M D Griffith

D Lo Jacono

J S Heridan

J Leontini

The Flow Around Stationary and Elastically-Mounted Circular Cylinders in Tandem and Staggered Arrangements

A numerical study is presented of the flow around two circular cylinders in tandem and staggered arrangements in a freestream, examining the fluid forces and vortex-shedding behaviour, as well as the oscillation of both cylinders when allowed to move and vibrate in response to the flow. The streamwise distance between the cylinder centres is 1.5 diameters, while the crossstream offset is varied from 0.0 to 5.0. The Reynolds number, based on cylinder diameter, D, and freestream velocity, U, is 200. Reduced velocity, U * = U f N D , where f N is the spring natural frequency, is varied from 0.0 to 14.0. Results are obtained using a sharp-interface immersed boundary finitedifference method. For the stationary cylinders a range of behaviours are observed over the cylinder offset range, including a difference in primary vortex-shedding frequency when the crossstream offset is greater than 1.5D. For the elasticmounting, in contrast to existing results in the literature, three modes of vortex-shedding and oscillation are observed over the U * range for the tandem arrangement. These modes are distinct in the phase difference between the front and rear cylinder oscillation, as well as the number of vortices shed from each cylinder.

Introduction

The vibration of an elastically-mounted circular cylinder in a flow is a canonical problem in fluid-structure interaction and a large volume of literature exists on the subject [START_REF] Leontini | The beginning of branching behaviour of vortex-induced vibration two-dimensional flow[END_REF][START_REF] Thompson | Threedimensional instabilities in the wake of a circular cylinder[END_REF][START_REF] Singh | Vortex-induced oscillations at low Reynolds numbers: Hysteresis and vortex-shedding modes[END_REF][START_REF] Williamson | Vortex-induced vibrations[END_REF]. Large amplitude oscillations occur when the vortex-shedding frequency matches with the cylinder oscillation frequency. This lock-in regime occurs over a range of natural frequencies for the elastic cylinder mounting [START_REF] Williamson | Vortex formation in the wake of an oscillating cylinder[END_REF]. The behaviour of the system is useful as a fundamental case for more irregular or complex geometries. For example, in applications where the potential for high-amplitude oscillation is critical, such as in the design of oil drilling risers and other marine structures. Similarly, highamplitude oscillation may be beneficial for the extraction of energy from VIV for power generation.

One such geometrical complexity to be considered is the presence of another, or several, cylinders in the vicinity of the single, isolated cylinder. When two stationary cylinders in crossflow are placed close enough together, their wakes begin to interfere. Figure 1 depicts the problem setup. The streamwise distance between the centres of the cylinders is defined as L and the cross-stream distance as T . For two cylinders, there are three arrangements possible: tandem, side-by-side and staggered. Tandem cylinders are arranged inline to the flow (L ≥ D, T = 0.0). Side-by-side cylinders are side-by-side with respect to the oncoming flow (L = 0.0, T ≥ D). For staggered cylinders, there is both a streamwise and cross-stream offset (L > 0, T > 0, also often defined in terms of a pitch ratio, P/D, where P is the distance between the cylinders, and an incidence angle, α. For stationary cylinders, a range of regime definitions have been proposed, depending on the proximity and interactions of the wakes of each cylinder [START_REF] Sumner | Two circular cylinders in cross-flow: A review[END_REF]. Tong, Cheng and Zhao [START_REF] Tong | Numerical simulations of steady flow past two cylinders in staggered arrangements[END_REF] defined four flow classifications: S-I, where only one vortex street exists with vortices shed from the downstream cylinder; S-II, again only one vortex street, but vortices shed from both cylinders; T-I, two vortex streets exist but with strong interactions; and T-II, two vortex streets but with weak interactions. For the S-I and S-II classifications, one cylinder sits in the wake of the other and, if the downstream cylinder is close enough, no vortices are able to shed from the upstream.

√ L 2 + T 2 ≥ D). Staggered
For elastically-mounted cylinders, Borazjani and Sotiropoulos [START_REF] Borazjani | Vortex-induced vibrations of two cylinders in tandem arrangement in the proximitywake interference region[END_REF] investigated the tandem cylinder arrangement, with an inline offset of L = 1.5D. The cylinders were found to oscillate at greater amplitudes than a single, isolated cylinder and also to experience greater lift force. Other studies have examined similar problem configurations: with two rigidly-coupled cylinders in tandem and side-by-side arrangement [START_REF] Zhao | Flow induced vibration of two rigidly coupled circular cylinders in tandem and side-by-side arrangements at a low Reynolds number of 150[END_REF]; with side-by-side cylinders with two degrees of freedom [START_REF] Huera-Huarte | Flow-induced vibrations of a side-by-side arrangement of two flexible circular cylinders[END_REF]; and with tandem cylinders with the upstream cylinder stationary and the downstream oscillating, [START_REF] Assi | On the wake-induced vibration of tandem circular cylinders: the vortex interaction excitation mechanism[END_REF].

The current study examines the tandem arrangement, with L = 1.5, as a starting point, over a range of reduced velocities. The work is then extended to the staggered arrangement by increasing the cross-stream offset, T .

Problem Definition

The geometry has been defined in figure 1. The two cylinders are aligned such that their centres are a distance L/D apart in the streamwise direction and T /D apart in the cross-stream direc-tion. The cylinders are arranged equidistant around the origin. In the results presented here, the upstream cylinder is positioned at y ≥ 0 and the downstream cylinder at y ≤ 0. The Reynolds number is defined as

Re = UD ν , ( 1
)
where U is the fluid freestream velocity, D the cylinder diameter and ν the kinematic viscosity. The ratio of the mass of each cylinder to the mass of the equivalent volume of fluid is defined as m * = 2.546, as used in Borazjani and Sotiropoulos [START_REF] Borazjani | Vortex-induced vibrations of two cylinders in tandem arrangement in the proximitywake interference region[END_REF] in their of study tandem vibrating cylinders. Each cylinder is elastically-mounted; the natural frequency of the springs is given as

f N = k/M/2π,
where k is the spring stiffness and M is the mass of the cylinder. A non-dimensional reduced velocity is defined such that U * = U/D f N . There is no damping added to the system. The y-position of a cylinder is defined as Y and the oscillation of each cylinder is defined by the equation:

M Ÿ + (2π f N ) 2 Y = F y , (2)
where Ÿ is the acceleration of the cylinder perpendicular to the freestream and F y is the lift force on the cylinder. The position of the cylinders can be described as:

Y 1 = Y 1 +Y 1 + T /2, (3)
Y 2 = Y 2 +Y 2 -T /2, ( 4
)
where Y is the mean position with respect to the cylinder starting point, Y is the oscillatory component of the cylinder motion and the subscripts 1 and 2 denote the front and rear cylinders, respectively.

Method

Simulations were carried out using a sharp-interface immersed boundary method to represent the cylinders on an underlying Cartesian grid, on which the flow is simulated by solving the incompressible Navier-Stokes equations using a finite-difference scheme [START_REF] Mittal | A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries[END_REF]. The vibration of each cylinder is found by solving equation 2 using a Newmark-β method. The underlying Cartesian grid was designed with a regular grid spacing around the origin, over a box-region measuring 4D in each direction. Grid spacings were then increased linearly to the domain boundaries. The inlet and lateral domain boundaries were located 15D from the origin, while the outlet boundary was located 40D downstream. Twice as many grid points were used in the streamwise direction than in the transverse direction; the number of grid points in each direction is restricted to the powers of 2, thereby leading to a grid size of 2 N+1 × 2 N , where N is a whole number. We denote each grid as MN, such that M10 corresponds to a grid size of 2048 × 1024 nodes.

A test of the sensitivity of the results to grid resolution was carried out. For the tandem cylinder arrangement of offset T = 0.0, results were obtained over the U * range for grids M8, M9, M10 and M11. For the grid M9, the results returned for A * MAX are within 1% of the result returned by the higher resolution M10 grid, while the root-mean-square value of the lift coefficient is within 2%. For all the results presented here for T ≤ 3.5, grid M9 was used. For the upper range of cylinder offset, T > 3.5, the box-region of regular grid spacing around the origin was increased to 8D in the y-direction to encompass the wider wake width and cylinder vibration that these cylinder arrangements produce. For this grid the number of total grid points in the y-direction was doubled for the M9 grid, maintaining the same transverse domain boundary distance, but using the extra grid points to increase the size of the box-region of regular grid spacing. Simulations run for values of T < 3.5 using both

C D 1 C D 2 C L 1 C L 2 C D ,C L T ∆ f
Figure 2: For stationary cylinders and L = 1.5, the variation with cross-stream offset, T , of the mean values of the drag and lift coefficients for the front and rear cylinders, denoted by subscripts 1 and 2, respectively. On the right axis, in solid squares ( ), the variation of the difference in the primary frequency of the oscillation of the two cylinders. The dotted lines refer to the mean drag and lift coefficients returned by a single cylinder, with the drag coefficient corrected by a ratio of the squares of the blockage ratios of the single and the double cylinder simulations, assuming a side-by-side arrangement.

grids showed negligible differences in oscillation amplitude and mean force coefficient.

Results

Stationary cylinders

The first set of results for stationary cylinders represents a limiting case of equation 2 where U * = 0, producing no flowinduced vibration. For inline cylinders, the current results are consistent with results presented in the literature for mean drag coefficient [START_REF] Tong | Numerical simulations of steady flow past two cylinders in staggered arrangements[END_REF]. Introducing a cross-stream offset, figure 2 plots the variation of the mean values of the lift and drag coefficients for both cylinders. For the inline cylinders, most of the drag is experienced by the front cylinder; the rear cylinder experiences a negative mean drag. The negative mean drag on the rear cylinder only occurs for offsets T < 0.2. The drag increases almost linearly up to offset T = 1.0, from which point it exceeds the drag on the front cylinder. The mean lift force is zero for both cylinders for the symmetric tandem configuration. With increasing offset, the mean lift becomes positive for the rear cylinder and negative for the front, indicating a mean force on the cylinders away from the centreline . Around T = 1.2, the drag on the front cylinder becomes positive again. Further increasing the offset from this value, the two values of C L slowly converge.

Beyond an offset of T = 1.5, a difference in the primary frequency of vortex-shedding, ∆ f , appears (calculated from frequency analysis of the signal for the coefficient of lift) and is associated with a loss of order in the vortex shedding. The primary frequency difference decreases with increasing offset, manifesting as a beating (of increasing period) in the lift signal of each cylinder. For T > 2.3, the vortex-shedding is ordered, with the values for C D and ∆ f converging to their values for the single cylinder. Note, that the value of the drag coefficient for the single cylinder has been corrected in an attempt to account for the difference in effective blockage ratio between one or two cylinders presenting fully to the freestream flow. Although the cylinders are at different streamwise positions and that strictly the blockage ratio for the two cylinder simulations is not different to that of a single cylinder, the actual effect on the cylinders will depend on the nature of the flow in the gap between the cylinders, which in turn depends on the fluid dynamics near the cylinders. From figure 2, the correction of the mean drag coefficient for the single cylinder empirically seems appropriate given the convergence of the drag coefficients as T → 5. Although only tests for offsets of T > 5.0 could confirm this.

