Nicolas Magaud
email: magaud@unistra.fr

Integrating an Automated Prover for Projective Geometry as a New Tactic in the Coq Proof Assistant

Recently, we developed an automated theorem prover for projective incidence geometry. This prover, based on a combinatorial approach using matroids, proceeds by saturation using the matroid rules. It is designed as an independent tool, implemented in C, which takes a geometric configuration as input and produces as output some Coq proof scripts: the statement of the expected theorem, a proof script proving the theorem and possibly some auxiliary lemmas. In this document, we show how to embed such an external tool as a plugin in Coq so that it can be used as a simple tactic.

Introduction

The Coq proof assistant [START_REF]The Coq Proof Assistant Reference Manual[END_REF][START_REF] Bertot | Interactive Theorem Proving and Program Development, Coq'Art : The Calculus of Inductive Constructions[END_REF] is a generic theorem prover, with huge capabilities. One of its main strengths is that it allows carrying out proofs either interactively or under some assumptions automatically. Its standard tactics allow to solve goals in some well-understood fragments of its underlying logic, e.g. first order logic using the tactic firstorder or linear arithmetic using the tactic lia. When the proofs get more technical or are outside of the scope of these automatic tactics, the user can take control and thus we are not limited any more by the power of automation. Contrary to what happens with SMT provers, like Z3 [START_REF] Mendonc ¸a De Moura | Z3: An Efficient SMT Solver[END_REF] or Vampire [START_REF] Kovács | First-Order Theorem Proving and Vampire[END_REF], which either succeed or fail on the goal, in Coq, the user can perform some proof steps interactively and then rely again on automated tools to solve the goal.

However, it requires a lot of expertise to be able to develop some new tactics in Coq to help the user proving theorems more easily. Most tactics are written using the Ltac tactic language [START_REF] Delahaye | A Tactic Language for the System Coq[END_REF], but writing tactics sometimes also requires to implement some features in OCaml in a Coq plugin.

In the context of geometry, we developed an independent theorem prover, implemented in C, which handles first-order statements. It takes as input a geometric configuration, written as plain text, and returns a Coq proof script, ready to be verified (type-checked) by Coq. We choose to proceed that way in order to make the development as easy as possible for a non-expert in Coq internals. The only requirements are to know the specification and the tactic languages of Coq, and thus to be able to produce some Coq files (actually a simple .v file).

In this article, we show how to integrate such an automated prover as a tactic in Coq, without modifying the interface of the automated prover.

In Sect. 2, we briefly present the automated prover, which we shall see as a blackbox in the rest of this document. In Sect. 3, we show how to translate a Coq goal into the input language of our prover. In Sect. 4, we investigate how to use the Coq script produced by our prover to solve the initial Coq goal. In Sect. 5, we discuss our implementation choices and explain how it could be extended to other external provers.

The automated prover

We work in the framework of projective incidence geometry, which is one of the simplest theory that can be used to capture most aspects of geometry. It is based on an incidence relation between points and lines. In its projective version, we assume that two coplanar lines always intersect. One of its main advantages is that it can be described using only a few axioms; thus it is a well-suited framework to try and automate proofs of theorems. This geometry can be described either in a synthetic way, writing statements using the incidence relation ∈, or in a more combinatorial way, using the rank of a set of points [START_REF] Michelucci | Incidence Constraints: a Combinatorial Approach[END_REF]. For instance, the property that a line has at least three distinct points can be expressed in a synthetic way as follows :

∀l : Line, ∃ABC : Point, A = B ∧ B = C ∧ A = C ∧ A ∈ l ∧ B ∈ l ∧C ∈ l.
It can also be implemented as the following statement using the matroid based description using ranks : ∀AB : Point, rk{A, B} = 2 ⇒ ∃C : Point, rk{A, B,C} = rk{B,C} = rk{A,C} = 2.

In the combinatorial approach, we exclusively deal with points and geometric reasoning is replaced by some computations relying on the combinatorial properties of the underlying matroid on which the rank properties are based [START_REF] Michelucci | Incidence Constraints: a Combinatorial Approach[END_REF]. Concretely, the rank of a set of two distinct points A and B is equal to 2. The rank of a set of three collinear points A, B, and C is also equal to 2. The rank of the whole plane in a two dimensional setting is 3. In a space of dimension n ≥ 3, the maximum rank of a set of points is n + 1. In the case n = 3, a set of points whose rank is 4 is not a plane and actually captures the whole space.

The above two approaches are shown to be equivalent [START_REF] Braun | Two Cryptomorphic Formalizations of Projective Incidence Geometry[END_REF] and the combinatorial one can be successfully used to automatically prove some emblematic theorems of 3D projective incidence geometry [4]. Among them we can cite Desargues' theorem and Dandelin-Gallucci's theorem [START_REF] Braun | Two New Ways to Formally Prove Dandelin-Gallucci's Theorem[END_REF]. The automated prover, named Bip for matroid Based Incidence Prover, is designed to prove equality between ranks of various sets of points. It is based on rank interval computations. For each subset of the powerset of the geometric configuration, we define the minimum and the maximum rank (in the worst case, when no information is known, the rank of each non-empty subset is between 1 and 4). We then use the matroid axioms, which specify the rank function, and we reformulate them as rewrite rules to incrementally reduce the size of the interval for each subset. This is achieved using a saturation algorithm, which is run on a valuated graph implementing the inclusion lattice of the point powerset, labeled by the minimum and maximum rank. Once the saturation graph is built, it is traversed to build a Coq proof script which actually proves the statement at stake. Technical details about the implementation can be found in [4] and the current implementation of the prover as well as several examples of applications are available in the git repository: https://github.com/pascalschreck/MatroidIncidenceProver.

In the next sections, we show how to integrate such a tool so that it can be simply used as a tactic in Coq.

3 Translating a Coq statement into the input language of the prover Provided that we define the theory of ranks in Coq (see Appendix A), as we first did in [START_REF] Magaud | A Case Study in Formalizing Projective Geometry in Coq: Desargues Theorem[END_REF], we can state geometric properties as Coq lemmas using equalities on the ranks of some sets of points.

A Coq statement featuring some rank properties can easily be translated into an input file for the automated prover. It simply consists in traversing the context and the goal, harvesting all variables of type Point and all statements of the form rk(e)=k. All other statements are simply dropped, as they could not be used by the automatic prover yet. Fig. 2 shows the correspondence between the Coq statement of a simple theorem in projective geometry, depicted in Fig. 1, and its translation into the input langage of our automated prover.

This translation can be easily implemented inside a Coq plugin, following the examples of the plugin tutorial available in the reference manual of Coq [START_REF]The Coq Proof Assistant Reference Manual[END_REF]. It produces a simple text file, which can be then used as input by the Bip prover. In the generated input of the Bip prover shown in the right part of Fig. 2, layers are a legacy tool which was used to decompose the context at stake. This allows to build smaller proof scripts which can be easily checked by Coq. In the current version of the prover, each deduced statement is stated as a lemma and thus layers are not needed anymore. Once the input file is generated, we simply execute the external prover from Coq using the Unix.system primitive of the OCaml library. It produces a Coq file (.v), with the appropriate prelude, which is ready to be verified by Coq.

An implementation of this translation as well as the mechanisms to use the produced proof inside Coq is available in this git repository: https://github.com/magaud/projective-prover. It works with Coq 8.12.2 (December 2020) and we are currently updating it to the most recent release of Coq.

4 Running the (generated) Coq script and proving the goal Assuming the automated prover manages to produce a Coq proof script which proves the goal at stake, we still need to load this Coq file inside Coq and use the externally proven lemma to actually prove the initial goal. Let us check what happens with our simple example. As the automated prover reorders the points in the sets at stake (they are ordered according to the order in which they were introduced, during the construction of the input file), the automatically generated statement and the initial one slightly differ. In our case, the prover produces the following statement in a file named pprove_ex2. Proving the initial goal ex2 from Sect.3 requires compiling all the automatically generated code leading to the proof of lemma LABC and loading it in Coq. Then the statement LABC can be almost directly applied to prove the statement at stake ex2. The slight differences between these two statements lie in the order of the points in each hypothesis or conclusion of the form rk(e) = n. Points need to be reordered according to the order in which they are introduced in the context. This is achieved by running the Ltac code solve_using2 which transforms the initial goal until its exactly matches the automaticallyproven statement.

Require Import pprove_ex2. solve_using LABC.

At this point, even if we can be fairly confident that the whole machinery works properly, we do not have a strong warranty that everything went as planned. The last step of the proof is, as usual in Coq, to type-check the built proof using the concluding command Qed. Once this step is completed, we are sure that our prover actually proved the initial statement provided by the user.

Discussion

We choose a simple but efficient approach to run the prover inside Coq. One of the main advantages of this approach is that it does not require the designer of the external prover to have any understandings of the internals of Coq. It simply requires the developer to be knowledgeable of the way Coq scripts are written. This is a skill every Coq user has. Such an approach thus makes every Coq user a potential tactic writer, provided we can build an interface linking Coq statements to the expected inputs of such an external prover. Indeed, the critical part of our tool is the translation of the statement from Coq to the input language of the prover. The proof generation does not need to be formally verified. Indeed, Coq will reject the proof script if it does not actually prove the statement at stake (either because statements do not coincide, or because the proof script is incorrect).

The connection from Coq to the automated prover is fairly straightforward. However the embedding of the automated prover into Coq is a bit more technical. It is not fully automated yet because calling a command (to load a compiled .vo file) from a tactic requires subtle interactions with the State Transaction Machine (which allows for faster and parallel executions of some parts of the proofs [START_REF] Barras | Asynchronous Processing of Coq Documents: From the Kernel up to the User Interface[END_REF]) to maintain consistency of the proof document. For the time being, we make the pprove tactic display the command and tactic to be applied to complete solving the goal. In the near future, we plan to integrate these two extra steps directly into the code of the pprove tactic.

We think this simple way of embedding the prover could be generalized to other external provers. So far, our automated prover is running from scratch every time we compute the proof again. We plan to add some memoization techniques in order to avoid recomputing the saturation every time. We could aim at a more incremental tool where the saturation mechanism is carried out when a new point is added to the context.

More integrated tools to make automated proofs exist [START_REF] Armand | A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses[END_REF], designed to embed SAT and SMT solvers inside Coq and ensure that they provide correct decision procedures. Their approach is safer than ours, but we argue that simply generating a Coq file is much easier to carry out by an average programmer and can be used as a first step towards integrating an automated tool into Coq.

Conclusions and Perspectives

We successfully embed the external prover Bip as a simple tactic to be used in Coq using Ltac. We proceed in two steps: we first develop a prover, which is completely independent from the internals of Coq. The second step consists in connecting this external prover to Coq. We call the prover from Coq and retrieve the external proof script it generates. We then simply feed this script to Coq to type-check it. The API of Coq is not intended to make it easy to embed some Coq proof scripts generated externally to prove a goal. We believe it would be a nice feature to ease this process by allowing a tactic to simply run a snippet of Coq code loaded from a file.

In the longer run, improving our prover requires to make it able to take synthetic geometry statements as input rather than sets of points and ranks. We carry on developing a way to automatically translate synthetic geometry statements into ranks equalities in Coq, so that the user deals with synthetic geometry, whereas the prover deals with sets of points and their ranks in the back-end. A draft implementation of this translation is available in the file translate.v of the git repository.

Finally, we think our example describes an efficient and straight-to-the-point approach to embed an automated prover inside Coq and is useful as a first step towards a more integrated embedding.

