Houssam Hajjoul

Julien Mathon

Hubert Ranchon

Pascal Carrivain

Isabelle Goiffon

Julien Mozziconacci

Benjamin Albert

Jean-Marc Victor

Olivier Gadal

Kerstin Bystricky

Aurélien Bancaud
email: abancaud@laas.fr

High-throughput chromatin motion tracking in living yeast

Keywords: chromatin, live cell imaging, high-throughput particle tracking, nuclear architecture, Brownian Dynamics Simulations

INTRODUCTION

Chromosome higher order architecture has been increasingly studied over the last decade thanks to technological breakthroughs in imaging and in molecular biology ranging from painting single chromosomes in fixed cells [START_REF] Cremer | Chromosome territories, nuclear architecture and gene regulation in mammalian cells[END_REF] to mapping physical interactions between genomic elements at the genome-wide level (Hi-C) [START_REF] Dekker | Mapping in vivo Chromatin interactions in yeast suggests an extended chromatin fiber with regional in compaction[END_REF]. It is now established that chromosome large scale organization plays important roles in all aspects of genomic transactions, allowing contact between distant chromatin loci [START_REF] Göndör | Chromosome crosstalk in three dimensions[END_REF] that trigger concomitant genomic processes in cis and in trans. Although several models have been proposed to describe the folding of chromosomes [START_REF] Lieberman-Aiden | Comprehensive Mapping of Long-Range Interactions reveals folding principles of the Human Chromosome[END_REF][START_REF] Bohn | Diffusion-Driven Looping Provides a Consistent Framework for Chromatin Organization[END_REF][START_REF] Bancaud | A fractal model for nuclear organization: current evidence and biological implications[END_REF], the physical principles governing this organization are still largely debated.

Despite its small size, budding yeast has become a unique model that recapitulates some of the main features of higher eukaryotes, including heterochromatin-like regions, and an organization mediated by the nuclear envelope (NE), the nucleolus, and the spindle pole body (SPB). Structural data obtained by statistical positioning of a gene in a yeast cell population led to a surprisingly simple model to define yeast nuclear architecture [START_REF] Zimmer | Principles of chromosomal organization: lessons from yeast[END_REF]: chromosome position can be predicted by few parameters such as genomic arm length, telomeres (TEL), and centromeres (CEN) tethered to the NE via nuclearenvelope-tethered proteins and to the SPB via microtubules, respectively [START_REF] Bystricky | Chromosome looping in yeast[END_REF][START_REF] Therizols | Chromosome arm length and nuclear constraint determine the dynamic relationship of yeast subtelomeres[END_REF][START_REF] Zimmer | Principles of chromosomal organization: lessons from yeast[END_REF]. This description was recently complemented by the first Hi-C comprehensive maps [START_REF] Rodley | Global identification of yeast chromosome interactions using genome conformation capture[END_REF][START_REF] Duan | A three-dimensional model of the yeast genome[END_REF], which confirmed an organization guided by nuclear landmarks, including TEL that congregate in foci [START_REF] Gotta | The clustering of telomeres and colocalization with Rap1, Sir3, and Sir4 proteins in wild-type Saccharomyces cerevisiae[END_REF][START_REF] Schober | Controlled exchange of chromosomal arms reveals principles driving telomere interactions in yeast[END_REF]. Recent Brownian dynamics (BD) simulations confirmed this structural model by recapitulating Hi-C and imaging data, assuming that physical tethering at TEL and CEN and volume exclusion were driving chromosome conformations [START_REF] Tjong | Physical tethering and volume exclusion determine higher-order genome organization in budding yeast[END_REF][START_REF] Wong | A predictive computational model of the dynamic 3D interphase nucleus[END_REF].

The large spatial fluctuations of chromosome loci inferred from particle tracking in living yeast suggested a highly dynamic character of chromosome architecture at the molecular level [START_REF] Marshall | Interphase chromosomes undergo constrained diffusional motion in living cells[END_REF][START_REF] Heun | Chromosome dynamics in the yeast interphase nucleus[END_REF][START_REF] Hihara | Local Nucleosome Dynamics Facilitate Chromatin Accessibility in Living Mammalian Cells[END_REF]. Chromatin dynamics appeared to be determined by nuclear constraints, in particular the NE [START_REF] Heun | Chromosome dynamics in the yeast interphase nucleus[END_REF][START_REF] Bystricky | Long range compaction and flexibility of interphase chromatin in budding yeast analysed by high-resolution imaging techniques[END_REF], and by the position along the chromosome, e.g. TEL [START_REF] Bystricky | Chromosome looping in yeast[END_REF]. Furthermore, a large body of data provides information on spatio-temporal dynamics in wild type vs. mutant cells (see e.g. [START_REF] Bystricky | Regulation of nuclear positioning and dynamics of the silent mating type loci by the yeast Ku70/Ku80 complex[END_REF])) and elucidates how chromatin properties are regulated by structural proteins. However the quantitative analysis of these movements remains controversial, and essentially two models have been used: (i) chromatin segments were suggested to undergo normal Brownian fluctuations at small time scales, and to be confined in regions of ~0.3 µm 2 at time scales longer than ~100 s [START_REF] Marshall | Interphase chromosomes undergo constrained diffusional motion in living cells[END_REF]; or (ii) the movement of GAL genes on chromosome II appeared to follow an anomalous behavior characterized by a diffusion coefficient of ~0.4 [START_REF] Cabal | SAGA interacting factors confine sub-diffusion of transcribed genes to the nuclear envelope[END_REF]). This anomalous behavior was also detected in bacteria [START_REF] Weber | Bacterial Chromosomal Loci Move Subdiffusively through a Viscoelastic Cytoplasm[END_REF]) and thoroughly studied using polymer models. In yeast the narrow temporal range of measurements within less than two decades were insufficient for a truly quantitative analysis of chromatin dynamics.

Here we develop high-speed live cell imaging and high-throughput image analysis techniques to monitor the spatio-temporal fluctuations over an extended temporal range spanning more than 4 decades (10 -2 to 10 3 s) of 9 chromosome loci on chromosomes III, IV, XII, and XIV of the yeast S. cerevisiae. We show that chromatin segments move subdiffusively, and that the characteristics of the anomalous response are largely conserved for every locus distant by more than ~50 kb from TEL and CEN. Similar dynamic behavior was also observed for two telomeric loci whenever they adopt a central localization in the nucleus, thus leading to a consistent picture for chromosome movement within the entire nuclear volume. We then demonstrate that these dynamics are consistent with the Rouse model using BD simulations and statistical analysis of the trajectories, and suggest that chromatin is a flexible polymer in yeast, characterized by a persistence length of less than 30 nm. Finally we show that the Rouse model is also relevant in mutants for proteins involved in chromatin structure, and propose that this model defines a consistent framework to study chromosome motion. Our findings significantly advance the quantitative understanding of chromosome dynamics and their implications for yeast genome architecture.

RESULTS AND DISCUSSION

The dynamics of chromosome loci are uniform throughout the nucleus and anomalous over a broad temporal range

We assayed the dynamics of chromatin in a collection of yeast strains each bearing a single fluorescently-labeled chromatin locus (see methods for details). The labels were inserted on chromosomes III, IV, XII, and XIV at loci distant from TEL and CEN (Fig. 1 and Fig. 2A). The chromosomes tested ranged in size from 300 kb to 1500 kb, which is wellsuited to assess whether the dynamics are affected by chromosome length. Motion was analyzed over a temporal range spanning more than four decades (15 ms to 400 s, Fig. 2B).

