Dorota Kostrz

Hannah K Wayment-Steele

Jing L Wang

Maryne Follenfant

Vijay S Pande

Terence R Strick
email: strick@ens.fr#gosse@ens.fr

Charlie Gosse

A modular DNA scaffold to study protein protein interactions at single-molecule resolution

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Kinetic characterization of molecular interactions provides essential mechanistic insights into

the functioning of biochemical pathways [START_REF] Rognoni | Dynamic force sensing of filamin revealed in single-molecule experiments[END_REF][START_REF] Kim | A mechanically stabilized receptor-ligand flexbond important in the vasculature[END_REF][START_REF] Marshall | Direct observation of catch bonds involving cell-adhesion molecules[END_REF]. With increasing frequency it also underpins the initial stages of drug screening and development, as well as later stages of drug refinement [START_REF] Copeland | The drug-target residence time model: A 10-year perspective[END_REF][START_REF] Schuetz | Kinetics for drug discovery: An industry-driven effort to target drug residence time[END_REF]. Indeed, two molecules with the same affinity for their target but different binding dynamics may have varied physiological effects in terms of safety and/or efficacy [START_REF] Swinney | Applications of binding kinetics to drug discovery[END_REF]. The most informative measurement strategies currently include biosensors such as surface plasmon resonance (SPR) and bio-layer interferometry [START_REF] Fang | Ligand-receptor interaction platforms and their applications for drug discovery[END_REF], kinetic isothermal titration calorimetry [START_REF] Burnouf | kinITC: A new method for obtaining joint thermodynamic and kinetic data by isothermal titration calorimetry[END_REF], and stopped-flow/quenched-flow [START_REF] Eccleston | Rapid kinetic techniques[END_REF].

Extremely successful, these techniques each have specific advantages and limitations but are overall demanding in terms of reagent quantity, in particular for the analysis of weaker interactions. More recently, single-molecule force-spectroscopy (SMFS) methods [START_REF] Garcia-Manyes | Steering chemical reactions with force-dependent[END_REF] have permitted high-resolution determination of association and dissociation rate constants of protein protein [START_REF] Sellers | Direct observation of the myosin-Va power stroke and its reversal[END_REF], protein DNA [START_REF] Hall | High-resolution dynamic mapping of histone-DNA interactions in a nucleosome[END_REF], and DNA DNA interactions [START_REF] Kilcherr | Single-molecule dissection of stacking forces in DNA[END_REF]. However, such approaches have not yet been widely adapted; indeed, protocols for attaching biomolecules to micron-size manipulators often involve significant modification of the biological system (e.g. single cysteine engineering prior to maleimide [START_REF] Schoeler | Mapping mechanical force propagation through biomolecular complexes[END_REF] or thiol conjugation [START_REF] Rognoni | Dynamic force sensing of filamin revealed in single-molecule experiments[END_REF][START_REF] Kim | A mechanically stabilized receptor-ligand flexbond important in the vasculature[END_REF][START_REF] Gao | Single reconstituted neuronal SNARE complexes zipper in three distinct stages[END_REF][START_REF] Dietz | Anisotropic deformation response of single protein molecules[END_REF], fusion of proteins through polypeptide linkers [START_REF] Rognoni | Dynamic force sensing of filamin revealed in single-molecule experiments[END_REF][START_REF] Kim | A mechanically stabilized receptor-ligand flexbond important in the vasculature[END_REF][START_REF] Gao | Single reconstituted neuronal SNARE complexes zipper in three distinct stages[END_REF]). Here we harness DNA nanotechnology to synthesize a generic and modular scaffold compatible with rapid SMFS implementation on a wide range of interacting partners.

Assembly of the dsDNA scaffold and functionalization with proteins

The scaffold is built of three linear segments of double-strand DNA (dsDNA) that are chemically junctured together, resulting in what we name J-DNA (Fig. 1a and Supp. Fig. 1). The structure of this tool is such that two DNA ends face each other and can be pulled apart with a controlled force, as if with tweezers (dsDNA break repair could for instance be studied in this way [START_REF] Wang | Dissection of DNA double-strand-break repair using novel singlemolecule forceps[END_REF]). These DNA ends, or tips, are made modular in nature and can be specifically engrafted with molecular partners for which one wishes to characterize the interaction (Fig. 1b). By monitoring the scaffold extension, for instance using magnetic tweezers to cycle between a low and a high force, one can specify whether the partners located at the tips are associated or dissociated (Fig. 2a). The leash connecting the two branches prevents the structure from disassembling in the absence of an interaction. The existence of this tether of known length also provides a mean to filter out events that do not comply with the expected gain in extension upon dissociation (Fig. 2b and inset Fig. 2c) [START_REF] Kim | A mechanically stabilized receptor-ligand flexbond important in the vasculature[END_REF][START_REF] Halvorsen | Nanoengineering a single-molecule mechanical switch using DNA self-assembly[END_REF][START_REF] Johnson | How do we know when single-molecule force spectroscopy really tests single bonds?[END_REF].

Although a variety of polymeric components have been employed to assemble such scaffolds, including polypeptide chains [START_REF] Rognoni | Dynamic force sensing of filamin revealed in single-molecule experiments[END_REF][START_REF] Kim | A mechanically stabilized receptor-ligand flexbond important in the vasculature[END_REF][START_REF] Gao | Single reconstituted neuronal SNARE complexes zipper in three distinct stages[END_REF] and DNA origamis [START_REF] Kilcherr | Single-molecule dissection of stacking forces in DNA[END_REF][START_REF] Halvorsen | Nanoengineering a single-molecule mechanical switch using DNA self-assembly[END_REF][START_REF] Koirala | Single-molecule mechanochemical sensing using DNA origami nanostructues[END_REF], each present specific drawbacks.

Using a leash made of an unstructured sequence of a few to tens of amino acids is challenging with respect to the expression and purification of large fusion constructs [START_REF] Rognoni | Dynamic force sensing of filamin revealed in single-molecule experiments[END_REF][START_REF] Kim | A mechanically stabilized receptor-ligand flexbond important in the vasculature[END_REF], a task that must be repeated as soon as either protein partner is to be changed. In comparison, thanks to the ease of modification and modularity of biologically-derived dsDNA, molecular partners can individually be engrafted on DNA origamis [START_REF] Halvorsen | Nanoengineering a single-molecule mechanical switch using DNA self-assembly[END_REF][START_REF] Koirala | Single-molecule mechanochemical sensing using DNA origami nanostructues[END_REF][START_REF] Nickels | Molecular force spectroscopy with a DNA origami-based nanoscopic force clamp[END_REF] and on J-DNA scaffolds, making combinatorial studies more straightforward. Yet, the latter two technologies differ by their mode of assembly: whereas J-DNA tweezers are fully covalent, DNA origamis rely on the pairing of hundreds of oligonucleotides, which may result in scaffold heterogeneity or even partial disassembly upon repeated loading. Furthermore, in addition to being chemically homogeneous and hydrophilic, dsDNA is also relatively stiff, with a persistence length of 52 nm [START_REF] Bouchiat | Estimating the persistence length of a worm-like chain molecule from force-extension measurements[END_REF]. We thus have here a polymer of choice for gently probing molecular interactions since it allows the use of forces in the fN range. In comparison, leashes made of a single strand of DNA or a polypeptide (with persistence length in the Å range) can only be employed for experiments over a few pN [START_REF] Rognoni | Dynamic force sensing of filamin revealed in single-molecule experiments[END_REF][START_REF] Kim | A mechanically stabilized receptor-ligand flexbond important in the vasculature[END_REF][START_REF] Kilcherr | Single-molecule dissection of stacking forces in DNA[END_REF][START_REF] Nickels | Molecular force spectroscopy with a DNA origami-based nanoscopic force clamp[END_REF]. We finally note that magnetic tweezers are particularly well-suited to measurements in the low force range, and also permit simultaneous monitoring of hundreds of molecules [START_REF] Ribeck | Multiplexed single-molecule measurements with magnetic tweezers[END_REF][START_REF] Vlaminck | Highly parallel magnetic tweezers by targeted DNA tethering[END_REF].

As a proof of principle we specifically modified the tips of the J-DNA tweezers with proteins FKBP12 and FRB whose interactions are mediated by the rapamycin class of compounds. These molecular partners constitute a good kinetic benchmarking system with both clinical and biotechnological relevance: rapamycin and its derivatives are widely-used immunosuppressive and antiproliferative drugs that modulate the mTOR signaling pathway [START_REF] Liu | FK506-binding protein 12 ligands: a patent review[END_REF][START_REF] Benjamin | Rapamycin passes the torch: a new generation of mTOR inhibitors[END_REF]; they are also chemical dimerizers employed to manipulate cell function [START_REF] Putyrski | Protein translocation as a tool: The current rapamycin story[END_REF][START_REF] Voss | Chemically induced dimerization: reversible and spatiotemporal control of protein function in cells[END_REF]. In fact, rapamycin first tightly binds to FKBP12 with an equilibrium dissociation constant on the order of 0.2 -0.5 nM; the resulting binary complex then binds FRB with a reported in the 10 nM range (Supp. Tab. 1) [START_REF] Banaszynski | Characterization of the FKBP.rapamycin.FRB ternary complex[END_REF][START_REF] Bierer | Two distinct signal transmission pathways in lymphocytes-T are inhibited by complexes formed between an immunophilin and either FK506 or rapamycin[END_REF][START_REF] Wear | Determination of the rate constants for the FK506 binding protein/rapamycin interaction using surface plasmon resonance: an alternative sensor surface for Ni2+nitrilotriacetic acid immobilization of His-tagged proteins[END_REF][START_REF] Kozany | Fluorescent probes to characterise FK506-binding proteins[END_REF][START_REF] Tamura | Fluorophore labeling of native FKBP12 by ligand-directed tosyl chemistry allows detection of its molecular interactions in vitro and in living cells[END_REF][START_REF] Lu | Quantitative analysis of ligand induced heterodimerization of two distinct receptors[END_REF].

