the ability of HDPBL to detect pockets in proteins that bind to hydrophobic ligands, polar ligands, and charged small probes as well as to characterize the binding sites of lipids for membrane proteins.

Fast and efficient purification of SARS-CoV-2 RNA dependent RNA polymerase complex expressed in Escherichia coli.

To stop the COVID-19 pandemic due to the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), which caused more than 2.5 million deaths to date, new antiviral molecules are urgently needed. The replication of SARS-CoV-2 requires the RNA-dependent RNA polymerase (RdRp), making RdRp an excellent target for antiviral agents. RdRp is a multi-subunit complex composed of 3 viral proteins named nsp7, nsp8 and nsp12 that ensure the ~30 kb RNA genome's transcription and replication. The main strategies employed so far for the overproduction of RdRp consist of expressing and purifying the three subunits separately before assembling the complex in vitro. However, nsp12 shows limited solubility in bacterial expression systems and is often produced in insect cells. Here, we describe an alternative strategy to co-express the full SARS-CoV-2 RdRp in E. coli, using a single plasmid. Characterization of the purified recombinant SARS-CoV-2 RdRp shows that it forms a complex with the expected (nsp7)(nsp8)2(nsp12) stoichiometry. RNA polymerization activity was measured using primer-extension assays showing that the purified enzyme is functional. The purification protocol can be achieved in one single day, surpassing in speed all other published protocols. Our construct is ideally suited for screening RdRp and its variants against very large chemical compounds libraries and has been made available to the scientific community through the Addgene plasmid depository (Addgene ID: 165451).

How cyanophage S-2L rejects adenine and incorporates 2-aminoadenine to saturate hydrogen bonding in its DNA.

Bacteriophages have long been known to use modified bases in their DNA to prevent cleavage by the host's restriction endonucleases. Among them, cyanophage S-2L is unique because its genome has all its adenines (A) systematically replaced by 2-aminoadenines (Z). Here, we identify a member of the PrimPol family as the sole possible polymerase of S-2L and we find it can incorporate both A and Z in front of a T. Its crystal structure at 1.5 Å resolution confirms that there is no structural element in the active site that could lead to the rejection of A in front of T. To resolve this contradiction, we show that a nearby gene is a triphosphohydolase specific of dATP (DatZ), that leaves intact all other dNTPs, including dZTP. This explains the absence of A in S-2L genome. Crystal structures of DatZ with various ligands, including one at sub-angstrom resolution, allow to describe its mechanism as a typical two-metal-ion mechanism and to set the stage for its engineering.

Physics approach to the variable-mass optimal-transport problem.

Optimal transport (OT) has become a discipline by itself that offers solutions to a wide range of theoretical problems in probability and mathematics with applications in several applied fields such as imaging sciences, machine learning, and in data sciences in general. The traditional OT problem suffers from a severe limitation: its balance condition imposes that the two distributions to be compared be normalized and have the same total mass. However, it is important for many applications to be able to relax this constraint and allow for mass creation and/or destruction. This is true, for example, in all problems requiring partial matching. In this paper, we propose an approach to solving a generalized version of the OT problem, which we refer to as the discrete variable-mass optimal-transport (VMOT) problem, using techniques adapted from statistical physics. Our first contribution is to fully describe this formalism, including all the proofs of its main claims. In particular, we derive a strongly concave effective free-energy function that captures the constraints of the VMOT problem at a finite temperature. From its maximum we derive a weak distance (i.e., a divergence) between possibly unbalanced distribution functions. The temperature-dependent OT distance decreases monotonically to the standard variable-mass OT distance, providing a robust framework for temperature annealing. Our second contribution is to show that the implementation of this formalism has the same properties as the regularized OT algorithms in time complexity, making it a competitive approach to solving the VMOT problem. We illustrate applications of the framework to the problem of partial two- and three-dimensional shape-matching problems.

Structural Studies of HNA Substrate Specificity in Mutants of an Archaeal DNA Polymerase Obtained by Directed Evolution.

Archaeal DNA polymerases from the B-family (polB) have found essential applications in biotechnology. In addition, some of their variants can accept a wide range of modified nucleotides or xenobiotic nucleotides, such as 1,5-anhydrohexitol nucleic acid (HNA), which has the unique ability to selectively cross-pair with DNA and RNA. This capacity is essential to allow the transmission of information between different chemistries of nucleic acid molecules. Variants of the archaeal polymerase from Thermococcus gorgonarius, TgoT, that can either generate HNA from DNA (TgoT_6G12) or DNA from HNA (TgoT_RT521) have been previously identified. To understand how DNA and HNA are recognized and selected by these two laboratory-evolved polymerases, we report six X-ray structures of these variants, as well as an in silico model of a ternary complex with HNA. Structural comparisons of the apo form of TgoT_6G12 together with its binary and ternary complexes with a DNA duplex highlight an ensemble of interactions and conformational changes required to promote DNA or HNA synthesis. MD simulations of the ternary complex suggest that the HNA-DNA hybrid duplex remains stable in the A-DNA helical form and help explain the presence of mutations in regions that would normally not be in contact with the DNA if it were not in the A-helical form. One complex with two incorporated HNA nucleotides is surprisingly found in a one nucleotide-backtracked form, which is new for a DNA polymerase. This information can be used for engineering a new generation of more efficient HNA polymerase variants.

Structural evidence for the binding of monocarboxylates and dicarboxylates at pharmacologically relevant extracellular sites of a pentameric ligand-gated ion channel.