This broad temporal analysis is more than 2 orders of magnitude larger than in previous studies performed in living yeast [START_REF] Heun | Chromosome dynamics in the yeast interphase nucleus[END_REF][START_REF] Bystricky | Long range compaction and flexibility of interphase chromatin in budding yeast analysed by high-resolution imaging techniques[END_REF][START_REF] Cabal | SAGA interacting factors confine sub-diffusion of transcribed genes to the nuclear envelope[END_REF] or in bacteria [START_REF] Weber | Bacterial Chromosomal Loci Move Subdiffusively through a Viscoelastic Cytoplasm[END_REF], and investigations on similar time domains were only conducted in mammalian cells for telomere dynamics [START_REF] Bronstein | Transient anomalous diffusion of telomeres in the nucleus of mammalian cells[END_REF]. The motion of chromosome loci was recorded using a bright field microscope, and analyzed using a customized high-throughput tracking software based on the Multiple-Target Tracing algorithm ( [START_REF] Sergé | Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes[END_REF]; J.M. and A.B. in preparation and Supplementary Fig. S1).

Because physical tethering of chromosomes may occur at the nuclear periphery [START_REF] Heun | Chromosome dynamics in the yeast interphase nucleus[END_REF][START_REF] Hediger | Live Imaging of Telomeres:: yKu and Sir Proteins Define Redundant Telomere-Anchoring Pathways in Yeast[END_REF], the nucleus was divided into two regions of equal surfaces, and every tracked locus was automatically assigned to a central or peripheral localization based on the segmentation of the first image of the acquisitions (see image in Fig. 1).

We first focused on loci located in the nuclear center, far from constraints imposed by the nuclear membrane, and representing ~60 % of the observed positions (Fig. 2A). We then characterized their motion by plotting the temporal evolution of the mean square displacement (MSD), which describes the average displacement after a given time lag τ:

𝑀𝑆𝐷(𝜏) = 〈(𝑟 ⃗(𝑡 + 𝜏) -𝑟 ⃗(𝑡)) 2 〉 (1)
with 𝑟 ⃗ the position vector, and 〈-〉 denoting the temporal average. We observed similar responses for every locus (data points in Fig. 2B), which appeared to fold onto a single master curve (solid line). This curve follows an anomalous diffusive behavior over a broad temporal range characterized by a power-law scaling response in t α with α=0.52+/-0.08 (α=1 for normal diffusion). This result is consistant with an earlier study describing the motion of GAL genes, which exhibited a non linear MSD response characterized by an exponent of ~0.4 in the temporal range of 4 to 80 s [START_REF] Cabal | SAGA interacting factors confine sub-diffusion of transcribed genes to the nuclear envelope[END_REF]), but it departs from other contributions showing normal diffusion and a plateau in the long time limit (see e.g. [START_REF] Heun | Chromosome dynamics in the yeast interphase nucleus[END_REF]).

The anomalous sub-diffusion response is associated with a slow increase in MSD over time.

Its persistence an extended period indicates that chromatin loci explore a broad region of the nucleus of �0.2 µ𝑚 2 ~450 nm in ~400 s. This estimate is consistent with the extent of "gene territories" of ~500 nm, which are obtained by statistical mapping of the position of loci in cell populations of ~2000 individuals [START_REF] Berger | High-resolution statistical mapping reveals gene territories in live yeast[END_REF]).

Next we studied the motion of chromosome loci located at the periphery, and observed that they frequently oscillated between nuclear center and periphery during the time course of the acquisition (Supplementary Fig. S1), suggesting that the localization classification based on a single image is somewhat artificial. We did not detect significant differences in the MSD response for peripheral or central localization for the three loci on chromosome XII (see e.g. position 240 kp in Fig. 2C) and on chromosome IV and XIV (not shown), so the anomalous diffusive response appears to be largely conserved and appropriate to describe chromosome segmental dynamics for loci distant by more than ~50 kb from TEL and CEN.

The dynamics of telomeres are anomalous in a central localization

In yeast, the 32 TEL tend to cluster near the NE, and the motion of tagged chromosome sites in the vicinity of a TEL is constrained [START_REF] Heun | Chromosome dynamics in the yeast interphase nucleus[END_REF][START_REF] Sage | Automatic tracking of individual fluorescence particles: application to the study of chromosome dynamics[END_REF].

Using our reference behavior for chromosome loci located halfway along chromosome arms, we set out to perform an MSD analysis on TEL 3R and 14L (Fig. 1; hereafter denoted Tel3R and Tel14L). Though TEL predominantly accumulate near the periphery (Fig. 3A, right panel), their positioning in the nuclear center can be detected with an occurrence of ~30%, and we analyzed their dynamics in this central region. The amplitude of spatial fluctuations in the short time regime appeared to be relatively similar compared to the reference response (Fig. 3A), although Tel3R appeared to be slightly less mobile after ~10 s than Tel14L, presumably because telomeric interactions between the two ends of chromosome XIV are much less frequent than that of chromosome III [START_REF] Bystricky | Chromosome looping in yeast[END_REF][START_REF] Duan | A three-dimensional model of the yeast genome[END_REF].

In contrast to the bulk of chromosomes, telomere dynamics appeared to be reduced at the nuclear periphery (Fig. 3B), in agreement with the idea that telomere peripheral localization is mediated by protein interactions involving among others SIR4 and YKU70/YKU80 [START_REF] Hediger | Live Imaging of Telomeres:: yKu and Sir Proteins Define Redundant Telomere-Anchoring Pathways in Yeast[END_REF][START_REF] Taddei | Separation of silencing from perinuclear anchoring functions in yeast Ku80, Sir4 and Esc1 proteins[END_REF][START_REF] Bupp | Telomere anchoring at the nuclear periphery requires the budding yeast Sad1-UNC-84 domain protein Mps3[END_REF][START_REF] Schober | Yeast telomerase and the SUN domain protein Mps3 anchor telomers and repress subtelomeric recombination[END_REF]. It has been shown that deletion of either YKU70 or SIR4 leads to delocalization of some TEL to the nuclear center [START_REF] Laroche | Mutation of yeast Ku genes disrupts the subnuclear organization of telomeres[END_REF][START_REF] Hediger | Live Imaging of Telomeres:: yKu and Sir Proteins Define Redundant Telomere-Anchoring Pathways in Yeast[END_REF], but it remains unclear whether this deletion affects TEL dynamics aside from chromosome III (Bystricky et al. 2009). We thus investigated the movements of Tel14L in wild-type and in SIR4 mutant strains. Deletion of SIR4 leads to a predominant localization of Tel14L in the center (62%), likely due to loss of anchoring to the nuclear membrane. Moreover telomere mobility is increased in SIR4 mutant strains when the tagged locus resides at the periphery and even more drastically at the nuclear center (Fig. 3B), confirming that physical interactions of the extremities of chromosomes are an essential player of their spatio-temporal dynamics. Overall this study tends to support the proposition of uniform fluctuations throughout the nucleus for chromatin loci provided that they are sufficiently distant from anchoring regions.

Chromosome segmental dynamics are consistent with the Rouse model

To interpret our results with a polymer model, we make the assumptions that chromosome conformation and dynamics are mainly determined by (i) the permanent tethering of CEN to the SPB and the more transient attachment of TEL to NE [START_REF] Zimmer | Principles of chromosomal organization: lessons from yeast[END_REF], and (ii) the level of crowding mediated by chromosomes and nuclear proteins.