Functionalization of the scaffold with protein partners can be carried out by a variety of methods. In a first implementation, we prepared the tips so that each of them present a 9-base 3' overhang specifically encoding for a complementary sequence that has been attached to each protein via N-terminal 4-azido-L-phenylalanine incorporation [START_REF] Chin | Addition of p-azido-Lphenylalanine to the genetic code of Escherichia coli[END_REF] followed by clicking to a 5' DBCO-modified oligonucleotide (Fig. 1b). After ligation, the J-DNA tweezers were assembled between an anti-digoxigenin treated glass surface and a streptavidin-coated magnetic bead thanks to the digoxigenin and biotin moieties that have been specifically incorporated at the extremity of each shanks (Fig. 1a) [START_REF] Duboc | Preparation of DNA substrates and functionalized glass surfaces for correlative nanomanipulation and colocalization (NanoCOSM) of single molecules[END_REF].

Force cycling in the presence of 500 nM rapamycin shows that the scaffolded FKBP12 and FRB proteins can be repeatedly probed for association and dissociation (Fig. 2a). When the magnetic trap is switched from a low force to a high force , nearly all scaffolds are found to be interacting (Fig. 2b).

No association is observed in the absence of rapamycin (Supp. Fig. 2a). Durations of individual interactions derived from a single scaffold are distributed according to single-exponential statistics with a mean lifetime of 26.0 ± 1.7 s (SEM, n = 395 events) for = 1.1 pN at = 21.7 o C (294.8 K) (Fig. 2c).

We proceeded to collect n = 100 to 400 rupture events from each of N = 50 individual scaffolds, and found that the mean lifetimes of individual scaffolds are themselves distributed according to Gaussian statistics (Supp. Fig. 2b); fitting this distribution gives a central value of = 28.6 ± 3.7 s (SD). The dispersion in population lifetimes is interpreted as a consequence of the dispersion in the applied force, which we evaluated to be around 20 % (Supp. Fig. 2c).

Analysis of FKBP12 interacting with rapamycin

At very low constant force (e.g. = = 0.04 pN) the system is seen to continuously and spontaneously associate and dissociate without a need for force cycling (Supp. Fig. 3a; mean lifetime for the closed conformation = 32.4 ± 2.7 s (SEM), n = 182 events analysed from N = 1 scaffold). However, when the concentration of rapamycin is decreased to 50 pM we instead observe distinct periods of frequent interactions interspersed by very long periods where no interaction takes place (Supp. Fig. 3b).

The latter idle periods reflect the absence of rapamycin from the scaffold: their duration obeys single exponential statistics (Supp. Fig. 3c) with a mean lifetime, , proportional to the inverse of rapamycin concentration (Supp. Fig. 3d). Interaction events within the active periods continue to obey singleexponential statistics (Supp. Fig. 3e), and their mean lifetime remains independent of rapamycin concentration and in the range of the value observed at 500 nM (Supp. Fig. 3f). Finally, correcting the duration of active periods to account for impossible dissociation of a drug encased in the ternary complex, we obtain a single-exponential distribution (Supp. Fig. 3g) with a mean lifetime, , also independent of rapamycin concentration (Supp. Fig. 3h).

Complementary experiments carried out using homomeric scaffolds (i.e. bearing either two FRB moieties or two FKBP12 ones), dimerized protein partners in solution, and rapamycin at less than 5 250 pM identify the FKBP12 rapamycin interaction as the most stable one (Supp. Fig. 4), in agreement with the literature (Supp. Tab. 1) [START_REF] Banaszynski | Characterization of the FKBP.rapamycin.FRB ternary complex[END_REF][START_REF] Bierer | Two distinct signal transmission pathways in lymphocytes-T are inhibited by complexes formed between an immunophilin and either FK506 or rapamycin[END_REF][START_REF] Wear | Determination of the rate constants for the FK506 binding protein/rapamycin interaction using surface plasmon resonance: an alternative sensor surface for Ni2+nitrilotriacetic acid immobilization of His-tagged proteins[END_REF][START_REF] Kozany | Fluorescent probes to characterise FK506-binding proteins[END_REF][START_REF] Tamura | Fluorophore labeling of native FKBP12 by ligand-directed tosyl chemistry allows detection of its molecular interactions in vitro and in living cells[END_REF][START_REF] Lu | Quantitative analysis of ligand induced heterodimerization of two distinct receptors[END_REF]. From the numbers provided in Supp. Fig. 3 we thus determine for the FKBP12 rapamycin ⇄ FKBP12 + rapamycin reaction both the dissociation and association rate constants: = (5.3 ± 0.57) × 10 -4 s -1 (SEM) and = (1.9 ± 0.18) × 10 6 M -1 s -1 (SEM) respectively. Combining both results yields = 0.28 ± 0.04 nM (SEM). Notably, these single-molecule data are zero-force ones and agree well with reported solution or SPR measurements (Supp. Tab. 1) [START_REF] Banaszynski | Characterization of the FKBP.rapamycin.FRB ternary complex[END_REF][START_REF] Bierer | Two distinct signal transmission pathways in lymphocytes-T are inhibited by complexes formed between an immunophilin and either FK506 or rapamycin[END_REF][START_REF] Wear | Determination of the rate constants for the FK506 binding protein/rapamycin interaction using surface plasmon resonance: an alternative sensor surface for Ni2+nitrilotriacetic acid immobilization of His-tagged proteins[END_REF][START_REF] Kozany | Fluorescent probes to characterise FK506-binding proteins[END_REF][START_REF] Tamura | Fluorophore labeling of native FKBP12 by ligand-directed tosyl chemistry allows detection of its molecular interactions in vitro and in living cells[END_REF][START_REF] Lu | Quantitative analysis of ligand induced heterodimerization of two distinct receptors[END_REF]. For instance the dissociation and association rate constants have been respectively

given as 1.6 × 10 -3 s -1 and 5.8 × 10 6 M -1 s -1 [START_REF] Banaszynski | Characterization of the FKBP.rapamycin.FRB ternary complex[END_REF] or 1.4 -1.6 × 10 -3 s -1 and 0.75 -0.85 × 10 6 M -1 s -1 [START_REF] Wear | Determination of the rate constants for the FK506 binding protein/rapamycin interaction using surface plasmon resonance: an alternative sensor surface for Ni2+nitrilotriacetic acid immobilization of His-tagged proteins[END_REF].

Analysis of FKBP12•rapamycin dissociating from FRB

With this dissociation mechanism elucidated, we next completed analysis of the forcedependence of the FKBP12 rapamycin FRB ⇄ FKBP12 rapamycin + FRB reaction using force cycling, at 21.7 o C and 500 nM rapamycin. For instance when was increased to 9.7 pN, the interaction lifetime dropped to = 11.2 ± 0.1 s (SD, n = 18423, N = 68, Supp. Fig. 2b). In fact the dissociation rate constant of the ternary complex, = 1/ , increases exponentially with force in agreement with the Arrhenius-Bell model: = exp -+ ! " # " ⁄ % (Eq. 1) with a pre-factor, the activation energy, ! the apparent distance to the transition state, # Boltzmann's constant, and the temperature (Fig. 3a) [START_REF] Schlierf | The unfolding kinetics of ubiquitin captured with singlemolecule force-clamp techniques[END_REF][START_REF] Evans | Probing the relation between force -lifetime -and chemistry in single molecular bonds[END_REF][START_REF] Popa | Direct quantification of the attempt frequency determining the mechanical unfolding of ubiquitin protein[END_REF]. By linear fitting of the data to the previous equation we obtained ! = 4.4 ± 0.1 Å (SEM)

and, for the dissociation rate constant at zero-force, & = (30.8 ± 0.4) × 10 -3 s -1 (SEM) -a value similar to the only reported one: 22 × 10 -3 s -1 (Supp. Tab. 1) [START_REF] Banaszynski | Characterization of the FKBP.rapamycin.FRB ternary complex[END_REF]. We further note that repeated measurements roughly gave a 10 % variation in ! , but only a 3 % variation in ln & (Supp. Fig. 5). Next, by performing the above measurements at different temperatures, we found that ! does not depend on this parameter (Fig. 3b), and we could further specify the activation energy from the dependence of ln & on 1 ⁄ : = 58.6 ± 1.7 kJ mol -1 (about 25 # for a single molecule; Fig. 3c).

To gain insight into the dissociation process, and more precisely to map the direction along which the chemical transformation is favoured [START_REF] Schoeler | Mapping mechanical force propagation through biomolecular complexes[END_REF][START_REF] Dietz | Anisotropic deformation response of single protein molecules[END_REF][START_REF] Brockwell | Pulling geometry defines the mechanical resistance of a beta-sheet protein[END_REF][START_REF] Carrion-Vazquez | The mechanical stability of ubiquitin is linkage dependent[END_REF][START_REF] Jagannathan | Direct observation of a forceinduced switch in the anisotropic mechanical unfolding pathway of a protein[END_REF], we generated versions of FKBP12 and FRB with internal 4-azido-L-phenylalanine labelling sites (R13AzF and E2052AzF, respectively). We then examined a total of four pulling directions by combining different pairs of protein partners labelled either at their N-terminus or internally (Fig. 4a). For each pulling direction the intercepts of the ln "% curves with the zero-force axis differs by ≈ 10 % (Fig. 4b), which is small but significantly superior to the 3 % observed on multiplicates (Supp. Fig. 5). In parallel, the slopes are modified by nearly a factor of three (Fig. 4b). As noted in the following paragraph, mutations can result in changes in the intercepts; however, we have never observed any differences in the slopes as long as the pulling direction remained constant (Supp. Fig. 6). We thus hypothesized that these variations in ! reflect the fact that work supplied by the magnetic tweezers is (to first approximation) the dot product of the force vector, ***+ , with the relative displacement vector of the centres of mass of the proteins at the transition state to rupture, , + [START_REF] Evans | Probing the relation between force -lifetime -and chemistry in single molecular bonds[END_REF]. In other words, the pulling axis which is overall most parallel to the natural dissociation axis should result in the highest force sensitivity, i.e. the largest ! [START_REF] Ainavarapu | Single-molecule force spectroscopy measurements of bond elongation during a bimolecular reaction[END_REF]. To test this model we first computed -. + , 0 *+ 1, the best plane-of-separation between the two proteins, and we assumed , + parallel to the normal vector , + (see Methods and Fig. 4a). Then, for each pulling direction, we represented ! as a function of the extent to which the normalized force vector + 2 3 projects onto the -. + , 0 *+ , , + 1 orthonormal basis (Fig. 4c). Results indicate a strong positive correlation of ! with + 2 3 • , + and a strong negative one with + 2 3 • . + . Consequently, the ternary complex should essentially dissociate by moving apart along the axis normal to the best plane-of-separation.