Figure 1 :

 1 Figure 1: A simple geometric configuration illustrating the statement of Fig. 2

Figure 2 :

 2 Figure 2: The Coq statement of a simple projective geometry theorem (left) and the corresponding input for the automated prover (right)

v 1 :

 1 Lemma LABC : forall A B C D , rk(A :: C :: nil) = 2 -> rk(A :: B :: D :: nil) = 3 -> rk(C :: D :: nil) = 2 -> rk(A :: C :: D :: nil) = 2 -> rk(A :: B :: C :: nil) = 3. Proof.

The name of the Lemma is automatically generated, starts from the L of Lemma, followed by all the names of the points used in the conclusion.

The code of solve_using is in the file Ltac_utils.v

A A few lines of code specifying the rank function and its properties

We outline the context describing the rank function which is loaded before starting the proof in Coq. The axioms describe the properties of the rank function and are used in the automatically built Coq proof script. See files basic_matroid_list.v and basic_rank_space_list.v for details.

Parameter Point : Set.

Parameter eq_dec : forall A B : Point, {A = B} + {˜A = B}.

B An example of an automatically generated file

The file pprove_ex2.v, which is 163-line long including comments, is automatically generated in the process of proving the statement ex2. It is available (or can be regenerated) from https://github. com/magaud/projective-prover/blob/master/theories/pprove_ex2.v. All statements, including intermediary statements have exactly the same hypotheses. In addition, there is exactly one statement for each deduction achieved during the saturation phase of the algorithm. The last statement LABC corresponds to the actual statement proved automatically. This lemma is then reused to prove the initial Coq goal: ex2 in our example.


P Maximiano Raimundo

M Obligado

A Cartellier

D Beneventi

A Forret

F Augier

Hydrodynamics of bubble columns in the heterogeneous regime: mechanisms, scale-up and modelling

Bubble column reactors, where gas is injected at the bottom of an initially stagnant liquid, are widely used in chemical engineering (e.g. for hydrogenation such as in Fischer-Tropsch synthetic fuels production), for bio-chemical transformations (aerobic bioreactors, algae production), waste management (wet oxidation) and flotation units (deinking of paper, extraction of rare metals). All these activities are also fundamental for the development of many recycling and renewable energies industries.

These reactors often operate in the heterogeneous regime, characterized by a strongly polydisperse distribution of bubble sizes, high gas concentrations (15 to 40%) and strong velocity fluctuations (≈ 25-30% times the mean). Owing to such flow complexity, no reliable scaling rules are available for reactor designers. This problem dramatically hampers optimization and process control. In particular, extrapolation between laboratory-scale and industrial-sized columns (diameter 5 to 10 m, height 20 to 40 m) is not controlled, and therefore the simulations lead to realistic results only via an ad-hoc adjustment depending on the size of the column [START_REF] Forret | Scale up of slurry bubble reactors[END_REF][START_REF] Rollbusch | Bubble columns operated under industrially relevant conditions -Current understanding of design parameters[END_REF].

Recently, two-fluid models have been significantly improved using kinetic theory concepts (Fox 2012). They are now able to handle coalescence and break-up on a sound basis (Marchisio andFox, 2013, Renze et al. 2014). Furthermore, the latest advances in Fox's group [START_REF] Capecelatro | On fluid-particle dynamics in fully developed cluster-induced turbulence[END_REF] are potentially apt in representing collective effects such as those observed in experiments. The above new contributions form a solid basis for definite progress towards the understanding of bubble column hydrodynamics.

In this work, we present well-controlled experiments (Maximiano's PhD, 2015) that span the largest range of parameters ever considered: diameter from 0.15 to 3m (figure 1), void fractions up to 35%, with a fixed bubble size distribution (i.e. no coalescence). We find that, contrary to common belief [START_REF] Ruzicka | On stability of a bubble column[END_REF], coalescence is not a necessary condition for homogeneous/heterogeneous transition to occur. Rather than emerging by way of large bubbles, heterogeneity arises from clusters of bubbles organized at mesoscale (≈a few tens bubble size). These clusters lead to large concentration gradients (0.1 to 10 times the mean) that generate strong shear as the relative velocity between cluster and void regions largely exceeds the terminal velocity of an isolated bubble. When accounting for this slip velocity in momentum exchange, 3D two-fluid simulations become able to reproduce scale-up within ±15% without any adjustment. We also confirmed the self-organization of these flows and clarified scaling laws. In particular, and contrary to intuition, the entrained liquid flow rate was shown to depend only on the column diameter and not on the injected gas flow rate (see figure 1c). Finally, we show some preliminary results from ongoing work: following recent advances in the context of particle-laden turbulent flows, joint velocity-concentration measurements based on Voronoï tessellations [START_REF] Monchaux | Preferential concentration of heavy particles: a Voronoï analysis[END_REF]) have been developed to characterize clusters dynamics as well as instantaneous velocity gradients which are believed to be the key to turbulence production (figure 1d).

Figure 1 :

 1 Figure 1: bubble columns of 1m and 3m in diameter, heights 5.7 (a) and 12m (b). Scaling of the entrained liquid flow rate in coalescence free conditions (c, from Maximiano PhD). Voronoï tessellations PDFs for differens values of superficial gas velocities 𝑣 "# (d).


Alan G Hinnebusch

Eunice Kennedy Shriver

Laura Plassart

† Ramtin

Christian Montellese

Dana Rinaldi

Natacha Larburu

Carole Pichereaux

Carine Froment

Simon Lebaron

Marie-Franc ¸oise O'donohue

Ulrike Kutay

Julien Marcoux

Pierre-Emmanuel Gleizes
email: pierre-emmanuel.gleizes@univ-tlse3.fr

Celia Plisson-Chastang
email: celia.plisson-chastang@univ-tlse3.fr

Ramtin Shayan

Ulrike Kutay Calmip

Celia Plisson-Chastang Inext Pid3684 -Vid

The final step of 40S ribosomal subunit maturation is controlled by a dual key lock

Preventing premature interaction of pre-ribosomes with the translation apparatus is essential for translational accuracy. Hence, the final maturation step releasing functional 40S ribosomal subunits, namely processing of the 18S ribosomal RNA 3 0 end, is safeguarded by the protein DIM2, which both interacts with the endoribonuclease NOB1 and masks the rRNA cleavage site. To elucidate the control mechanism that unlocks NOB1 activity, we performed cryo-electron microscopy analysis of late human pre-40S particles purified using a catalytically inactive form of the ATPase RIO1. These structures, together with in vivo and in vitro functional analyses, support a model in which ATP-loaded RIO1 cooperates with ribosomal protein RPS26/eS26 to displace DIM2 from the 18S rRNA 3 0 end, thereby triggering final cleavage by NOB1; release of ADP then leads to RIO1 dissociation from the 40S subunit. This dual key lock mechanism requiring RIO1 and RPS26 guarantees the precise timing of pre-40S particle conversion into translation-competent ribosomal subunits.

Introduction

Synthesis of eukaryotic ribosomes relies on a large array of ribosome biogenesis factors (RBFs) that coordinate the multiple steps of pre-ribosomal RNA (pre-rRNA) modification, cleavage, and folding, together with ribosomal protein (RP) assembly [START_REF] Bohnsack | Uncovering the assembly pathway of human ribosomes and its emerging links to disease[END_REF]. Progression through this process, defined by the timely association or dissociation of RBFs and RPs to pre-ribosomal particles and the gradual maturation of pre-rRNAs, is tightly monitored from one stage to the next. These monitoring mechanisms not only ensure quality control along this intricate biosynthetic pathway, but also prevent binding of immature ribosomal subunit precursors (pre-ribosomes) to mRNAs or to components of the translation apparatus. Such interactions would not only interfere with ribosome biogenesis, but also affect translation accuracy. The recent discovery of congenital diseases or cancers linked to ribosome biogenesis defects and translation dysregulation underscores the importance of the control mechanisms that license newly formed ribosomal subunits to enter the translation-competent pool of ribosomes [START_REF] Aubert | Pre-Ribosomal RNA processing in human cells: from mechanisms to congenital diseases[END_REF][START_REF] Bohnsack | Uncovering the assembly pathway of human ribosomes and its emerging links to disease[END_REF][START_REF] Sulima | How Ribosomes Translate Cancer[END_REF].

After initial assembly in the nucleolus, pre-40S particles are rapidly transported to the cytoplasm [START_REF] Rouquette | Nuclear export and cytoplasmic processing of precursors to the 40S ribosomal subunits in mammalian cells[END_REF], where translation takes place. Cytoplasmic precursors to the 40S ribosomal subunits (pre-40S particles) closely resemble their mature counterparts [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF][START_REF] Larburu | Structure of a human pre-40S particle points to a role for RACK1 in the final steps of 18S rRNA processing[END_REF], which possess binding sites for numerous components of the translation machinery including factors of the translation initiation complex, tRNAs and mRNAs. Thus, pre-40S particles would be especially prone to premature interactions with the translation apparatus without the presence of several RBFs (Bystin/ENP1, LTV1, RIO2, TSR1, DIM2/PNO1, NOB1), which occupy the binding sites of translation partners near their 'head' and 'platform' domains [START_REF] Larburu | Structure of a human pre-40S particle points to a role for RACK1 in the final steps of 18S rRNA processing[END_REF][START_REF] Strunk | A translation-like cycle is a quality control checkpoint for maturing 40S ribosome subunits[END_REF]. These two structural domains undergo several remodeling steps in the cytoplasm leading to the gradual release of these RBFs [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF][START_REF] Zemp | CK1d and CK1e are components of human 40S subunit precursors required for cytoplasmic 40S maturation[END_REF][START_REF] Zemp | Distinct cytoplasmic maturation steps of 40S ribosomal subunit precursors require hRio2[END_REF]. This maturation process ends with the cleavage of the 18S rRNA 3 0 end and the dissociation of the last RBFs, DIM2, and NOB1, which converts pre-40S particles into functional subunits. Interfering with this late stage can result in the incorporation of immature 40S subunits in the translation pool [START_REF] Belhabich-Baumas | The Rio1p ATPase hinders premature entry into translation of late pre-40S pre-ribosomal particles[END_REF][START_REF] Parker | A kinase-dependent checkpoint prevents escape of immature ribosomes into the translating pool[END_REF].

Up to this final stage, the 3 0 end of the 18S rRNA is extended with remnants of the internal transcribed spacer 1 (ITS1). In human cells, this last precursor to the 18S rRNA (called 18S-E pre-rRNA) is generated in the nucleolus by endonucleolytic cleavage of earlier pre-rRNAs 78 or 81 nucleotides downstream of the mature 3 0 end [START_REF] Preti | Gradual processing of the ITS1 from the nucleolus to the cytoplasm during synthesis of the human 18S rRNA[END_REF][START_REF] Sloan | Both endonucleolytic and exonucleolytic cleavage mediate ITS1 removal during human ribosomal RNA processing[END_REF][START_REF] Tafforeau | The complexity of human ribosome biogenesis revealed by systematic nucleolar screening of Pre-rRNA processing factors[END_REF]. This 3 0 tail is then gradually trimmed by exonucleases before and after nuclear export, including PARN in the nucleus [START_REF] Montellese | Poly(A)-specific ribonuclease is a nuclear ribosome biogenesis factor involved in human 18S rRNA maturation[END_REF]. However, processing of the 18S rRNA 3 0 end is finalized by endonuclease NOB1, which cleaves at the so-called site 3. NOB1 is already incorporated into the pre-40S particle in the nucleolus on the platform domain near site 3, but it is restricted from cleaving the rRNA by DIM2, another RBF, which contacts NOB1 in the particle and masks the cleavage site on the RNA [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF][START_REF] Larburu | Structure of a human pre-40S particle points to a role for RACK1 in the final steps of 18S rRNA processing[END_REF]. This conformation also maintains a large gap between the catalytic site of NOB1 and its substrate. Dissociation of NOB1 and DIM2 from the pre-40S particles only occurs at the final processing stage, which produces mature 18S rRNA. In addition, NOB1 occupies the mRNA binding cleft and prevents the association of pre-40S particles with mRNAs until this ultimate maturation step [START_REF] Parker | A kinase-dependent checkpoint prevents escape of immature ribosomes into the translating pool[END_REF]. Thus, NOB1 and DIM2 constitute a critical checkpoint controlling the release of nascent 40S subunits into the translating pool.