Crowding is expected to screen out hydrodynamic effects, which otherwise induce long range interactions in between chromosome segments [START_REF] Doi | The theory of polymer dynamics[END_REF], so that nearestneighbor elastic interactions between consecutive chromosome segments dominate their local dynamics. This approximation, which leads to the "Rouse" regime [START_REF] Rouse | A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers[END_REF], has been extensively documented for concentrated solutions of synthetic polymers (see e.g. [START_REF] Ewen | Neutron Spin Echo Investigations on the Segmental Dynamics of Polymers in Melts, Networks and Solutions[END_REF])), and was recently validated in vivo for the bacterial chromosome [START_REF] Weber | Bacterial Chromosomal Loci Move Subdiffusively through a Viscoelastic Cytoplasm[END_REF].

Chromosomes are modeled by a Rouse chain, which is composed of a series of N elastic segments of length b. The motion of each bond is determined by its elasticity defined by the stiffness 3k B T/b 2 with 𝑘 𝐵 𝑇 the thermal energy, and its viscous drag 𝜁. Assuming that chromosomes are tethered at CEN and TEL, the MSD of monomers can be solved analytically in the short time regime (see Model section):

𝑀𝑆𝐷(𝜏) ~ � 12𝑏 2 𝑘 𝐵 𝑇 𝜋𝜁 � 1 2 � 𝜏 1 2 �
(2)

The Rouse segmental dynamics are characterized by an anomalous diffusive response uniform along the chain, in good agreement with our data. We wished to test the predictions of the Rouse model further by extracting the histogram of the displacement after a time lag of 0.18, 1.0 and 1.6 s from the trajectories of locus 240 on chromosome XII (Fig. 4A). The histograms were first fitted with a normal diffusion model (Fig. 4A, left panel and equation in inset), which relies on one fitting parameter, the diffusion coefficient D. The diffusion coefficient of 4.8, 2.2, 1.8 10 -3 µm 2 /s was very different for τ=0.18, 1.0, and 1.6 s, respectively, showing the inconsistency of this model. We then used the formalism described in [START_REF] Guérin | Non-Markovian polymer reaction kinetics[END_REF] to compute the histogram of the displacement for a Rouse chain tethered at its extremities (see expression in Model section). One single parameter was sufficient to reproduce the three distributions (Fig. 4A, right panel), and the quality of the fitting was significantly improved (note the departure of the red fit from the conventional model), hence strongly supporting the relevance of the Rouse model to describe the segmental dynamics of yeast chromosomes.

We then performed BD simulations of yeast chromosome dynamics in a volume the geometry of which is consistent with yeast nuclear size, and using the structure derived from Hi-C experiments as the initial state [START_REF] Duan | A three-dimensional model of the yeast genome[END_REF]. We assumed that chromosomes were attached to the SPB at their CEN (i.e., neglecting the contribution of microtubules connecting SPB to kinetochores), and freely diffusing at their TEL (chromosome III is represented in the left panel of Fig. 5B). The computed MSD for loci distant from CEN (>400 nm; blue dataset in the right panel of Fig. 5B) reproduced our the anomalous diffusive response associated to a power-law scaling of ~0.54 over a temporal domain of four orders of magnitude that we observed experimentally (dashed line in Fig. 5B, right panel). The motion is more restricted for segments located at 10-100 nm from the CEN (pink dataset) vs. at a distance comprised between 200-400 nm (red dataset). In addition, superposing the conformations of chromosome III during 10 6 time steps shows an elongated state of diameter ~300 nm. This conformation is associated with volume exclusion between chromosomes (see also Supplementary Fig. S4B), an effect that was recently shown to be a key parameter of yeast nuclear architecture [START_REF] Tjong | Physical tethering and volume exclusion determine higher-order genome organization in budding yeast[END_REF]. We thus conclude that the dynamics of chromosome loci in living yeast are accurately described by the Rouse model.

The Rouse dynamics imply that chromosome segments search for target sites by compact exploration (de Gennes 1982), meaning that they systematically visit neighboring sites as they look for targets during repair or transcription activation [START_REF] Condamin | First-passage times in complex scale-invariant media[END_REF]).

Because the probability that chromosome loci find a nearby target is increased [START_REF] Guigas | Sampling the cell with anomalous diffusion -the discovery of slowness[END_REF], the Rouse dynamics are likely efficient to create specific chromosome contacts in cis or in trans over distances of less than ~400 nm, which are explored in a few minutes (Fig. 2B). The notion of territoriality remains controversial, whether it is absent based on the observation that broken ends of chromosomes are free to search the entire genome for appropriate partners [START_REF] Haber | Lack of chromosome territoriality in yeast: Promiscuous rejoining of broken chromosome ends[END_REF], or partial as telomere colocalisation and coordinated movement would indicate [START_REF] Bystricky | Chromosome looping in yeast[END_REF]. Future BD simulation studies should therefore evaluate whether and how compact exploration is related to chromosome territoriality in the yeast genome.

MSD fluctuations suggest that chromatin is highly flexible

The level of flexibility of a chromatin fiber is a matter of debate. In vitro single molecule experiments have shown that the persistence length l p of nucleosome arrays is 20-30 nm [START_REF] Cui | Pulling a single chromatin fiber reveals the forces that maintain its higher-order structure[END_REF][START_REF] Bancaud | Structural plasticity of single chromatin fibers revealed by torsional manipulation[END_REF][START_REF] Celedon | Magnetic tweezers measurement of single molecule torque[END_REF][START_REF] Kruithof | Single-molecule force spectroscopy reveals a highly compliant helical folding for the 30 nm chromatin fiber[END_REF]. Conversely, analyses based on polymer models of in vivo distance measurements or Hi-C experiments [START_REF] Bystricky | Long range compaction and flexibility of interphase chromatin in budding yeast analysed by high-resolution imaging techniques[END_REF][START_REF] Dekker | Mapping in vivo Chromatin interactions in yeast suggests an extended chromatin fiber with regional in compaction[END_REF][START_REF] Tjong | Physical tethering and volume exclusion determine higher-order genome organization in budding yeast[END_REF]) provided estimates of ~200 nm and 66-134 nm, respectively. Physical modeling of the mechanical properties nucleosome arrays predicts a persistence length smaller than 30 nm for chromatin [START_REF] Ben-Haïm | Chromatin: a tunable spring at work inside chromosomes[END_REF][START_REF] Schiessel | DNA folding: structural and mechanical properties of the two-angle model for chromatin[END_REF], except in the case of highly ordered arrays with strong nucleosome-nucleosome interactions [START_REF] Wedemann | Computer simulation of the 30-nanometer chromatin fiber[END_REF], in which case l p increases to ~250 nm.

The amplitude of spatial fluctuations can be qualitatively linked to the flexibility of chromatin using the Rouse model, given that the bond length b and the viscous drag coefficient 𝜁 are equal to 2l p and 6𝜋η𝑙 𝑝 with η the viscosity, respectively (de Gennes 1979).

