Sabine F Bensamoun
email: sabine.bensamoun@utc.fr

Y Tatarenko

M Li

P Pouletaut

M Kammoun

J R Hawse

V Joumaa

W Herzog

S Chatelin

Multiscale analysis of Klf10's impact on the passive mechanical properties of murine skeletal muscle

Keywords: multiscale, mechanical properties, Klf10, mouse, skeletal muscle

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

HIGHLIGHTS

 Role of Klf10 on the passive behavior of muscle at three organizational scales.

 Klf10 impacts differentially the passive properties of the soleus and EDL muscles.

 Lack of Klf10 expression does not change the passive behavior of myofibrils.

 Disruption of Klf10 on skeletal muscle is primarily at the microscopic scale.

GRAPHICAL ABSTRACT ABSTRACT

Skeletal muscle is a hierarchical structure composed of multiple organizational scales. A major challenge in the biomechanical evaluation of muscle relates to the difficulty in evaluating the experimental mechanical properties at the different organizational levels of the same tissue.

Indeed, the ability to integrate mechanical properties evaluated at various levels will allow for improved assessment of the entire tissue, leading to a better understanding of how changes at each level evolve over time and/or impact tissue function, especially in the case of muscle diseases.

Therefore, the purpose of this study was to analyze a genetically engineered mouse model (Klf10 KO: Krüppel-Like Factor 10 knockout) with known skeletal muscle defects to compare the mechanical properties with wild-type (WT) controls at the three main muscle scales: the macroscopic (whole muscle), microscopic (fiber) and submicron (myofibril) levels. Passive mechanical tests (ramp, relaxation) were performed on two types of skeletal muscle (soleus and extensor digitorum longus (EDL)).

Results of the present study revealed muscle-type specific behaviors in both genotypes only at the microscopic scale. Interestingly, loss of Klf10 expression resulted in increased passive properties in the soleus but decreased passive properties in the EDL compared to WT controls.

At the submicron scale, no changes were observed between WT and Klf10 KO myofibrils for either muscle; these results demonstrate that the passive property differences observed at the microscopic scale (fiber) are not caused by sarcomere intrinsic alterations but instead must originate outside the sarcomeres, likely in the collagen-based extracellular matrix. The macroscopic scale revealed similar passive mechanical properties between WT and Klf10 KO hindlimb muscles.

Introduction

Striated skeletal muscle represents approximately 40 % of the human body mass that is multifunctional and highly adaptive to physiological and pathological conditions that may result in muscle hypertrophy (due to increased mechanical load) or atrophy (inactivity, chronic disease states) [START_REF] Adams | Skeletal muscle unweighting: spaceflight and ground-based models[END_REF]. From a structural point of view, striated skeletal muscle tissue is a complex, hierarchical system which can be classified into four primary scales [START_REF] Tatarenko | Passive and active mechanical tests at different scales of the skeletal muscle: a literature review[END_REF]: macroscopic (mouse muscle diameter: about 1-3 cm), mesoscopic (mouse single fascicle diameter: about 0.5-30 mm), microscopic (mouse single muscle fiber diameter: 10-100 µm) and submicron (mouse single myofibril diameter: about 1-3 µm). The macroscopic scale is represented by the whole muscle and the different collagen sheaths. Both in vivo and in vitro techniques are currently used to characterize the morphological and mechanical properties of an entire skeletal muscle. The mesoscopic scale corresponds to the fascicles, which are surrounded by the perimysium tissue and is poorly characterized in the literature (Meyer and Lieber, 2011). The microscopic scale is defined by a single muscle fiber that is surrounded by the endomysium tissue, and in vitro mechanical techniques have been used to analyze its mechanical properties. Structural analysis and orientation of fibers within a muscle can be determined with specialized imaging techniques, such as diffusion tensor imaging [START_REF] Correia | 3D elastic tensor imaging in weakly transversely isotropic soft tissues[END_REF], ultrasound [START_REF] Ternifi | Ultrasound image processing to estimate the structural and functional properties of mouse skeletal muscle[END_REF] and multiphoton microscopy [START_REF] Syverud | Quantitative, Label-Free Evaluation of Tissue-Engineered Skeletal Muscle Through Multiphoton Microscopy[END_REF]. The submicroscopic scale is composed of myofibril filaments which can be mechanically assessed by only a few research groups around the world [START_REF] Herzog | The role of titin in eccentric muscle contraction[END_REF][START_REF] Linke | Stretching molecular springs: elasticity of titin filaments in vertebrate striated muscle[END_REF].