The RIO1 ATPase was shown to play a critical function in the last maturation step of the 18S rRNA [START_REF] Widmann | The kinase activity of human Rio1 is required for final steps of cytoplasmic maturation of 40S subunits[END_REF], but the molecular mechanism driving the accurate activation of rRNA cleavage by NOB1 remains poorly known. RIO1 associates with pre-40S particles briefly before the final cleavage step. Like RIO2, another ATPase of the same family that intervenes earlier in pre-40S particle maturation, RIO1 adopts different conformations depending on its nucleotide binding state [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF]. The absence of RIO1 or suppression of its catalytic activity impairs both rRNA cleavage and release of NOB1 and DIM2 in yeast and human cells [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF][START_REF] Turowski | Rio1 mediates ATP-dependent final maturation of 40S ribosomal subunits[END_REF][START_REF] Widmann | The kinase activity of human Rio1 is required for final steps of cytoplasmic maturation of 40S subunits[END_REF], suggesting that RIO1 association to pre-40S particles as well as its ATPase activity are both required to yield functional small ribosomal subunits.

Ribosomal protein RPS26/eS26, which is in close contact with the 18S rRNA 3 0 end on the mature small ribosomal subunit, was also shown to be necessary for efficient cleavage by NOB1 in yeast and in human cells [START_REF] O'donohue | Functional dichotomy of ribosomal proteins during the synthesis of mammalian 40S ribosomal subunits[END_REF][START_REF] Pen ˜a | Prefabrication of a ribosomal protein subcomplex essential for eukaryotic ribosome formation[END_REF][START_REF] Schu ¨tz | Molecular basis for disassembly of an importin:ribosomal protein complex by the escortin Tsr2[END_REF], but its interplay with RIO1, DIM2, and NOB1 remains unclear. Indeed, the precise timing of association of this ribosomal protein to pre-ribosomal particles is a matter of debate. Studies performed in yeast cells suggested that Rps26 is imported into the nucleus and is dissociated from its importin by the RBF Tsr2 in a non-canonical way [START_REF] Schu ¨tz | A RanGTP-independent mechanism allows ribosomal protein nuclear import for ribosome assembly[END_REF]. Tsr2 was proposed to then chaperone the incorporation of Rps26 into nucleolar pre-ribosomal particles [START_REF] Pen ˜a | Prefabrication of a ribosomal protein subcomplex essential for eukaryotic ribosome formation[END_REF][START_REF] Schu ¨tz | Molecular basis for disassembly of an importin:ribosomal protein complex by the escortin Tsr2[END_REF]. However, RPS26 has not been found so far in cryo-electron microscopy (cryo-EM) structures of nucle(ol)ar small ribosomal subunit precursors in yeast or human, and was only detected in late cytoplasmic ones [START_REF] Ameismeier | Structural basis for the final steps of human 40S ribosome maturation[END_REF][START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF]. Consistently, western blot and proteomics analysis failed to clearly identify RPS26 in nuclear or in early cytoplasmic human pre-40S particles [START_REF] Larburu | Structure of a human pre-40S particle points to a role for RACK1 in the final steps of 18S rRNA processing[END_REF][START_REF] Wyler | Tandem affinity purification combined with inducible shRNA expression as a tool to study the maturation of macromolecular assemblies[END_REF]. One cannot exclude that association of RPS26 to nuclear precursors might be highly labile and becomes more stable only during later maturation steps, but evidence is still lacking to date for the presence of human RPS26 in early precursors.

Here, we have used cryo-EM to solve the structures of human pre-40S particles trapped with a catalytically inactive form of RIO1 in this final maturation stage. Image analysis revealed two distinct structural states, prior and after 18S rRNA cleavage. In the pre-cleavage state, DIM2 and NOB1 are still in place, while the postion of RIO1 is not clearly defined and RPS26 is absent. In contrast, the post-cleavage state displays RIO1 and RPS26 stably associated with 40S particles, which contain mature 18S rRNA. In vivo assays confirmed the central role of RPS26 for triggering both processing of the 18S-E pre-rRNA and the release of DIM2, NOB1, and RIO1. In vitro, cleavage of the 18S-E pre-rRNA was partially stimulated by ATP binding to RIO1 in RPS26-depleted pre-40S particles and was enhanced by adding back purified RPS26. These data suggest a model in which ATP-bound RIO1 and RPS26 cooperatively displace DIM2 to activate the final cleavage of the 18S rRNA 3 0 end by NOB1.

Results

Pre-40S particles purified with a catalytically deficient form of RIO1 display pre-and post-18S rRNA processing structural states

In order to characterize the final cytoplasmic maturation steps undergone by human pre-40S particles, we purified pre-40S particles from a human cell line overexpressing a tagged version of a catalytically inactive form of RIO1 mutated on aspartic acid 324 (D324A) [START_REF] Widmann | The kinase activity of human Rio1 is required for final steps of cytoplasmic maturation of 40S subunits[END_REF]. Autophosphorylation of this mutant in the presence of ATP was previously shown to be strongly impaired [START_REF] Widmann | The kinase activity of human Rio1 is required for final steps of cytoplasmic maturation of 40S subunits[END_REF], and free Pi release activity reduced by at least 50% in its Chaetomium thermophilum D281A ortholog [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF]. Protein and RNA composition of the affinity-purified complexes, hereafter called RIO1(kd)-StHA pre-40S particles, were analyzed using SDS-PAGE, northern blot, and bottom-up proteomics (Figure 1). SDS-PAGE revealed a complex protein pattern with a typical trail of low-molecular-weight bands corresponding to RPs. Northern blot showed that the 18S-E pre-rRNA was the only 18S rRNA precursor precipitated by this bait, while no rRNA of the large ribosomal subunit could be detected (Figure 1-figure supplement 1). Bottom-up proteomics confirmed that the catalytically dead version of RIO1 associates with the methylosome, a complex composed of proteins PRMT5 and MEP50 that methylates proteins involved in gene expression regulation [START_REF] Guderian | RioK1, a new interactor of protein arginine methyltransferase 5 (PRMT5), competes with pICln for binding and modulates PRMT5 complex composition and substrate specificity[END_REF], in addition to late pre-40S particles [START_REF] Montellese | Poly(A)-specific ribonuclease is a nuclear ribosome biogenesis factor involved in human 18S rRNA maturation[END_REF][START_REF] Widmann | The kinase activity of human Rio1 is required for final steps of cytoplasmic maturation of 40S subunits[END_REF]. Of note, these purified pre-40S particles contain all RPs of the small subunit (RPSs), including the late binding RPS10 and RPS26, but only a handful of ribosome biogenesis factors, namely RIO1 (the bait), DIM2, NOB1, and TSR1 (Figure 1, Figure 1figure supplement 2). Other proteins also co-purified with RIO1(kd)-StHA: while some can unambiguously be identified as components of the translation apparatus (eIF4A, RPLs, etc.), it is not known whether others belong to the methylosome or to (pre-)ribosomal particles.

We then performed cryo-EM and single-particle analysis on the particles purified using RIO1(kd)-StHA as bait. 2D classification assays performed with RELION [START_REF] Scheres | RELION: implementation of a Bayesian approach to cryo-EM structure determination[END_REF] yielded class sums corresponding to pre-40S particles as well as various views of the methylosome [START_REF] Timm | Cryo-electron microscopy structure of a human PRMT5:mep50 complex[END_REF]; Figure 2, Figure 2-figure supplement 1). Pre-40S views were selected for further processing; an extensive 3D classification scheme resulted in two distinct 3D structures, hereafter called state A and state B, that likely reflect two successive pre-40S maturation steps (Figure 2, Figure 2-figure supplement 1). Both structures, which represented ~21% (state A) and ~57% (state B) of the pre-40S particles comprised within the analysis, were refined to overall resolutions of 3.2 and 3.0 A ˚, respectively, according to RELION's gold-standard FSC (Figure 2-figure supplements 1 and 2).

State A harbored an rRNA scaffold closely resembling that of the mature 18S rRNA. On the head region, the three-way junction formed by rRNA helices h34, h35, and h38 is fully formed [START_REF] Mohan | Molecular mechanics of 30S subunit head rotation[END_REF], while RPS3, RPS10, and RPS12 occupy their final position. Like in many other pre-40S structures [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF][START_REF] Heuer | Cryo-EM structure of a late pre-40S ribosomal subunit from Saccharomyces cerevisiae[END_REF][START_REF] Mitterer | Conformational proofreading of distant 40S ribosomal subunit maturation events by a long-range communication mechanism[END_REF][START_REF] Scaiola | Structure of a eukaryotic cytoplasmic pre-40S ribosomal subunit[END_REF], the upper part of rRNA h44, located on the intersubunit side, appears detached from the body (Figure 3a). Low-pass filtering of the cryo-EM map of state A also revealed the presence of TSR1 in this region (Figure 3-figure supplement 1). Combined with the bottomup proteomic analysis that revealed the presence of this RBF among the co-purified proteins, this suggests that TSR1 might still be loosely and/or flexibly bound to pre-40S particles at this maturation state. Of note, the presence of TSR1 in late pre-40S particles and mature 40S subunits was recently observed by others [START_REF] Thoms | Structural basis for translational shutdown and immune evasion by the Nsp1 protein of SARS-CoV-2[END_REF], reinforcing the idea that TSR1 could stay associated with small ribosomal subunits until their entry into translation initiation. On the platform region, the cryo-EM density map allowed to unambiguously position nucleotide A1870, belonging to the ITS1 after the 3 0 end of the mature 18S rRNA. In this state, DIM2 protects this region of the 18S-E pre-rRNA and impedes endonucleolytic cleavage by NOB1, located right next to DIM2 (Figures 2 and3b). These results suggest that RIO1(kd)-StHA pre-40S particles in structural state A are in an immature state in which the rRNA scaffold harbors a quasi-mature conformation, but the remaining nucleotides of the ITS1 have not yet been cleaved off by NOB1. Furthermore, NOB1 and DIM2 are the only two RBFs that can clearly be distinguished, while RIO1(kd)-StHA, the protein used as purification bait, cannot be clearly positioned on this cryo-EM map. This suggests that RIO1(kd)-StHA is not structurally stabilized onto state A pre-40S particles. Indeed, while this manuscript was under revision, a cryo-EM study focusing on similarly late human pre-40S particles revealed that RIO1 can adopt several positions in maturing pre-40S particles [START_REF] Ameismeier | Structural basis for the final steps of human 40S ribosome maturation[END_REF].