Injecting this term in Eq. ( 2) implies that the amplitude of the MSD increases with the square root of the polymer persistence length. The extent of spatio-temporal fluctuations therefore increases as the rigidity of the fiber increases, in qualitative opposition to free diffusion of an isolated tracer that increases as the diameter of the particle decreases. The MSD response can then be predicted for a persistence length comprised between 50 and 200 nm, given that the nuclear viscosity is η~7+/-3 10 -2 P based on GFP diffusion coefficient measurements [START_REF] Kawai-Noma | Dynamics of yeast prion aggregates in single living cells[END_REF][START_REF] Slaughter | Mapping dynamic protein interactions in MAP kinase signaling using live-cell fluorescence fluctuation spectroscopy and imaging[END_REF]). This conjecture exceeds our measurements by a factor of 10 to 20 (dashed lines in Fig. 5A). In contrast, fitting of our data with the Rouse model leads to an amplitude of the MSD of 1.0 +/-0.2 10 -2 µm 2 /s -1/2 (solid line in Fig. 5A),

suggesting that the persistence length of chromatin in living yeast is ~5 nm. This length scale is coherent with the dimensions of a single nucleosome, which is a ~5 nm by ~10 nm disk-like structure. Hence the analysis of chromosome motion suggests that chromatin is a flexible polymer in vivo.

Because the Rouse model is a simplified model that does not take volume exclusion between monomers into account, we wished to strengthen our conclusions by running BD of a single chain composed of self-avoiding segments (see model section). The extracted MSD

shows an anomalous diffusive response, as well as the dependence on the persistence length and the viscous drag (Eq. ( 2)) expected from the Rouse model (Fig. 5B). This analysis showed that the numerical prefactor of Eq. ( 2) is underestimated by 1.4, suggesting that volume exclusion enhances the rate of spatial exploration. This difference implies that the persistence length of ~5 nm is overestimated, and a correct estimate may be as small as ~3

nm. This length scale, which is comparable to the DNA diameter, is unrealistic and points to an additional parameter related to the chromosomal environment.

Each MSD curve represented in Fig. 2B is the average response over a population of ~100 cells. The clonal variability of the spatio-temporal dynamics is not shown in this graph, although this variability is large, as inferred from the distribution of average displacements after a time lag of 0.1, 0.6, and 4.0 s for ~70 loci on chromosome XII (position 830, Fig. 5C).

Because the difference between the average and the maximal or minimal MSD is about threefold, this variability is unlikely related to changes in persistence length, which should vary over two orders of magnitude from 0.3 to 30 nm. We rather suggest that this variability is associated with the existence of dynamic chromosomal contacts, as previously indicated in e.g. the dynamic random loop model derived to interpret distance measurements in human cells [START_REF] Mateos-Langerak | Spatially confined folding of chromatin in the interphase nucleus[END_REF]. Dynamic and random contacts should transiently restrict spatial exploration (Supplementary Fig. S5), reduce the effective diffusion of a genomic site over a population average, and hence lead to an apparent persistence length smaller than chromatin intrinsic properties. We propose that chromosome loci with maximal mean square displacements in the short time regime represent the "interaction-free" limit, because their motion is not hindered by distant contacts. Given that the difference between the average and the maximal MSD is less than three-fold (Fig. 5C), we can evaluate an upper limit for the persistence length of 3 2 x3 nm <30 nm. Consequently, chromatin appears as a flexible polymer, and its persistence length can be qualitatively estimated to be less than ~30 nm.

Chromatin structural proteins alter chromosome mobility

Finally we investigated whether the dynamics of chromosomes was altered in the absence of chromatin structural proteins or chromatin assembly proteins. We first considered the HMG-like protein Spt2 in S. cerevisiae, which interacts with the histones H3 and H4 [START_REF] Horn | The SIN domain of the histone octamer is essential for intramolecular folding of nucleosomal arrays[END_REF]. The statics and the dynamics of one locus on chromosome XIV were assayed in WT and mutant spt2 cells, showing an accumulation at the periphery for the mutant and similar MSD responses in the short time regime (Fig. 6, right and left panels, respectively). We then performed the same analysis with Hho1p [START_REF] Levy | Yeast linker histone Hho1p is required for efficient RNA polymerase 1 processivity and transcriptional silencing at the ribosomal DNA[END_REF], which is considered as the linker histone analog in S. cerevisiae, though its structure differs from linker histone in other organisms because it bears two globular domains. So far it remains unclear whether and how this protein participates in chromatin condensation. The deletion of hho1 increases the proportion of spots detected in the nuclear center compared to wild type, and increases ~1.5-fold the amplitude of chromatin loci displacements (Fig. 6). Given that the ratio Hho1p vs. nucleosome remains poorly estimated (comprised between 1:37 to 1:4 [START_REF] Freidkin | Specific distribution of the Saccharomyces cerevisiae linker histone homolog HHO1p in the chromatin[END_REF][START_REF] Downs | Suppression of Homologous Recombination by the Saccharomyces cerevisiae Linker Histone[END_REF]), these enhanced dynamics may be associated with the reduced frequency of chromosome interactions mediated by the two domains of Hho1 and/or with an onset in flexibility due to conformational changes at the nucleosome level. Finally, we probed the role of the nucleosome assembly chaperone Asf1, which is involved in replication-dependent and replication-independent chromatin assembly [START_REF] Loyola | Histone chaperones, a supporting role in the limelight[END_REF]. As for hho1, the labeled locus appeared to be more frequently central than in wild type nuclei, and its mobility was 2.2-fold increased. The Rouse model therefore seems to account for the dynamics of chromosome loci in WT cells, as well as in hho1, asf1 and spt2 mutants, suggesting that this approach is sufficiently generic to perform systematic motion analyses.

CONCLUSION

We demonstrate that the motion of chromosome loci in living yeast is characterized by anomalous sub-diffusion with an exponent of 0.52 over a temporal domain spanning more than 4 orders of magnitude. We then show that this response, which appears to be relevant for the analysis of WT and mutant cells, is consistent with the Rouse dynamics. Because the Rouse regime is characteristic of polymers in crowded environments, our result strengthens the relevance of polymer models for the description of the yeast genome [START_REF] Gehlen | Chromosome positioning and the clustering of functionally related loci in yeast is driven by chromosomal interactions[END_REF][START_REF] Tjong | Physical tethering and volume exclusion determine higher-order genome organization in budding yeast[END_REF][START_REF] Wong | A predictive computational model of the dynamic 3D interphase nucleus[END_REF]). In addition the Rouse dynamics is associated to compact exploration, implying that chromosome loci efficiently search for nearby targets. We speculate that this property guides chromosome interactions in cis and trans, and envision that this hypothesis can be tested using BD simulations in combination with Hi-C experiments aiming to evaluate the number of chromosome contacts as a function of the genomic distance.

Further the amplitude of chromatin spatio-temporal fluctuations shows that this polymer is

flexible. Yet the cell-to-cell variability of the amplitude of chromosome movements only allows for a qualitative determination of the persistence length of less than 30 nm. We propose that this variability is associated to dynamic interactions between chromosomes, and future BD simulations may confirm or invalidate this conjecture, in turn providing new insights on the statics and the dynamics of the yeast genome.

The folding of interphase chromosomes in metazoans involves loops of variable sizes defining topological domains of 0.2 to 5 Mb [START_REF] Nora | Spatial partitioning of the regulatory landscape of the X-inactivation centre[END_REF][START_REF] Sexton | Three-Dimensional Folding and Functional Organization Principles of the Drosophila Genome[END_REF]. Because the dimension of these domains, which can be described as end-tethered chromosome fragments, is consistent with the length of yeast chromosome arms, we speculate that the Rouse model is relevant to higher-order eukaryotes. This model has recently been implemented in numerical simulations [START_REF] Bohn | Diffusion-Driven Looping Provides a Consistent Framework for Chromatin Organization[END_REF], showing that the dynamics of loop formation may interfere with the segmental motion of human chromosomes, an hypothesis that remains to be tested quantitatively in vivo.