There have been studies aimed at analyzing tissues at different structural levels. [START_REF] Brynnel | Downsizing the molecular spring of the giant protein titin reveals that skeletal muscle titin determines passive stiffness and drives longitudinal hypertrophy[END_REF] compared the passive properties between two fiber types (slow twitch and fast twitch) of muscles in mice. Moreover, for the same animal model (rabbit), Ward et al. (2020) compared the passive mechanical properties between fibers, bundles, fascicles and whole muscle. Meyer et al. (2011) and [START_REF] Wood | Intrinsic stiffness of extracellular matrix increases with age in skeletal muscles of mice[END_REF] compared the passive properties between fibers and bundles in mice, and [START_REF] Marcucci | Fibre and extracellular matrix contributions to passive forces in human skeletal muscles: An experimental based constitutive law for numerical modelling of the passive element in the classical Hill-type three element model[END_REF] compared the mechanical behavior between slow and fast fibers and bundles in humans. These models, based on experimental data, illustrated the importance of each scale on the global tissue response, and the difficulty in experimentally determining the mechanical properties at each scale of interest.

One of the major challenges in the biomechanical assessment of skeletal muscle relates to the current inability to integrate the mechanical properties at each primary scale and to evaluate changes of these properties over time to better understand the development and progression of muscle disorders and diseases. Indeed, some studies have demonstrated the impact of alterations in the structural and functional properties at different levels from the same tissue (tendon [START_REF] Aghaei | Wave propagation across a functionally graded interphase between soft and hard solids: Insight from a dynamic surface elasticity model[END_REF]; myocardium [START_REF] Tueni | On the structural origin of the anisotropy in the myocardium: Multiscale modeling and analysis[END_REF]; soleus muscle [START_REF] Bensamoun | Macroscopic-microscopic characterization of the passive mechanical properties in rat soleus muscle[END_REF]). In addition, it has been demonstrated that genetic disorders resulting in muscle disease, such as Duchenne muscular dystrophy [START_REF] Desguerre | A new model of experimental fibrosis in hindlimb skeletal muscle of adult mdx mouse mimicking muscular dystrophy[END_REF], have a strong effect on different structural scales leading to changes in whole muscle mechanical properties. A recent publication [START_REF] Pouletaut | Multiscale mechanical characterization of rodent skeletal muscle[END_REF] provided a better understanding of passive mechanical properties at the macro-micro and submicron scales, for healthy slow and fast twitch muscles.

The results have demonstrated that the Young's modulus and passive stresses have higher values for the slow twitch (soleus) compared to the fast twitch (EDL: extensor digitorum longus) muscle at only the macroscopic scale. This study showed the relevance of the choice of the scale to study the impact of muscle type.

As a continuation of Pouletaut's study, a genetically modified mouse model, in which the Krüppel-like factor 10 (Klf10) gene was knocked-out, has been utilized in the present study, given that deletion of Klf10 is known to result in passive mechanical changes at the microscopic scale (i.e. slow and fast muscle fiber) [START_REF] Kammoun | Impact of TIEG1 Deletion on the Passive Mechanical Properties of Fast and Slow Twitch Skeletal Muscles in Female Mice[END_REF][START_REF] Kammoun | Impact of TIEG1 on the structural properties of fast and slow twitch skeletal muscle[END_REF]. Thus, the purpose of this study was to analyze the passive mechanical properties at the macroscopic, microscopic and submicron scales (Fig. 1), on mouse soleus and EDL muscles, to determine how the macroscopic mechanical behavior of muscle is impacted by the properties of its subcomponents at the microscopic and submicron scales in both healthy and Klf10 knockout muscle tissues.