On the contrary, the cryo-EM map corresponding to state B harbored a density located on the intersubunit side, at the back of the head region, into which the X-ray structure of RIO1 could unambiguously be fitted [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF]. Of note, RIO1 occupies a position strongly overlapping with that of RIO2 in earlier pre-40S maturation states [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF]; Figure 3figure supplement 1). This observation explains why both ATPases are not found together in pre-40S particles and confirms that RIO1 replaces RIO2 at the back of the head [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF][START_REF] Knu ¨ppel | Insights into the evolutionary conserved regulation of rio ATPase activity[END_REF][START_REF] Widmann | The kinase activity of human Rio1 is required for final steps of cytoplasmic maturation of 40S subunits[END_REF]. The C-terminal domain of RIO2 was shown to be deeply inserted within the body of human pre-40S particles [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF]. In contrast, the C-terminal domain of RIO1 is not resolved here; furthermore, the upper part of rRNA helix h44 occupies its mature position, which would preclude insertion of the C-terminal domain of RIO1 at the same position as the C-terminal domain of RIO2. Indeed, the strong sequence divergence of the C-termini of RIO proteins suggests that these domains play a major role in the functional specificity of these proteins, which is supported by the structural difference observed here.

As previously observed in the structure of wild-type RIO1 solved by X-ray crystallography [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF], our cryo-EM map revealed that the catalytic pocket of mutant RIO1 encloses an ADP together with phospho-aspartate pD341 (Figure 3c, Figure 3-figure supplement 2). Thus, the D324A RIO1 mutation does not fully prevent ATP hydrolysis, but rather blocks the release of its reaction products. ATP hydrolysis is thought to be accompanied by a significant conformational change of RIO1 [START_REF] Knu ¨ppel | Insights into the evolutionary conserved regulation of rio ATPase activity[END_REF][START_REF] Ku ¨hlbrandt | Biology, structure and mechanism of P-type ATPases[END_REF], which might be essential for stable association of RIO1 to pre-40S particles. Blocking of RIO1 in this conformation is likely to explain why this point mutation traps the protein on the particles. Furthermore, the RIO1(kd) catalytic pocket appears to be closed through a pi-stacking interaction between phenylalanine F328 and 18S rRNA G1639 (Figure 3c). This highly conserved nucleotide plays a crucial role in tRNA translocation, which puts RIO1 in a good position to probe this mechanism (see Discussion).

In state B, the rRNA scaffold harbors a fully mature conformation. Contrary to what was observed on the platform in state A, no density corresponding to nucleotides belonging to the ITS1 could be detected, suggesting that the 18S rRNA 3 0 end is mature. Furthermore, neither NOB1 nor DIM2 could be found in this area; instead, a cryo-EM density sheathing the 18S rRNA 3 0 end revealed the presence of RPS26 (Figure 3d). These observations indicate that state B corresponds to particles after rRNA cleavage by NOB1. This conclusion was further supported by the analysis of the 3 0 -end of the 18S rRNA by RNase H digestion assays (Figure 4a). As expected, early and intermediate cytoplasmic pre-40S particles purified using tagged forms of LTV1 or DIM2 as baits [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF][START_REF] Wyler | Tandem affinity purification combined with inducible shRNA expression as a tool to study the maturation of macromolecular assemblies[END_REF] contained a large majority of 18S-E pre-rRNAs. Most of the 18S-E precursors in these particles included 4 to 9 nucleotides of the ITS1 (Figure 4 supplement 1). In stark contrast, this experiment showed that RIO1(kd)-StHA pre-40S particles mostly contained mature 18S rRNA (Figure 4b,c).

We conclude that states A and B of the pre-40S particles here isolated with RIO1(kd)-StHA correspond to two very late maturation stages, just before and right after cleavage of the 18S rRNA 3 0 end. These data indicate that rRNA cleavage and release of NOB1 and DIM2 coincide with the association of RIO1 in a stable conformation within the pre-40S particle and the incorporation of RPS26 in its final location. RIO1 enzymatic activity, and more specifically the release of the ATP hydrolysis products, seems required for its own dissociation from the particle rather than for the 18S-E pre-rRNA processing by NOB1.

RPS26 is required for efficient rRNA cleavage and release of NOB1 and DIM2

States A and B of the RIO1(kd)-StHA pre-40S particles harbor two distinct conformations of the platform domain: in state A, the 18S-E pre-rRNA 3'-end is protected by DIM2, which prevents endonucleolytic cleavage by NOB1; in state B, the platform displays a mature conformation, with RPS26 replacing DIM2. Both RPS26 and RIO1 were shown to be necessary for processing of the 18S-E pre-rRNA to occur in human cells [START_REF] O'donohue | Functional dichotomy of ribosomal proteins during the synthesis of mammalian 40S ribosomal subunits[END_REF][START_REF] Widmann | The kinase activity of human Rio1 is required for final steps of cytoplasmic maturation of 40S subunits[END_REF], which argues for the two proteins being involved in transition from state A to state B. Accommodation of RPS26 in its mature position requires prior release of DIM2, which occupies the binding site of RPS26.

In order to assess the role of RPS26 binding to pre-40S particles in 18S rRNA maturation as well as DIM2 and NOB1 release, we analyzed the RNA and protein composition of intermediate and late pre-40S particles purified from cells depleted of RPS26 using a specific siRNA (siRPS26). The level of 18S-E pre-rRNA cleavage in pre-40S particles was measured by RNase H analysis in pre-40S particles isolated using different baits (RIO1(kd)-StHA or RIO1(wt)-StHA, HASt-LTV1) (Figure 5a,b). The amount of 18S-E pre-rRNA within early cytoplasmic pre-40S particles purified with HASt-LTV1 remained unchanged upon RPS26 depletion (Figure 5a), consistent with the absence of RPS26 in these particles [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF][START_REF] Larburu | Structure of a human pre-40S particle points to a role for RACK1 in the final steps of 18S rRNA processing[END_REF][START_REF] Wyler | Tandem affinity purification combined with inducible shRNA expression as a tool to study the maturation of macromolecular assemblies[END_REF]. In contrast, we observed a strong defect of 18S-E pre-rRNA processing in RIO1(kd)-StHA particles upon knockdown of RPS26, as evidenced by a ~60% decrease of the 18S/(18S + 18S-E) ratio when compared to the same particles isolated from cells treated with scramble siRNA. Similar observations were obtained when purifying pre-40S particles with a wild-type version of RIO1 as bait (RIO1(wt)-StHA pre-40S particles). These experiments indicate that the absence of RPS26 impedes 18S-E pre-rRNA maturation and that the action of RPS26 in 18S-E pre-rRNA cleavage takes place within RIO1-containing late cytoplasmic pre-40S particles.

We then used western blot analyses to monitor how RPS26 depletion influences the release of NOB1 and DIM2 (Figure 5c). As expected from previous studies [START_REF] Larburu | Structure of a human pre-40S particle points to a role for RACK1 in the final steps of 18S rRNA processing[END_REF][START_REF] Wyler | Tandem affinity purification combined with inducible shRNA expression as a tool to study the maturation of macromolecular assemblies[END_REF], we did not detect RPS26 in early cytoplasmic HASt-LTV1 pre-40S particles. Consistently, knockdown of RPS26 did not influence the presence of NOB1 and DIM2 in these early cytoplasmic pre-40S particles, as attested by measuring the NOB1/RPS19 or DIM2/RPS19 ratios (Figure 5d), nor did it affect the dissociation of ENP1 and RIO2. In contrast, we observed a strong increase of NOB1 and DIM2 levels relative to RPS19 in RIO1(kd)-StHA pre-40S particles purified from RPS26-depleted cells when compared to control cells (Figure 5c,d), which suggests that the absence of RPS26 prevents the release of NOB1 and DIM2 and traps the particles in state A. This hypothesis was further supported when we analyzed pre-40S particles purified using wild-type RIO1 as bait (RIO1(wt)-StHA). We have previously shown that RIO1(wt)-StHA does not co-purify efficiently with pre-40S particles when compared to the catalytically inactive version of RIO1 [START_REF] Montellese | USP16 counteracts mono-ubiquitination of RPS27a and promotes maturation of the 40S ribosomal subunit[END_REF][START_REF] Widmann | The kinase activity of human Rio1 is required for final steps of cytoplasmic maturation of 40S subunits[END_REF], which was confirmed here by the very low amount of both pre-40S RBFs and RPS19 detected by western blot (Figure 5c). However, upon RPS26 depletion, RIO1(wt)-StHA co-purified with late cytoplasmic pre-40S particles, as attested by the presence of NOB1 and DIM2 (Figure 5c), as well as that of 18S-E pre-rRNA (Figure 5a). These data indicate that RIO1 association with late cytoplasmic pre-40S particles is stabilized in the absence of RPS26, while the release of NOB1 and DIM2 is inhibited.

Comparative proteomics analyses of RIO1(kd)-StHA-associated pre-40S particles in the absence or presence of RPS26 confirmed that no other RPS was lost upon RPS26 depletion (Figure 5-figure supplement 1). This experiment also revealed a significant decrease of EIF1AD co-purification with RIO1(kd)-StHA upon RPS26 depletion (log 2 (fold change) = À2.1, corresponding to a 4.2-fold decrease; p-value=8.9E-3). EIF1AD was recently shown to be a new RBF present in late pre-40S particles in direct contact with RIO1 [START_REF] Ameismeier | Structural basis for the final steps of human 40S ribosome maturation[END_REF]. But whether RPS26 depletion affects EIF1AD association to RIO1 within or out of pre-40S particles cannot be distinguished by this experiment. To assess incorporation of EIF1AD in RIO1(kd)-StHA pre-40S particles, we evaluated the ratio of EIF1AD relative to RPS19 within pre-40S particles by western blot and observed a mild 1.3-fold reduction upon RPS26 depletion (Figure 5-figure supplement 2). As a comparison, the levels of NOB1 or DIM2 relative to RPS19 increased by a factor of 1.6 and 2, respectively (Figure 5c,d,Figure 5-figure supplement 2). These results indicate that loss of RPS26 does not strongly impact the presence of EIF1AD onto RIO1(kd)-StHA pre-40S particles. The stronger decrease observed by mass spectrometry may be also related to EIF1AD association with RIO1(kd)-StHA out of the pre-40S particles and be an indirect effect of RPS26 depletion. Altogether, these data lead us to conclude that RPS26 intervenes directly in the mechanism triggering rRNA cleavage by NOB1 at site 3 and dissociation of NOB1, DIM2, and RIO1 from pre-40S particles.

ATP binding by RIO1 and addition of RPS26 stimulate in vitro rRNA cleavage by NOB1 in RPS26-depleted pre-40S particles RIO protein kinases have been proposed to act as conformation-sensing ATPases rather than kinases [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF]. Previous studies in the yeast Saccharomyces cerevisiae have shown that rRNA cleavage by Nob1 in cytoplasmic pre-40S particles purified with tagged Rio1 was stimulated in vitro by ATP binding to Rio1 [START_REF] Turowski | Rio1 mediates ATP-dependent final maturation of 40S ribosomal subunits[END_REF]. The D324A point mutation introduced in RIO1(kd)-StHA does not hamper fixation of ATP [START_REF] Widmann | The kinase activity of human Rio1 is required for final steps of cytoplasmic maturation of 40S subunits[END_REF], but the structure of RIO1(kd) in state B shows that the hydrolysis products are trapped in the catalytic site (Figure 3c). However, this defective catalytic activity does not block maturation of the 3 0 -end of 18S rRNA within RIO1(kd)-StHA pre-40S particles. This suggests that ATP binding to the human RIO1 catalytic site is sufficient for 18S-E pre-rRNA cleavage, similar to what was shown in yeast. In order to check whether ATP binding to RIO1 favors rRNA cleavage by NOB1, we purified RIO1(wt)-StHA and RIO1(kd)-StHA human pre-40S particles from RPS26 depleted cells to enrich pre-cleavage state A and performed in vitro cleavage assays.