MODEL

Dynamics

The motion of an end-tethered Rouse chain can be studied analytically using normal mode decomposition [START_REF] Vandoolaeghe | A Rouse-tube model of dynamic rubber viscoelasticity[END_REF], and the MSD of the n th -segment (𝑀𝑆𝐷 𝑛 ) reads:

𝑀𝑆𝐷 𝑛 (𝜏) = 4𝑁𝑏 2 𝜋 2 ∑ 1 𝑝 2 �1 -𝑒 -𝜏 𝜏 𝑝 � � 𝑠𝑖𝑛 2 � 𝑝𝜋𝑛 𝑁 � ∞ 𝑝=1
(3) with 𝜏 𝑝 the relaxation time of each mode 𝜏 𝑝 = 𝜏 𝑅 /𝑝 2 and 𝜏 𝑅 = 𝐿 2 𝜁/3𝜋 2 𝑘 𝐵 𝑇 the Rouse time identified as the longest relaxation time of the chain. Note that this equation is valid in 3D, and its 2D version is readily obtained with a multiplication by 2/3 assuming that the motion is isotropic. The temporal evolution of the MSD is plotted in Supplementary Fig. S4As). In the short time limit (𝜏 ≪ 𝜏 𝑅 ), equation ( 3) is dominated by the terms with large p, and it can be simplified to obtain Equation ( 2) given in the main text. In addition, the formalism described in ( [START_REF] Guérin | Non-Markovian polymer reaction kinetics[END_REF] ; see details in Supplementary Materials) enables to extract the distribution of the displacement R for the n th segment after a time lag τ :

𝑃 𝑛 (𝑅, 𝜏) = 𝑅 Ψ n (𝜏) 𝑒𝑥𝑝 -� 𝑅 2 2Ψ n (τ) � (4) Ψ n (𝜏) = 2𝑏 2 𝑁 ∑ sin 2 �𝑝 𝑛𝜋 𝑁+1 � * � 1-exp �- 2𝜁𝑏 2 𝜏 k B T �1-cos�𝑝 𝜋 𝑁+1 ��� 1-cos�𝑝 𝜋 𝑁+1 � � 𝑁 𝑝=1 (5)
The movements of chromosomes, which were modeled by a series of bead linked by springs or ball-in-socket joints, was also analyzed by BD. The size of each bead was set to 15 nm in diameter, and it was assumed to contain ~3 nucleosomes, so that the full genome consists of 27,000 beads. Chromosomes were constrained in a sphere of 2 µm in diameter, and the CEN were fixed to the SPB using harmonic constraints. We used the Langevin dynamics algorithm implemented in the NAMD software [START_REF] Phillips | Scalable molecular dynamics with NAMD[END_REF]) with an appropriate in-house force field. The Langevin equation for the n th monomer has the form:

𝑚 𝑛 𝑑 2 𝑥 𝑛 𝑑𝑡 2 (𝑡) = -𝑔𝑟𝑎𝑑 𝑥 𝑛 𝐸 + 𝑓 𝑛 (𝑡) -𝑚 𝑛 𝑏 𝑛 𝑑𝑥 𝑛 𝑑𝑡 (𝑡) (7)
where the random force f n (t) is derived from a Gaussian distribution with the properties:

〈𝑓 𝑛 (𝑡)〉 = 0 (8) 〈𝑓 𝑛 (𝑡)𝑓 𝑛 (0)〉 = 2𝑘 𝐵 𝑇𝜁𝑚 𝑛 𝛿(𝑡) (9)
with 𝜁 the friction coefficient. The energy E of each bead is the sum of three contributions associated to the confinement in the nucleus, the elasticity of the chain, and the repulsive interactions between monomers, which are expressed as:

𝐸 = 𝐸 𝑐𝑜𝑛𝑓 + 𝐸 𝑠𝑝𝑟𝑖𝑛𝑔 + 𝐸 𝑉𝑑𝑊 (10)
𝐸 𝑐𝑜𝑛𝑓 (𝑟 < 𝑟 1 ) = 0 and 𝐸 𝑐𝑜𝑛𝑓 (𝑟 > 𝑟 1 ) = 𝐸 1 (𝑟 -𝑟 1 ) 4 (11)

with r the distance of the bead to the center of the nucleus, and r 1 the radius of the nucleus.

𝐸 𝑠𝑝𝑟𝑖𝑛𝑔 (𝑛, 𝑛 + 1) = 𝑘 𝑠 (𝑟 𝑛 -𝑟 𝑛+1 ) 2 (12) 𝐸 𝑉𝑑𝑊 (𝑖, 𝑗) = 𝑈 �� 𝑅 𝑚𝑖𝑛 �𝑟 𝑖 -𝑟 𝑗 � � 12 -2 � 𝑅 𝑚𝑖𝑛 �𝑟 𝑖 -𝑟 𝑗 � � 6 � (13)
The parameters of this model can be found in Table 1. BD were run during 3.10 7 time steps, starting from the conformation obtained by Hi-C [START_REF] Duan | A three-dimensional model of the yeast genome[END_REF]) equilibrated during 10 6 time steps. We also performed BD to investigate whether spatio-temporal fluctuations were different for 1, 4, or 10 segments, or for one segment of large diameter along the chain.

We did not detect differences on the MSD response (not shown), in agreement with our observation of similar dynamics with Lac or Tet labeling, which measure ~10 and 7 kb in length, respectively.

MATERIALS AND METHODS

Plasmids and strains:

All the strains we used are described in the Supplemental table 1.

Cell culture

Cells were grown in YPD or YNB at 30°C starting from a fresh overnight culture.

They were diluted at 10 6 cells/ml, and harvested when OD600 reached 4.10 6 cells/ml and rinsed twice with the corresponding SC media. Cells were then spread on a SC media patch containing 2% agarose and 2% glucose coated slide. A coverslip was deposited over the cells, and the construction was finally sealed with "VaLaP" (1/3 vaseline, 1/3 lanoline, 1/3 paraffin). Live microscopy was limited to 20 minutes after mounting the coverslip. Extreme care was taken to ensure that cells are at approximately equal stages of growth based on their shapes, as inferred from a single image of transmission light microscopy, and based on the nucleus shape using the roundness parameter R that was defined as:

𝑅 = 4𝜋 × 𝑆𝑢𝑟𝑓𝑎𝑐𝑒/𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 2 (14)
with Surface the number of pixels after segmentation of the nucleus, and Perimeter the outline in pixels (see Supplementary Fig. S2). We considered nuclei with R>0.8 to avoid mitotic phenotypes.

Live cell imaging

Yeast cells were imaged at room temperature with a BX-51 upright microscope equipped with a laser diode (Lumencor), a 100X oil immersion objective (NA=1.4), and an EMCCD camera (Andor DU-897), as described in [START_REF] Hajjoul | Lab-on-Chip for fast 3D particle tracking in living cells[END_REF]). The excitation emission at 470+/-10 nm was set to 7.53 W/µm 2 , about 100 times less than the value which is necessary for normal cells growth [START_REF] Carlton | Fast live simultaneous multiwavelength fourdimensional optical microscopy[END_REF]), and we observed consecutive rounds of divisions during ~2 hours (not shown). For slow acquisitions of inter-frame intervals of 2 s or more, we used a 100X oil immersion objective with a variable NA set to ~1.1-1.2. The acquisition was performed with a shutter synchronized with the camera to minimize photobleaching, and we checked for drifts by monitoring the position of the center of the manuscript. We are grateful to Charlotte Galimow for strain construction and initial characterization of gene position.