Vibrating Cylinders, T = 0.0 Borazjani and Sotiropoulos [START_REF] Borazjani | Vortex-induced vibrations of two cylinders in tandem arrangement in the proximitywake interference region[END_REF] present results for T = 0.0 and L = 1.5 and for the reduced velocity range 3 ≤ U * ≤ 14. The same parameter space has been simulated using our method, giving the results in figure 3, showing maximum displacement, A * MAX , for each cylinder for comparison. We calculate A * MAX as the mean of the greatest 10% of local peaks of Y . Across the three parameters presented there are differences with the results from the literature [START_REF] Borazjani | Vortex-induced vibrations of two cylinders in tandem arrangement in the proximitywake interference region[END_REF]. For the single isolated cylinder, the values of A * MAX for the range 4 ≤ U * ≤ 7, for the current study are greater than those reported previously. For the tandem arrangement, the oscillation amplitude of the front cylinder is greater, while that of the rear cylinder is reduced slightly for 5 ≤ U * ≤ 7. Similarly for the lift and drag, some variation in the results can be seen (not shown here).

The comparison shows the variations with U * of oscillation amplitude, A * MAX , and the root-mean-square coefficients of lift and drag (not plotted) are similar between the two studies, but there are significant variations between the two studies for some values of U * . We put these differences down principally to the different domain sizes used in each study, as well as differences in grid resolution. Borazjani and Sotiropoulos [START_REF] Borazjani | Vortex-induced vibrations of two cylinders in tandem arrangement in the proximitywake interference region[END_REF] used an inlet length and lateral clearance of 8D and an outlet length of 24D. Therefore, there is a significant difference in blockage ratio between the two studies: for a single cylinder, 6.25% against 3.33% for the current study. In an attempt to account for this difference, we ran the results for a single, isolated cylinder again, but with a domain size reduced to that used in [START_REF] Borazjani | Vortex-induced vibrations of two cylinders in tandem arrangement in the proximitywake interference region[END_REF]. This produced only marginal differences in the returned results for A * MAX . There is also a significant difference in timestep used between the two studies; δt = 0.02 in [START_REF] Borazjani | Vortex-induced vibrations of two cylinders in tandem arrangement in the proximitywake interference region[END_REF] and δt = 0.004 in the current. This difference is mostly due to the higher grid resolution used in the current study. To examine the effect of timestep, we have also run both grid domain sizes using timesteps of δt = 0.004 and 0.002, to examine any sensitivity to temporal resolution. We found no significant effect resulting from this change in timestep.

For zero cross-stream offset, T = 0.0, Borazjani and Sotiropoulos [START_REF] Borazjani | Vortex-induced vibrations of two cylinders in tandem arrangement in the proximitywake interference region[END_REF] defined two flow states which we summarize here. State 1 refers to those cases where the front cylinder oscillated more than the rear, for U * ≤ 4.0, and state 2, where the rear cylinder oscillated more, for U * ≥ 7.0. They classed the cases in between these two ranges as critical cases in the transition between the two states. Using the vortex-shedding pattern classification of Williams and Roshko [START_REF] Williamson | Vortex formation in the wake of an oscillating cylinder[END_REF], state 1 consists of a 2S vortexshedding pattern, where a single vortex of each sign is shed from the rear cylinder, with the rear cylinder enveloped by shear layers beginning at the front cylinder. State 2 consists of a 2P vortex-shedding pattern, with vortices of each sign shed from both cylinders with complex vortex interaction and merging in the near-wake. The critical case for U * = 5.0 shows similarity to state 2, but does not show a 2P ordering, with complex interactions resulting from fast moving vortex pairs merging with earlier-shed vortices, producing a less ordered wake.

We propose that the two states described in the literature [START_REF] Borazjani | Vortex-induced vibrations of two cylinders in tandem arrangement in the proximitywake interference region[END_REF] are better described as vortex-shedding modes, and that the critical case (U * = 5.0 and 6.0) is in fact its own distinct vortexshedding mode, rather than a transition case. Mode 1 refers to those cases where the rear cylinder oscillation is small, U * ≤ 4.0, and is synonymous with the state 1. Mode 2 is present for U * = 5.0 and 6.0, while mode 3, (synonymous with state 2) exhibits large rear cylinder oscillation and is present for U * ≥ 7.0. Plots of vorticity contours throughout the oscillation for representative cases of each of the three modes are shown in figure 4. For mode 1, shown for U * = 4.0, the rear cylinder sits in the wake of the front throughout the oscillation cycle. The oscillation of the rear cylinder is comparatively small and lags the oscillation of the front cylinder by γ = 4π/5, or 0.4 of an oscillation cycle. Vorticity that forms on the front cylinder merges with vorticity of the same sign on the rear cylinder. Vortices are shed only from the rear cylinder. One vortex of each sign is shed each cycle, forming a regular vortex street. Given the vortices shed from the rear cylinder, we denote this mode as 2S R . The mode exists for cases of U * = 3.0 and U * = 4.0, with simulations requiring long run times (750U * ) to reach a statistically-converged solution.

Mode 2 exists for U * = 5.0 and 6.0. For these cases, the rear cylinder oscillates more than it does for mode 1, coming out fully from behind the front cylinder. The cylinders oscillate out of phase, γ = π. In contrast to mode 1, vortices do not form on the rear cylinder, instead only a small amount of vorticity is deposited in a trail. Instead a vortex pair forms in the periodically larger space now available between the cylinders. As this pair forms it is cut off by the rear cylinder, its orientation rolling before meeting freestream fluid and convecting at high velocity downstream. The vortex pairs overtake earlier pairs, merge and form an irregular vortex street. Because of the two vortex pairs formed each cycle, which mostly form on the front cylinder, we denote this mode 2P F , Mode 3 exists for U * ≥ 7.0 and is characterised by large oscillation of the rear cylinder, with the oscillation of the rear cylinder lagging the front cylinder by γ ≈ π/2. Similar to mode 2, the rear cylinder traverses the wake of the front, but instead of a vortex pair forming in the gap, the rear cylinder effectively cuts through the shear layers of the front cylinder (the second to third images of figure 4). In a complex interaction, negative and positive vorticity from the front cylinder is subsumed by the vortex formation on the rear cylinder each half cycle. Each cycle, this vortex mingling creates two pairs of unequal strength vortices. To account for the complex formation of these vortex pairs, the mode is denoted as a 2P. These three vortex-shedding modes cover the T = 0.0 parameter space.

Conclusions

Results for the flow around tandem and staggered cylinder pair configurations for stationary cylinders have been presented, exhibiting a variation with transverse offset of the the lift and drag coefficients on the cylinders and of the difference of the primary frequency of vortex-shedding. The results are consistent with published results in the literature. The flow around and vibration of elastically-mounted cylinders for the tandem arrangement has also been presented, with three distinct modes of oscillation and vortex-shedding identified across the range of U * and characterized by differences in phase lag between the cylinder oscillations and in the number of vortices shed from each cylinder. Future work will extend into the cross-stream offset parameter space for the elastically-mounted cylinders.

Figure 1 :

 1 Figure 1: A sketch of the setup.

Figure 3 :

 3 Figure 3: For T = 0.0 and L = 1.5, the variation with U * of the maximum displacement of the each cylinder. Solid symbols represent results from the current study, while hollow ones are from Borazjani and Sotiropoulos [2].

mode 1 ,Figure 4 :

 14 Figure 4: For the tandem cylinder arrangement (T = 0), vorticity contours for three cases, U * = 4.0, 5.0 and 8.0, describing the three vortex-shedding modes, 2S R , 2P F and 2P. Each series of images depicts an entire oscillation cycle, beginning with the front cylinder at its maximum displacement. Contours vary in the range -1 ≤ ω z ≤ 1.

Acknowledgements

This work was financially supported by the Australian Research Council (ARC) through Discovery Projects grant DP150103177. Computational resources provided by the National Computational Infrastructure (NCI) under project IZ4 through the National Computational Infrastructure Merit Allocation Scheme (NCMAS), and by Swinburne University of Technology's Centre for Astrophysics and Supercomputing.


A Sareen

J Zhao

D Lo Jacono

J Sheridan

K Hourigan

M C Thompson

Vortex-Induced Vibration of a Transversely Rotating Sphere

).

Introduction

Vortex-induced vibration (VIV) of structures can occur in a variety of engineering situations, such as bridges, transmission lines, offshore structures, heat exchangers, tethered structures, pipelines, and other hydrodynamic and hydroacoustic applications. This led to several comprehensive studies on VIV in the past (see [START_REF] Sarpkaya | Vortex-Induced Oscillations[END_REF] and [START_REF] Parkinson | Phenomena and modelling of flow-induced vibrations of bluff bodies[END_REF]). Since such vibrations impact on the fatigue life of structures, they can lead to structural failures and are an important source of fatigue damage of offshore oil exploration and production risers. Numerous studies have focused on suppressing such flow-induced vibrations, especially for cylinders. However, there are no such studies for basic symmetrical three-dimensional bodies like spheres. In spite of its ubiquitous practical significance, there are few studies on the VIV response of a sphere and its suppression. The question that arises is, how can the VIV of such a simple 3D geometry be suppressed? Previous numerical studies on the effect of rotation on rigidly mounted rotating spheres at low Reynolds numbers (Re ≤ 300) ( [START_REF] Poon | Flow past a transversely rotating sphere at Reynolds numbers above the laminar regime[END_REF], [START_REF] Kim | Laminar flow past a sphere rotating in the transverse direction[END_REF]) revealed suppression of the vortex shedding for a certain range of spin ratios. So can the structural vibrations of a sphere be suppressed by an imposed rotation once the sphere is free to oscillate? The previous investigations on the VIV of spheres by [START_REF] Govardhan | Vortexinduced vibrations of a sphere[END_REF] and [START_REF] Jauvtis | Multiple Modes of Vortex-Induced Vibration of a Sphere[END_REF], revealed that the sphere exhibits two modes of vibration, namely, mode I and mode II when the oscillation frequency is of the order of the static body vortex shedding. They showed that the vortex phase φ v (phase difference between the vortex force and the body displacement) gradually changes from ∼ 50 degrees to ∼ 150 degrees from mode I to mode II. But it is still unknown, how the vibration response of the sphere changes when a transverse rotation is imposed. This is the first study reporting the effect of an imposed transverse rotation on the VIV response of a sphere. In the current study, an elastically mounted sphere free to oscillate in the transverse direction is considered over a wide range of parameter space of reduced velocities and rotational rates. The Reynolds number (based on sphere diameter and flow velocity) for the current study varies from 5000 to 30,000.