GLIC is a bacterial homologue of the pentameric ligand-gated ion channels (pLGICs) that mediate the fast chemical neurotransmission of nerve signalling in eukaryotes. Because the activation and allosteric modulation features are conserved among prokaryotic and eukaryotic pLGICs, GLIC is commonly used as a model to study the allosteric transition and structural pharmacology of pLGICs. It has previously been shown that GLIC is inhibited by some carboxylic acid derivatives. Here, experimental evidence for carboxylate binding to GLIC is provided by solving its X-ray structures with a series of monocarboxylate and dicarboxylate derivatives, and two carboxylate-binding sites are described: (i) the `intersubunit' site that partially overlaps the canonical pLGIC orthosteric site and (ii) the `intrasubunit' vestibular site, which is only occupied by a subset of the described derivatives. While the intersubunit site is widely conserved in all pLGICs, the intrasubunit site is only conserved in cationic eukaryotic pLGICs. This study sheds light on the importance of these two extracellular modulation sites as potential drug targets in pLGICs.

Structural basis for allosteric transitions of a multidomain pentameric ligand-gated ion channel.

Pentameric ligand-gated ion channels (pLGICs) are allosteric receptors that mediate rapid electrochemical signal transduction in the animal nervous system through the opening of an ion pore upon binding of neurotransmitters. Orthologs have been found and characterized in prokaryotes and they display highly similar structure-function relationships to eukaryotic pLGICs; however, they often encode greater architectural diversity involving additional amino-terminal domains (NTDs). Here we report structural, functional, and normal-mode analysis of two conformational states of a multidomain pLGIC, called DeCLIC, from a Desulfofustis deltaproteobacterium, including a periplasmic NTD fused to the conventional ligand-binding domain (LBD). X-ray structure determination revealed an NTD consisting of two jelly-roll domains interacting across each subunit interface. Binding of Ca2+ at the LBD subunit interface was associated with a closed transmembrane pore, with resolved monovalent cations intracellular to the hydrophobic gate. Accordingly, DeCLIC-injected oocytes conducted currents only upon depletion of extracellular Ca2+; these were insensitive to quaternary ammonium block. Furthermore, DeCLIC crystallized in the absence of Ca2+ with a wide-open pore and remodeled periplasmic domains, including increased contacts between the NTD and classic LBD agonist-binding sites. Functional, structural, and dynamical properties of DeCLIC paralleled those of sTeLIC, a pLGIC from another symbiotic prokaryote. Based on these DeCLIC structures, we would reclassify the previous structure of bacterial ELIC (the first high-resolution structure of a pLGIC) as a "locally closed" conformation. Taken together, structures of DeCLIC in multiple conformations illustrate dramatic conformational state transitions and diverse regulatory mechanisms available to ion channels in pLGICs, particularly involving Ca2+ modulation and periplasmic NTDs.

Structural basis for the increased processivity of D-family DNA polymerases in complex with PCNA.

Replicative DNA polymerases (DNAPs) have evolved the ability to copy the genome with high processivity and fidelity. In Eukarya and Archaea, the processivity of replicative DNAPs is greatly enhanced by its binding to the proliferative cell nuclear antigen (PCNA) that encircles the DNA. We determined the cryo-EM structure of the DNA-bound PolD-PCNA complex from Pyrococcus abyssi at 3.77 Å. Using an integrative structural biology approach - combining cryo-EM, X-ray crystallography, protein-protein interaction measurements, and activity assays - we describe the molecular basis for the interaction and cooperativity between a replicative DNAP and PCNA. PolD recruits PCNA via a complex mechanism, which requires two different PIP-boxes. We infer that the second PIP-box, which is shared with the eukaryotic Polα replicative DNAP, plays a dual role in binding either PCNA or primase, and could be a master switch between an initiation and a processive phase during replication.

Statistical Physics Approach to the Optimal Transport Problem.

Originally defined for the optimal allocation of resources, optimal transport (OT) has found many theoretical and practical applications in multiple domains of science and physics. In this Letter we develop a new method for solving the discrete version of this problem using techniques derived from statistical physics. We derive a strongly concave free energy function that captures the constraints of the OT problem at a finite temperature. Its maximum defines an optimal transport plan, or registration between the two discrete probability measures that are compared, as well as a pseudodistance between those measures that satisfies the triangular inequalities. The computation of this pseudodistance is fast and numerically stable. The temperature dependent OT pseudodistance is shown to decrease monotonically with respect to the inverse of the temperature and to converge to the standard OT distance at zero temperature, providing a robust framework for temperature annealing. We illustrate applications of this framework to the problem of image comparison.

Optimal transport at finite temperature.

Optimal transport (OT) has become a discipline by itself that offers solutions to a wide range of theoretical problems in probability and mathematics. Despite its appealing theoretical properties, solving the OT problem involves the resolution of a linear program whose computational cost can quickly become prohibitive whenever the size of the problem exceeds a few hundred points. The recent introduction of entropy regularization, however, has led to the development of fast algorithms for solving an approximate OT problem. The successes of those algorithms have resulted in a popularization of the applications of OT in several applied fields such as imaging sciences and machine learning, and in data sciences in general. Problems remain, however, as to the numerical convergence of those regularized approximations towards the actual OT solution. In addition, the physical meaning of this regularization is unclear. In this paper, we propose an approach to solving the discrete OT problem using techniques adapted from statistical physics. Our first contribution is to fully describe this formalism, including all the proofs of its main claims. In particular we derive a strongly concave effective free energy function that captures the constraints of the optimal transport problem at a finite temperature. Its maximum defines a pseudo distance between the two set of weighted points that are compared, which satisfies the triangular inequalities. The temperature dependent OT pseudo distance decreases monotonically to the standard OT distance, providing a robust framework for temperature annealing. Our second contribution is to show that the implementation of this formalism has the same properties as the regularized OT algorithms in time complexity, making it a competitive approach to solving the OT problem. We illustrate applications of the framework to the problem of protein fold recognition based on sequence information only.