Author contributions: H.H., J.M. designed the study, performed data analysis; H.R. ∆t (s)

  developed analytical models; I.G. generated new strains; J.M., P.C. performed Brownian dynamics simulations; B.A. provided new strains; P.C., J.M.V. designed models; O.G., K.B. developed the manuscript; A.B. designed the study, developed models, and wrote the paper.

Figure 1 :

 1 Figure 1: Collection of loci used to monitor chromosome spatio-temporal dynamics. Arrows

Figure 2 :

 2 Figure 2: Chromatin dynamics in living budding yeast. (A) The upper panel shows

Figure 3 :

 3 Figure 3: Telomere dynamics in living budding yeasts. (A) The left plot represents the MSD

Figure 4 :

 4 Figure 4: Rouse model for chromosome segmental dynamics. (A) The two graphs represent

Figure 5 :

 5 Figure 5: Assaying chromatin flexibility from MSD analysis. (A) The MSD response plotted

Figure 6 :

 6 Figure 6: Chromatin structural/modifying proteins and chromosome dynamics. The left plot

  Figure 4

Table 1 :

 1 Set of parameters to run Brownian dynamics simulations.

Acknowledgements:

We thank the University Paul Sabatier for PhD fellowship funding (to JM). This work was partly supported by the ANR program JC08_341867, by the CNRS program PIR, and by the LAAS-CNRS technology platform, a member of the French Basic Technology Research Network. We are grateful to Nathalie Daigle for critical reading of the

nucleus in the first and last image of the recording. Optimal inter-frame intervals of ~20 ms were reached by cropping regions of interest, and using a 2*2 binning with the Andor iQ imaging software. The loss in pixel size resolution was compensated with a 2X lens placed in the microscope light path.

We focused on 2D single particle tracking, and checked that similar information were retrieved with 3D tracking using micro-mirrors ( [START_REF] Hajjoul | Lab-on-Chip for fast 3D particle tracking in living cells[END_REF][START_REF] Hajjoul | Optimized micromirrors for Threedimensional single-particle tracking in living cells[END_REF], Supplementary Fig. S3). We note that 2D acquisitions may bias MSD responses for loci preferentially localized at the periphery, because in some cases central loci in the projected view may be peripheral in the 3D nucleus.

Data analysis

Video sequences consisted in 300 consecutive images, and we displayed MSD traces on 150 time intervals at most in order insure the statistical relevance of mean displacements.

The movement of chromosome loci were systematically analyzed using a custom software that was developed in Matlab (Mathworks, Natick, MA; [START_REF] Sergé | Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes[END_REF]. This software, which will be described in detail elsewhere, enabled us to extract (x,y) coordinates by Gaussian fitting, to reconstruct the trajectories, and to compute the MSD and the step distribution function. Note that the MSD in fixed cells was 20-to 30-fold lower than in living cells (Supplementary Fig. S3B).

Mozziconacci, 4,5 Benjamin Albert 2,3 , Pascal Carrivain, 4,5 Jean-Marc Victor, 4,5 Olivier Gadal 2,3 , Kerstin Bystricky 2,3 , Aurélien Bancaud 1,3 Supplementary material contains: 1supplementary text, and 5 figures Supplementary Material

1-Model for step distribution analysis

We use the method developed by Guérin et al. to derive the step distribution function.

We first define the Rouse modes for an end-tethered polymer chain, which requires to diagonalize the Hessian matrix. This matrix of size N 2 relates the elastic forces acting on each monomer, and it is tridiagonal:

Note that this matrix is slightly different from that described in [START_REF] Guérin | Non-Markovian polymer reaction kinetics[END_REF] to account for the difference in boundary conditions. Its eigenvalues are:

Its eigenvectors are:

Using Supplementary Eq. A29-A30 of the work of Guérin et al., we deduce the temporal evolution of a diffusive observable X:

In our case, we focus on the dynamics of a segment located at position n along the chromosome, and the terms b j are defined by the following equations:

These solutions are obtained with dimensionless variables, and we have to define the useful units of time and length:

and 𝑙 = 𝑏 (S7)

Using the set of equations (S2,4,5,6,7), one can derive equation ( 5) and ( 6) given in the main text.

Supplementary Table 1: Strain list Supplementary Figures


Patrick Castel

Recent developments in cancer care in France. Competition or coordinated care?

Patrice [START_REF] Pinell | The birth of a scourge: the anti-cancer war in France 1890-1940[END_REF] has analysed the birth of a national policy to fight against cancer in France at the beginning of the 20 th century and how this policy came to be articulated around a restricted number of hospitals specialised in cancer care. In those times, their characteristics were innovative, since these hospitals should manage research activities and treat patients at the same time while defending a multidisciplinary approach to cancer care. This meant that each medical speciality was to participate in the therapeutic decision process. The defence and promotion of radiotherapy as an emerging technique beside the dominant surgery methods was a major concern for the founders of these cancer centres.

From their creation to the 1970s, these Cancer Centres were the main organisations in charge of cancer patients in France. In 1965, the French government entrusted them with organising consultations for patients in other hospitals in their regions. Until 1972, physicians appointed to the National Commission in charge of advising the government to define a national cancer policy were exclusively drawn from the Cancer Centres, as well.

But from then on, things changed. Cancer Centres have faced increasing competition (by Teaching Hospitals and general healthcare organisations) and their legitimacy has been challenged by other healthcare actors and organisations (especially by organ specialists who contested their pathology-oriented and multidisciplinary approach). In this paper, I will sketch out two reform projects which greatly contributed to reinstate cancer centres as cornerstones in the French oncology sector. This movement shared two important characteristics with other past reforms (see P. Pinell):

• it was a centralised, national impetus;

• it aimed at normalising medical practices and the organisation of cancer care.

As we will see, this reform program clearly leaned on previous achievements as well as on some of the CC's organisational and cultural characteristics. But it was specific in two main ways:

• it aimed at defending and promoting medical oncology as an emerging speciality inside and outside cancer centres whereas radiotherapy and surgery had been the dominant specialities until then; • normalisation was to be achieved through randomised clinical trials and (evidence-based) practice guidelines.

I focused my paper on three dimensions of this reform, so that it may facilitate discussions and international comparisons during the workshop:

• reasons why this reform was launched;

• conditions that might have facilitated its implementation;

• some current characteristics of the organisation of cancer care in France2 .

Reasons underlying normalisation

At the beginning of the 1990s, a group of 5 physicians at the head of cancer centres launched a reform program with the goal of normalising medical practices inside and outside cancer centres. They argued that the National Federation of Cancer Centres, an employers' association which was created in 1964 and whose board was composed of the 20 directors of CCs, should develop evidence-based guidelines and sponsor clinical trials. The reasons vary why they decided to design this reform.

Common interest and similar career paths

The CCs' reformers shared a number of distinctive features and a personal adherence to the evidence-based medicine program. They belonged to what [START_REF] Marks | The Progress of Experiment: Science and Therapeutic Reform in the United States, 1900-1990[END_REF] would have called therapeutic reformers: they believed in the necessity to improve efficiency and reduce the heterogeneity of medical practices through the development of rational methods.

First, their medical specialisation contrasted with those of the previous directors in the centre in which they were nominated. Three of them were the first medical oncologists to be nominated at the head of a Cancer Centre while the fourth was the first radiotherapist following three surgeons and a pathologist: in other words, they shared a disciplinary interest in the face of surgery as another, still dominant treatment technique.