In this study, we seek to understand the following fundamental questions: How does the imposed transverse rotation affect the VIV response of the sphere? Does it suppress the vortex shedding at this high Reynolds number? Does the sphere continue to vibrate in the absence of vortex shedding?

In the first section, we will elaborate on the experimental methods used in the current study followed by a section on Results and Discussions in which, the findings from the current study are presented and discussed in detail.

Experimental Details

The experiments were conducted in the recirculating freesurface water channel of the Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Monash University, Australia. The test section of the water channel has dimensions of 600mm in width, 800mm in depth, and 400mm in length.

The free-stream velocity in the present experiments was varied continuously in a range of 0.05 ≤ U ≤ 0.45m/s, corresponding to the pump frequency range of 5 -50Hz. The free-stream turbulence levels were less than 1% for the current experiments.

Mass ratio The schematic for the experimental setup is shown in figure 2.

m * m/(πρD 3 /6) Amplitude ratios A * y , A * x A x /D, A y /D Normalised velocity U * U/( f n D) Scaled normalised velocity U * s (U * / f * )S Reynolds number Re UD/µ Strouhal number S f vo D/U Transverse frequency ratio f * f / f n Damping ratio ζ c/2 k(m + m A ) Rotation ratio α Dω/2U
An air-bearing system with a low damping ratio was used to provide low-friction motion in the transverse direction. More details of the hydroelastic facility can be found in [START_REF] Zhao | Flow-Induced Vibration of Circular and Square Cylinders with Low Mass and Damping[END_REF]. The body displacement was measured using a non-contact (magnetostrictive) linear variable differential transformer (LVDT). The fluctuating lift and drag forces were measured by a six-axis force sensor (ATI mini40/IP68), which was attached at the upper end of the rig. The sphere was driven at various rotational speeds using a miniature low-voltage LV172 Parker stepper motor. For each data set, the raw analog voltages were acquired at 100Hz for 300 seconds at each flow velocity, and were converted to digital signals using a differential DAQ board system. The data sampling and recording were controlled via customised LabVIEW 8.5 VI programs, while the data processing and analysis were performed using MATLAB codes.

The spherical model used in the present study was a precision solid ball of diameter 80mm manufactured from acrylic plastic. The diameter of the supporting rod was approximately 27 times smaller than the sphere. The rotating driving shaft was covered with a non-rotating cylindrical shroud 6.35mm in diameter so as to avoid any interference from the rotating shaft.

The top surface of the sphere was one diameter away from the free-surface in order to avoid any free surface effects. [START_REF] Mirauda | Dynamic Response of a Sphere Immersed in a Shallow Water Flow[END_REF] reported that the free surface effect only kicks in when the immersed length is less than 0.5 times the sphere diameter for a tethered sphere. Free decay tests in water and air were performed to obtain the natural frequency and damping ratio of the system before each series of experiments.

Results and Discussions

Validation experiment: VIV of a non-rotating sphere Figure 3 shows the classic one-degree of freedom vibration response of a sphere compared to the one reported by [START_REF] Govardhan | Vortexinduced vibrations of a sphere[END_REF]. The mass ratio and the damping ratio for the current experiment were 7.8 and 0.004 compared to 7 and 0.004, respectively, by [START_REF] Govardhan | Vortexinduced vibrations of a sphere[END_REF]. In figure 3, the non-dimensional amplitude of oscillations (defined as A * = √ 2A rms /D) is plotted against the scaled U * , which is defined as U * S = (U * / f * )S, where S is the Strouhal number for the sphere. The lock-in starts at U * = 4 -5 for the sphere, which corresponds to a U * s of 0.7 -0.875. It can be noted that the vibration response gradually progresses to mode II from mode I, as opposed to the case of cylinders, where a sudden jump is observed between the vibration branches. In the case of cylinders, the sudden jump in ampli-Figure 3: Comparison of the amplitude response obtained in the current study to that of [START_REF] Govardhan | Vortexinduced vibrations of a sphere[END_REF]. The mass ratio for the current study is 7.8 compared to a mass ratio of 7 in their study. The damping ratio was same in both the studies (ζ = 0.004).

Figure 4: The variation of the total and vortex phase with the reduced velocity compared to the data by [START_REF] Govardhan | Vortexinduced vibrations of a sphere[END_REF]. The mass ratio for the current experiment was 12 compared to 31.1 in their study.

tudes is associated with a sudden jump in the total phase difference (phase difference between the total fluid force in the transverse direction to the body displacement). However, in spheres, the vortex phase gradually changes from ∼ 50 degrees to ∼ 160 degrees, as shown in figure 4. Figure 4 shows the variation of the total and vortex phase difference with the reduced velocity in comparison to the ones reported by [START_REF] Govardhan | Vortexinduced vibrations of a sphere[END_REF] for somewhat different experimental conditions.

For a very light tethered body, a desynchronised region can be observed between the two modes [START_REF] Govardhan | Vortexinduced vibrations of a sphere[END_REF]. For elastically mounted bodies of higher mass, the transition is evident only as a dip in the amplitude response. Figure 5 shows the variation of the nondimensional frequency f * = f / f n (the ratio of the dominant oscillation frequency to the natural frequency in the water) with the reduced velocity. During lock-in (U * ∼ 4), the oscillation frequency stays close to the natural frequency of the system.

VIV of a rotating sphere

A non-dimensional rotation ratio α is the main parameter characterising the flow past rotating bluff bodies. It is defined as α = Dω/2U, where ω is the rotation rate of the sphere in radians per second. It signifies how fast the surface of the sphere is spinning relative to the incoming flow velocity. For investigating the effect of α on the vibration response of the sphere, U * was varied from 3 to 14 in increments of 0.5. The response was studied for 5 rotation ratios α = 0.0, 0.2, 0.3, 0.4 and 0.5. For this set of experiments, the mass ratio of the system was 14, the natural frequency in water was 0.28Hz, and the damping ratio was 0.0059.

In figure 6, we see a classic VIV response for α = 0, when the sphere is not rotating. When α is gradually increased from 0 to 0.3, the response shape looks similar to the non-rotating case, but the amplitude of vibration decreases. For α ≥ 0.4, we see a drastic drop in the response. For all these cases, the amplitude suddenly drops after reaching the maximum amplitude of oscillations. As the α is increased, the synchronisation region (parameter space for which the resonance is observed) becomes narrower. The magnitude of peak oscillation also decreases consistently with the rotation up to α = 0.5.

The peak amplitude occurs for a smaller U * with increasing α. The dominant frequency of oscillations stayed close to the natural frequency of the system for all the α values as shown in figure 7. This indicates that the rotation does not completely suppress the vortex shedding and the sphere remains locked-in for all the cases. Figure 8 shows how the mean displacement of the sphere varies with increasing rotation. The mean displacement initially is zero for the non-rotating case but increases with the α, which is an effect of the Magnus force acting on the sphere in the direction of rotation. Vorticity measurements by [START_REF] Govardhan | Vortexinduced vibrations of a sphere[END_REF] showed planar symmetric vortex loops emanating from the two sides of a non-rotating sphere undergoing VIV. The transverse rotation imposes asymmetry in the flow, causing the loops to bend towards one side due to the Magnus effect, which in consequence increases the 'lift force' in the direction of rotation. In the case of cylinders, some novel asymmetric wake patterns were observed with the transverse rotation, which led to an increase in the oscillation amplitude up to 1.9 times the diameter [START_REF] Bourguet | Flow-induced vibrations of a rotating cylinder[END_REF]. However, the flow past a sphere is three-dimensional and complex. How the transverse rotation changes the wake patterns and the forces experienced by the sphere, is currently under investigation.

Conclusions

A series of experiments was performed to investigate the effect of transverse rotation on the VIV response of an elastically mounted sphere in terms of amplitude and frequency response. The amplitude of oscillations was lowered with increasing rotation. The synchronisation regime became narrower and the peak response occurred at a lower U * compared to the non-rotating case. The frequency of oscillation remained close to the natural frequency of the system for all the cases.

Figure 1 :

 1 Figure1: Definition sketch for the cross-flow VIV of a rotating sphere (Top view). The sphere undergoes free vibrations in the transverse direction to the free-stream U ∞ in the x-direction. The sphere rotates in the clockwise direction with rotational rate ω. Here k is the spring constant, and c is the damping of the system.

Table 1 :

 1 Non-dimensional parameters. The added mass m A , is given by m A = C A m d , where m d is the displaced fluid mass and C A is the added mass coefficient (0.5 for a sphere). In the above parameters, f n is the natural frequency of the system, D = sphere diameter, k = spring constant, ρ = fluid density, U = free stream velocity, µ = viscosity, m = total oscillating mass, c = structural damping, ω = rotational speed of the sphere, f vo = non-oscillating body vortex shedding frequency, f = oscillation frequency, and A x , A y are the oscillation amplitudes in x and y directions respectively.

Figure 2 :

 2 Figure 2: Schematic of the experimental setup used for the current study.

Figure 5 :

 5 Figure 5: The frequency response corresponding to the same experimental conditions as figure 3.

Figure 6 :

 6 Figure 6: The variation of vibration amplitude response with the reduced velocity for different α.

Figure 7 :

 7 Figure 7: The variation of the non-dimensional frequency of oscillation of the sphere with the reduced velocity for different α.

Figure 8 :

 8 Figure 8: The variation of mean displacement of the sphere with the reduced velocity for different α.

Acknowledgements

AS acknowledges the support of a Monash Graduate Scholarship (MGS) and Monash International Postgraduate Research Scholarship (MIPRS). The research was supported by an Australian Research Council Discovery Project grant (DP150102879).


Delphine Trochet
email: d.trochet@institut-myologie.org

Bernard Prudhon

Lylia Mekzine

Mégane Lemaitre

Maud Beuvin

Laura Julien

Sofia Benkhelifa-Ziyyat

Mai Thao Bui

Norma Romero

Marc Bitoun
email: m.bitoun@institut-myologie.org

Benefits of therapy by Dynamin 2 mutant specific silencing are maintained with time in a mouse model of dominant centronuclear myopathy

Dominant dynamin 2 (DNM2) mutations are responsible for the autosomal dominant centronuclear myopathy (AD-CNM), a rare progressive neuromuscular disorder ranging from severe neonatal to mild adult forms. We previously demonstrated that mutant-specific RNA interference is an efficient therapeutic strategy to rescue the muscle phenotype at the onset of the symptoms in the AD-CNM Knock-in-Dnm2 R465W/+ mouse model. Our objective was to evaluate the long-term benefit of the treatment along with the disease time course. We demonstrate here that the complete rescue of the muscle phenotype is maintained for at least one year after a single injection of adeno-associated virus expressing the mutant specific shRNA. This was achieved by a maintained reduction of the mutant Dnm2 transcript. Moreover, this long-term study uncovers a pathological accumulation of DNM2 protein occurring with age in the mouse model and prevented by the treatment. Conversely, a physiological DNM2 protein decrease with age was observed in muscles from wild-type mice. Therefore, this study highlights a new potential pathophysiological mechanism linked to mutant protein accumulation and underlines the importance of DNM2 protein expression level for proper muscle function. Overall, these results strengthen the allele-specific silencing approach as a robust, safe, and efficient therapy for AD-CNM.