Analysis of variants of the interaction and of new scaffold designs

We first validated the ability of the method to analyse medically-relevant analogues of rapamycin: everolimus and deforolimus [START_REF] Liu | FK506-binding protein 12 ligands: a patent review[END_REF][START_REF] Benjamin | Rapamycin passes the torch: a new generation of mTOR inhibitors[END_REF]. ln "% data sets were recorded in our standard conditions (N-terminal protein attachments, 21.7 o C, and 500 nM of drug). For such analysis we typically collected for each force point at least n = 2000 events from at least N = 10 scaffolds. Both compounds showed a modest 30 % increase in the lifetime of the ternary complex extrapolated to zero-force:

1 & ⁄
is equal to 32.5 ± 0.4 s (SEM) for rapamycin, 41.4 ± 0.9 s (SEM) for everolimus, and 44.8 ± 1.8 s (SEM) for deforolimus (Supp. Fig. 6, Supp. Table 2). Secondly, we determined the effect of a number of FKBP12 and FRB mutations anticipated to modify ternary as well as binary interactions (Supp. Fig. 6, Supp.

Tab. 2) [START_REF] Choi | Structure of the FKBP12-rapamycin complex interacting with the binding domain of human FRAP[END_REF][START_REF] Decenzo | FK506-binding protein mutational analysis: Defining the active-site residue contributions to catalysis and the stability of ligand complexes[END_REF]. The Y82F FKBP12 mutation resulted in only a slight increase (15 %) in the lifetime of the ternary complex relative to wildtype, 1 & ⁄ = 37.7 ± 1.1 s (SEM), while the D37V FKBP12 mutation made the ternary complex more than twice more stable relative to wildtype, 1 & ⁄ = 70.6 ± 1.3 s (SEM). It is interesting to note that these mutations, which have been selected from the crystal structure of the ternary complex to reduce hydrogen bonding between rapamycin and FKBP12 [START_REF] Choi | Structure of the FKBP12-rapamycin complex interacting with the binding domain of human FRAP[END_REF][START_REF] Decenzo | FK506-binding protein mutational analysis: Defining the active-site residue contributions to catalysis and the stability of ligand complexes[END_REF], in fact result in more stable ternary complexes. We consequently investigated the association of rapamycin to FKBP12

variants by measuring the active-period duration at low rapamycin concentration. Force-cycling experiments ( = 1.1 pN, Supp. Fig. 7) indicate that rapamycin binding to Y82F FKBP12 is twice as longlived as to wild-type (respectively, 15600 ± 2300 s SEM, n = 51, N = 11 vs. 8900 ± 1400 s SEM, n = 41, N = 4). However, rapamycin binding to D37V FKBP12 is much more unstable (134 ± 22 s SEM, n = 38, N = 4) than to wild-type. We thus identify a mutation which, intriguingly, can induce a destabilization of the binary complex in favour of a stabilization of the ternary complex. On the FRB side, the Y2105A mutation is expected to disrupt both a hydrophobic interaction with rapamycin and hydrogen bonding with FKBP12 [START_REF] Choi | Structure of the FKBP12-rapamycin complex interacting with the binding domain of human FRAP[END_REF][START_REF] Leone | The FRB domain of mTOR: NMR solution structure and inhibitor design[END_REF]. Accordingly, the lifetime of the ternary complex is dramatically reduced:

1 & ⁄ =
6.2 ± 0.2 s (SEM). We note that a camera with a 90 Hz framerate allows us to observe short-lived (≈ 50 ms) interactions between Y2105A FRB and the FKB12 rapamycin complex (Supp. Fig. 8).

Finally, we introduce two modifications of the scaffold that illustrate the modularity of our approach. First, in order to make SMFS experiments universally accessible to other biological systems, we devised a second engrafting strategy based on standard protein expression tools: we fused the genetically-encoded CLIP-and SNAP-tags to the N-termini of the proteins of interest (Fig. 5a) [START_REF] Keppler | Labeling of fusion proteins of O6-alkylguanine-DNA alkyltransferase with small molecules in vivo and in vitro[END_REF][START_REF] Hinner | How to obtain labeled proteins and what to do with them[END_REF].

These protein tags bind specifically and covalently to the benzylcytosine (BC) and benzylguanine (BG) small molecules, respectively. Thus, by preparing J-DNA tweezers bearing a BC group at one DNA tip and a BG group at the other, we could simply assemble CLIP-FKBP12 and SNAP-FRB onto the scaffold by incubation. Results obtained with this approach are identical to those obtained with the N-terminal 4azido-L-phenylalanine labelling strategy (Fig. 5b), proving that SMFS outcomes are robust with respect to tip modifications. We further note that the CLIP-and SNAP-protein tags are already widely accepted in cellular biology, where they are used for fluorescent labelling and monitoring of proteins in vivo [START_REF] Gautier | An engineered protein tag for multiprotein labeling in living cells[END_REF]; therefore, we anticipate both rapid adoption as well as fast implementation of this alternative engraftment strategy.

In a second implementation we modified the leash length of the original scaffold so as to be able to tune association efficacy. During cycling experiments the likelihood of detecting an interaction decreased from 85 to 6 % when we increased the leash length from ≈ 0.7 to ≈ 2.7 kbp (Supp. Fig. 9), as expected for a dilution effect. In fact, J-factor measurements indicate that the 700 base-pair value of our initial design is certainly an optimal one with respect to complex formation at nearly zero-force: smaller loops are associated with a high enthalpic cost in term of bending energy whereas larger loops are associated with a high entropic cost because distant molecular partners have to enter in collision [START_REF] Allemand | Loops in DNA: an overview of experimental and theoretical approaches[END_REF].

Conclusions

The single-molecule tool we have developed provides precise, accurate, and model-independent measurements of the lifetime of rapamycin protein interactions. Rate constants are determined with error bars lower than 10 % and the obtained values are in agreement with those found in the literature (Supp. Tab. 1, Supp. Tab. 2) [START_REF] Banaszynski | Characterization of the FKBP.rapamycin.FRB ternary complex[END_REF][START_REF] Wear | Determination of the rate constants for the FK506 binding protein/rapamycin interaction using surface plasmon resonance: an alternative sensor surface for Ni2+nitrilotriacetic acid immobilization of His-tagged proteins[END_REF]. Importantly, our experiments necessitate less than 1 % of the amount of protein reagents required for any other kinetic method: 250 samples can be prepared with as little as 12 fmol of SNAP-and CLIP-tag conjugates, which is largely enough to measure the three rate constants we have determined for the binary and ternary complexes (see Methods). At present, 50 ms to 5000 s long rupture events can be assessed with an applied force between 30 fN to 10 pN, covering a wide range of biological interactions. Importantly, the dsDNA leash uniquely enables one to probe engrafted complexes using extremely low forces, thereby advantageously placing oneself in solution-like conditions. All other performances are setup-dependent and can readily be improved (magnetic actuation down to 20 ms, force up to 100 pN). In fact, J-DNA scaffolds are also expected to comply with SMFS apparatuses having different working ranges (e.g. optical tweezers, atomic force microscope).

The modularity and simplicity of J-DNA tweezers make established single-molecule metrics (i.e.

position of the transition state in space and energy, direction of the dissociation axis) accessible to researchers in drug design. Direct application can readily be foreseen for a large variety of active compounds stabilizing protein protein interactions through the formation of a ternary complex (drugs, among which immunosuppressants [START_REF] Liu | FK506-binding protein 12 ligands: a patent review[END_REF][START_REF] Bier | Stabilization of protein-protein interactions in chemical biology and drug discovery[END_REF] and PROTACs [START_REF] Neklesa | Targeted protein degradation by protacs[END_REF][START_REF] Roy | SPR-measured dissociation kinetics of PROTAC ternary complexes influence target degradation rate[END_REF], as well as dimerizers used in chemical biology [START_REF] Putyrski | Protein translocation as a tool: The current rapamycin story[END_REF][START_REF] Voss | Chemically induced dimerization: reversible and spatiotemporal control of protein function in cells[END_REF]). In addition, the ability to scrutinize the force-dependence of dissociation kinetics should be significant for medicines targeting the cytoskeleton [START_REF] Bier | Stabilization of protein-protein interactions in chemical biology and drug discovery[END_REF] or mediating recognition between cancer and immune cells [START_REF] Del Bano | Taking up cancer immunotherapy challenges: Bispecific antibodies, the path forward?[END_REF]. Ultimately, other classes of nanomaterials, both organic and inorganic, should be amenable to such investigations. two branches, divided into shank and tip, held together by a leash. Freely-swivelling junctures between branches and leash minimize transmission of steric constraints between the segments. One of the shanks is attached to a glass surface and the other one to a magnetic bead, the two handles of the micron-size manipulator we are using, i.e. magnetic tweezers. Each tip can be specifically functionalized with a given biomolecule, here either the FRB domain of the mTOR kinase or the FKBP12 immunophilin.

In our first implementation the length of the dsDNA segments is around 700 and 1300 bp for the shanks, 41 and 47 bp for the tip, and 690 bp for the leash (drawing not to scale). b, For engraftment an azide moiety is first introduced at a desired location in the peptidic backbone using unnatural amino acid incorporation. This chemical group is next reacted with an oligonucleotide bearing a 5' DBCO group. The single-strand DNA sequence now connected to the protein is complementary to the one present at one of the tip of the tweezers. The protein can thus be specifically addressed by hybridization before undergoing covalent enzymatic ligation. Extension changes (inset) are fit to a Gaussian statistic, providing a mean value of 170 ± 1.5 nm (SD, n = 56 rupture events analysed). Red lines are fits to the data.