Material and Methods

Animals

In agreement with our previous studies characterizing the role of Klf10 on the mechanical properties of adult female mouse skeletal muscle, we used 3-month-old WT (wild type) and KLF10 KO (knockout) female mice generated from heterozygous breeding. All mice were maintained in a temperature-controlled room (22 ± 2°C) with a light/dark cycle of 12 hours. Animals had free access to water and were fed a standard laboratory chow ad libitum.

Anesthesia was performed via an isoflurane vaporizer (MiniHUB V2, TEM SEGA) device by inhalation from 3 mg.L -1 to 1.5 L.min -1 during muscle dissection. Following dissection, mice were euthanized by cervical dislocation according to the guidelines for the care and use of experimental animals. The protocol was approved by the French ministry of higher education, research, and innovation (Permit Number: DUO-4776) as well as the local ethics committee (CREMEAP; Permit Number: APAFIS #8905-2021011109249708).

Macroscopic scale 2.2.1. Preparation of the skeletal muscles and experimental set up

Soleus (NWT = 9, NKO = 6) and EDL (NWT = 9, NKO = 8) muscles were carefully harvested from the left hindlimb to ensure that muscles were not stretched during dissection and with confirmation that no residual tissue from surrounding muscles was carried forward. For muscle isolation, a suture (Sofsilk TM , 4-0, 1.5Metric) was tied around the distal and proximal tendons; then tendons were cut and removed, and muscles were placed in a bath containing a physiological solution (50 mL sodium bicarbonate, 10 mL calcium chloride dihydrate, 9.6 g.L - 1 Krebs-Henseleit buffer powder) maintained at a temperature of 25 °C, pH 7.3 and a constant oxygenation (95 % O2 and 5 % CO2) to mimic the in vivo environment (Fig. 1). Subsequently, the proximal and the distal parts of the muscle were connected to a dual mode force transducer (300C-LR dual-mode muscle lever, Aurora Scientific, Ontario, Canada) and to a hook, respectively. A pair of flat platinum electrodes, connected to an external stimulator set at 1 A, were placed on each side of the muscle. A SI610A Dynamics Muscle Control v5.420 software (Aurora Scientific, Ontario, Canada) was used to control the displacement of the lever arm to stretch the muscle at different velocities.

Prior to performing the passive mechanical tests, the muscle was placed at its optimal length (Lo), i.e. the length where the muscle developed its maximal isometric force. Optimal length was obtained for each muscle as follows. First, the muscle was set to its resting length (Lr), which corresponds to the length where muscle develops a stable force of 10 mN [START_REF] Canon | Passive stiffness of rat soleus muscle from weaning to senescence[END_REF][START_REF] Toscano | Passive stiffness of rat skeletal muscle undernourished during fetal development[END_REF], by applying three successive tetanus and three successive twitch contractions. Each stimulation was spaced 30 s apart and both impulses were performed at a 40 Hz frequency for a period of 0.7 s (tetanus test) and instantaneously (twitch test). Between each stimulation, a stretch was applied to the muscle to keep the initial force level of 10 mN constant.

Once Lr had been determined in this manner, the optimal length (Lo) was obtained by applying successive twitch impulses, spaced 30 s apart, and by increasing the muscle length by increments of 0.25 mm between each twitch until the muscle reached its maximal isometric force.

Passive mechanical properties using ramp and relaxation tests

Preconditioning of the muscle samples was performed at Lo. Each sample underwent a stretch-release cycle, repeated two times spaced 5 min apart [START_REF] Canon | Passive stiffness of rat soleus muscle from weaning to senescence[END_REF]. The decrease of the hysteresis value was used to control the efficiency of the preconditioning.