Introduction

Autosomal dominant centronuclear myopathy (AD-CNM, MIM #160150) is a rare congenital myopathy characterized by progressive muscle weakness, mainly affecting limb and facial muscles. Age of onset and severity of symptoms are variable ranging from severeneonatal to mild-adult forms. [START_REF] Romero | Centronuclear myopathies: A widening concept[END_REF] Histological hallmarks in muscle biopsies consist of nuclear centralization in absence of regenerative process associated with atrophy and predominance of type 1 fibers and radial arrangement of sarcoplasmic strands radiating from the central nuclei. [START_REF] Romero | Centronuclear myopathies: A widening concept[END_REF] AD-CNM results from heterozygous mutations in the DNM2 gene which encodes dynamin 2 (DNM2) [START_REF] Böhm | Mutation spectrum in the large gtpase dynamin 2, and genotype-phenotype correlation in autosomal dominant centronuclear myopathy[END_REF][START_REF] Bitoun | Mutations in dynamin 2 cause dominant centronuclear myopathy[END_REF] and to date thirty-seven mutations (mainly missense) have been identified. [START_REF] Böhm | Mutation spectrum in the large gtpase dynamin 2, and genotype-phenotype correlation in autosomal dominant centronuclear myopathy[END_REF][START_REF] Biancalana | Some DNM2 mutations cause extremely severe congenital myopathy and phenocopy myotubular myopathy[END_REF][START_REF] Casar-Borota | A novel dynamin-2 gene mutation associated with a late-onset centronuclear myopathy with necklace fibres[END_REF][START_REF] Catteruccia | Centronuclear myopathy related to dynamin 2 mutations: Clinical, morphological, muscle imaging and genetic features of an Italian cohort[END_REF][START_REF] Chen | Clinical, pathological, and genetic features of dynamin-2-related centronuclear myopathy in China[END_REF][START_REF] Fujise | Imaging-based evaluation of pathogenicity by novel DNM2 variants associated with centronuclear myopathy[END_REF][START_REF] Kierdaszuk | A novel mutation in the DNM2 gene impairs dynamin 2 localization in skeletal muscle of a patient with late onset centronuclear myopathy[END_REF][START_REF] Neto | DNM2 mutations in a cohort of sporadic patients with centronuclear myopathy[END_REF][START_REF] Reumers | Clinical, genetic, and histological features of centronuclear myopathy in the Netherlands[END_REF] Dominant DNM2 mutations also cause rare cases of Charcot-Marie-Tooth peripheral neuropathy (CMT, MIM #606482) [START_REF] Züchner | Mutations in the pleckstrin homology domain of dynamin 2 cause dominant intermediate Charcot-Marie-Tooth disease[END_REF] and hereditary spastic paraplegia. [START_REF] Sambuughin | Adult-onset autosomal dominant spastic paraplegia linked to a GTPaseeffector domain mutation of dynamin 2[END_REF] DNM2 belongs to the superfamily of large GTPases and is involved in endocytosis and intracellular vesicle trafficking through its role in deformation of biological membranes by oligomerization at the neck of membranes invagination leading to the release of vesicles. [START_REF] Antonny | Membrane fission by dynamin: what we know and what we need to know[END_REF][START_REF] Ferguson | Dynamin, a membrane-remodelling GTPase[END_REF] Furthermore, several studies have highlighted the role of DNM2 as a regulator of actin and microtubule cytoskeletons. [START_REF] Ferguson | Dynamin, a membrane-remodelling GTPase[END_REF][START_REF] Durieux | Dynamin 2 and human diseases[END_REF] DNM2 mutations in AD-CNM are thought to lead to a gain of function and/or a dominant negative effect through the potential formation of abnormal stable DNM2 oligomers associated with mis-regulated GTPase activity. [START_REF] Kenniston | Dynamin GTPase regulation is altered by PH domain mutations found in centronuclear myopathy patients[END_REF][START_REF] Wang | Dynamin 2 mutants linked to centronuclear myopathies form abnormally stable polymers[END_REF] In addition, absence of haploinsufficiency in AD-CNM is supported by data from patients and absence of phenotype developed by heterozygous knockout mice expressing 50% Dnm2. [START_REF] Cowling | Reducing dynamin 2 expression rescues X-linked centronuclear myopathy[END_REF][START_REF] Ferguson | Coordinated Actions of Actin and BAR Proteins Upstream of Dynamin at Endocytic Clathrin-Coated Pits[END_REF] Consequently, AD-CNM fulfils all the criteria for the development of allele-specific silencing therapy by RNA interference (RNAi) devoted to silence the mutated mRNA without affecting the normal transcript. [START_REF] Trochet | Therapy for Dominant Inherited Diseases by Allele-Specific RNA Interference: Successes and Pitfalls[END_REF] Indeed, we have established the proof-of-concept of allele-specific RNA silencing therapy in a knock-in mouse model of DNM2-linked CNM (KI-Dnm2 R465W/+ ) and patient-derived cells. [START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] The KI-Dnm2 R465W/+ mouse model (thereafter called KI-Dnm2 R465W ) harbors the most frequent DNM2-CNM mutation (30% of AD-CNM patients) and progressively develops features of the human disease including impairment of force generation, muscle atrophy and morphological abnormalities of the muscle fibers. [START_REF] Durieux | A centronuclear myopathydynamin 2 mutation impairs skeletal muscle structure and function in mice[END_REF] We showed that adeno-associated virus (AAV)-mediated allele-specific RNAi targeting the R465W mutant allele is able to completely prevent this muscle phenotype in young mice while partially restore muscle function in older mice probably due to a viral transduction defect. [START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] In the present study, we aim at establishing the long-term benefit of mutant-specific silencing after a single AAV-shRNA injection in young KI-Dnm2 R465W mice and to improve the treatment efficacy in older mice.

Results

Therapeutic benefit on muscle phenotype is maintained long-term

To assess the long-term maintenance of phenotype restoration, a single intramuscular injection of AAV1 expressing or not the R465W mutant-specific shRNA (i.e. AAV1-sh9 and AAV1-control) was performed in tibialis anterior muscle (TA) of the KI-Dnm2 R465W mice at 1 month of age (10 11 viral genomes (vg)/TA) and mice were sacrificed after 1 year. Heterozygous (HTZ) KI-Dnm2 R465W mice received the therapeutic AAV1-sh9 in the right TA and AAV1control in the contralateral muscle. The wild-type (WT) mice received the AAV1-control in the left muscle and PBS in the contralateral muscle.

A 18% reduction in muscle mass was observed in untreated HTZ muscle while a single injection of AAV-sh9 restored muscle mass close to WT values (Figure 1A). Measurement of fiber diameter performed on transversal TA sections immunolabelled with Laminin antibody showed a reduced mean fiber size in HTZ muscle compared to WT which was corrected in the treated muscle (Figure 1B). In addition, fiber size distribution in the treated muscle was similar to the WT with the exception of persistence of medium-sized fibers and a slightly lower number of large fibers (Figure 1C and SupS1). Muscle histopathology was studied on transversal TA sections stained with hematoxylin and eosin (HE), succinate dehydrogenase (SDH), and reduced diphosphopyridine nucleotide diaphorase (DPNH) (Figure 1D and SupS2). The disease-specific histopathological abnormalities, i.e. central accumulation of oxidative cell compartments within fibers, were observed in 18% of fibers in HTZ control muscles and absent in AAV1-sh9 treated muscles (Figure 1E, shown by asterisks in Figure 1D). Moreover, global DNPH and SDH staining in entire muscle section showed an increased oxidative staining in the posterior region of the untreated HTZ muscles compared to WT which was also abolished in AAV1-sh9 treated muscles (Fig SupS2). Absence of myofiber with central nuclei in HE confirmed that the AAV-sh9 was not toxic and did not induced muscle degeneration (Figure 1D lower panel). Transient activation of the ubiquitin-proteasome and autophagy pathways was previously demonstrated in the heterozygous Knock-in model at 2 months of age. [START_REF] Durieux | A centronuclear myopathydynamin 2 mutation impairs skeletal muscle structure and function in mice[END_REF] Therefore, we assessed the expression of Gabarapl1, p62, Atg 4, Murf1, and Atrogin 1 in the TA muscle of the 13-month-old mice by RT-qPCR. With the exception of p62 expression which slightly decreased in HTZ mice, we found similar expression of all genes in untreated WT and HTZ mice, whereas Murf1 and Gabarapl1 expression decreased in heterozygous treated mice (Fig SupS3). We have recently reported a reduction of the satellite cell content in muscle of KI-Dnm2 R465W mice associated with a decreased expression of Pax7. [START_REF] Almeida | Satellite cells deficiency and defective regeneration in dynamin 2-related centronuclear myopathy[END_REF][START_REF] Fongy | Nuclear defects in skeletal muscle from a Dynamin 2-linked centronuclear myopathy mouse model[END_REF] Therefore, we analyzed Pax7 expression in TA muscles from WT, HTZ-control and HTZ-sh9 treated mice by quantitative real-time PCR and immunostaining. We confirmed a decrease of ~60% in Pax7 expression in HTZ-untreated muscle compared to the WT by qPCR and Pax7 expression was not improved in the AAV1-sh9 treated HTZ mice (Figure 1F and Fig SupS4). Finally, force measurements showed that absolute and specific forces were significantly reduced in TA muscle from untreated HTZ mice (-30% and -20%, respectively) and were restored to normal values in treated HTZ mice (Figures 1G and1H). Overall, these results showed a long-term benefit of allele-specific silencing therapy since muscle mass, morphology and function were maintained one year after a single injection of the therapeutic AAV.

Viral genome persists in HTZ muscle after a 1-year treatment

We measured persistence of AAV in HTZ and WT muscles after 1 year through quantification of viral genomes (vg) per nanogram of genomic DNA. A similar amount of vg was found in HTZ muscles injected with AAV1-sh9 and AAV1-control (960 vg/ng) (Figure 2A) also supporting absence of toxicity of the long-term expression of the sh9 RNA and a similar persistence of both virus in HTZ muscles. In contrast, AAV1-control values were almost tenfold higher in WT muscle (~8800 vg/ng) (Figure 2A). We looked at potential immune response induced in HTZ muscle by long-term expression of shRNA through the potential induction of interferon response by semi-quantitative RT-PCR. Similar expression of two interferon-induced genes (Oas1 and Stat1) was observed in HTZ-control, HTZ-sh9 and WT muscles (Figure 2B) ruling out abnormal immune response in HTZ muscles. This result along with absence of fibrosis and signs of muscle necrosis-regeneration in HE-stained muscle sections (Figure 1D) confirmed safety of long-term expression of the therapeutic molecule. In addition, given that viral genome amount 1 month after AAV injection were comparable between 1-month-old WT and HTZ mice (Fig. SupS5), our results also suggested a partial loss of viral genome in the HTZ muscle with time independent of muscle regeneration but without significant impact on the therapeutic benefit at one year.