Methods

Synthesis of J-DNA tweezers

General strategy

J-DNA scaffolds were prepared as described previously [START_REF] Wang | Dissection of DNA double-strand-break repair using novel singlemolecule forceps[END_REF] with the exception of a few modifications (see Supp. Fig. 1 for a graphical depiction). Briefly, the tweezers still consist of two linear dsDNA segments, the two branches, connected by a third one, the leash. However, those three respective elements are now ≈ 690, 1330, and 690 bp long (a variant with a leash ≈ 2.7 kbp in size has also been used but only for a single experiment, the one of Supp. Fig. 9). In addition to those new dimensions, the tips of the branches are now functionalized and serve as attachment points for the molecular partners: in a first implementation two single-strand overhangs generated by Nb.BbvCI nicking can be used for ligation of oligonucleotide-conjugated proteins; in a second implementation incorporation of benzylguanine (BG) and benzylcytosine (BC) allow for direct immobilization of SNAPand CLIP-tagged proteins [START_REF] Gautier | An engineered protein tag for multiprotein labeling in living cells[END_REF][START_REF] Keppler | A general method for the covalent labeling of fusion proteins with small molecules in vivo[END_REF].

Oligonucleotides sequences (5' to 3' direction) Biolabs/Trilink). Furthermore, the underlined sequence is the Nb.BbvCI nicking site.

J-DNA tweezers with a 690 bp leash and functionalized by Nb.BbvCI-generated ssDNA overhangs

Oligonucleotides L 1 , L 2 , TS 1 , and TS 2 were synthesized by Trilink Inc. and resuspended in formamide (Merck) at 37 °C, so as to obtain a 10 μg/μL final concentration. Typically, ≈ 100 μg of each L i was combined with an equimolar amount of the associated TS i and incubated 12 h at 25 °C, in order to yield the corresponding J i product by click-chemistry coupling (Step a1 in Supp. Fig. 1). Both J 1 and J 2 branched oligonucleotides were then purified by electrophoresis on an 8 M urea, 8 % acrylamide/bisacrylamide (29:1) gel as previously described [START_REF] Wang | Dissection of DNA double-strand-break repair using novel singlemolecule forceps[END_REF]. Subsequently, J 1 and J 2 were used as primers in the PCR amplification of a ≈ 2.0 kbp fragment of the Charomid 9-5 ΔSbfI template with the Expand High Fidelity polymerase system (Roche) (Step a2 in Supp. Fig. 1) -the used template is a derivative of the Charomid 9-5 plasmid in which the native SbfI site has been removed by SbfI digestion, fill-in, and religation with the Quick Blunting kit (New England Biolabs). The resulting branched PCR product, which is the precursor of the tips and shanks of the J-DNA tweezers, was purified using the NucleoSpin Gel and PCR Clean-up kit (Macherey-Nagel).

% Tween-20, 0.5 mg/mL BSA, 2 mM DTT) supplemented with 1 mM ATP and 2 mM DTT (Step b2 in Supp.

Fig. 1). Reaction volumes of 50 μL containing 20 -200 nM of each protein conjugate and 50 pM of J-DNA were incubated for at least 4 h at 16 °C. Then, glycerol was added to a final concentration of 10 % and assembled scaffolds were aliquoted, frozen in liquid N 2 , and stored at -80 °C.

One of the above conjugation reactions between a DBCO-labelled oligonucleotide and an AzFcontaining protein, followed by purification, is sufficient for at least 100 -150 subsequent engraftment reactions. One of the latter ligations onto the J-DNA tweezers requires as little as 1 -10 pmol of each oligonucleotide-protein conjugate. Yet, it provides enough material for at least 40 single-molecule experiments. Therefore, one conjugation reaction enables to perform at least 4000 -6000 singlemolecule experiments.

Coupling of SNAP and CLIP protein tags to small-molecule substrates BG and BC

The SNAP-and CLIP-tagged proteins respectively react with the BG and BC groups that are located at the tips of the BG/BC-containing J-DNA tweezers, forming a stable thioether covalent bond [START_REF] Gautier | An engineered protein tag for multiprotein labeling in living cells[END_REF][START_REF] Keppler | A general method for the covalent labeling of fusion proteins with small molecules in vivo[END_REF]. Typically, reaction volumes of 15 μL containing 2 μM of each fusion protein and 1 nM of BG/BCcontaining J-DNA in mTOR buffer were incubated overnight at 25 °C (Step b2' in Supp. Fig. 1). Reaction mixtures were then diluted 20-fold with mTOR buffer and glycerol was added to a final concentration of 10 %. Finally, the assembled scaffolds were aliquoted, frozen in liquid N 2 , and stored at -80 °C.

The previous assembly reaction requires as little as 12 fmol of each SNAP-and CLIP-fused

protein. Yet, the obtained amount of J-DNA tweezers conjugated with proteins is sufficient for at least 250 single-molecule experiments.

Single molecule experiments workflow

Reagents

Stock solutions of rapamycin (Sigma-Aldrich) and deforolimus (MedChem Express) were prepared by dissolution at 50 μM in dimethyl sulfoxide (DMSO, Sigma-Aldrich) whilst everolimus (Sigma-Aldrich) was supplied in acetonitrile and diluted to 100 μM in the latter solvent. Single-use aliquots of stock solutions were stored at -80 °C.

Magnetic tweezers operation

Details on this well-known single-molecule techniques [START_REF] Strick | The elasticity of a single supercoiled DNA molecule[END_REF][START_REF] Gosse | Magnetic tweezers: Micromanipulation and force measurement at the molecular level[END_REF] can be found in Supplementary information.

Data analysis

We used custom routines in the Xvin software suite (PicoTwist). For cycling-force experiments traces of DNA extension versus time were analyzed to determine (i) ∆6, the duration of the interaction, which corresponds to the dwell-time in low-extension state at high force; (ii) ∆!, the extension change upon dissociation, which corresponds to the difference in bead height before and after rupture at high force (Fig. 2). We excluded from analysis all the events for which rupture did not occur within the same force-traction cycle as the one in which binding was first observed. Indeed, they could not be reliably assessed for continuity. For presentation purposes time-traces are offset in extension so that the maximal extension is that expected from the worm-like chain model for a ≈ 2.7 kbp DNA at the given extending force -in the case of the longer 2.7 kbp leash of Supp. Fig. 9 we used a ≈ 4.7 kbp contour length.

Roughly 100 -500 events were collected from each scaffold molecule monitored. Event durations were represented in histogram form using the appropriate bin size (optimal bin sizes were typically ≈ 10 % of the mean lifetime, i.e. ≈ 1 s bins for events with mean lifetimes of ≈ 10 s and ≈ 5 s bins for events with mean lifetimes of ≈ 50 s). Error bars in histograms are equal to the square root of the number of events in that bin and represent the statistical (Poissonian) counting error (i.e. the standard deviation in counts). Histograms were fitted to single-exponential decays after removing the first bin (for which missed events may lead to undercounting) and after weighting points by error bars. For each scaffold molecule, a lifetime ± SEM was thus obtained. SEM typically progressed as SD/(number of events) 1/2 as expected for a stochastic process. We then averaged together lifetimes obtained on different scaffold molecules and computed the population variance (except in Supp. Fig. 2b, where enough scaffolds were collected to give a Gaussian fit to the population distribution).

Fig. 1 |

 1 Fig. 1 | Structure of the junctured-DNA (J-DNA) tweezers and first generic strategy used to attach a given protein at a given tip. a, The molecular scaffold is constituted of three linear dsDNA segments:

Fig. 2 |

 2 Fig. 2 | Experiment design and initial results on a single molecule. a, Sketch of the force-cycling procedure applied to the J-DNA scaffold using magnetic tweezers. The scaffold is engrafted with FKBP12 and FRB, and rapamycin is present in solution at 500 nM, a saturating concentration for the FKBP12 rapamycin interaction ( = 0.2 -0.5 nM) but not for the rapamycin FRB one ( > 1 µM) (Supp. Tab. 1) [29, 30, 31, 32, 33, 34]. A reference bead stuck on the surface is monitored to correct for microscope drift. (1) The tweezers are initialized in a high-force, high-extension state. (2) The force is lowered, bringing the tips into proximity and (3) allowing FKBP12 and FRB to bind via their interaction with rapamycin. (4) The force is returned to its initial value and the resulting DNA extension reports on the association state of the proteins. Eventually, the scaffold recovers its initial high-extension state (1) after dissociation of the ternary complex. b, Representative time-trace of DNA extension as the tweezers are cycled between a low force, = 0.001 pN, for 15 s and a high force, = 1.1 pN, for 125 s. Each interaction event is characterized by its duration, ∆6, and by the change in DNA scaffold extension following tweezers opening, ∆!. Data were collected at = 21.7 o C in the mTOR buffer (20 mM K•HEPES, pH 7.8, 100 mM KCl, 5 mM MgCl 2 , 0.1 % Tween-20, 0.5 mg/mL BSA, 2 mM DTT). Blue points: raw data obtained at 31 Hz. Red line: raw data averaged over 1 s. Green line: force modulation pattern. c, The histogram of interaction durations is fit by a single-exponential distribution, yielding 26.0 ± 1.7 s for the mean lifetime of this scaffold in the closed configuration (SEM, n = 395 rupture events analysed).

Fig. 3

 3 Fig. 3 |Influence of force and temperature on dissociation of the FKBP12 rapamycin FRB complex. a, Force-dependence, at four different temperatures, of the dissociation rate constant. All were measured upon force cycling except the ones at 0.03 pN, which were determined upon analysis of spontaneous fluctuations. Linear fitting according to the Arrhenius-Bell model provides, for each dataset, !

Fig. 4 |

 4 Fig. 4 | Influence of the pulling direction on dissociation of the FKBP12 rapamycin FRB complex. a, Structure of the ternary complex with the positions of the mutated amino acids indicated in cyan and the directions of the force vectors materialized by green, black, blue, and red lines. Arrows represent a set of basis vectors oriented so as to emphasize the best plane-of-separation between the two proteins (. + and 0 *+ are grey and in-plane, , + is blue and normal). b, Force-dependence of the dissociation rate constant. Curves are color-coded as per the structural depiction in (a). The black dataset is that for the original labelling position presented in Fig. 3a. Linear fitting according to the Arrhenius-Bell model yields: ! = 1.9 ± 0.2 Å and ln & = -3.65 ± 0.03 (SEM) for the green curve; ! = 4.4 ± 0.1 Å and ln & = -3.48 ± 0.01 (SEM) for the black curve; ! = 5.6 ± 0.2 Å and ln & = -3.53 ± 0.03 (SEM) for the blue curve; and ! = 5.9 ± 0.3 Å and ln & = -3.30 ± 0.04 (SEM) for the red curve. c, Plot of the apparent distance to the transition state as a function of the projection of the normalized force vector + 2 3 = + || + || 9 on the different unit vectors of the -. + , 0 *+ , , + 1 basis. Each coloured pill corresponds to a given pulling direction, and includes three points. For each pill, the abscissae are + 2 3 • : *+ with either : *+ = . + (dark grey), 0 *+ (light grey), or , + (blue). Data were collected at 21.7 o C in the mTOR buffer supplemented with 500 nM rapamycin; error bars represent SEM; all were measured upon force cycling ( = 0.001 pN) except the one at = = 0.03 pN, which was determined upon analysis of spontaneous fluctuations.