Based on the conditions established in yeast [START_REF] Lebaron | Proofreading of pre-40S ribosome maturation by a translation initiation factor and 60S subunits[END_REF], we added either ATP or AMP-PNP (a non-hydrolysable analog of ATP) to purified pre-40S particles and monitored 18S rRNA 3 0 -end maturation using RNase H digestion. As shown in Figure 6 , 18S-E pre-rRNA cleavage was stimulated both by ATP and AMP-PNP in particles purified with RIO1(wt)-StHA or with RIO1(kd)-StHA, albeit a bit more efficiently by ATP as previously observed in yeast (Figure 6a,b). This result reinforces the idea that, like in yeast, ATP binding to RIO1 stimulates 18S-E cleavage at site 3 [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF][START_REF] Turowski | Rio1 mediates ATP-dependent final maturation of 40S ribosomal subunits[END_REF]. Given the position of RIO1 in the vicinity of DIM2 and NOB1 revealed by the cryo-EM analysis, RIO1 might favor DIM2 displacement and subsequent activity of NOB1 through an ATP-driven local conformational change. Indeed, superimposition of state A and state B atomic models showed steric hindrance between the C-terminal regions of DIM2 and RIO1 (Figure 6-figure supplement 1); similarly, putative clashes between RIO1 and DIM2 were also seen by others [START_REF] Ameismeier | Structural basis for the final steps of human 40S ribosome maturation[END_REF]. These structural observations support a mechanism of competition between RIO1 and DIM2.

We next sought to assess the role of RPS26 and produced recombinant human RPS26 (Figure 6figure supplement 2). Addition of RPS26 to the pre-40S particles depleted of RPS26 stimulated cleavage by NOB1 to the same extent as addition of ATP (Figure 6a,c). Importantly, the addition of RPS26 together with ATP significantly increased the fraction of cleaved 18S rRNA when compared to single addition of one or the other (Figure 6a,c). These data show that in vitro cleavage by NOB1 in pre-40S particles is stimulated by both RIO1 and RPS26 and support the hypothesis of a cooperative action of RPS26 and RIO1 in triggering the final step of 18S rRNA maturation.

Discussion

A previous cryo-EM analysis of human pre-40S particles purified using DIM2 as bait revealed several successive structural states, in which the latest one carried NOB1, DIM2, TSR1, as well as a long alpha-helix attributed to LTV1 [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF]. Here, by purification of a pre-40S particle via a catalytically inactive form of RIO1, we have uncovered two later structural states in which only the last RBFs found in pre-40S particles, namely NOB1, DIM2, and RIO1, were clearly detected. In addition, one of these states is posterior to 18S-E pre-rRNA cleavage at site 3, as indicated by detection of the mature 3 0 end of the 18S rRNA, presence of RPS26, and absence of NOB1 and DIM2. These structures arguably correspond to the ultimate maturation stages of the pre-40S particles. Our results point towards a coordinated action of RIO1 and RPS26 in triggering the last 18S rRNA processing step by NOB1, following a sequence represented in Figure 7 and discussed below.

The cooperative action of RIO1 and RPS26 unlocks 18S-E rRNA cleavage

Our results show that RIO1 binds to pre-40S particles in the same region as RIO2, which suggests that recruitment of RIO1 may simply follow the release of RIO2. The absence of a clear density for . In vitro cleavage of the 18S-E pre-rRNA within pre-40S particles is stimulated by ATP addition. HEK cell lines expressing tagged versions of wild-type RIO1 'RIO1(wt)' or of the catalytically inactive 'RIO1(kd)' were treated with RPS26 siRNAs for 48 hr to enrich particles in state A. Pre-40S particles were purified and incubated for 1 hr in buffer alone (mock condition) or in the presence of either 1 mM ATP, 1 mM AMP-PNP, 2 mg of RPS26, or 2 mg of RPS26 plus 1 mM ATP. (a) RNAse H assays were performed on the RNAs extracted from the particles. (b) The variation of cleavage efficiency upon addition of ATP or AMP-PNP is indicated by the 18S/(18S + 18S-E) ratio. The data correspond to five independent experiments. Statistical analysis was performed with a unilateral paired Wilcoxon test ('sample greater than mock') indicating p-values of 0.031 for all samples. (c) The variation of cleavage efficiency upon addition of ATP and/or RPS26 is indicated by the 18S/(18S + 18S-E) ratio. The data correspond to three to six independent measurements for each point. Statistical analysis was performed with a unilateral unpaired Wilcoxon test ('sample greater than mock' or '+RPS26+ATP greater than +RPS26'). The online version of this article includes the following figure supplement(s) for figure 6: RIO1 in pre-cleavage state A suggests that RIO1 is initially flexibly associated, while DIM2 and NOB1 are stably bound. A recent cryo-EM study performed on human pre-40S particles revealed significant changes in RIO1 position before 18S-E pre-rRNA cleavage [START_REF] Ameismeier | Structural basis for the final steps of human 40S ribosome maturation[END_REF]. We hypothesize that we could not precisely position RIO1 in the pre-cleavage state A herein described because our cryo-EM analysis was performed on a significantly smaller scale.

In contrast, state B shows RIO1 in a stable conformation, while DIM2 and NOB1 are absent in this post-cleavage particle. Despite its overall impaired ATPase activity, the catalytic pocket of the RIO1-D324A mutant is occupied by ADP+pAsp341 (Figure 3c, Figure 3-figure supplement 2). This suggests that transition of pre-40S particles to state B involves ATP binding as well as the ATP hydrolysis activity of RIO-D324A, while trapping of ADP in the catalytic site prevents release from the matured particle. The structure of RIO1 was shown to switch to a so-called 'active' form when complexed either with ATP or with its hydrolysis products ADP/pAsp [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF]. ATP fixation in the catalytic pocket of RIO1 might trigger its stabilization on the head of the pre-40S particle and bring RIO1 to contact DIM2. Furthermore, our data reveal a possible steric clash between the C-terminal domains of RIO1 and DIM2 (Figure 6-figure supplement 1). This suggests that RIO1 stabilization on pre-40S particles initiates DIM2 dislodging to uncover site 3 and allows rRNA cleavage by NOB1. Accordingly, our in vitro assays show that binding of ATP or AMP-PNP to RIO1 stimulates cleavage by NOB1 in human pre-40S particles (Figure 6), as concluded before in yeast [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF]. Also supporting this scenario, recent in vitro studies in yeast have shown that Rio1 forms a trimeric complex with Dim2 and Nob1 in the presence of AMP-PNP and not ADP [START_REF] Parker | A kinase-dependent checkpoint prevents escape of immature ribosomes into the translating pool[END_REF]. In addition, overexpression of Rio1 in yeast is sufficient to displace a catalytically inactive form of Nob1 from pre-40S particles [START_REF] Parker | A kinase-dependent checkpoint prevents escape of immature ribosomes into the translating pool[END_REF]. The recent study by [START_REF] Ameismeier | Structural basis for the final steps of human 40S ribosome maturation[END_REF] reached similar conclusions regarding the role of RIO1. It also uncovered the role of EIF1AD as a new ribosome biogenesis factor. The structures published in this study suggest that both factors may functionally interact upstream of RPS26 incorporation. Nevertheless, the action of RIO1 is not sufficient to efficiently trigger 18S-E pre-rRNA cleavage together with DIM2 and NOB1 dissociation pre-40S particles, as shown by the blocking of RIO1-StHA pre-40S particles in the pre-cleavage state upon RPS26 knockdown. RPS26 is the only component of the mature small ribosomal subunit missing in state A. Its binding site overlaps with that of DIM2, and its final positioning on the 40S subunits is thus directly dependent on the release of DIM2. Importantly, addition of RPS26 was sufficient to stimulate in vitro cleavage of the 18S-E pre-rRNA in RPS26 depleted pre-40S particles, and it increased cleavage efficiency in the presence of ATP. While establishment of the full interaction of RIO1 with the head domain may provide a driving force to displace DIM2, RPS26 may potentiate its activity by competing with DIM2 binding. We propose a model in which displacement of DIM2 upon RIO1 binding in its final position (corresponding to state B) triggers the recruitment of RPS26 to the pre-40S particle, which in turn further displaces DIM2 from cleavage site 3. This cooperative action of RIO1 and RPS26 would then lead to a putative, probably short-lived cleavage-competent state (Figure 7), in which NOB1 can reach its substrate and process the 3 0 -end of the 18S rRNA. The status of ATP hydrolysis within RIO1 in this state is not known, and thus marked as 'ATP*' in Figure 7. The release of ADP and dephosphorylation of phospho-aspartate pAsp341 would then trigger a conformational change within RIO1 allowing its dissociation from pre-40S particles, as proposed for yeast Rio1 as well as other RIO kinases family members [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF][START_REF] Ferreira-Cerca | ATPase-dependent role of the atypical kinase Rio2 on the evolving pre-40S ribosomal subunit[END_REF][START_REF] Knu ¨ppel | Insights into the evolutionary conserved regulation of rio ATPase activity[END_REF][START_REF] Turowski | Rio1 mediates ATP-dependent final maturation of 40S ribosomal subunits[END_REF]. Along this view, RIO1 and RPS26 function as the two keys of a dual key lock that ensures a strict control of the ultimate steps of 40S subunit maturation before entry in translation.

Human 40S subunit precursors do not form 80S-like particles

In yeast, expression of the Rio1-D244A mutant (equivalent to human RIO1-D324A) was shown to promote the accumulation of 80S-like particles, with which it co-purifies. In these 80S-like particles, pre-40S particles containing unprocessed 20S pre-rRNA, the last precursor to the 18S rRNA in yeast, are associated with large ribosomal subunits [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF][START_REF] Turowski | Rio1 mediates ATP-dependent final maturation of 40S ribosomal subunits[END_REF]. Such particles were also observed with a number of other mutations targeting late-acting small ribosomal subunit biogenesis factors [START_REF] Lebaron | Proofreading of pre-40S ribosome maturation by a translation initiation factor and 60S subunits[END_REF][START_REF] Parker | A kinase-dependent checkpoint prevents escape of immature ribosomes into the translating pool[END_REF][START_REF] Scaiola | Structure of a eukaryotic cytoplasmic pre-40S ribosomal subunit[END_REF][START_REF] Strunk | A translation-like cycle is a quality control checkpoint for maturing 40S ribosome subunits[END_REF] and were proposed to host the cleavage of the 20S pre-rRNA. Association of late pre-40S particles with large ribosomal subunits might serve as a checkpoint to verify that they are translation-competent after their final maturation [START_REF] Lebaron | Proofreading of pre-40S ribosome maturation by a translation initiation factor and 60S subunits[END_REF][START_REF] Strunk | A translation-like cycle is a quality control checkpoint for maturing 40S ribosome subunits[END_REF][START_REF] Turowski | Rio1 mediates ATP-dependent final maturation of 40S ribosomal subunits[END_REF]. In addition, yeast 80S-like particles containing 20S pre-rRNA have been shown to be able to associate with polysomes and thus enter into the translating pool of ribosomes [START_REF] Belhabich-Baumas | The Rio1p ATPase hinders premature entry into translation of late pre-40S pre-ribosomal particles[END_REF][START_REF] Parker | A kinase-dependent checkpoint prevents escape of immature ribosomes into the translating pool[END_REF][START_REF] Soudet | Immature small ribosomal subunits can engage in translation initiation in Saccharomyces cerevisiae[END_REF], suggesting some permissiveness between final pre-40S maturation and translation initiation events. In stark contrast, we found little evidence that human RIO1(kd)-StHA pre-ribosomal particles strongly associate with 60S subunits, neither by proteomics and northern blot, nor by cryo-EM single-particle analysis. Our results rather suggest that final rRNA maturation can occur within free pre-40S particles. Though ribosome biogenesis appears globally conserved within eukaryotic species, substantial differences in the pre-rRNA processing pathways, as well as in the dynamics of RBF association with pre-ribosomes in mammals and yeast, have been demonstrated (for review, [START_REF] Cerezo | Maturation of pre-40S particles in yeast and humans[END_REF][START_REF] Henras | An overview of preribosomal RNA processing in eukaryotes: pre-ribosomal RNA processing in eukaryotes[END_REF]. The absence of 80S-like particles in late human pre-40S particles might constitute a significant difference in the maturation pathway of human pre-ribosomal particles compared to yeast.