After a rest of 5 min, soleus and EDL muscles underwent a ramp test with the stretch-release cycle consisting of a stretch of 25% of optimal length (Lo ≈ 10 mm) at a slow velocity of 1.67% Lo.s -1 (about 0.167 mm.s -1 ) followed by a release at the same velocity, allowing for the measurement of the instantaneous force (Fi_Ramp) reached at the maximum of the stretch. The force-displacement curve was recorded, and a stress-strain curve was generated to measure the Young's modulus (E) in the linear part of the loading curve between 60 and 80% of the maximal strain [START_REF] Hollenstein | Mechanical Characterization of the Liver Capsule and Parenchyma[END_REF].

After a rest of 5 min, the viscoelastic properties were characterized through a relaxation test using a fast stretching velocity of 5 Lo.s -1 (about 50 mm.s -1 ) with an amplitude of stretch of 25% Lo. Three parameters were measured: 1) the dynamic force (Fd), corresponding to the maximum force reached at the end of the stretch, 2) the static force (Fs_Relax), corresponding to the steady state force reached at the end of the holding period (i.e. at 250 s), and 3) the half time of relaxation (t1/2).

All forces (Fs_Ramp, Fd, Fs_Relax) were normalized relative to the initial cross-sectional (CSA) area of the respective muscle to determine the dynamic (σd), the instantaneous (σi_Ramp) and the static (σs_Relax) stresses. The cross-sectional area was calculated using the following equation [START_REF] Del Prete | Measuring Mechanical Properties, Including Isotonic Fatigue, of Fast and Slow MLC/mIgf-1 Transgenic Skeletal Muscle[END_REF]:

𝐶𝑆𝐴(𝑚𝑚 2 ) = 𝑚 (𝑚𝑔) 𝐿 𝑓 (𝑚𝑚) * 1.06 (𝑚𝑔 .𝑚𝑚 -3 ) (1)
where 1.06 (mg.mm -3 ) is the density of mammalian skeletal muscle, (m) is the muscle mass and (Lf) the optimal fiber length which was calculated by multiplying the value Lo with the muscle length ratio (0.44 for the EDL and 0.71 for soleus) as indicated in the literature [START_REF] Del Prete | Measuring Mechanical Properties, Including Isotonic Fatigue, of Fast and Slow MLC/mIgf-1 Transgenic Skeletal Muscle[END_REF].

Following completion of the passive testing, muscles were removed from the bath and weighed using an analytical laboratory balance (BP61S, SARTORIUS, Göttingen, Germany).

Microscopic scale 2.3.1. Preparation of muscle fibers and experimental set up

Skinned muscle fibers from an additional 5 WT and 5 KO mice were isolated from soleus (NWT = 17, NKO = 16) and EDL (NWT = 16, NKO = 15) muscles from the left hindlimb. Following disection, muscles were permeabilized at 4 °C in a skinning solution with successive added percentages of glycerol (12.5, 25 and 50 %) [START_REF] Kammoun | Impact of TIEG1 Deletion on the Passive Mechanical Properties of Fast and Slow Twitch Skeletal Muscles in Female Mice[END_REF][START_REF] Toursel | Passive tension of rat skeletal soleus muscle fibers: effects of unloading conditions[END_REF][START_REF] West | Power output of skinned skeletal muscle fibres from the cheetah (Acinonyx jubatus)[END_REF]. The muscle samples were then stored in 50% glycerol / 50% relaxing solution at -20 °C for a maximum of 5 weeks. Subsequently, using a light microscope (Leica TM M80, Wetzlar, Germany), muscle fibers were isolated and placed in a small bath (14 x 4 mm) (Fig. 1) filled with the relaxing solution, corresponding to the skinning solution, at a controlled temperature of 25 °C.