Fig. 5 |

 5 Fig. 5 | Second generic strategy used to engraft a given protein at a given tip of the J-DNA tweezers. a, The protein of interest is fused to a genetically-encoded protein tag complementary to a small molecule located at one of the tip of the scaffold. The two entities react together to form a covalent adduct. The present illustration is given for the CLIP/benzylcytosine couple but the SNAP/benzylguanine one works similarly. b, Force-dependence of the dissociation rate constant of the ternary FKBP12 rapamycin FRB complex engrafted via CLIP-and SNAP-tags: ! = 4.7 ± 0.2 Å and ln & = -3.45 ± 0.03 (SEM) for the red curve. These measurements are compared with the ones obtained for protein components engrafted via oligonucleotidic intermediates (same dataset as the one presented in Fig. 3a: ! = 4.4 ± 0.1 Å and ln & = -3.48 ± 0.01 (SEM) for the black curve). Data were collected at 21.7 o C in the mTOR buffer supplemented with 500 nM rapamycin; error bars represent SEM; all were measured upon force cycling ( = 0.001 pN) except the one at = = 0.03 pN, which was determined upon analysis of spontaneous fluctuations.

  notation X indicates DBCO-dT (Glen Research), Y Azido-dT, Pho a 5' phosphate group, Z O 2 -benzylcytosine-dT (New England Biolabs/Trilink), and Q O 6 -benzylguanine-dA (New England

Acknowledgements

This work was supported by the following grants: T-DropTwo (Labex NanoSaclay); T-DropThree (Idex Paris-Saclay); NanoRep (PSL University); Gephyrip (Labex Memolife); J-DNA (PSL-Valorisation). T.R.S. is part of the "Equipe Labellisée" program of the Ligue Nationale Contre la Cancer. H.K.W.S. and J.L.W. respectively acknowledge the National Science Foundation and the China Scholarship Council for PhD fellowships. We are finally thankful to Alix Thomas and Leah Friedman for preliminary experiments, as well as to the groups of Jie Yan and Felix Hausch for discussions on unpublished data.

Data Availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Author Contributions

D.K., T.R.S., and C.G. conceived the experiments; J.L.W. contributed unique reagents; D.K. and M.F. prepared reagents and carried out measurements; D.K. and T.R.S. carried out primary data analysis; D.K., H.K.W.S., V.S.P., T.R.S., and C.G. carried out advanced data analysis and modelling; D.K., T.R.S., and C.G. wrote the paper.

Competing interests

The authors declare no financial or non-financial competing interests.

Additional Information

Supplementary information is available in the online version of the paper. Reprints and permission information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to either T. R. Strick or C. Gosse. In parallel, the leash precursor was synthesized as follow. Its ≈ 630 bp backbone was amplified by PCR using the Platinum Pfx DNA polymerase (Invitrogen), the Charomid 9-5 ΔSbfI template, and the Charo-3600-MluI and Charo-4230-SbfI primers. The blunt-end PCR product was then digested with SbfI and cloned into the pUC18 vector using the SbfI/SmaI restriction site. The resulting DNA plasmid, 690_pUC18, was amplified and purified using the NucleoBond Xtra maxiprep kit (Macherey-Nagel), and digested with the MluI and SbfI restriction enzymes. The digestion products were separated using by electrophoresis on a 1 % agarose gel and extracted using the NucleoSpin Gel and PCR Clean-up kit (Macherey-Nagel).

Next, the L 1 and L 2 oligonucleotides of the branched PCR product, which have not participated in the amplification reaction, were annealed in equimolar ratio to the O1-Comp and O2-Comp oligonucleotides, respectively (Step a3 in Supp. Fig. 1). This reaction took place at a final concentration of ≈ 270 nM in each strand, for 1 h at room temperature in 1× CutSmart buffer (New England Biolabs).

This assembly was subsequently combined with the leash precursor at ≈ 130 nM final concentration each in 1× CutSmart buffer, along with 10 units (U) of SbfI-HF, 10 U of MluI-HF, 10 U of NsiI-HF, 5 U of AscI, 1000 U of T4 DNA ligase (New England Biolabs), 1 mM ATP, and 1 mM DTT (Step a4 in Supp. Fig. 1).

After overnight incubation at 25 °C the mixture was heat inactivated at 65 °C for 20 min. Then, in a one pot reaction taking place at 37 °C for 8 -16 h, the tips were nicked with 30 U of Nb.BvCI (New England Biolabs) and the extremities of the shanks were digested with 100 U of XbaI and 50 U of SacI (New England Biolabs) (Step a5 in Supp. Fig. 1). The product was separated on a 1.5 % agarose gel at 37 °C and extracted using the NucleoSpin Gel and PCR Clean-up kit (Macherey-Nagel).

Finally, the ≈ 2.7 kbp construct obtained above was ligated at the SacI site to a ≈ 1 kbp dsDNA fragment multiply labeled with biotin and at the XbaI site to a ≈ 1 kbp dsDNA fragment multiply labeled with digoxigenin (Step a6 in Supp. Fig. 1). Those labeled DNA fragments were synthesized by PCR as previously described [START_REF] Duboc | Preparation of DNA substrates and functionalized glass surfaces for correlative nanomanipulation and colocalization (NanoCOSM) of single molecules[END_REF][START_REF] Revyakin | Single-molecule DNA nanomanipulation: improved resolution through use of shorter DNA fragments[END_REF], in the presence of dUTP-biotin and dUTP-digoxigenin (Roche), respectively. The ligation reaction was conducted for 3 h at room temperature, in 10 μL of 1× T4 DNA ligase buffer (New England Biolabs) containing 3 nM of construct, 10 nM each of biotin and digoxygeninlabeled ≈ 1 kbp fragments, and 200 U of T4 DNA ligase. The enzyme was then inactivated and the resulting J-DNA tweezers were aliquoted and stored at -20 o C.

J-DNA tweezers with a 690 bp leash and functionalized by small recognition molecules BG and BC

Preparation was as above, except for two modifications. First, oligonucleotides TS 1 and TS 2 were replaced with oligonucleotides TS 3 and TS 4 . Second, Nb.BbvCI was omitted when performing the one pot digestion with XbaI and SacI.

J-DNA tweezers with a 2.7 kbp leash and functionalized by Nb.BbvCI-generated ssDNA overhangs Preparation was similar to the one of the scaffold with the 690 bp leash, with two variations.

The ≈ 2.7 kbp precursor of the leash was now generated from the 690_pUC18 plasmid from which the native SacI site has been removed using the Quick Blunting kit (New England Biolabs). Digestion with the MluI and SbfI restriction enzymes yielded products of the same lengths than in the original protocol but we now purified the longer one. Second, higher amounts of enzyme were used to digest the product resulting from the ligation of the 2.0 kbp branched PCR product to the 2.7 kbp leash: 50 U of Nb.BbvCI, 200 U of XbaI, and 100 U of SacI.

Protein design and production

Standard protocols inspired by previously published reports are described in details in Supplementary information.

Assembly of the proteins at the tips of the J-DNA tweezers

General strategy

Two strategies were used in our work. In the first one, AzF-containing FRB and FKBP12 proteins were coupled via click chemistry to DBCO-modified oligonucleotides, each complementary to a specific 9-base overhang present at one of the tips of the J-DNA tweezers. Each protein could thus be addressed to the scaffold via hybridization and ligation of its accompanying oligonucleotide to a specific tip. In the second strategy, the J-DNA tweezers were prepared with BG-and BC-functionalized tips, and SNAP-FRB and CLIP-FKBP12 covalently coupled to the tweezers simply by mixing the three components together.

Oligonucleotides sequences (5' to 3' direction)

DBCO-P1

XATATGAGGC

DBCO-P2

XTGTAAGAGC

In the present notations X indicates DBCO-dT.

Recognition by hybridization of complementary oligonucleotides and ligation

Between 40 and 50 μg of DBCO-labelled oligonucleotides were resuspended in 5 μL of water and combined with ≈ 70 μL of 170 μM AzF-containing protein in 50 mM Tris-HCl, pH 7.5 buffer containing 300 mM NaCl and 10 % glycerol. This equimolar mixture was incubated for 2 h at 25 °C for FKBP12 derivatives or overnight at 4 °C for FRB ones (Step b1 in Supp. Fig. 1). These conditions typically yielded 50 % labeling of proteins, as estimated using Cy5-DBCO fluorescent dye (Sigma-Aldrich) as a model reagent and measuring the reaction yield by gel electrophoresis. Typically, FRB A2020AzF and FRB E2052AzF were covalently labeled with DBCO-P1 and, in consequence, were closer to the magnetic bead, whilst FKBP12 M0AzF and FKBP12 R13AzF were covalently labeled with DBCO-P2, situating them closer to the glass surface. Incidentally, for experiments involving homotypic scaffolds (i.e. scaffold functionalized with either two FKBP12 or two FRB; see Supp. Fig. 4), either FKBP12 M0AzF or FRB A2020AzF was covalently labeled with both DBCO-P1 and DBCO-P2. Conjugated proteins were purified by gel filtration chromatography using a Superdex 75 Increase column (GE Healthcare) equilibrated in 50 mM Tris-HCl, pH 7.5, 300 mM NaCl, and 10 % glycerol, collecting 200 -250 μL fractions. Concentration of oligonucleotide-protein conjugates was estimated with a DS 11 FX+ Spectrophotometer/Fluorimeter (DeNovix) using theoretical epsilon values at 280 nm (ε 280 ) of 32070 M -1 cm -1 for FRB A2020AzF and FRB E2052AzF , 30580 M -1 cm -1 for Y2105A FRB A2020AzF , 12590 M -1 cm -1 for FKBP12 M0AzF , D37V FKBP12 M0AzF and FKBP12 R13AzF , and 11100 M -1 cm -1 for Y82F FKBP12 M0AzF .