RIO1 probes tRNA translocation capacities of pre-40S particles

The function of RIO1 in the release of DIM2 and NOB1 echoes the roles that other NTPases play in pre-ribosomal particle remodeling along the maturation pathway. Their nucleotide-hydrolyzing activity was shown to power the release of other RBFs, as well as their own release, contributing to the unidirectionality of the maturation [START_REF] Hedges | Release of the export adapter, Nmd3p, from the 60S ribosomal subunit requires Rpl10p and the cytoplasmic GTPase Lsg1p[END_REF][START_REF] Kargas | Mechanism of completion of peptidyltransferase centre assembly in eukaryotes[END_REF][START_REF] Knu ¨ppel | Insights into the evolutionary conserved regulation of rio ATPase activity[END_REF][START_REF] Micic | Coupling of 5S RNP rotation with maturation of functional centers during large ribosomal subunit assembly[END_REF][START_REF] Mitterer | Conformational proofreading of distant 40S ribosomal subunit maturation events by a long-range communication mechanism[END_REF][START_REF] Weis | Mechanism of eIF6 release from the nascent 60S ribosomal subunit[END_REF][START_REF] Zemp | Distinct cytoplasmic maturation steps of 40S ribosomal subunit precursors require hRio2[END_REF]. NTPases might also have additional roles than conformational switches and probe the correct conformation of functional sites. For example, proper formation of the peptidyl-transferase center (PTC) in the large subunit may be checked by Nog2 and adjacent GTPases Nog1 and Nug1, which binds at or adjacent to the PTC (discussed by [START_REF] Klinge | Ribosome assembly coming into focus[END_REF]. RIO1 binds to the same place as RIO2, which prevents premature engagement of pre-40S particles in translation by physically obstructing the mRNA groove and tRNA interaction sites [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF][START_REF] Heuer | Cryo-EM structure of a late pre-40S ribosomal subunit from Saccharomyces cerevisiae[END_REF][START_REF] Larburu | Structure of a human pre-40S particle points to a role for RACK1 in the final steps of 18S rRNA processing[END_REF][START_REF] Scaiola | Structure of a eukaryotic cytoplasmic pre-40S ribosomal subunit[END_REF][START_REF] Strunk | A translation-like cycle is a quality control checkpoint for maturing 40S ribosome subunits[END_REF]. Furthermore, in the post-cleavage state B herein described, 18S rRNA G1639 appears to lock the RIO1(kd) catalytic pocket in its 'active' conformation [START_REF] Ferreira-Cerca | Dominant Rio1 kinase/ATPase catalytic mutant induces trapping of late pre-40S biogenesis factors in 80S-like ribosomes[END_REF] through a pi-stacking interaction with phenylalanine F328 (Figure 3c). Such an interaction does not seem to be established with RIO2, whose catalytic pocket is more distant from this guanosine [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF]. The N7-methylated G1639 is universally conserved and is involved in the correct positioning of tRNA in the P-site as well as its transfer to the E-site thanks to a switch mechanism [START_REF] Malygin | HCV IRES interacts with the 18S rRNA to activate the 40S ribosome for subsequent steps of translation initiation[END_REF][START_REF] Selmer | Structure of the 70S ribosome complexed with mRNA and tRNA[END_REF]. Through its cycle of association, ATPase hydrolysis, and subsequent dissociation from pre-40S particles, RIO1 might thus act as a conformational and functional probe that assesses the tRNA translocation capacities of the small subunit and couples triggering of the last maturation step to functional proofreading of the ribosome. Cell culture and treatment with siRNA duplexes HEK293 cells were cultured in Dulbecco's modified Eagle's medium supplemented with 10% fetal bovine serum and 1 mM sodium pyruvate. HEK293 FlpIn TRex cell lines (Invitrogen, RRID:CVCL_ U427) and expressing HASt-DIM2, HASt-LTV1, RIO1(wt)-StHA, and RIO1(D324A)-StHA have been described previously [START_REF] Wyler | Tandem affinity purification combined with inducible shRNA expression as a tool to study the maturation of macromolecular assemblies[END_REF]. Cell lines used in this study were not further authenticated after obtaining them from the indicated source. All cell lines were tested negative for mycoplasma using MycoAlert test (Lonza). None of the cell lines used in this study were included in the list of commonly misidentified cell lines maintained by International Cell Line Authentication Committee.

Materials and methods

Key resources table

To knockdown expression of the corresponding human protein genes, siRNA duplex of RPS26 (5 0 -GGACAAGGCCAUUAAGAAAdTdT-3 0 ) or EIF1AD (5 0 -ACCGCAGACAGUAUCAUGAGA-3 0 ) (Eurogentec) was added at a final concentration of 500 nM to 100 mL of cell suspension (50 Â 10 6 cells/ mL diluted in Na phosphate buffer, pH 7.25, containing 250 mM sucrose and 1 mM MgCl 2 ). After electrotransformation at 240 V, cells were plated and collected 48 hr later. Control cells were electro-transformed with a scramble siRNA. Knockdown efficiency of siRNAs was assessed by quantitative PCR, using HPRT1 as an internal control.

TAP purification of human pre-40S particles

To purify pre-ribosomal particles, the protocol described in [START_REF] Wyler | Tandem affinity purification combined with inducible shRNA expression as a tool to study the maturation of macromolecular assemblies[END_REF] was adapted as follows: expression of N-terminally HASt-tagged or C-terminally StHA-tagged bait proteins in stable HEK293 cells was induced with tetracycline (0.5 mg/mL) 24 hr prior to harvest. Cells were detached with PBS containing 0.5 mM EDTA and lysed in lysis buffer (10 mM Tris-HCl, pH 7.6, 100 mM KCl, 2 mM MgCl 2 , 1 mM DTT, 0.5% NP-40, supplemented with protease and phosphatase inhibitors) using a dounce homogenizer. Lysed cells were centrifuged (4500 g, 12 min), and the lysate was incubated with EZview Red Anti-HA Affinity Gel (Sigma-Aldrich) for 2 hr in an overhead shaker. For electron microscopy studies, beads were washed six times with TAP buffer (20 mM Tris-HCl, pH 7.6, 100 mM KCl, 2 mM MgCl 2 , 1 mM DTT) and eluted by incubation in TAP buffer supplemented with 0.2 mg/ mL HA peptide (Sigma-Aldrich). Eluates were washed and concentrated by Vivacon 2, 100 kDa MWCO centrifugal devices (Sartorius). For subsequent analyses by silver staining, western blotting, and mass spectrometry, beads were washed three times with TAP buffer and bound material was eluted with SDS sample buffer.

Protein digestion and nano-LC-MS/MS analysis Analysis of RIO1(kd)-StHA particles composition

Following TAP purification, 100 mL of concentrated RIO1 pre-40S particles, corresponding to 3.5 mg of protein, was reduced by incubation for 5 min at 95˚C with 5 mL of Laemmli buffer containing 30 mM DTT and then alkylated with 90 mM iodoacetamide for 30 min at room temperature in the dark. The reduced/alkylated sample was then loaded onto SDS-PAGE gel (stacking 4% and separating 12% acrylamide). For one-shot analysis of the entire mixture, no fractionation was performed, and the electrophoretic migration was stopped as soon as the protein sample entered the separating gel as one single band. The proteins, revealed with Instant Blue (Expedeon) for 20 min, were found in one blue band of around 5 mm width. Single slice containing the whole sample was cut and washed before the in-gel digestion of the proteins overnight at 37˚C with a solution of modified trypsin (sequence grade, Promega, Charbonnie `res, France). The resulting peptides were extracted from the gel by one round of incubation (15 min, 37˚C) in 1% formic acid-acetonitrile (40%) and two rounds of incubation (15 min each, 37˚C) in 1% formic acid-acetonitrile (1:1). The extracted fractions were airdried. Tryptic peptides were resuspended in 14 mL of 2% acetonitrile and 0.05% trifluoroacetic acid (TFA). Nano-LC-MS/MS analysis was performed in duplicate injections using an Ultimate 3000 nanoRS system (Dionex, Amsterdam, The Netherlands) coupled with an LTQ-Orbitrap Velos mass spectrometer (Thermo Fisher Scientific, Bremen, Germany) operating in positive mode. Five microliters of each sample was loaded onto a C18-pre-column (300 mm inner diameter  5 mm) at 20 mL/ min in 2% ACN, 0.05% TFA. After 5 min of desalting, the pre-column was switched online with the analytical C18 nanocolumn (75 mm inner diameter  15 cm, packed in-house) equilibrated in 95% solvent A (5% ACN, 0.2% FA) and 5% solvent B (80% ACN, 0.2% FA). Peptides were eluted by using a 5-50% gradient of solvent B for 105 min, at a flow rate of 300 nL/min. The LTQ-Orbitrap Velos was operated in data-dependent acquisition mode with the XCalibur software. Survey scans MS were acquired in the Orbitrap, on the 300-2000 m/z (mass to charge ratio) range, with the resolution set to a value of 60,000 at m/z 400. Up to 20 of the most intense multiply charged ions (>2+) per survey scan were selected for CID (collision-induced dissociation) fragmentation, and the resulting fragments were analyzed in the linear ion trap (LTQ). Dynamic exclusion was used within 60 s to prevent repetitive selection of the same peptide.