Passive mechanical tests performed with single muscle fibers

Single muscle fibers were attached at each extremity with an aluminium T-clip (Photofabrication, St Neots, UK) respectively connected to a force transducer (5 mN) and to a motor (1400A -802D Permeabilized Fiber Test Apparatus -Aurora Scientific). Immediately prior to mechanical testing, each fiber was manually stretched to a sarcomere length of 2.4 µm by the same operator. The control of this length was performed with the placement of a region of interest over 3 sarcomeres using ASI 900B video sarcomere length tools (Aurora Scientific, Aurora, Ontario, Canada). After, its slack length (Ls ≈ 2 mm) was measured using an optical microscope (Leica TM DM IL LED, Wetzlar, Germany), composed of a 10 mm graticule in the eyepiece, at a magnification of 20X. The average fiber diameter was determined using several measurements along the fiber length. Subsequently, each fiber underwent two preconditioning tests followed by two passive mechanical tests (ramp stretch, stress-relaxation) as previously described [START_REF] Kammoun | Impact of TIEG1 Deletion on the Passive Mechanical Properties of Fast and Slow Twitch Skeletal Muscles in Female Mice[END_REF]. Preconditioning tests were performed to limit the impact of the viscous effect on the myofibrils [START_REF] Rehorn | The passive properties of muscle fibers are velocity dependent[END_REF]. Accordingly, each fiber was stretched to 150% Ls (about 3 mm) at velocity of 0.00167 Ls.s -1 (about 0.00333 mm s -1 ) and relaxed at the same velocity. After a 5 min rest period at the slack length, this preconditioning test was repeated twice. The hysteresis loop was plotted for each preconditioning run. The hysteresis area was calculated and the decrease in the hysteresis value was used to control the efficiency of preconditioning [START_REF] Kammoun | Impact of TIEG1 Deletion on the Passive Mechanical Properties of Fast and Slow Twitch Skeletal Muscles in Female Mice[END_REF].

The first passive mechanical test was a ramp stretch. The fibers were stretched to 150 % Ls (about 3 mm) with a velocity of 0.033 Ls.s -1 (about 0.066 mm s -1 ) and released at the same velocity, allowing the measurement of the instantaneous force (Fi_Ramp) reached at the end of the stretch. As with the whole muscle test, the Young's modulus (E) was calculated using an identical method [START_REF] Hollenstein | Mechanical Characterization of the Liver Capsule and Parenchyma[END_REF].

The second passive mechanical test was a relaxation test. Over a period of 60 s, the fiber was rapidly stretched to 150 % Ls (about 3 mm) at a high velocity of 3.3 Ls.s -1 (about 6.6 mm s -1 ) and released to its slack length. The dynamic force Fd, corresponding to the maximal force value, reached at the end of the stretch, and the static force Fs_Relax measured at the end of the test, before the fiber was released, were recorded. In addition, the half time of relaxation was measured.

All measured forces (Fi_Ramp, Fd, Fs_Relax) were divided by the initial average anatomical cross-sectional area of the fiber to obtain dynamic (d), instantaneous (i_Ramp) and static (s_Relax) stresses.

Submicron scale 2.4.1. Preparation of the myofibrils and experimental set up

Myofibrils were extracted from the soleus (NWT = 11, NKO = 11) and EDL (NWT = 11, NKO = 11) muscles of an additional 6 WT and 6 KO mice. To isolate the myofibrils, muscles were first skinned as described above. A small piece of the skinned muscles (about 5 mm in length and 2 mm in width) was placed in a microcentrifuge tube containing rigor solution and vortexed to separate individual myofibrils [START_REF] Joumaa | The origin of passive force enhancement in skeletal muscle[END_REF].

Passive mechanical test performed with myofibrils

Myofibrils were placed in a bath on the stage of an inverted microscope and attached to a glass needle at one end, and to a nanolever at the other end (Fig. 1), allowing for length changes and force measurements, respectively [START_REF] Powers | Titin force enhancement following active stretch of skinned skeletal muscle fibres[END_REF]. The sarcomere striation pattern of the myofibrils was projected onto a linear photodiode array for determination of individual sarcomere lengths. The diameter of the myofibrils was measured at a magnification of 250X and used to determine the cross-sectional area of myofibrils. Subsequently, myofibrils were set at an average sarcomere length of 2.4 µm. They were then passively stretched at a speed of 0.1 µm.s -1 to an average sarcomere length of 3.4 µm. The stretch was held for 20 seconds until a steady-state force was reached, and then released. Passive force reached at steady-state, i.e at the end of the test, was determined and converted to static stress (s) by dividing the recorded force by the cross-sectional area of each myofibril.