Oligonucleotide-protein conjugates were ligated onto the Nb.BbvCI-nicked J-DNA tweezers using T4 ligase (New England Biolabs) in mTOR buffer (20 mM K•HEPES, pH 7.8, 100 mM KCl, 5 mM MgCl 2 , 0.1

Experimental conditions

All assays were conducted in mTOR buffer (20 mM K•HEPES, pH 7.8, 100 mM KCl, 5 mM MgCl 2 , 0.1 % Tween-20, 0.5 mg/mL BSA, 2 mM DTT). Rapamycin and rapalogs were used at a final concentration of 500 nM unless stated otherwise and the concentration of dimethyl sulfoxide or acetonitrile in the mTOR buffer was always at 1 or 0.5 % v/v, respectively. For Fig. 3a, data collected at 21.7 o C and for high forces greater than 30 fN were obtained at 390 nM rapamycin.

Temperature was set at 21.7 o C unless stated otherwise.

Flow cell preparation

Flow cells for single-molecule experimentation were prepared as extensively described elsewhere [START_REF] Duboc | Preparation of DNA substrates and functionalized glass surfaces for correlative nanomanipulation and colocalization (NanoCOSM) of single molecules[END_REF][START_REF] Revyakin | Single-molecule DNA nanomanipulation: improved resolution through use of shorter DNA fragments[END_REF], starting from two glass coverslips (#1, ≈ 180 μm thick, Menzel-Glaser), one of them having been sandblasted to provide two 2-mm in diameter access ports. Those coverslips are spincoated first with MCC Primer 80/20 (MicroChem) and second with a polystyrene solution (0.1 % w/v in toluene). Then, they are assembled thanks to two thicknesses of parafilm M (75 μm, Bemis North America) into which a channel (1 mm × 50 mm) has been cut open. Further surface functionalization with antidigoxigenin (Roche) and passivation are achieved in the closed fluidic channel, as described [START_REF] Duboc | Preparation of DNA substrates and functionalized glass surfaces for correlative nanomanipulation and colocalization (NanoCOSM) of single molecules[END_REF][START_REF] Revyakin | Single-molecule DNA nanomanipulation: improved resolution through use of shorter DNA fragments[END_REF].

J-DNA tweezers assembly

J-DNA tweezers are attached to streptavidin-coated magnetic bead at the biotin-labeled end (i.e. via the ≈ 690 bp long branch) and to the antidigoxigenin-treated glass surface at the dioxigeninlabeled end (i.e. via the ≈ 1330 bp long branch).

More precisely, 1-μm-diameter streptavidin-coated magnetic beads (MyOne Streptavidin C1, Life Technologies) were first prepared by washing 5 μL of stock solution (10 mg/mL) with 200 μL of mTOR buffer. After magnetic concentration and disposal of the supernatant, the particles were resuspended in 35 μL of mTOR buffer. Then, 0.5 -1.4 μL of solution of functionalized J-DNA tweezers, at 50 pM, were added. This mixture was incubated for 2 min at room temperature, injected in the flow cell and incubated for an additional 10 min before washing away the unattached beads with mTOR buffer.

After mounting of the microfluidic chamber onto the microscope stage, 30 -70 scaffolds can typically be observed per field of view and handled with magnetic tweezers. Among them up to 30 % have both tips filled with proteins.

In experiments using homotypic scaffolds (Supp. Fig. 4), J-DNA constructs were assembled under the magnetic tweezers and exposed for 15 min to 50 nM rapamycin and 50 nM of complementary protein dimer (i.e. either FRB-PEG 4 -FRB or FKBP12-PEG 4 -FKBP12). Free components were then washed out with 4 -5 mL of mTOR buffer, and 50 nM of the appropriate protein dimer reintroduced into the chamber before beginning measurements.

In experiments carried out at limiting concentrations of rapamycin (Supp. Fig. 7), scaffolds were assembled under the magnetic tweezers and exposed for 15 min to 50 nM rapamycin. Free rapamycin was then washed out with 4 -5 mL of mTOR buffer before beginning measurements. From the ratio of the used volumes, the concentration of the remaining rapamycin was estimated to be lower than 250 pM (the microfluidic chamber with fillports is ≈ 20 μL in volume).

Analysis of pulling vector direction

A support vector machine (SVM) model in Scikit-learn (http://scikit-learn.org/stable/about.html) was used to estimate the plane of separation between the two interacting protein faces. A SVM is a classification algorithm that identifies a hyperplane between categories and that maintains the largest distance to data points of different categories. This was leveraged to identify a plane with the largest distance to the nearest coordinate of either protein. It was observed that the normal vector to the separation plane (, + , depicted in blue in Fig. 4a) was oriented similarly to the longest rotational axis of the protein complex. This was used to identify a second vector (. + , depicted in grey and pointing toward the reader in Fig. 4a) that was parallel to the separation plane and closest in orientation to the secondlongest rotational axis. A third vector (0 *+ , depicted in grey and vertical in Fig. 4a) was identified as the vector that completed the basis.


Marguerite Léang

Ludovic Pauchard

Lay-Theng Lee

Frédérique Giorgiutti- Dauphiné

Imbibition on a porous layer: dynamical and mechanical characterization

Solvent penetration in porous layers was analyzed using dynamical and mechanical characterization. Spreading dynamics of a solvent drop in a porous substrate provided parameters of the porous medium such as permeability and porosity. These measurements are relevant for many porous systems, for example paintings or porous varnishes and resins... We present direct visualizations of the drop as well as of the wet zone during the imbibition process and we evidence three distinct regimes. Experiments performed with various porous systems and different solvents highlight a universal behavior. The mechanical properties during the imbibition process are deduced through indentation testing measurements. We show that solvent penetration is responsible for the appearance of a viscous component in the system. A characteristic time depending on the solvent and on the porous medium is then deduced. The system recovers its initial mechanical properties and no swelling nor cracking is observed contrary to the case of paintings. This result tends to prove that visco-plastic properties are required to observe swelling or cracking.

Introduction

The phenomenon of imbibition in porous media is widely encountered in industrial situations or in the domain of cultural heritage particularly when restauration operations are carried out to remove and to replace the varnish layer of a painting. Indeed, the most common treatment used by curators to remove varnish consists in using organic solvents [START_REF] Stolow | Recent advances in conservation: contributions to the IIC Rome Conference[END_REF] applied to solubilize the old varnish and to remove it. Generally, when a solvent penetrates in a porous layer, it can cause swelling or inversely a decrease of volume after solvent evaporation, and consequently, it can induce additional stresses on the matter which lead to the formation of cracks. In addition, the solvent can modify the interactions between the components of the porous medium and consequently implies modifications of the mechanical properties of the porous layer.

To prevent these undesirable effects, one needs to study the dynamics of solvent penetration in a porous substrate and a Laboratoire F.A.S.T, Univ. Paris-Sud, CNRS, Université Paris-Saclay, F-91405, Orsay, France; † Corresponding author, e-mail: fred@fast.u-psud.fr b Laboratoire Léon Brillouin, UMR12 CEA-CNRS, Bât. 563 CEA Saclay, 91191 Gif sur Yvette Cedex, France.

the potential modifications induced on the matter such as: dissolution, variations of the mechanical properties, modifications of interactions between various components of porous medium or changes in the stress field due to swelling for example.

The aim of the presented work is to explain the physical mechanisms that come into play in imbibition processes and to identify physical macroscopic parameters, as relevant parameters, to describe the imbibition process for various porous systems which could be paintings, varnish or resins.

To this end, we propose to study the imbibition process of three different solvents in porous model systems formed after controlled drying of colloidal dispersions. The use of model systems has been motivated by the intent to deal with a well known and controlled system [START_REF] Giorgiutti-Dauphiné | [END_REF] . The problem of solvent imbibition process on a porous medium has been studied by various authors; the widely used geometry is the case of a liquid droplet deposited on a porous substrate. Different situations have been addressed: the case of a porous medium partly or entirely filled with liquid 3,4 , the case of a drop whose size is small or comparable to the size of the porous layer 5 . The wetting properties, the viscosity of the liquid or its volatility are the main parameters considered. Each pa-

Soft Matter Accepted Manuscript

Published on 12 February 2019. Downloaded by University of New England on 2/12/2019 2:59:25 PM.

rameter will play a role on respectively the spreading of the drop, the viscous flow in the drop or/and the diffusion in the porous and the evaporation. Davis et al. 6 and then Alleborn et al. 7 used lubrication theory combined with Darcy's law to model spreading and sorption of a two-dimensional drop on a dry or saturated porous substrate. They obtained numeric profiles of the drop and of the wet zone, during the imbibition process. Some authors have included dynamic contact angle and contact angle hysteresis in their model or some employed Brinkman's equation to solve the flow in the porous medium 8,[START_REF] Press | Wetting and spreading dynamics[END_REF] . Nevertheless, there are very few experimental visualizations, to our knowledge, of both the drop and the wet zone in the porous medium during the imbibition process [START_REF] Ogawa | [END_REF]11 . In the present work, we propose an experimental study of the imbibition process based on direct visualization of simultaneously spreading and sorption of a drop on a porous substrate. The experimental profiles validate the numerical results obtained by solving both the lubrication and Darcy's equations in the work of Alleborn and Raszillier (2004). We performed experiments with three different solvents and two porous media and founded a universal behavior for the imbibition dynamics. In addition, we can estimate permeability of the porous substrate in two directions: parallel and perpendicular to the flow. We then present then indentation measurements conducted on the porous substrate before and after imbibition process to measure the impact of solvent penetration on the mechanical properties of the porous layer. Finally, we estimate dissolution of the porous media due to imbibition process.