Analysis of RIO1(kd)-StHA particles composition upon RPS26 depletion

Each protein sample corresponding to RIO1(kd)-StHA pre-40S particles purified from RPS26 depleted cells and control cells (64 and 94 mg of proteins in 300 mL of 40 mM Tris-HCl, 4% SDS, respectively) was reduced with 6 mL of 1 M DTT (20 mM final) during 10 min at 95˚C under agitation, cooled to room temperature, and alkylated with 19 mL of 1 M iodoacetamide (60 mM final) during 30 min in the dark. Then, each sample was digested with trypsin using the S-Trap Micro spin column protocol (Protifi, Huntington, NY) according to the manufacturer's instructions [START_REF] Hailemariam | S-Trap, an ultrafast Sample-Preparation approach for shotgun proteomics[END_REF]. The pooled digested peptide extracts were dried down and resuspended with 0.05% TFA in 2% ACN at a concentration of 3.8 mg/mL, vortexed, and sonicated for 10 min before injection. Peptides samples were analyzed in triplicate injections using an UltiMate 3000 RSLCnano LC system (ThermoScientific, Dionex) coupled with an Orbitrap Fusion Tribrid mass spectrometer (Thermo Scientific, Bremen, Germany) operating in positive mode. Five microliters of each sample were loaded onto a 300 mm ID Â 5 mm PepMap C18 pre-column (Thermo Scientific, Dionex) at 20 mL/min in 2% ACN, 0.05% TFA. After 5 min of desalting, peptides were on-line separated on a 75 mm ID Â 50 cm C18 column (in-house packed with Reprosil C18-AQ Pur 3 mm resin, Dr. Maisch; Proxeon Biosystems, Odense, Denmark) equilibrated in 95% of buffer A (0.2% formic acid [FA]), with a gradient of 5% to 25% of buffer B (80% ACN, 0.2% FA) for 75 min and then 25-50% for 30 min at a flow rate of 300 nl/min. The instrument was operated in data-dependent acquisition mode using a top-speed approach (cycle time of 3 s). Survey scans MS were acquired in the Orbitrap over 400-2000 m/z with a resolution of 120,000 (at 200 m/z), an automatic gain control (AGC) target value of 4e5, and a maximum injection time of 50 ms. Most intense multiply charged ions (2 + to 7+) per survey scan were selected at 1.6 m/z with quadrupole and fragmented by higher energy collisional dissociation (HCD). The monoisotopic precursor selection was turned on, the intensity threshold for fragmentation was set to 50,000, and the normalized collision energy was set to 35%. The resulting fragments were analyzed in the Orbitrap with a resolution of 30,000 (at 200 m/z), an AGC target value of 5e4, and a maximum injection time of 60 ms. Dynamic exclusion was used within 60 s with a 10 ppm tolerance, to prevent repetitive selection of the same peptide. For internal calibration the 445.120025 ion was used as lock mass.

Bioinformatic MS data analysis

Mascot (Mascot server v2.6.1; http://www.matrixscience.com) database search engine was used for peptide and protein identification using automatic decoy database search to calculate a false discovery rate (FDR). MS/MS spectra were compared to the SwissProt H. sapiens database (supplemented with the sequence of the D324A RIO1 mutant). MS mass tolerance was set at 5 ppm and MS/MS mass tolerance was set at 0.8 Da and 0.02 Da for data acquired on LTQ-Orbitrap Velos and Orbitrap Fusion Tribrid mass spectrometers, respectively. The enzyme selectivity was set to full trypsin with two missed cleavages allowed. Protein modifications were fixed carbamidomethylation of cysteines, variable phosphorylation of serine, threonine and tyrosine, variable oxidation of methionine, variable acetylation of protein N-terminus. Proline software [START_REF] Bouyssie | Proline: an efficient and user-friendly software suite for large-scale proteomics[END_REF] was used for the validation and the label-free quantification of identified proteins in each sample. Mascot identification results were imported into Proline. Search results were validated with a peptide rank = 1 and at 1% FDR both at PSM level (on adjusted e-value criterion) and protein set level (on modified Mudpit score criterion). Label-free quantification was performed for all proteins identified: peptides were quantified by extraction of MS signals in the corresponding raw files, and post-processing steps were applied to filter, normalize, and compute protein intensities. For analysis of RIO1(kd)-StHA pre-40S particles composition, protein abundances were summarized in iBAQ values by dividing the protein intensities by the number of observable peptides [START_REF] Schwanha ¨usser | Global quantification of mammalian gene expression control[END_REF]. Proteins with a ratio of observed peptide sequences over observable peptide sequences inferior to 30% were filtered out. Additionally, only the two most intense iBAQ logs (1E6 to 1E8) were represented in Figure 1, Figure 1-figure supplement 2. For analysis of RIO1(kd)-StHA pre-40S particle composition upon RPS26 depletion, after log2-transformation of the data, an unpaired two-tailed Student's t-test was performed and proteins were considered significantly enriched when their absolute log2-transformed fold change was higher than two and their p-value lower than 0.01. A volcano plot was drawn to visualize significant protein abundance variations between the two compared conditions and represents Àlog10 (p-value) according to the log2 ratio (Figure 5-figure supplement 1).

Grid preparation and cryo-EM images acquisition

Cryo-EM grids were prepared and systematically checked at METI, Toulouse. Immediately after glow discharge, 3.5 mL of purified hRIO1(kd)-StHA particles (with RNA concentrations of ~60 ng/mL as estimated by Nanodrop measurement) was deposited onto QUANTIFOIL holey carbon grids (R2/1, 300 mesh with a 2 nm continuous layer of carbon on top). Grids were plunge-frozen using a Leica EM-GP automat; temperature and humidity level of the loading chamber were maintained at 20˚C and 95%, respectively. Excess solution was blotted with a Whatman filter paper no. 1 for 1.7-1.9 s, and grids were immediately plunged into liquid ethane (À183˚C).

Images were recorded on a Titan Krios electron microscope (FEI, ThermoFisher Scientific) located at EMBL, Heidelberg, Germany. The cryo-electron microscope was operating at 300 kV and was equipped with a Gatan K2 summit direct electron detector using counting mode. Automatic image acquisition was performed with SerialEM, at a magnification corresponding to a calibrated pixel size of 1.04 A ˚and a total electron dose of 29.88 e-/A ˚2 over 28 frames. Nominal defocus values ranged from À0.8 mm to À2.8 mm.

Single-particle analysis

Nine thousand four hundred and ninety-four stacks of frames were collected at EMBL. Frame stacks were aligned to correct for beam-induced motion using MotionCor2 [START_REF] Zheng | MotionCor2: anisotropic correction of beam-induced motion for improved cryo-electron microscopy[END_REF]. Contrast transfer function (CTF) and defocus estimation were performed on the realigned stacks using CTFFIND4 [START_REF] Rohou | CTFFIND4: Fast and accurate defocus estimation from electron micrographs[END_REF]. After selection upon CTF estimation quality, maximum resolution on their power spectra, and visual checking, 'good' micrographs were retained for further analysis. The 2,126,610 particles were automatically picked and then extracted in boxes of 384 Â 384 pixels, using the RELION 3.0 Autopick option. All subsequent image analysis was performed using RELION 3.0 [START_REF] Zivanov | New tools for automated high-resolution cryo-EM structure determination in RELION-3[END_REF]; Figure 2-figure supplement 1). A first 2D classification was performed (on particles images binned by a factor of 8) to sort out ill-picked and methylosome particles. The 1,287,445 remaining particles were binned by a factor of 4 and subjected to a 3D classification in five classes, using the 40S subunit atomic model derived from the human ribosomal 3D structure (PDB-ID 6EK0) [START_REF] Natchiar | Visualizing the role of 2'-OH rRNA methylations in the human ribosome structure[END_REF] low-pass filtered to 60 A ˚, as initial reference. One class harbored full 40S morphology and good level of details. The 484,429 particles from this class were re-extracted without imposing any binning factor, and a consensus 3D structure was obtained using RELION's 3D auto-refine option, with an overall resolution of 2.9 A ˚for FSC = 0.143 according to gold-standard FSC procedure. Particles were then submitted to focused 3D classifications with signal subtraction around the platform domain, to remove information coming from the body and head of the pre-40S particles, according to Scheres, 2016. Two of the five 3D classes yielded reconstructions with clear features. The first one, hereafter named state A, contained 104,844 particles and was further auto-refined to 3.1 A ˚resolution according to gold-standard FSC procedure; the second one (state B) comprised 276,012 particles and was auto-refined to 2.9 A ˚resolution. Subsequently, particles corresponding to the states A and B 'platform only' classes were retrieved from the dataset without signal subtraction and submitted to auto-refinement, yielding maps of 'full' states A and B particles solved to 3.22 and 2.96 A ˚, respectively (Figure 2-figure supplement 1b, c). Because significant motion of the head and platform regions compared to the body was observed, multi-body refinement [START_REF] Nakane | Characterisation of molecular motions in cryo-EM singleparticle data by multi-body refinement in RELION[END_REF] was performed for both states by dividing pre-40S particles in three main domains: body, head, and platform. Multi-body refinement of state A gave rise to body, head, and platform domains solved to 3.14, 3.17, and 3.30 A ˚, respectively, after post-processing, while that of state B yielded resolutions of 2.98, 2.96, and 2.98 A ˚for the body, head, and platform regions, respectively (Figure 2-figure supplement 1c). Local resolution of all cryo-EM maps was estimated using the ResMap software [START_REF] Kucukelbir | Quantifying the local resolution of cryo-EM density maps[END_REF]

Interpretation of cryo-EM maps

Atomic models of pre-40S particle (PDB-ID 6G51) [START_REF] Ameismeier | Visualizing late states of human 40S ribosomal subunit maturation[END_REF] or the mature 40S subunit (PDB-ID 6EK0) [START_REF] Natchiar | Visualizing the role of 2'-OH rRNA methylations in the human ribosome structure[END_REF] were first fitted in the cryo-EM maps of interest as rigid body using the 'fit' command in UCSF Chimera [START_REF] Pettersen | UCSF Chimera-a visualization system for exploratory research and analysis[END_REF]. Body, head, and platforms domains were modeled separately in the post-processed multi-body 'bodies' maps and then adapted to the composite full maps to generate whole atomic models using UCSF Chimera and Coot [START_REF] Emsley | Features and development of coot[END_REF].

Final atomic models of states A (pre-cleavage) and B (post-cleavage) pre-40S particles were refined using REFMAC5 [START_REF] Murshudov | REFMAC5 for the refinement of macromolecular crystal structures[END_REF] and Phenix_RealSpace_Refine [START_REF] Adams | PHENIX: a comprehensive Python-based system for macromolecular structure solution[END_REF], with secondary structure restraints for proteins and RNA generated by ProSMART [START_REF] Nicholls | Conformation-independent structural comparison of macromolecules with ProSMART[END_REF] and LIBG [START_REF] Brown | Tools for macromolecular model building and refinement into electron cryo-microscopy reconstructions[END_REF]. Final model evaluation was done with MolProbity [START_REF] Chen | MolProbity: all-atom structure validation for macromolecular crystallography[END_REF]. Overfitting statistics were calculated by a random displacement of atoms in the model, followed by a refinement against one of the half-maps in REFMAC5, and Fourier shell correlation curves were calculated between the volume from the atomic model and each of the halfmaps in REFMAC5 (Supplementary file 1).

Maps and models visualization was done with Coot and UCSF Chimera; figures were created using UCSF Chimera and ChimeraX [START_REF] Goddard | UCSF ChimeraX: meeting modern challenges in visualization and analysis[END_REF].

RNase H digestion assay and RNA analysis

For RNase H digestion assays, 250 ng of pre-40S purified RNAs were denatured at 95˚C for 6 min with a RNA/DNA/RNA reverse probe hybridizing in the 3 0 -end of 18S rRNA (probe RNaseH_3_Hyb1: 5 0 -UGUUACGACUUUUACTTCCUCUAGAUAGUCAAGUUC-3 0 ; 0.5 mL at 100 mM). After annealing by cooling down to room temperature for 20 min, the reaction mixture was diluted to 30 mL with a reaction mix containing 1X RNase H reaction buffer, 25 mM DTT, 0.5 U/l RNasin (Promega), and 50 U RNase H (New England Biolabs), and incubated at 37˚C for 30 min. The reaction was then blocked by addition of 0.3 M sodium acetate, pH 5.2 and 0.2 mM EDTA, and the RNAs were recovered by ethanol precipitation after phenol-chloroform-isoamylalcohol (25:24:1) extraction.