Statistical analysis

The SystatTM V11 software (Systat Software Inc., CA, USA) was used for all statistical analyses. Non-parametric two-sample Mann-Whitney tests were used to compare all parameter values at a given scale between the WT and KLF10 KO genotypes. Results were considered significant for p < 0.05. At the macroscopic scale (Fig. 3), all passive parameters (i_Ramp, E, ds_Relax,t1/2) obtained for WT controls and Klf10 KO soleus muscle were within the same range (Fig. 3A, Table 1A).

Results

Comparison between Klf10 KO and WT soleus across scales

However, none of these reached statistical significance (Table 2).

At the microscopic scale, a significant difference (P < 0.01) was observed for all of the parameters analyzed (Fig. 3B, Table 1B, Table 2), excepted for the half relaxation time, between fibers extracted as a function of mouse genotype.

At the submicron scale, no significant difference was found for the static stresses (s) of myofibril filament between WT and Klf10 KO animals (Fig. 3C, Table 1C, Table 2). Of note, there was much more variability between individual myofibrils isolated from Klf10 KO mice.

To conclude, particularly at the microscopic scale, there were significantly higher values (P < 0.01) in the passive stresses and Young's modulus of the Klf10 KO soleus fibers. At the macroscopic scale (Fig. 5A), all passive parameters (i_Ramp, E, ds_Relax) for the Klf10 KO were slightly higher compared to the WT control (Table 3A). However, none of these, including the half relaxation time, reached statistical significance (Table 4).

Comparison between Klf10 KO and WT EDL across scales

At the microscopic scale (Fig. 5B), a significant difference (P < 0.01) was observed for all of the parameters analyzed (Table 3B,Table 4), excepted for the half relaxation time, between WT and Klf10 KO fibers.

At the submicron scale, no significant difference was found for the static stresses (s) of myofibril filaments between WT and Klf10 KO animals (Fig. 5C, Table 3C, Table 4).

Overall, particularly at the microscopic scale, there were significant lower values (P < 0.01) in the passive stresses and Young's modulus of the EDL muscle in the absence of Klf10 expression.

Discussion

Klf10 is known to be highly expressed in skeletal muscle [START_REF] Subramaniam | Identification of a novel TGF-β-regulated gene encoding a putative zinc finger protein in human osteoblasts[END_REF][START_REF] Subramaniam | Tissue, cell type, and breast cancer stage-specific expression of a TGF-β inducible early transcription factor gene[END_REF], and we have previously reported multiple scale impacts through phenotypic differences in the skeletal muscle organization: increase of fiber diameter [START_REF] Kammoun | Impact of TIEG1 on the structural properties of fast and slow twitch skeletal muscle[END_REF], shorter sarcomere length [START_REF] Kammoun | Novel role of Tieg1 in muscle metabolism and mitochondrial oxidative capacities[END_REF], etc. We have also discovered substantial differences in mitochondrial localization and function [START_REF] Kammoun | Novel role of Tieg1 in muscle metabolism and mitochondrial oxidative capacities[END_REF], particularly in the soleus muscle. At the molecular level, we have also demonstrated significant impacts of Klf10 on muscle metabolism [START_REF] Baroukh | Serum and soleus metabolomics signature of Klf10 knockout mice to identify potential biomarkers[END_REF].

The basis for the present study was to analyze the impact of Klf10 gene deletion on the passive mechanical properties of fast and slow twitch skeletal muscles at the macroscopic, microscopic and submicron scales. More specifically, at each scale, we have evaluated only the linear elastic properties of this tissue and have compared the results to those obtained from WT littermate controls. Future directions of this work will be to apply different strain rates to the muscle tissue, with passive mechanical tests, which would allow for the study of the non-linear responses such as Meyer's study (Meyer et al., 2011b). In addition, it is of interest to use the same amplitude of strain for all specimens in order to compare the mechanical behaviors between the scales.