Specific silencing of mutated allele is maintained over time

Expression of Dnm2 transcript was quantified by semi-quantitative RT-PCR normalized with ATPase transcript. A significant decrease in the Dnm2 mRNA content was observed in sh9-expressing HTZ muscle compared to untreated HTZ and WT muscles (-20%) (Figure 3A) and confirmed by qPCR (Fig. SupS6A). Allele-specific silencing was checked using Dnm2 RT-PCR and EcoNI enzymatic digestion to discriminate mutated (undigested) from WT allele (digested) (Figure 3B). A significant decrease of mutant/WT ratio was observed in treated muscle (-30%) due to specific silencing of the mutant transcript and unchanged expression of the WT Dnm2 mRNA (Figure 3B). A second RT-PCR assay using primers designed for specific amplification of either WT or mutant alleles confirmed these results (Fig. SupS6B). The DNM2 protein expression was then quantified using western blot and densitometric analysis. In untreated HTZ muscles, a two-fold increase in DNM2 expression was observed compared to WT muscles while DNM2 expression was similar in WT and HTZ treated muscle (Figure 3C).

Altogether, these data demonstrated that allele-specific silencing was maintained 1 year after a single AAV1-sh9 intramuscular injection. These results also highlighted an age-related accumulation of the DNM2 protein without increase in mRNA expression in muscle of HTZ mice at 1 year of age.

Dynamin 2 protein is down-regulated with age in normal mouse muscle

The increased DNM2 protein expression in HTZ muscles compared to WT muscles of 13month-old mice (Figure 3C) suggested a change of DNM2 expression with age. To test this hypothesis, we investigated the DNM2 expression in TA muscles from WT and HTZ KI-Dnm2 R465W mice at 1 month, 3 months and 6 months of age using western blot (Figure 4A). In WT muscle, the DNM2 content remained stable between 1 and 3 months and was then decreased by half at 6 months of age. In HTZ muscle, the DNM2 protein content was higher at 1 month of age compared to WT, and returned to amount comparable with WT in 3-month-old mice, in accordance with previous observation at this age. [START_REF] Buono | Reducing dynamin 2 (DNM2) rescues DNM2related dominant centronuclear myopathy[END_REF] Then, between 3 and 6 months of age, the DNM2 protein content remained stable in HTZ muscle, leading to a 2-fold higher protein content compared to WT at 6 months of age. Together these data support a physiological decrease in DNM2 protein content in wild-type muscle from 3 to 6 months of age which was impaired in presence of the R465W DNM2 mutation.

We then investigated whether this physiological decrease of DNM2 occurred at transcriptional level by quantifying Dnm2 mRNA in tibialis anterior muscle in 1-and 9-monthold mice using semi-quantitative RT-PCR. As shown in Figure 4B, the level of Dnm2 mRNA was similar in these muscles regardless of the age and genotype. Therefore, as for the accumulation of mutant protein observed in mutant muscle (Figure 3C), the physiological decrease of DNM2 protein content in WT muscle results from post-translational event which is altered in HTZ mice.

We then wondered if the physiological decrease in DNM2 protein content with aging in WT mice was muscle-specific. We investigated the DNM2 expression in several muscles (quadriceps, gastrocnemius, and heart) and non-muscle tissues (liver and brain) from WT mice at 1 and 9 months of age using western blot (Figure 4C). DNM2 protein content was quantified by densitometry and normalized with total protein detected by Stain-Free. In WT brain and liver, no significant decrease in DNM2 protein expression was highlighted with age (Figure 4C, p = 0.82 and 0.41 respectively). In muscle tissues, while the significance threshold is not reached (p=0.057 for all of them), we observed a decrease in DNM2 protein amount between 1 and 9 months with a more important decrease in quadriceps and gastrocnemius muscles than in heart.

DNM2 protein content was also compared between WT and HTZ mice at the age of 9 months (Fig. SupS7). No difference was found between the two genotypes in brain and heart while an increase in protein content was observed in quadriceps and gastrocnemius but below the significant threshold (p=0.057). Altogether these results supported a skeletal musclespecific physiological decrease of DNM2 protein with age in WT mice that would be impaired in HTZ mice.

Dynamin 2 expression is also down-regulated with age in healthy human muscle

We then investigated the relevance of age-related variation in DNM2 protein in human. To this end, we assessed DNM2 expression in muscle biopsies from healthy subjects and CNM patients at various ages (ranging from 1 month to 60 years old) by western blot (Figure 5A).

For analysis, we grouped the control samples as younger or older than 20 years old (n=6 for both group, Figure 5B). We observed that DNM2 expression was ~30% lower in the older group compared with the younger (p<0.05). Moreover, when plotting individual DNM2 expression level as a function of age, we observed a negative correlation (r=-0.7, p<0.05) in controls samples. Considering CNM samples, spearman correlation was non-significant (r=0.70, p=0.17) and the number of patients was not sufficient to constitute a group of age, however at matched aged we observed a level of DNM2 that tends to be higher in CNM patients (Figure 5C and SupS8).

High dose of therapeutic AAV does not improve the transduction defect occurring in old mice

We previously highlighted a viral transduction defect in 6-month-old mice compared to 1month-old HTZ mice explaining the lower efficacy of the treatment in old mice. [START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] Therefore, we wanted to explore the possibility to improve treatment efficacy in old mice by using a 10fold increase in therapeutic AAV1-sh9 compared to the dose used in our previous study (10 11 vg/TA). A single intramuscular injection was performed in TA of HTZ mice at 6 months of age (10 12 vg/TA). HTZ mice received an AAV1-sh9 in the right TA and PBS in the contralateral muscle. The WT mice received only PBS in both TA since such amount of virus in a WT mouse muscle leads to muscle regeneration. Mice were sacrificed after 3 months to perform molecular analysis and force measurements. We did not show significant variation in the total Dnm2 transcript in treated mice and only a slight reduction of the mutant transcript (Figure 6B). As already reported with a lower dose [START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] , a significant improvement of contractile properties occurred but muscle mass was unchanged (Figure 6A). We then evaluated the viral genome amount in HTZ muscles injected with high dose of virus (10 12 vg/TA) in comparison with HTZ muscle samples injected with low dose of virus (10 11 vg/TA). We found 382 vg/ng of DNA in the latter muscles versus 1055 vg/ng in muscle injected with the tenfold higher dose (Figure 6C). A virus loss subsequent to muscle regeneration due to potential toxicity was ruled out by absence of central nuclei observed in HE staining (Figure 6D). Overall, despite improvement of muscle contractile properties, a 10-fold increase of therapeutic AAV1-sh9 was unable to bypass the transduction defect in 6-month-old KI-Dnm2 mice.

Discussion

High efficacy and specificity of RNA interference (RNAi) to silence morbid genes have been at the origin of numerous clinical trials. These two properties of RNAi have been also used to specifically target the mutated allele without affecting the normal allele in dominant inherited diseases even when the two sequences only differed by one nucleotide. Proof of concept of allele-specific RNAi (AS-RNAi) was achieved for almost 20 diseases in patient-derived cells and/or animal models including the DNM2-linked dominant centronuclear myopathy. [START_REF] Trochet | Therapy for Dominant Inherited Diseases by Allele-Specific RNA Interference: Successes and Pitfalls[END_REF][START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] Here, we addressed a key point for preclinical development of AAV-mediated therapy for AD-CNM which is the long-term maintenance of therapeutic benefit in vivo.

The long-term expression of transgene is one of the advantage of AAV delivery as transgene expression has been detected up to 10 years after single injection in non-dividing tissues. [START_REF] Buchlis | Factor IX expression in skeletal muscle of a severe hemophilia B patient 10 years after AAV-mediated gene transfer[END_REF] However, a decrease of transgene expression starting from 7 months after AAV injection in mice has been also reported. [START_REF] Bish | Adeno-associated virus (AAV) serotype 9 provides global cardiac gene transfer superior to AAV1, AAV6, AAV7, and AAV8 in the mouse and rat[END_REF] To the best of our knowledge, only one study addressed the long-term maintenance of AAV-mediated AS-RNAi therapy in vivo showing a decrease in treatment benefit with time in a mouse model of cardiomyopathy through an undetermined mechanism [START_REF] Jiang | Allele-specific silencing of mutant Myh6 transcripts in mice suppresses hypertrophic cardiomyopathy[END_REF] highlighting a potential limitation for the preclinical development of this therapy. Here, we report a rescue of muscle mass, force and histological phenotypes developed by the heterozygous KI-Dnm2 R465W mice [START_REF] Durieux | A centronuclear myopathydynamin 2 mutation impairs skeletal muscle structure and function in mice[END_REF] one year upon a single AAV1-sh9 injection performed at the beginning of symptoms demonstrating the long-term maintenance of the therapeutic benefit previously demonstrated after a 3-month treatment. [START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] Specific reduction of Dnm2 mutant is therefore able to revert the impairment of the muscle contractile properties and prevent the development of muscle atrophy and histological features. In addition, we confirmed in TA muscle the decreased expression of the Pax7 satellite cells marker previously reported in gastrocnemius muscle [START_REF] Almeida | Satellite cells deficiency and defective regeneration in dynamin 2-related centronuclear myopathy[END_REF] , that was not restored after treatment. The capability of AAV vector to efficiently transduce satellite cells is controversial with studies supporting absence of transduction [START_REF] Arnett | Adeno-associated viral vectors do not efficiently target muscle satellite cells[END_REF] or efficient transduction using serotypes 8 and 9 or even with serotype 1 despite a lower efficacy. [START_REF] Kwon | In Vivo Gene Editing of Muscle Stem Cells with Adeno-Associated Viral Vectors in a Mouse Model of Duchenne Muscular Dystrophy[END_REF] Therefore, the absence of Pax7 rescue might result from limited transduction of satellite cells with AAV1 vector that may be improved in the future by other serotypes. Nevertheless, our results show that the correction of Pax7 expression is not a prerequisite to prevent fiber atrophy.