RNAs were then separated on a 12% polyacrylamide gel (19:1) in 1X TBE buffer containing 7 M urea. RNAs were transferred to Hybond N + nylon membrane (GE-Healthcare, Orsay, France) and crosslinked under UV light. Membrane pre-hybridization was performed at 45˚C in 6X SSC (salinesodium citrate), 5X Denhardt's solution, 0.5% SDS, and 0.9 mg/mL tRNA. The 5 0 -radiolabeled oligonucleotide probe 3 0 18S (5 0 -GATCCTTCCGCAGGTTCACCTACG-3 0 ) was added after 1 hr and incubated overnight at 45˚C. Membranes were washed twice for 10 min in 2X SSC and 0.1% SDS and once in 1X SSC and 0.1% SDS, and then exposed. Signals were acquired with a Typhoon Trio Phos-phorImager and quantified using the ImageLab software.

The RNA ladder corresponds to a 131 nucleotides sequence comprising the 3'18S probe and the T7 promoter sequence (Supplementary file 1). Using the oligonucleotides Lad_S and Lad_AS (Supplementary file 1), the DNA template for the RNA ladder was produced by PCR. Then, RNA was synthesized by in vitro transcription of the PCR products using the T7 RNA polymerase (Promega kit). Then, alkaline hydrolysis was performed on 500 ng of the synthesized RNA incubated in 50 mM sodium carbonate, pH 10.3, 1 mM EDTA for 5 min at 95˚C.

Overexpression and purification of hRPS26-His

hRPS26-HisTag construct was cloned into pET29b vector using NdeI/KpnI (GenScript). Escherichia coli BL21-CodonPlus (DE3) strain carrying pET29b-hRPS26-HisTag was induced by addition of 0.5 mM IPTG and incubated O.N at 20˚C. Cells were pelleted and lysed by sonication in 20 mM HEPES, 50 mM NaCl, 2 mM EDTA, 10% glycerol, 20 mM Imidazole, and (EDTA)-free protease inhibitor (cOmpleteTM, Roche). The extract was treated with 750 U of Benzonase 30 min at room temperature under agitation and then clarified by centrifugation and filtration (0.22 mm). The recombinant protein was purified from the soluble fractions using FPLC (fast protein liquid chromatography, A ¨kta-Basic, GE-Healthcare), by a nickel-attached HiTrap chelating column (HisTrap 1 mL, GE-Healthcare) with a linear gradient of 20-500 mM imidazole. The eluted fractions containing His-tagged proteins were pooled, dialyzed, and concentrated on Amicon 10 kDa MWCO centrifugal devices (Sartorius) with dialysis buffer (50 mM Tris-HCl [pH 7.5], 0.1% Triton, 1 mM DTT, 10% glycerol, 5 mM MgCl 2 ). The purity of the protein was finally checked by SDS-PAGE 12% followed either by Coomassie blue staining or by western blot (Figure 6-figure supplement 2).

In vitro pre-ribosome maturation assay

The method of pre-40S particle purification described above was followed, and instead of elution, beads were then washed three times with 1 mL of TAP buffer. Most of the supernatant was discarded, and 50 mL of buffer X (50 mM Tris-HCl pH 7.5, 150 mM NaCl, 5 mM MgCl2, 1 mM DTT, 1% Triton, and 10% glycerol) added to the beads (suspended in approx. 20 mL of remaining TAP buffer) to reach a final volume of 70 mL. Nucleotides at a final concentration of 1 mM and/or 2 mg of hRPS26 were added when required. Reactions were incubated at 37˚C for 1 hr, and RNAs were then immediately extracted with Tri Reagent.

Figure 2 .

 2 Figure 2. Cryo-EM and single-particle analysis reveal two distinct structural states, pre-(state A) and post-(state B) 18S-E rRNA cleavage. Surface views of cryo-EM maps of RIO1(kd)-StHA pre-40S particles in structural state A (left) and state B (right). Ribosomal proteins, rRNA segments, and RBFs of interest have been segmented and colored as indicated on the figure. Image processing details are shown in Figure 2-figure supplements 1 and 2. The online version of this article includes the following figure supplement(s) for figure 2: Figure supplement 1. Cryo-EM image processing scheme.Figure supplement 2. Details of the cryo-EM structures/model validation.

Figure 3 .

 3 Figure 3. Structural details of RIO(kd)-StHA pre-40S particles. (a) The upper part of 18S rRNA helix h44 is in an immature position in structural state A. The cryo-EM density map corresponding to this helix has been segmented (beige density); the atomic model of rRNA h44 in structural state A is represented in golden; superimposed 18S rRNA h44 as found in structural state B and in the mature 40S subunit (PDB 6EK0 Natchiar et al., 2018) are in green and blue, respectively. (b) Close-up on the platform domain of structural state A. Segmented cryo-EM density corresponding to 18S-E pre-rRNA is shown as a grey mesh. The 3 0 -end of the mature 18S rRNA (nucleotides 1865-1869) is shown in black, while A1870 in the ITS1 is in red. The 18S rRNA is otherwise shown as a gray ribbon. DIM2 is in orange; RPS3a is in turquoise. NOB1 was removed from this representation for the sake of clarity. (c) The catalytic pocket of RIO1 is in an 'active' state within structural state B pre-40S particles, and carries an ADP and a phospho-aspartate (pD341). The cryo-EM density corresponding to ADP, p-Asp, and magnesium is shown as a green mesh. RIO1 is shown in green; ADP in dark gray, Mg 2+ in dark violet, and 18S rRNA G1639 closing RIO1 catalytic domain by a pi-stacking interaction (yellow dashed line) with RIO1 Phe 328 in light gray. (d) Close-up on the platform domain of structural state B. Segmented cryo-EM density corresponding to 18S rRNA 3 0 -end is shown as a light gray mesh. 18S rRNA 3 0 -end (nucleotides 1865-1869) is shown in black, while otherwise as gray ribbon. RPS26 is in magenta and RPS3a in turquoise. The online version of this article includes the following figure supplement(s) for figure 3: Figure supplement 1. Details of the structural analysis of hRIO1(kd)-StHA pre-40S particles.Figure supplement 2. RIO1(kd) carries an hydrolyzed ATP in its catalytic site.

Figure 4 .

 4 Figure 4. Late RIO1(kd)StHA pre-40S particles contain a high proportion of mature 18S rRNA. (a) Diagram representing steps of the pre-40S rRNA digestion by RNase H. (b) RNase H assays were performed on RNAs extracted from pre-40S particles purified with the mentioned StHA-tagged bait and separated on a 12% polyacrylamide gel. The 18S rRNA and its precursors were revealed by the 3 0 18S radiolabeled probe. Bands are separated with single nucleotide resolution, as shown in Figure 4-figure supplement 1. (c) Signals corresponding to the 18S-E and 18S rRNAs were quantified by phosphorimaging and represented by the 18S/(18S + 18S-E) ratio for the different purified pre-40S particles. The average of three independent experiments is shown, with the standard deviation indicated on top of the histogram. The online version of this article includes the following figure supplement(s) for figure 4: Figure supplement 1. Assessment of the size of the ITS1 in purified pre-40S particles.

Figure 5 .

 5 Figure 5. RPS26 is required for rRNA cleavage at site 3 as well as NOB1 and DIM2 release. HEK cell lines expressing tagged version of LTV1, the catalytically inactive RIO1-D324A (RIO1 (kd)) or wild-type RIO1 (RIO1(wt)) were treated with scramble or RPS26 siRNAs for 48 hr. (a) RNase H assays were conducted as in Figure 4 on rRNAs of pre-40S particles purified with the mentioned StHA-tagged bait, either from RPS26-depleted or from control cells (scramble siRNA). (b) Signals corresponding to the 18S-E and 18S rRNA detected in (a) were quantified and represented as the 18S/(18S + 18S-E) Figure 5 continued on next page

Figure 5

 5 Figure 5 continued ratio for the different pre-40S particles. Error bars, s.d. (n = 3) (c) Cell extracts and purified particles were analyzed by western blot using the indicated antibodies. (d) Bands corresponding to DIM2 and NOB1 (in the eluates) were quantified, corrected for pre-40S particle loading (using RPS19) and normalized to the control condition (set to 1). Error bars, s.d. (n = 3). The online version of this article includes the following figure supplement(s) for figure 5: Figure supplement 1. Comparative proteomics of RIO1(kd)-StHA particles composition upon RPS26 depletion. Figure supplement 2. Western blot analysis of EIF1AD association to pre-40S particles upon depletion of RPS26.

Figure supplement 1 .

 1 Figure supplement 1. Superimposition of atomic models of states A and B reveals overlapping distances (gray lines) between atoms of Proline 351 from RIO1 (green) and of Arginine 247 from DIM2 (orange).Figure supplement 2. Purification of recombinant hRPS26-His.

Figure supplement 2 .

 2 Figure supplement 1. Superimposition of atomic models of states A and B reveals overlapping distances (gray lines) between atoms of Proline 351 from RIO1 (green) and of Arginine 247 from DIM2 (orange).Figure supplement 2. Purification of recombinant hRPS26-His.

Figure 7 .

 7 Figure 7. Model of the pre-40S last maturation steps triggered by RIO1 and RPS26. Upper and lower panels represent interface and platform views of the small ribosomal subunit, respectively. A putative ITS1 cleavage-competent state is shown to illustrate the transition between the pre-cleavage (state A) and post-cleavage (state B) structures that were resolved in this study. Status of ATP hydrolysis within RIO1 for this maturation state is not known, and thus marked as 'ATP*'.

Figure

Plassart, Shayan, et al. eLife 2021;10:e61254. DOI: https://doi.org/10.7554/eLife.61254

Acknowledgements

This work was funded by the Agence Nationale de la Recherche (ANR 16-CE11-0029), the CNRS, the University of Toulouse-Paul Sabatier, the Re ´gion Occitanie, the European Union (Fonds Europe ´ens de De ´veloppement Re ´gional, FEDER), and Toulouse Me ´tropole. UK received funding from the Swiss National Science Foundation (grant 31003A_166565 and the NCCR 'RNA and disease'). Cryo-EM image acquisition was performed on the METI facility (CBI, Toulouse) and at the EMBL in Heidelberg with financial support from the iNext European initiative. Cryo-EM image analysis was performed using HPC resources from CALMIP (Grant 2018). We would like to thank the engineers and staff working on these facilities for their great help, as well as Marion Aguirrebengoa for her help on statistical analysis and Odile Burlet-Schiltz for her support.

Additional information

Funding

Data availability

Mass spectrometry proteomics data have been deposited to the ProteomeXchange Consortium via the PRIDE partner repository with the dataset identifier PXD019270. Cryo-EM maps have been deposited in the Electron Microscopy Data Bank (EMDB), under the accession codes : EMD-11440 (State A multi-body composite map); EMD-11441 (State B multi-body composite map); EMD-11446 (State A, head); EMD-11445 (State A, body); EMD-11447 (State A, platform); EMD-11443 (State B,

Additional files

Supplementary files

. Supplementary file 1. Cryo-EM data collection, atomic models refinement, and validation statistics.

. Transparent reporting form