Secondly, they had been actively involved in (international) research activities, a fact which strongly contrasted with other directors of the National Federation's board. In particular, the three medical oncologists had been appointed as research fellows in some of the most famous American institutions who developed new medical treatments through experimental research and multicentre clinical trials3 .

As concerns the guidelines project, its instigator, a paediatric oncologist, could not abide by the heterogeneity among treatments which were prescribed by physicians in his centre, since they could imply inequalities among patients. He was all the more sensitive to this issue in that the international community of paediatric oncologists had been involved for many years in the question of the harmonisation of their practices [START_REF] Castel | Les dimensions politiques de la rationalisation des pratiques médicales[END_REF].

Normalisation for legitimacy

But the normalisation program was also based on more utilitarian grounds: it aimed at reinstating cancer centres as leaders in the French oncology sector. Indeed, from the 1980s on, these centres had faced increasing criticisms by regulatory bodies and other healthcare actors and organisations. If they were to survive, they had to prove that they were still useful.

First, general (for-profit and non-profit) hospitals had greatly increased their participation in cancer care. Cancer Centres possessed only 22 percent of the French radiotherapy equipment by the end of the 1970s, while they had heavily based their development on this technique. Moreover, the emergence of chemotherapy allowed new categories of physicians, who were not specialised in radiotherapy or surgery, to enter the field of cancer care 4 . As a consequence, the number of new cancer patients treated in the CCs stagnated during the 1980s whereas the total number of cancer patients grew. Furthermore, the number of hospitals relying on CCs' physicians for cancer consultations stagnated to around 150 during the 1980s.

Secondly, some healthcare organisations promoted an alternative medical model that challenged the CCs'. They were organised around physicians specialised in the treatment of specific organs (gynaecologists, urologists, gastro-enterologists, etc.), cancer being only one among many other pathologies they treated, whereas Cancer Centres claimed that only physicians specialised in the knowledge of the pathology as a whole (oncologists) were able to propose the appropriate treatments. The Teaching Hospitals, created in 1958 (i.e. after the CCs), were particularly threatening for CCs. Having become the keystone of the French healthcare system, since they were perceived as offering the best and most advanced treatments, to train physicians and to conduct medical research for all pathologies, they began to claim from the 1980s on that Cancer Centres were no longer useful and argued that their physicians, specialised in organ treatments and at the forefront of clinical research, were thus more qualified to treat cancer.

In this competitive context, several public reports raised the question of maintaining these atypical hospitals: they were costly and did not show any evidence of their added value.

The normalisation program was conceived as an answer to all these challenges.

First, it was expected that the sponsorship of (multicentre) clinical trials and the elaboration of guidelines by CCs would contribute to prove the pre-eminence of their physicians and of their pathology-oriented and multidisciplinary approach in the oncology sector. For instance, through the guidelines project, they came up to regulatory bodies' expectations which tried to promote a quality approach in the French healthcare sector in order to curb expenditures [START_REF] Setbon | La qualité des soins, nouveau paradigme de l'action collective ?[END_REF][START_REF] Kerleau | L'hétérogénéité des pratiques médicales, enjeu des politiques de maîtrise des dépenses de santé[END_REF]. Furthermore, homogeneity of practices inside CCs was expected to reinforce their professional legitimacy 5 .

Secondly, both activities -guidelines' elaboration and clinical research -could help to differentiate these centres and their physicians from other healthcare organisations. They were intended to make clear the "added value" of cancer centres in the French oncology sector. At that time, there was not any national cancer guideline in France although, given the increasing number of randomised controlled trials, reformers were convinced that professionals would welcome some help to stay well informed on current treatments. As concerns clinical research, objectives were twofold. On the one hand, an increasing participation of CCs' physicians in clinical trials could differentiate them from "rank-and-file" practitioners who only treated individual patients. On the other hand, the NFCC should (and indeed would) become the main public sponsor of clinical trials in France and thus differentiate CCs from Teaching Hospitals -since the latter had not developed such a co-ordinated activity at the national level.

Last but not least, the guidelines project was seen by the directors as a way to set the rules in the oncology sector. In particular, it was a tool to defend 1) the usefulness of radiotherapy and medical treatments besides surgery and 2) the medical approach and organisation of cancer care which CCs' physicians have developed [START_REF] Pinell | The birth of a scourge: the anti-cancer war in France 1890-1940[END_REF]. Thus, one of the first guidelines elaborated by the CCs was entitled "Standards, Options and Recommendations concerning good practices in the multidisciplinary organisation of cancer care" (Chardot, Fervers et al., 1995).

5 By the end of the 1980s, the instigator of the guidelines project (recently appointed as director of his centre), analysed that heterogeneity of practices inside his centre was indeed an obstacle to the regional legitimacy of his centre. Because of this heterogeneity, physicians of other hospitals explicitly cast in doubt the quality of the advice that CC's physicians offered them.

Favourable conditions and social skilfulness

The reformers of Cancer Centres can be defined in Fligstein's words as "socially skilled actors" ( 2001). On the one hand, they succeeded in making sense of the situation that directors and physicians of Cancer Centres were encountering and in redefining their collective interests and identity. On the other hand, they were pragmatic enough to use the resources at hand and induce co-operation among actors.

Collective identity as a resource for change

While pushing for drastic reform along the lines which they sketched out, the group of reformers argued that their program was in line with, and therefore able to protect and to enhance, the founding project of Cancer Centres [START_REF] Pinell | The birth of a scourge: the anti-cancer war in France 1890-1940[END_REF] of which directors and physicians are very proud. They underlined that the two distinctive organisational features of Cancer Centres (their specialisation around the pathology and their multidisciplinary organisation), were seriously threatened by other medical approaches. They also recalled that the initial missions of Cancer Centres were not only to treat patients but also to have an influence on general cancer care : their proposal to produce medical guidelines and to develop research were presented as a way to regain scientific legitimacy and leadership.

The insistence on multi-disciplinarity, on collegiality and on a pathology-centred approach to cancer care was capitalising on the specific competence and skills [START_REF] Selznick | Leadership in administration[END_REF] of Cancer Centres, which was their historical identity. Indeed, this identity was used as a basis and as a tool of mobilisation in favour of change. And this model did in fact provide peculiar resources to push along other important dimensions of the reform. For instance, thanks to their multidisciplinary organisation, physicians in Cancer Centres had grown accustomed to showing their patients' records to each other and to discuss with each other the best therapeutic strategy, it transpired that they were ready to understand the utility of guidelines as a co-ordinating mechanism. These meetings would also prove to be a resource to enrol patients in NFCC's trials: since many cases were collegially discussed, medical oncologists had the opportunity to screen patients more easily and remind their colleagues that these patients could be enrolled in federal trials.

Federal resources

Reformers capitalised on other existing collective patterns to implement their program. Not to mention that the unified classification of tumours which was formalised years ago was a sine qua non condition to develop clinical trials and guidelines. Reformers also involved physicians who had been active in inter-centre scientific groups. These groups had conducted smaller clinical trials and had organised "open" collective reflection on some scientific topics since the 1970s. For instance, at the beginning of the guidelines' project, 26 out of 28 federal task groups were animated by a physician who had previous responsibilities in these intercentre groups. These groups constituted a valuable resource for this project since physicians who had participated in them had learnt how to collaborate with each other and were interested in harmonising practices. Furthermore, their leaders had acquired a kind of legitimacy inside the CC's professional community. Last but not least, the traditional close relationships between CCs and the National League Against Cancer certainly facilitated that this association of patients accepted funding these federal projects.