Our study identified a 2-fold increase in DNM2 protein content in heterozygous Tibialis anterior muscle from 6-month-old mice, not seen at mRNA level suggesting that this posttranscriptional regulation results from mutant protein accumulation/absence of degradation. Of note, an increase in DNM2 protein without increase in mRNA expression has been also reported in XLCNM disease. [START_REF] Cowling | Reducing dynamin 2 expression rescues X-linked centronuclear myopathy[END_REF] DNM2 protein accumulation was not observed at younger age in this KI-Dnm2 R465W model (in neonates and 2-month-old mice) [START_REF] Durieux | A centronuclear myopathydynamin 2 mutation impairs skeletal muscle structure and function in mice[END_REF][START_REF] Buono | Reducing dynamin 2 (DNM2) rescues DNM2related dominant centronuclear myopathy[END_REF] , while intracellular accumulations have been already observed by immunofluorescence in isolated HTZ muscle fiber. [START_REF] Durieux | A centronuclear myopathydynamin 2 mutation impairs skeletal muscle structure and function in mice[END_REF] However, in the recent model of severe CNM KI-Dnm2 S619L/+ , a 2-fold increase in DNM2 protein level was also demonstrated at 2 months of age [START_REF] Muñoz | Physiological impact and disease reversion for the severe form of centronuclear myopathy linked to dynamin[END_REF] . In accordance with these observations, transgenic zebrafish models expressing the R465W and S619L mutants showed a protein mislocalization and aggregation that correlate with the severity of the CNM mutations. [START_REF] Zhao | Insights into wildtype dynamin 2 and the consequences of DNM2 mutations from transgenic zebrafish[END_REF] Finally, the propensity of several DNM2 mutants to form abnormally stable oligomers compare to WT has been already reported in vitro. [START_REF] Muñoz | Physiological impact and disease reversion for the severe form of centronuclear myopathy linked to dynamin[END_REF] Autophagy and the ubiquitin-proteasome system are the two major intracellular quality control and recycling mechanisms that are responsible for degradation of misfolded or aggregated proteins. [START_REF] Kocaturk | Crosstalk between mammalian autophagy and the ubiquitin-proteasome system[END_REF] Interestingly, autophagy was shown to be directly impacted by Dnm2 mutation. [START_REF] Durieux | A Centronuclear Myopathy -Dynamin 2 Mutation Impairs Autophagy in Mice[END_REF][START_REF] Puri | A DNM2 Centronuclear Myopathy Mutation Reveals a Link between Recycling Endosome Scission and Autophagy[END_REF] Therefore, the DNM2 oligomers/polymers formed by the DNM2 R465W mutant could be initially efficiently handle by intracellular quality control system, who would become overloaded and/or mis-functional with time leading to the increase in DNM2 protein level. However, we confirmed that the abnormal activation of the ubiquitin-proteasome and autophagy genes observed at 2 months of age in heterozygous mice that normalizes at 8 months [START_REF] Durieux | A centronuclear myopathydynamin 2 mutation impairs skeletal muscle structure and function in mice[END_REF] remains normalized at 13 months. The decrease in Murf1 and Gabarapl1 expression observed in treated heterozygous mice could be due to a direct regulation of these genes by DNM2.

Altogether, the propensity to aggregate shared by several Dnm2 CNM mutation (and not seen in CMT-related mutation [START_REF] Zhao | Insights into wildtype dynamin 2 and the consequences of DNM2 mutations from transgenic zebrafish[END_REF] ), the correlation between the degree of aggregation and the severity of the disease [START_REF] Muñoz | Physiological impact and disease reversion for the severe form of centronuclear myopathy linked to dynamin[END_REF] and this study, and our observation of increase with age in parallel of the disease progression, argue in favor of their contribution to pathogenesis. Along the same lines, it is noteworthy that overexpression of WT DNM2 by itself could trigger muscle defects [START_REF] Cowling | Increased expression of wild-type or a centronuclear myopathy mutant of dynamin 2 in skeletal muscle of adult mice leads to structural defects and muscle weakness[END_REF][START_REF] Liu | Mice lacking microRNA 133a develop dynamin 2-dependent centronuclear myopathy[END_REF] underlying the importance of a tiny DNM2 level regulation for proper muscle development, maturation, and maintenance.

Our study also led to identify a physiological decrease of DNM2 protein content in healthy muscle with age and this age-related decrease seems to be muscle-specific. Our results argue for the relevance of this DNM2 decrease with age in human muscle from healthy controls, while the level of DNM2 expression in CNM patients remains in the range of young controls regardless of their age. In the literature, few studies have investigated the localization or the level of DNM2 in patients. Normal expression of Dynamin 2 mRNA and protein has been reported in fibroblasts from CNM patients. [START_REF] Bitoun | Dynamin 2 mutations associated with human diseases impair clathrin-mediated receptor endocytosis[END_REF][START_REF] Echaniz-Laguna | Subtle central and peripheral nervous system abnormalities in a family with centronuclear myopathy and a novel dynamin 2 gene mutation[END_REF][START_REF] Koutsopoulos | Dynamin 2 homozygous mutation in humans with a lethal congenital syndrome[END_REF] In addition, aggregates have been reported in one late-onset patient with a normal protein amount [START_REF] Kierdaszuk | A novel mutation in the DNM2 gene impairs dynamin 2 localization in skeletal muscle of a patient with late onset centronuclear myopathy[END_REF] and recently abnormal western blot profile was reported for a severe young CNM patient. [START_REF] Muñoz | Physiological impact and disease reversion for the severe form of centronuclear myopathy linked to dynamin[END_REF] Altogether these data may suggest that the level of DNM2 required for proper muscle function would vary according to muscle maturation stage and this process would be impaired more or less early according to the DNM2 mutation, leading to unbalanced WT/mutant protein ratio with age and reinforcing under this postulate the asset of a mutant specific approach.

AAVs transgene expression results from a complex multistep process including AAV entry by endocytosis, microtubule-dependent endosomal trafficking, endosome escape, nuclear import, capsid uncoating allowing single-strand DNA release and double strand conversion. [START_REF] Nonnenmacher | Intracellular transport of recombinant adenoassociated virus vectors[END_REF] Given the known functions of DNM2, several steps of AAV processing could be additively affected by DNM2 dysfunction. Our study shows an AAV transduction defect in the KI-Dnm2 R465W/+ model which is probably already present in young mice. Indeed, the amount of viral genome detected after one year in mice injected at one month of age is lower in HTZ than in WT mice, while this amount is comparable after one month. This argues for a higher rate of viral genome loss with time in HTZ muscles that would be independent of regeneration.

However, the benefit on contractile properties despite undetectable silencing of the mutated allele in 6-month-old mice supports a low therapeutic threshold and is encouraging to persevere in the improvement of AAV-transduction in our model. Notably, insulin treatment [START_REF] Carrig | Insulin Therapy Improves Adeno-Associated Virus Transduction of Liver and Skeletal Muscle in Mice and Cultured Cells[END_REF] , removal of capsid phosphorylation sites [START_REF] Qiao | Adeno-Associated Virus Serotype 6 Capsid Tyrosine-to-Phenylalanine Mutations Improve Gene Transfer to Skeletal Muscle[END_REF] or stimulation of autophagy [START_REF] Hösel | Autophagy determines efficiency of liver-directed gene therapy with adeno-associated viral vectors[END_REF] have been reported to improve transduction efficiency. Otherwise, other serotypes or non-viral delivery can be considered alone or in combination with AAV treatment. In the latter case the non-viral delivery could transiently improve the muscle state in order to enhance the transduction capabilities at the time of AAV injection.

To date there is no curative treatment available for AD-CNM patients, despite a treatment with acetylcholinesterase inhibitor reported to improve muscle strength in few DNM2-CNM patients. [START_REF] Gibbs | Neuromuscular junction abnormalities in DNM2-related centronuclear myopathy[END_REF] We have previously succeeded to correct the DNM2 mRNA by trans-splicing, but with a low efficiency. [START_REF] Trochet | Reprogramming the Dynamin 2 mRNA by Spliceosome-mediated RNA Trans-splicing[END_REF] Non-allele specific Dnm2 RNAi (i.e. targeting both alleles of Dnm2) mediated by antisense oligonucleotides was also reported to efficiently improve the progression of the disease in two AD-CNM mouse models (i.e. KI-Dnm2 R465W/+ and KI-Dnm2 S619L/+ ). [START_REF] Buono | Reducing dynamin 2 (DNM2) rescues DNM2related dominant centronuclear myopathy[END_REF][START_REF] Muñoz | Physiological impact and disease reversion for the severe form of centronuclear myopathy linked to dynamin[END_REF] Unfortunately, the long-term benefits have not been reported using this approach. The proofof-concept of AS-RNAi therapy in vitro and in vivo [START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] and our current demonstration of longterm efficacy in an animal model enlarge the therapeutic possibilities for the disease. In addition to efficiency and specificity provided by RNAi, AS-RNAi introduces a third property of safety since 50% expression is preserved from the healthy untargeted allele. This may be of particular importance in a context of physiological decrease with age of the DNM2 expression.

In conclusion, the demonstration that time does not impair the treatment benefit nor the level of mutant silencing associated with the prevention of protein accumulation and absence of toxicity confirms allele-specific RNA interference mediated by AAV delivery as a strategy of choice to treat autosomal dominant centronuclear myopathy due to Dynamin 2 mutations.

Materials and Methods

Data Analysis and Statistics

Graphics and statistical analyses were performed with GraphPad Prism software version 9.

Values were expressed as means ± SEM. The number of samples (n), representing the number of independent biological replicates, was indicated in the figure legends. For molecular analysis the experiments were repeated at least three times per biological replicate and averaged. We used nonparametric statistical tests to analyze our data since the normality could not be assume or tested or the variance were not equal between groups. Statistical comparisons between two groups were performed using unpaired two-tailed Mann-Whitney U-test as specified. Spearman correlation analysis was used to evaluate the strength of relationship between DNM2 protein content and age. Statistical tests applied are indicated in the figure legends. P values < 0.05 were considered as statistically significant. In most of the figures, the gels are cropped for more conciseness but samples presented were run on a same gel.

Total RNA extraction and cDNA analysis

Total RNAs were isolated from muscle by TRIZOL reagent (Life Technologies, France) following standard protocol after disruption using Fastprep Lysing Matrix D and Fastprep apparatus (MP Biomedical, France). Total RNA (1 µg) were submitted to reverse transcription using the Superscript III reverse transcriptase kit (Life Technologies) and oligo-dT primers.