Imbibition dynamics

Material and methods

The porous media of interest in this work are obtained during the drying of aqueous dispersions of silica colloidal particles: Ludox SM-30 and HS-40 commercially available from Sigma-Aldrich. The radius of silica particle is noted a and the initial particle volume fraction is φ p,0 (see Table 1). The pH value is in the range of 9 -10 to ensure that a high negative charge density is born by the particles; the DLVO theory is expected to apply and the dispersions are used without previous treatment. A liquid layer is formed by depositing a controlled volume of dispersion in a non-porous substrate (glass Petri dish), then the layer is left to dry from the free surface. The relative humidity is kept constant, RH = 54 ± 2%, at room temperature. Solvent evaporation concentrates the dispersion until the formation of a porous layer of approximately constant thickness in the centre of the container. The volume of dispersion initially deposited is chosen to obtain a solid layer thickness of around 1 mm.

As drying proceeds, shrinkage is frustrated by adhesion with the substrate. It causes large tensile stresses which lead to the formation of cracks which divide the layer into polygonal adjacent fragments. Table 2 Main characteristics of the solvents used for imbibition processes at T = 20 • C. M W is the molecular weight; ρ, the density; γ, the surface tension and η, the dynamic viscosity [START_REF]CRC Handbook of Chemistry and Physics[END_REF][START_REF] Sheely | [END_REF] .

neutron imaging techniques to deduce the porosity 1φ p of their structure, where φ p is the particle volume fraction. The permeability K is deduced from the Kozeny-Carman law based on the size of the nanoparticles [START_REF] Kozeny | Über kapillare leitung des wassers im boden: aufstieg, versickerung und anwendung auf die bewässerung[END_REF][START_REF] Carman | [END_REF] . The main properties of the porous structure are reported in Table 1. One should note that we have considered fragments with no cracks as the presence of cracks will enhance and modify solvent penetration. Three kinds of solvents are imbibed into the porous layers: water, ethyl acetate and glycerol. The choice of water and ethyl acetate has been motivated given their ordinary use by curators. Glycerol is not used in restoration but is a limiting case for the model due to its high viscosity and non-volatility. We have reported the main properties of the different solvents at

T = 20 • C in Table 2.
The experimental setup used to follow the dynamics of imbibition is presented in figure 1. A fragment of uniform thickness is selected. The thickness of a fragment is measured by successively focusing on the top (air-layer interface) and on the bottom (layer-substrate interface) of the deposited film in transmitted light. The accuracy of this method is to within 3 µm. Horizontality is adjusted by 3 screws on the sample holder. The experimental set-up allows us to image a fragment and provides both side and top view using two cameras (Marlin F131B, Allied Vision Technologies). Acquisition frequency is 1.875 frame per second (fps) for glycerol imbibition dynamics, whereas for water and ethyl acetate, we used a fast-speed camera Eo Sens 6546 CF 25-290 (Mikrotron GmbH) with a 200 fps frequency. A drop of a given volume is then deposited with a micropipette (Fisherbrand). The drop characteristic size is smaller than the capillary length ensuring an initial spherical cap shape for the sessile drops. The imbibition process takes place during a low duration in comparison with the evaporation timescale t D , less than < 1/100 (see Table 3). Thus, the whole drop that is deposited is assumed to penetrate into the porous layer. The drop and the wet area in the porous medium are illuminated by transmitted light, simultaneously. The two main advantages of the setup are the following. Firstly, the wet region can be followed with time by imaging successive profiles (see images in figure 1). Secondly, the axisymmetry of the deposited sessile drop and the wet region are easily followed using the top-view camera. Hence, the quantification of the profiles of both the sessile drop and the imbibed region reveals the conservation of the volume of liquid all along the imbibition process. This important point allows us to determine the volume of the imbibed region at each time.

The main parameters involved during the drop imbibition are reported in figure 2: the drop radius r d (the maximum radius is r dmax = r d (t 0 ), reached at time t 0 ), the drop contact angle θ (the initial contact angle is noted θ 0 ), the vertical penetration depth z imb at the center of the drop. h d is the drop height at its center, and the initial drop height is h d,0 .

Dynamics of drop imbibition

The same scenario is observed for the three used solvents and both porous media: the imbibition process can be decomposed in three distinct stages. In the first stage, the drop spreads on the porous fragment; the drop radius increases whereas the contact angle decreases (images 1-3 in figure 3(a) for glycerol). In a second step, the surface area of the drop contact base is constant: the contact line is pinned by surface defects and the contact angle still decreases (see images from 3 to 4 in figure 3(a)). Simultaneously, the solvent starts penetrating in the porous. Both radii, respectively of the drop and of the wet area are the same. In the last stage, the drop is no more pinned and its radius decreases as well as its contact angle. The radius of the wet area remains constant and equal to the maximum value of the drop radius whereas the vertical penetration increases (see figure 3(a), images from 4 to 10). At the end of the process, there is no more solvent outside the porous and the wet area is axisymmetric.

The time variations of the dimensionless drop radius, r d /r dmax , and dimensionless contact angle, θ /θ 0 , are plotted in figure 4 for different initial drop volumes. Note that time t 0 corresponds to the end of the spreading stage of the drop and is chosen as a time reference.

We observe a brutal change of the slope for the drop radius correlated with the contact angle. These curves attest of a good reproducibility of the process. The data for experiments on two porous and with three solvents have been scaled with the Darcy's time, t Darcy , defined as the time for the drop to penetrate in the porous medium, hence 16 : t Darcy = ηh 2 d (t 0 )(1φ p )/K P cap with η the viscosity of the solvent; h d (t 0 ), the height of the drop when the drop radius is maximum (at the end of the spreading stage t 0 ); (1φ p ) is the porosity of the medium; K is the permeability determined by neutron imaging (see values in Table 1) and P cap is the capillary pressure which is the pressure of liquid in the pores of the system. Here, we take P cap ∼ γ a where γ is the solvent superficial tension and a, the particle ra- Note that for a kind of porous, Darcy's time of ethyl acetate is bigger than those of water. A possible explanation can be capillary condensation in the pores 18 . In fact, ethyl acetate evaporates faster than water and condensation of ethyl acetate vapour can take place in the void spaces. This can modify the wettability of the silica particle surface. Thus, ethyl acetate penetrates faster and easier in the porous media than water, leading to a bigger imbibition speed inside the porous media. The drying timescale t D is defined as the drop mean height divided by the solvent evaporation rate V E , for constant relative humidity. This evaporation rate has been measured by the mass loss with time of a volume of 5mL, in a Petri Dish, at ambient temperature and with a relative humidity of 50% [START_REF] Boulogne | Oil Gas 8 | 1-9 J o u r n a l N a me[END_REF] . A typical length for drop penetration is L imb = 100 µm. Table 3 shows the evaporation rate for water and ethyl acetate and the corresponding drying timescales.

All the curves collapse into a universal imbibition curve when plotted with the scaling time t/t Darcy . A deviation is observed for dimensionless times about 10; at that time, the drop is very small and the resolution of the corresponding images do not provide enough precisions on the drop profiles. We have plotted as well, the height of the wet area z imb , scaled with the height of the initial drop h d,0 . Again a universal behavior is evidenced.

The porosity values of the different porous media were deduced from neutron imaging techniques. We used a cold neutron imaging spectrometer. It allows performing radiography and tomography with fields of view ranging from 20 to 100mm using a CMOS ANDOR NEO camera. Radiography can be performed with a field of view of 200 * 400mm 2 by using a FUJI image plate. The incident neutron beam has a diameter of 20mm, with a wavelength between 2 and 30 Angstrom. The spatial resolution is between 100 and 130 micrometers. The neutron beam passes over the sample (a fragment of the porous medium, obtained by drying, with a uniform thickness over the whole fragment) and we measured the transmitted light on an image formed thanks to a scintillator and a camera. By dividing the transmitted light of a sample filled with water with the transmitted light of a dry sample, we obtained the thickness of the sample traversed by the neutron beam and we deduce, knowing the total thickness of the sample, its porosity.

Another key parameter of the porous medium is the permeability which can be deduced from two different ways: using the Kozeny-Carman law or by direct measurements. This last method is based on the dynamics of the imbibition front depicted by the spatiotemporal diagrams presented on figure 5. We have recorded with time the vertical and the horizontal dashed lines to produce spatiotemporal diagrams of respectively the vertical and the radial imbibition front in the porous medium. We deduce the temporal evolution of the wet area z imb and its radial spreading r imb . At the beginning of the imbibition process, evolutions of the fronts are linear and then become proportional to √ t to finally saturate. This behavior is similar to the dynamic of the capillary rise 20 as the liquid penetration in the porous medium is due to a pressure gradient in the pores of the system, that is the capillary pressure. There are then three stages in the capillary rise dynamics which depend on the dominant physical mechanisms. The first stage is regime dominated by the inertial forces, the second regime is called the Washburn's regime where inertial forces become negligible compared to the viscous ones. The evolution of the imbibition front in the case of a porous medium is then given by [START_REF] Dullien | Porous Media: Fluid Transport and Pore Structure[END_REF][START_REF] Hassanein | [END_REF] :

z imb = γcos(θ p )r e f f 2ηT 2 √ t (1)
with γ, the solvent surface tension; θ p , the contact angle between solvent and particle surface (θ p is taken to be zero due to silica particle hydrophilicity); r e f f , the effective radius of the porous and T , the tortuosity. The tortuosity is deduced from the porosity values through the relation 23,24,25 : T = 1/ 1φ p and the permeability expresses as: K = (1φ p )/24Tr 2 e f f , which is given by Bear [START_REF] Bear | Dynamics of fluids in porous media[END_REF] . By fitting the curves (6f) representing the evolution of the imbibition front with time, with the Washburn's law, one can deduce the value of r e f f . The results have been compared to values obtained with neutron imaging techniques (Table 4) and are equivalents (the experiment, in that case, consists of recording the imbibition front in a vertical fragment one end is in contact with a water bath) [START_REF] Léang | [END_REF] . It turns out that the effective radius is always lower than the particle size, a, typically of factor 3 for the different colloidal systems we used. In the case of the sessile drop experiment, the fit of the curves in 6f with the Washburn's law, provides expressions for the two permeabilities in the two directions vertical and radial ones, respectively, K vertical and K radial . The results are reported in Table 4. The permeability in the radial direction K radial is always higher than the one in the vertical direction K vertical . This observation can be related to results of previous work with the same systems in SANS experiments [START_REF] Boulogne | [END_REF] . It has been shown that particles are closer in the direction of the drying flux, consequently, permeability of the final porous medium should be lower in this direction. These results are confirmed with our experimental values : K vertical ≤ K radial . This suggests a non completely homogeneous porous medium, due to the vertical drying flux conducting to vertical compression of particles.