Centralisation, informal hierarchy and "medical oncologisation"

A more centralised and unified organisational field Traditionally, the federation was an employers' organisation with weak prerogatives. While there were of course differences in the influence of individual directors, the organisational model seemed more like a confederation of highly autonomous centres than like a unified organisation. The situation today is quite different. By the end of the 1990s, the National Federation has grown bigger, stronger and more influent: 1) it has gained a significant increase in resources (see Annex 1), 2) its legitimacy to initiate and lead collective projects for the 20 Cancer Centres has been acknowledged and enacted, and 3) strategic orientations of Cancer Centres are congruent with the federal reform. The Federation also defines the clinical trials which are to be developed, decides when a trial needs to be ended earlier than expected because of too small accrual, while also monitoring these trials -thus intervening in medical practices.

Furthermore, the Federation is more influential. Cancer Centres' strategic plans are very similar to each other and congruent with the reform. Each strategic plan emphasises that the Cancer Centre intends henceforth to be a centre for assistance and expertise for other healthcare organisations in their particular region rather than their competitor. And the development of research activities and the improvement of the quality of care through treatment protocols and patients' participation are identified as priorities in every Cancer Centre, even in the centres which had been focused previously only on care.

Nowadays, this trend toward centralisation continues with the creation of a national cancer institute in 2004. This new public agency intends to regulate the organisation of cancer care and research. It is the result of a longstanding initiative by NFCC's reformers, which allied with some others opinion leaders who worked in Teaching Hospitals. It therefore comes as no surprise if this institute carries on former major projects of the NFCC and intends to generalise the creation of multidisciplinary staffs. Furthermore, it is now presided by the former director of the NFCC's project for clinical research. This represents an adoption of CCs' medical model which they have defended and promoted all along the reform.

A regional reorganisation of cancer care

At the regional level, CCs' physicians play a leading role in the creation of co-operative networks for the elaboration and implementation of regional treatment protocols adapted to the characteristics and resources of the local healthcare system in order to be relevant and accessible for everyday practice6 . Local networks for the implementation of guidelines became the organisational infra-structure for exchange around difficult cases and the de facto grading of regional cancer-care: the "normal" cases for small non-profit and for-profit hospitals, the difficult cases for the Cancer Centres and the Teaching Hospital(s). 55% of CCs' patients are recruited outside their nearby territory, reflecting their role of support for the other organisations. Even when they do not treat patients, CCs' physicians do participate very often in the treatment decisions. In 2000, Cancer Centres' physicians were invited to 200 hospitals to discuss medical cases of local patients. This shows an increase in comparison to the 1980s (see above). Furthermore, between 1995 and 2000, the number of medical records which have been seen by CCs' physicians during these meetings has grown up from 33.000 to 50.000.

Evolution of physicians' work and intra-professional legitimacy

Decision in the medical field is becoming more and more a collective process. Not only are physicians expected to conform to guidelines, but they have to participate in multidisciplinary staffs where therapeutic decisions for their own patients are collegially discussed. Even when no available guideline fits with specific cases, physicians have to justify therapeutic decisions using scientific references (and especially the results of clinical trials). This is not a "pure" de-professionalisation process, since:

• only physicians participate (for example, patients and economists are excluded from guidelines' elaboration); • they can refuse to participate in clinical trials;

• medical audits are very rare and do not lead to sanctions (so far).

This has more to do with a "lateral control regime" (Laszega, 2000), consisting in increasing informal and horizontal control among peers. However, one may notice that medical oncologists are becoming more and more central in the organisation of cancer care in France, although at the same time nobody denies that surgery remains the most efficient treatment for most cancers. This will require further (comparative) analyses but one may argue that this is much due to the normalisation process. First, medical oncologists are the most involved specialists in clinical research. Secondly, and consequently, since specific therapeutic decisions and guidelines have to be grounded on the results of clinical research, medical oncologists are more likely to intervene in, and master, processes of collective deliberation. Thirdly, the development of multidisciplinary staffs allows medical oncologist to intervene earlier in patients' trajectories, whereas they were more dependent on surgeons' decisions before.

Conclusion: some perspectives of comparison

It cannot be denied that institutional conditions favoured the emergence and the relative easy acceptance of this reform by other CCs' actors. First, as we wrote above, the emphasis on the development of clinical research in Cancer Centres as well as the commitment to producing guidelines corresponds to a major trend in modern medicine [START_REF] Marks | The Progress of Experiment: Science and Therapeutic Reform in the United States, 1900-1990[END_REF][START_REF] Timmermans | The gold standard[END_REF][START_REF] Daly | Evidence-Based Medicine and the Search for a Science of Clinical Care[END_REF]. Secondly, it corresponds to the rise of medical oncology as a speciality strongly linked with clinical research [START_REF] Löwy | Between Bench and Bedside[END_REF][START_REF] Cambrosio | Rationalisation et médecine des preuves en oncologie : quelques remarques à propos des pratiques biomédicales (Commentaire)[END_REF]. For instance, in the middle of the 1980s, medical oncologists became the dominant speciality at the NFCC's board (see Annex 2) -even if their colleagues had a far smaller experience in (international) clinical research than the reformers. Thirdly, it was in line with growing considerations for quality by regulation bodies, which facilitated their (financial and political) support.

International comparisons should allow us to weigh the impact of these broad factors on the social phenomena that we described. To what extent can we observe convergent changes on an international scale? Comparisons should address the following dimensions:

1) categories of actors and organisations who (possibly) gave the initial impulse to changes in the organisation of cancer care; 2) initial content of the projects for change and reasons why they are thus designed; 3) processes of implementation; 4) evolution in cancer care.

One may first hypothesise that the relative development of cancer treatment modalities in different countries [START_REF] Pickstone | Contested Cumulations: Configurations of Cancer Treatments through the Twentieth Century[END_REF] impacts the change process. In the same vein, can the relative development of cancer hospitals in different countries and their characteristics be related to organisational changes? Indeed, we saw that some of the historical characteristics of cancer centres seemed to facilitate the emergence and the diffusion of the reform inside CCs. To what extent is this true? Other differences may depend on the organisation and funding of the respective healthcare systems. In France, on the one hand, the competition between Teaching Hospitals and Cancer Centres and, on the other hand, the informal hierarchical relationships between hospitals may explain the dynamics of the reform. For instance, French oncology networks should not be confused with American HMO or English trusts. These peculiarities may impact change processes in the different countries.

Sciences Po, Centre de Sociologie des Organisations ; CNRS. p.castel@cso.cnrs.fr

I am well aware that every topic deserves further developments and, most of all, that the logical link between the three should be explicated.

Two of them, who later were to assume the leadership of national scientific projects, had been research fellows at the Fred Hutchinson Cancer Research in Seattle. This institution specialised in haematology and in particular in bone marrow transplantation which was a new technique intended to allow the prescription of higher doses of chemotherapy to patients. When they came back to France, they both became director of a bone marrow transplant service in their respective centres, founded the French association of bone marrow transplantation and became advisers for the Ministry of Health in this area. Later on, they spent some months in the NCI laboratories of Prof. Steven Rosenberg, who was a much reputed specialist of Interleukin 2.

In France, oncologists are not the only physicians allowed to prescribe chemotherapy.

This entails two activities. First, it means initiating and monitoring the discussion process at the regional level through which federal review monographs are transformed into decision algorithms and into specific recommendations of one among several scientifically appropriate treatments.

ANNEX 1 Evolution of the budget of the Federation

 1991 1992 1993 1994 1995 1996 1997 1998 1999