The cDNAs were amplified by PCR under the following conditions: 96°C for 5 min, cycles of 30 s at 96°C, 30 s at the appropriate temperature (58 to 62°C), 30 s at 72°C, and a final step of 7 min at 72°C. Semi-quantitative RT-PCR was used to determine the total Dnm2 expression, the appropriate number of PCR cycles has been selected in order to have the amplification in the exponential range (i.e. 23 cycles to amplify Gapdh and 28 cycles for Dnm2). Sequences of the primers were indicated previously [START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] . To quantify allele-specific silencing, an assay was developed using EcoNI restriction enzyme allowing discrimination between wild-type and mutant cDNAs. Dnm2 PCR products (393 base-pair) containing the mutation was EcoNI digested and run on agarose gel. EcoNI digests only RT-PCR product amplified from the WT leading to 2 fragments (247 and 146 base-pair) allowing discrimination between WT and mutated alleles. The densitometric ratio between the non-digested band (mutated) and the sum of the signal for the two digested bands (wild-type) is done and compared with untreated conditions where this ratio is set to 1 to estimate the efficiency of the siRNA on the mutated allele. The digestion of murine Dnm2 amplicons was performed after 32 cycles at the end of the exponential phase of amplification. For this assay, the half of the PCR products was digested using 2U of EcoNI (New England Biolabs, France) for 2 h at 37°C. Image acquisition of PCR products after agarose gel electrophoresis was performed using a Geni2 gel imaging system (Ozyme, France) and associated-signal was quantified using ImageJ Software (NIH; http://rsbweb.nih.gov/ij).

Semi-quantitative RT-PCR was also used to determine the total expression of two interferoninduced genes (Oas1 and Stat1) with appropriate number of PCR cycles selected in order to have the amplification in the exponential range (i.e. 34 cycles to amplify OasI, 36 cycles to amplify Stat1). Sequences of the primers were indicated previously. [START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] Pax7, Gabarapl1, p62 Atg4, Murf1 and Atrogin 1 mRNA quantification was performed by real-time PCR using a Lightcycler 480 II (Roche, Switzerland) and 1X SYBR Green (Roche, Switzerland) reactions using 0.5 µM of forward and reverse primers, and 5 µL of cDNA diluted at 1:10 in nucleasefree water. PCR cycles were a 5 min 95°C pre-incubation step followed by 45 cycles with a 95°C denaturation for 10 s, 58°C or 60°C annealing for 15 s and 72°C extension for 15 s.

Protein extraction and western blot

Frozen TA muscles and tissues were mechanically grinding in liquid nitrogen using a ceramic mortar and pestle precooled in dry ice. Powder was then weighed and homogenized in cold lysis buffer (200 µl per 30 mg of powder) containing 50 mM of Tris-HCl pH 7.5, 150 mM NaCl, 1 mM EDTA, NP40 1% supplemented with protease inhibitor cocktail 1% (Sigma-Aldrich, France). Samples was then incubated under agitation in cold-room for 4 hours and sonicated on ice. After centrifugation (14,000 g, 4°C, 15 min), protein concentration in the supernatant was determined with the BCA Protein Assay Kit (Thermo Scientific Pierce, France). Ten µg of proteins were mixed with loading buffer (50 mM Tris-HCl, SDS 2%, glycerol 10%, 2-mercaptoethanol 1% and bromophenol blue) and denaturated at 90°C for 5 min. For TA, protein extracts samples were separated on SDS-PAGE 10% and transferred onto PVDF membranes (0.45 µm pore size, Life Technologies) overnight at 100 mA at 4°C. The other protein extracts (i.e. mouse tissues and human muscles) were separated on 10% Mini-PROTEAN® TGX Stain-Free (Bio-Rad) and the gel was transferred on nitrocellulose membrane using Transblot Turbo RTA transfer kit for 8 minutes at 2.5A. Total protein loading was determined by stain free staining. After transfer, membranes were blocked for 1 h at room temperature in PBS containing non-fat dry milk 5% and Tween-20 0.1% and then exposed to rabbit polyclonal anti-Dynamin 2 antibody (Abcam ab3457, dilution 1:1000 or ab65556 dilution 1:4000, United Kingdom) or rabbit polyclonal anti-GAPDH antibody (Sc-25778 dilution 1:2000, Santa Cruz, France) in PBS-Tween-20 0.1%, milk 1% overnight at 4°C. Membranes were rinsed in PBS-Tween-20 0.1% and incubated 1h at room temperature with horseradish peroxidase-conjugated secondary antibody (anti-rabbit from Jackson ImmunoResearch, United Kingdom) in PBS-Tween-20 0.1%. Chemiluminescence was detected using ECL detection Kit (Merck-Millipore, Germany) in a Chemidoc Imaging Systems (Biorad, France) and signal quantification was performed using ImageJ software.

AAV production

A cassette containing the small hairpin (sh) RNA under the control of H1 RNA polymerase III promoter has been inserted in a pSMD2 expression plasmid. The small-hairpin (sh)-9 RNA was generated from the Dnm2 19 nucleotides siRNA targeting the mouse mutation (c.1393 A>T, p.R465W) and harboring a mismatch with the wild type sequence in position 9 of the sense strand. This siRNA has been previously selected for its efficacy and allele specificity. [START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] The shRNA maker function of the Serial Cloner software was used to generate shRNA sequences (available on request) for subsequent subcloning in the pH1-Super plasmid. Sense and antisense sh9-RNA (Eurogentec, Belgium) was annealed using annealing solution (pSilencer kit, Ambion) according to manufacturer's instructions and inserted in BglII -HindIII sites in pH1-Super plasmid. The cassette pH1-sh9RNA was then inserted in the pSMD2 between BamH1 and SalI sites. AAV vectors (serotype 1) were produced in HEK293 cells after transfection of the pSMD2-shRNA plasmid or empty pSMD2 plasmid, the pXX6 plasmid coding for viral helper genes required for AAV production and the pRepCap plasmid (p0001) coding for AAV1 capsid as described previously. Viral particles were purified on iodixanol gradients and concentrated on Amicon Ultra-15 100K columns (Merck-Millipore). The concentration of viral genomes (vg/ml) was determined by quantitative real-time PCR on a LightCycler480 (Roche diagnostic, France) by using TaqMan probe in the inverted terminal repeat (ITR) sequences. A control pSMD2 plasmid was tenfold serially diluted (from 10 7 to 10 1 copies) and used as a control to establish the standard curve for absolute quantification.

Sequences of primers and probes are available on request or indicated previously. [START_REF] Trochet | Allele-specific silencing therapy for Dynamin 2-related dominant centronuclear myopathy[END_REF] Adenoassociated virus (AAV) serotype 1 vectors containing shRNA specific of the mutant allele (AAV-sh9) and a control (AAV-control) were produced.

Mice and in vivo transduction

The dynamin 2 mutant mouse line was established on C57Bl/6 background at the Mouse Clinical Institute (MCI, Illkirch, France; http:// www-mci.u-strasbg.fr) [START_REF] Durieux | A centronuclear myopathydynamin 2 mutation impairs skeletal muscle structure and function in mice[END_REF] . All mice used in this study were housed on a 12-h light/dark cycle and received standard diet and water ad libitum in the animal facility of Sorbonne University (Paris, France). Male heterozygous KI-Dnm2 R465W mice were injected at 1 and 6 months of age under isoflurane anesthesia. We chose male mice since the characterization of the model has been done on male, the WT littermates were used as controls. Two intramuscular injections of 30 µl within 24h interval were performed using 29G needle in TA muscles. AAV-sh9 and AAV-control were injected at 1 month of age and at 6 months of age in order to achieve 10 11 and 10 12 vg/muscle respectively. Age-matched WT mice non-injected or injected with the AAV-control or PBS were used as control.

For 1-month old mice injected for 1 year, 23 heterozygous mice have been injected (i.e. 23 right TA with the AAV1-sh9 and 23 left TA with the AAV1-control) and 11 wild-type mice (i.e. 11 right TA with the AAV1-control and 11 left TA with PBS), all of them were analyzed for the muscle force. We decided to inject a high number of mice to prevent potential lost due to death of mice considering the long period. Eleven heterozygous TA of each conditions and 14 wild-type TA were then used for molecular biology, 9 heterozygous TA of each condition and 8 wild-type were used for histology. For 6-month old mice injected for 3 months with high dose of AAV1-sh9, 5 heterozygous mice have been injected (i.e. 4 TA with the AAV1-sh9 and 6 TA with the PBS) and 11 wild-type mice (i.e. 11 TA with PBS), all of them were analyzed for the muscle force, molecular biology and histology.

Muscle contractile properties

The isometric contractile properties of TA muscles were studied in situ on mice anesthetized with 60 mg/kg pentobarbital. The distal tendon of the TA muscle was attached to a lever arm of a servomotor system (305B Dual-Mode Lever, Aurora Scientific). The sciatic nerve was stimulated by a bipolar silver electrode using a supramaximal (10 V) square wave pulse of 0.1 ms duration. Absolute maximal isometric tetanic force was measured during isometric contractions in response to electrical stimulation (frequency of 25-150 Hz; train of stimulation of 500 ms). All isometric contraction measurements were made at optimal muscle length. Force are expressed in grams (1 gram = 9.8 mNewton). Mice were sacrificed by cervical dislocation and TA muscles were weighted. Specific maximal force was calculated by dividing absolute force by muscle weight.

Histomorphological analyses

TA muscles were frozen in liquid nitrogen-cooled isopentane. Transverse sections of TA muscle (8 µm thick) were stained with hematoxylin and eosin (HE), Succinate Dehydrogenase staining (SDH) and reduced diphosphopyridine nucleotide diaphorase staining (DPNH) by standard methods. Light microscopy was performed using an Axioscope Z1 Slide scanners (Zeiss, France) at 20X magnification. Exposure settings were identical between compared samples and viewed at room temperature. Histomorphological abnormalities were manually counted on SDH staining using cell counter plugin Fiji software [START_REF] Schindelin | Fiji: An open-source platform for biological-image analysis[END_REF] , 8 untreated and 8 treated heterozygous Tibialis anterior sections from different animals were counted

Immunocytochemistry

For immunocytochemistry, muscle cryosections (8 µm thick) were fixed in paraformaldehyde 4% (15 min at room temperature). After washing in PBS, cryosections were permeabilized in Triton X-100 0.5% in PBS for 10 min at room temperature and blocked in PBS-Triton X-100 0.1%, BSA 5% and Donkey serum 5% for 30 min. Samples were incubated with rabbit anti-Laminin (Abcam ab11575) overnight at 4°C, in PBS with Triton X-100 0.1% and BSA 1%.