Evolution of the mechanical properties before and after drop imbibition

The mechanical properties of a porous medium strongly depend on its moisture content. This section is devoted to compare the elastic behavior of a porous medium before and after drop imbibition. In this way measurements using indentation testing (CSM Instrument Micro-Hardness Tester -Anton Paar) were investigated on HS-40 and SM-30 layers of 1 mm thick. A typical experiment consists in the measurement of an applied force, F, using a spherical indenter (Rockwell indenter of radius R indent = 200 µm) as a function of the penetration depth, p, as shown in figure 6.

The maximum penetration depth of the indenter is always smaller than the solvent penetration depth (≈ 500 µm), except at the end of solvent evaporation from the porous media. Assuming the material purely elastic within the limits of small deformations, the elastic response is well fitted using the Hertz contact law over a range of indentation depth such as p < 1.2 µm (figure 6). Hence, according to the classical Hertzian model, the applied indentation force F is determined by [START_REF] Fischer-Cripps | Nanoindentation[END_REF] :

F = 4 √ R indent 3 E 1 -ν 2 p 3 2 (2)
with the Poisson ratio ν = 0.2 [START_REF] Di Giuseppe | [END_REF] . Typical elastic behavior of a porous medium before drop imbibition is shown in figure 6. It has to be noted, the water moisture content in the porous layer is not zero since the humidity rate of the surroundings is finite. Within the first minutes following the drop deposition, measurements using indentation testing do not allow us to estimate elastic response. Once the drop is totally penetrated inside the layer, measurements are possible in the wet region. The load-displacement measurements are then characteristic of a low elastic modulus. Further measurements show recovery with time of the elastic behavior of the porous layer (figure 6). Figure 6 reports the case of ethyl acetate imbibition into HS-40 porous layers. Similar behaviors are obtained with SM-30 porous layers and with water imbibition, the timescales involved being different. The elastic moduli which are deduced from load-displacement curves and equation 2, are shown in figure 7. Using the poroelastic theory it has been shown that the drying stress linearly increases with time 31 . However, this model stated a constant elastic modulus with time. The recovery with time of the elastic behavior can be pointed out by the following simple arguments. Consider X being the current moisture content of the porous medium after drop imbibition. E 0 is the elastic modulus of the medium without solvent content addition, the linearity between stress, σ , applied to the porous medium and its strain, ε 0 , writes: σ = E 0 ε 0 in the condi- tions of applicability of the Hooke's law. We observe no swelling of the material when water penetrated into the porous media, however, there is an additional deformation ε(X) due to imbibition that we assumed to be proportional to the quantity of solvent which has penetrated in the porous medium. The degree of solvent saturation affects thus the elastic response of the porous medium and this results in larger strain, ε + ε(X), and specific elastic modulus, E(X), such as: σ = E(X)(ε 0 + ε(X)). The solvent molecules and silica structures are assumed to be incompressible. Consequently, the strain resulting from the moisture content can be written: ε(X) = ε 0 V X where V is the volume per solvent molecule. The evaporation rate of the solvent is assumed to be constant during the main solvent removal period and is defined as:

V E = -V S 0
dX dt where S 0 is the evaporation surface. Finally the experimental results can be fitted by the law:

E(X)/E 0 = 1/ 1 + α(1 -t/t D ) (3)
where α is a coefficient of the influence of the moisture content on the elastic properties of the material 32 . This highlights the effect of solvent evaporation in the timing recovery of the elastic behavior of a porous medium previously imbibed. In order to observe swelling and cracking as a result of solvent imbibition and solvent evaporation, visco-plastic properties seem to be required 32,33,34 .

Conclusion

We investigated the imbibition dynamics of three different solvents on two porous media. These porous media were characterized previously by neutron imaging. We implemented a set-up which permitted us to (i) verify the axisymmetry of deposited drops from a top view; (ii) to follow the drop profiles and the liquid front profiles inside the porous media.

We described the imbibition dynamics by quantifying the drop radius, the drop contact angle, and the vertical penetration depth at the centre of the drop. A relevant characteristic time for imbibition is determined to be Darcy's timescale: a universal behavior for different solvents and porous media is shown. These dynamics are completed with mechanical properties of porous media, before and after imbibition. Particularly, viscoelasticity was measured by creep measurements and show different characteristic times for water and ethyl acetate. Moreover, the fitting of micro-indentation loading curves with the Hertz's contact law permitted the determination of Young's modulus of the porous media before and after drop imbibition. recovery of mechanical properties was evidenced as solvent evaporated. This result tends to prove that visco-plastic properties are required to observe swelling or cracking.

5 Acknowledgment

Fig. 1

 1 Fig. 1 (a) Experimental set-up composed of a sample holder, two cameras which acquire transmitted images. (b) Successive images during the imbibition of a glycerol drop on a porous system formed by drying Ludox HS-40.

Fig. 2

 2 Fig. 2 Scheme of the drop on the porous substrate: definition of the experimentally measured lengths: r d is the drop radius, h d is its height at the drop centre, θ is the drop contact angle with the porous medium. Inside the porous medium, z imb is the vertical penetration depth at the centre of the drop.

Fig. 3

 3 Fig. 3 Evolution of a drop of three solvent spreading and then imbibing porous fragment of Ludox HS-40 (particle radius a = 8nm). (a) The initial volume of glycerol drop: 0.1 µL. (b) The initial volume of water drop: 0.2 µL. (c) The initial volume of ethyl acetate: 0.08 µL. Scale bar : 1 mm.

Fig. 4 (

 4 Fig. 4 (a) Time evolution of the dimensionless drop radius, r d /r d,max , contact angle, θ /θ 0 , and vertical penetration, z imb /h d,0 , with the dimensionless time (t + t 0 )/t Darcy , where t 0 corresponds to the end of the drop spreading stage. Colours: different solvents penetrating in different porous media. Vertical dotted line: drop radius change is correlated to drop contact angle change. Inset : z imb as a function of time, log-log scale. The initial contact angle, θ 0 , of Water, Glycerol and Ethyl acetate on the porous surfaces are 31 ± 2 • , 20 ± 2 • and 18 ± 2 • , respectively.

Fig. 5

 5 Fig. 5 Time evolution of vertical and the radial fronts. (a) Side view of a drop deposited on the surface of a porous medium. (b) Spatio-temporal diagram along the yellow dashed line, r = 0, in (a). (c),(d) Spatio-temporal diagrams obtained along the red and the blue horizontal lines represented in (e), i.e in the drop, and in the wet zone. (e) Images of the drop imbibition at different times. The numbers in (b)-(d) correspond to the images in (e). Scale bar: 0.5mm. (f) Position for the imbibition front with time in vertical and radial directions; the Washburn regime corresponds to the zone (2).

Fig. 6 Fig. 7

 67 Fig. 6 Spherical indentation load-displacement (applied force F vs. penetration depth p) in HS-40 porous layers. The present test shows a series of measurements performed before imbibition (•). Then each series of dots correspond to an indentation load-displacement performed after ethyl acetate imbibition and during the stiffness recovery. The measurements (dots) are fitted by dashed lines according to equation 2.

  These fragments have been characterized through

	System	Colloidal dispersion	Porous medium
		2a	φ p,0	pH	1 -φ p	K
	(nm)				(m 2 )
	SM-30	10	0.15 ± 0.04 9.9 0.33 ± 0.02	2.10 -20
	HS-40	16	0.22 ± 0.01 9.8 0.31 ± 0.03 3.7.10 -20
	Table 1 Main properties of silica dispersions (particle diameter 2a) and
	porous media. φ p,0 is the initial particle volume fraction of the
	dispersions. The volume fraction of the voids in the porous media is
	denoted 1 -φ p with φ p , the particle volume fraction. The values have
	been determined by neutron imaging; K is the permeability calculated
	from Kozeny-Carman law 12,13 . Measurements uncertainties are
	averaged over three different samples.
	Solvent	M W	ρ	γ	η
			(g.mol -1 )		(mN.m -1 ) (mPa.s)
	water		18	1	72.8	1
	ethyl acetate	88.1	0.9	23.9	0.46
	glycerol	92	1.26	63	1499

Table 3

 3

	Porous	HS-40 SM-30
	Solvent	t Darcy	t Darcy	V E	t D
		(s)	(s)	(m.s -1 )	(s)
	water	10	11	5.10 -8	2000
	ethyl acetate	13	15	1.10 -7	1000

shows values of t Darcy for water and for ethyl acetate on HS-40 and SM-30 porous.

Table 3

 3 Comparison of Darcy's time, t Darcy as a function of solvents and of porous media HS-40 and SM-30. V E is the evaporation rate. The drying timescales t D is defined as: t D = L imb /V E where L imb = 100 µm is a typical length for drop penetration in the porous media.

Table 4

 4 Comparison or mean pore radius determined by Washburn's law for vertical and radial imbibition dynamics of a drop inside 2 porous media and mean pore radius determined by neutron imaging. a : particle radius composing the porous media, κ KC : Kozeny-Carman permability, κ Bear : Bear's law permeability. r e f f vert , κ Bear vert : vertical imbibition, mean pore radius and Bear's permeability respectively; r e f f radial , κ Bear radial : radial imbibition, mean pore radius and Bear's permeability respectively.

Published on 12 February 2019. Downloaded by University of New England on 2/12/2019 2:59:25 PM. View Article Online DOI: 10.1039/C8SM02295J

We acknowledge financial support through the Funding agency: Investissement d'Avenir LabEx PALM (Grant number : ANR-10-LABX-0039). We also acknowledge Laboratory Léon Brillouin (LLB) and CEA Saclay for giving neutron beamtime on IMAGINE (G3 bis), neutron imaging spectrometer. Many thanks go to E. Rabot (LLB) and F. Ott (LLB) for their help and advice on IMAGINE. We also thank S. Kwok and B. Cabane for fruitful discussions. We acknowledge F. Gibert (LLB), J. Amarni, A. Aubertin, L. Auffray and R. Pidoux (FAST-University Paris Sud) engineering and technical support and Sofia Carrasco.

Soft Matter Accepted Manuscript