After PBS-Triton X-100 0.1% washes, samples were incubated with Goat anti-rabbit AlexaFluor568 secondary antibody (Life Technologies, France) for 60 min at room temperature. For satellite cell staining, transverse 8 µm-cross-sections were fixed with 4% paraformaldehyde, blocked in PBS containing 5% FCS and 0.01% triton-X100, and then incubated overnight with primary antibody against PAX7 (1:20; DSHB, US) and labelled with AlexaFluor 568 (1:300, Life Technologies, France). Slides were then stained with 4',6diamidino-2-phenylindole (DAPI) for nuclei staining. The slides were mounted with Vectashield mounting medium (Vector Laboratories, United Kingdom). Fluorescent images acquisition was performed at 20X magnification on Axioscope Z1 Slide scanners (Zeiss, France) for Laminin and on a Nikon Ti2 microscope, driven by Metamorph Software (Roper), equipped with a motorized stage and a Yokogawa CSU-W1 spinning disk head coupled with a Prime 95 sCMOS camera (Photometrics) for PAX7. For quantification of fibre size, images of TA muscle sections labelled with anti-laminin antibody were used to automatically determine the Feret diameter of each fibre after manual segmentation using the Fiji software. The normal distribution of the values was plotted using Microsoft Excel software (8 heterozygous untreated, 8 heterozygous treated and 6 wild-type Tibialis anterior sections from different animals were analyzed). Satellite cells were counted using the "cell counter" plugin of ImageJ. Tibialis from each condition (WT (n=6), untreated heterozygous (n=5) and treated heterozygous (n=5) were imaged at 20 X magnification and at least 5 different fields were analyzed (corresponding to an average of 900 fibers).

Viral genome quantification

Viral infection efficacy was evaluated through quantification of viral genomes in injected muscles. Genomic DNA was extracted from mouse muscle sections using DNA purification kit (Promega, France) according to the manufacturer's protocol. Copy numbers of AAV genomes were quantified on 100 ng of genomic DNA by quantitative real-time PCR on a LightCycler480 (Roche diagnostic, France) by using TaqMan probe. A linearized plasmid containing ITR sequences was used to establish the standard curve for absolute quantification. Sequences of primers also used for viral titration are available on request.

Human biopsies

Twelve control human muscle samples from patients ranging from ages 3 to 60 years old were

Study approval

Animal studies conform to the French laws and regulations concerning the use of animals for Semi-quantitative Dnm2 and Atpase RT-PCR of mRNA extracted from tibialis anterior muscle at 9 months and quantification of Dnm2 expression normalized to Atpase (n≥3). C. DNM2 and GAPDH western blot and total protein stain free extracted from WT brain, liver, quadriceps, gastrocnemius and heart at 1 and 9 months of age. The histograms show quantification of DNM2 protein signal by densitometry using total protein loading (stain free) as loading control (WT-1M n=4, WT-9M n≥3). WT: wild-type. SF: protein stain free. Data information: In scatters blot, bars represent mean ± SEM. Statistical analysis was performed using a two-tailed Mann-Whitney U-test. *P < 0.05. A. Representative DNM2 western blot of total protein extracted from human muscle biopsies. GAPDH and total protein loading was used as loading control. B. Histograms showing quantification of DNM2 protein signal by densitometry using total protein loading (stain free) as loading control (<20y n=6, >20y n=6). C. Individual plot of densitometry of bands corresponding to DNM2 normalized to total protein stain free as a function of age. Controls patients are represented by black plots (n=12) and CNM patients by red plots (n=5). Individual plot represents mean ±SEM of 1 to 4 technical duplicates. Statistical analysis was performed using spearman correlation (*P < 0.05). SF: protein stain free.

  Relative expression was calculated as mean values of 2 -ΔΔCT normalized using the Atpase housekeeping gene. Primers sequences are Pax7 Fw-GAG TTC GAT TAG CCG AGT GC, Rv-GTG TTT GGC TTT CTT CTC GC, Atpase Fw-CCCCCTGTTCAGGTCTACGG, Rv-GACGGTGCGCTTGATGTAGG, Atrogin1 Fw -GCCTTCAAAGGCCTCACG and Rv -CTGAGCACATGCAGGTCTGGG, Murf1 Fw -CGACCGAGTGCAGACGATCATCTC and Rv-GTGTCAAACTTCTGACTCAGC, Gabarap11 Fw-CATCGTGGAGAAGGCTCCTA and Fw-ATACAGCTGGCCCATGGTAG, P62, Atg4 Fw-ACAGATGATCTTTGCCCAGG and Rv-TAGACTTGCCTTCGCCAACT, P62 Fw-GCTCAGGAGGAGACGATGAC and Rv-AGGGGTCTAGAGAGCTTGGC.

  obtained from the MyoBank-AFM bank of tissues for research, a partner in the EU network EuroBioBank, or from the Morphological Unit of the Institute of Myology (Paris, France) in accordance with European recommendations and French legislation. The five CNM-patient's biopsies were obtained from the Morphological unit, and are ranging from age 1 month to 48 years and harbor different DNM2 missense mutations (i.e. the DNM2 E611K, R369W, A618T, R465W and R522H).

  research and were approved by an external Ethical committee (APAFIS#21085-2019060719395546) delivered by the French Ministry of Higher Education and Scientific Research).

Figures and legends Figure 1 :

 legends1 Figures and legendsFigure 1: Muscle phenotypic rescue persists at least one year long. A. Muscle mass relative to body weight in milligrams/grams from WT and AAV-shRNA-injected mice (HTZ n=23, WT n = 22). B. Histogram of the mean Feret diameter (WT n=6, HTZ n=8). C. Combined frequencies of fibre size in TA muscles (WT n=6, HTZ n =8 of each conditions). D. Histochemical staining of TA sections from WT and AAV-injected HTZ mice. HE: haematoxylin-eosin staining. SDH: Succinate Dehydrogenase staining. Asterisks indicate fibers with abnormal central accumulations. Scale bars = 50 µm. E. Quantification of histological abnormality. Scatter plot represents individual percentages of histological abnormality from heterozygous control or treated mice (HTZ-ctl n = 6, HTZ treated n = 4). F. Relative Pax7 mRNA expression in WT, HTZ control and HTZ muscles injected with AAV-sh9. WT was used as the normalizer sample (WT n= 11, HTZ n = 11). G. Absolute maximal force (g: grams) H. Specific maximal force developed by TA muscles (In G and H HTZ n = 23, WT n = 22). Data information: In scatters blot (A, B, E-H), bars represent mean ± SEM. Statistical analysis was performed using a two-tailed Mann-Whitney U-test. *P < 0.05, **P < 0.01 and ***P < 0.001 compared to WT.

Figure 2 :

 2 Figure 2: Viral amount and expression of interferon-induced genes in AAV-injected mice A. Quantification of the viral genomes (vg) per ng of genomic DNA in mice injected with AAV-sh9 or control. WT muscles injected with PBS were included as negative control (HTZ n = 11, WT-control n=6, WT-PBS n=5). B. Quantification of expression of the interferon-induced genes Oas1 and Stat1 mRNA relative to Gapdh mRNA by RT-PCR in muscle from 13-monthold mice treated at 1 month of age. Left panel: Oas1 expression. Right panel: Stat1 expression. (HTZ-control n = 11, HTZ-control n=11, WT-PBS n=11). Data information: Scatter plot bars represent mean +/-SEM. Statistical analysis was performed using a two-tailed Mann-Whitney U-test. *P < 0.05, ns: non-significant.

Figure 3 :

 3 Figure 3: Specific silencing on mutant allele and protein is maintained over time A. Semi-quantitative Dnm2 and Atpase RT-PCR products and quantification of Dnm2 expression normalized to Atpase (HTZ n≥10, WT n = 12) B. EcoNI digestion profile of Dnm2 PCR products and quantification of the mutant/WT, mutant/Atpase and WT/Atpase ratios (HTZ, WT n = 11). C. DNM2 western blot and quantification of signal by densitometry. GAPDH was used as loading control (HTZ, WT n = 8). Data information: In scatter plots (A, B and C), the bars are mean values and error bars indicate SEM. ***P < 0.001, **P < 0.01, *P < 0.1 two-tailed using a Mann-Whitney U-test comparison. HTZ: heterozygous, WT: wildtype, Mut: Mutant.

Figure 4 :

 4 Figure 4: DNM2 protein expression in wild-type mouse muscle and non-muscle tissues with agingA. DNM2 western blot of total protein extracted from tibialis anterior at 1, 3 and 6 months of age and quantification of signal by densitometry. GAPDH was used as loading control (n≥3) B. Semi-quantitative Dnm2 and Atpase RT-PCR of mRNA extracted from tibialis anterior muscle at 9 months and quantification of Dnm2 expression normalized to Atpase (n≥3). C. DNM2 and GAPDH western blot and total protein stain free extracted from WT brain, liver, quadriceps, gastrocnemius and heart at 1 and 9 months of age. The histograms show quantification of DNM2 protein signal by densitometry using total protein loading (stain free) as loading control (WT-1M n=4, WT-9M n≥3). WT: wild-type. SF: protein stain free. Data information: In scatters blot, bars represent mean ± SEM. Statistical analysis was performed using a two-tailed Mann-Whitney U-test. *P < 0.05.

Figure 5 :

 5 Figure 5: DNM2 protein expression in healthy human muscle and CNM muscle.

Figure 6 :

 6 Figure 6: High dose of therapeutic AAV-sh9 does not improve the benefit in old mice A. Muscle mass relative to body weight in milligrams/grams, absolute maximal force in grams and specific maximal force (in grams/mg) developed by TA muscles from WT and AAVinjected HTZ mice (WT n = 8, HTZ-control n=7 and HTZ-sh9 n=4). B. Quantification of Dnm2 expression normalized to Atpase from semi-quantitative Dnm2 and Atpase RT-PCR (left) and quantification of the mutant/WT ratio from EcoNI digestion profile of Dnm2 PCR (right) (WT ≥ 4, HTZ-Ctl n=4 and HTZ-sh9=4). C. Quantification of the viral genomes (vg) per ng of DNA in HTZ 6-month-old mice injected with AAV1-sh9 at low (n = 4) or high dose (n=4). D. Representative Haematoxylin-Eosin staining (HE) staining of TA sections from WT and AAVinjected HTZ mice. Data information: In Histogram/scatters blot (A-C), bars represent mean ± SEM. Statistical analysis was performed using Mann-Whitney U-test. *P < 0.05, **P < 0.01 and ***P < 0.001.

Acknowledgments

We thank the Histomics Platform from the Brain and Spinal cord Institute (Paris, France) for light microscopy imaging, the MyoBank-AFM and the Histopathology Laboratory from the Institut de Myologie (Paris, France) for providing human muscles samples, the Penn Vector Core, Gene Therapy Program (University of Pennsylvania, Philadelphia, USA) for providing pAAV1 plasmid (p0001). We would like to thank Catherine Coirault for fruitful discussions and comments. This work was supported by the Institut National de la Santé et de la Recherche Médicale (INSERM), INSERM transfert (CoPoC grant), the Association Institut de Myologie

Author contributions

DT and MBi conceived and designed the experiments. DT, BP, LM, ML, MBe, and MBi performed the experiments. LJ and SBZ produced the AAV vector. MTB and NR provided the human muscle samples and helpful discussions. DT, LM and MBi analysed the data. DT and MBi wrote the manuscript.

Conflict of interest statement:

The authors have declared that no conflict of interest exists.

Key words: allele-specific silencing; gene therapy; dominant centronuclear myopathy; Dynamin 2; RNA interference, in vivo long-term benefits

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