An efficient way to describe the mechanical behaviors of a muscle at different scales is through finite element modeling [START_REF] Wheatley | Skeletal muscle tensile strain dependence: Hyperviscoelastic nonlinearity[END_REF][START_REF] Wheatley | Finite element analysis of skeletal muscle: a validated approach to modeling muscle force and intramuscular pressure[END_REF]. Such modeling includes a constitutive law with multiscale parameters (mechanical behavior of the underlying components, microscopic and macroscopic architecture, fast and slow fibers, etc.) by homogenization methods [START_REF] May-Newman | Homogenization modeling for the mechanics of perfused myocardium[END_REF][START_REF] Röhrle | A physiologically based, multi-scale model of skeletal muscle structure and function[END_REF][START_REF] Subramaniam | Tissue, cell type, and breast cancer stage-specific expression of a TGF-β inducible early transcription factor gene[END_REF], 2019). The macroscopic behavior of the tissue is predicted by complex scale shifting operations representing the intersecting phenomena between the components. In spite of these different elements, the multiscale link between mechanical properties of muscle fibers and the global homogenized functional behavior of striated skeletal muscle remains underexplored. One of the reasons for this state of affairs is that the development and validation of such muscle models requires not only the measurement of experimental data of anatomical and morphological types, but also functional (or mechanical) data at both the macroscopic, microscopic and submicron scales.

To begin to address this void, we sought to evaluate the biomechanical properties of skeletal muscle at various scales and to explore how such mechanical evaluation may reveal known structural phenomena. Results from the present study indicate that only the passive mechanical behaviors at the microscopic scale were significantly different between Klf10 KO and WT animals for both of the muscles analyzed (soleus and EDL). It should be noted that opposite variations in the passive mechanical parameters for soleus and EDL were observed whereby the KO fibers showed higher and lower values compared to WT fibers, respectively. These results demonstrated that Klf10 has a fiber-type specific impact on skeletal muscle at the microscopic scale. This may be due to the different roles of Klf10 on the oxidative and glycolytic signaling pathways [START_REF] Kammoun | Impact of TIEG1 on the structural properties of fast and slow twitch skeletal muscle[END_REF][START_REF] Kammoun | Novel role of Tieg1 in muscle metabolism and mitochondrial oxidative capacities[END_REF].

To gain insight into the origin of the Klf10 KO passive behaviors observed at the different scales, myofibril filaments were tested as they represent the primary mechanical properties of the sarcomere without the confounding effect of any extra-cellular passive components.

Interestingly, similar values were found between WT and Klf10 KO myofibrils for both muscles. Since the primary, and virtually exclusive, passive forces in myofibrils originate from the sarcomeric protein titin, it is safe to assume that the titin isoforms in Klf10 KO and WT are similar and have similar mechanical properties. Indeed, a complementary analysis [START_REF] Kammoun | Krüppel-like factor 10 regulates the contractile properties of skeletal muscle fibers in mice[END_REF] on the molecular weights of titin for WT and Klf10 KO mice showed that there is no difference in titin isoforms. Therefore, it may reasonably be concluded that the changes in the passive properties found at the fiber level do not originate from sarcomeric structures. Thus, the observed fiber-type specific changes in passive force in Klf10 KO mice are likely in the collagenbased extracellular matrix surrounding the fiber.

Of future interest is to additionally incorporate characterization at the mesoscopic scale (i.e. the fascicle), but at present established and validated techniques have not been reported (Meyer et al., 2011a). Fascicles are surrounded by the perimysium and are composed of fibers also surrounded with collagenous extracellular tissues (endomysium). Therefore, it is likely that the extracellular matrix contributes to the overall mechanical properties of the whole muscle. Indeed, [START_REF] Brashear | Passive stiffness of 19 fibrotic skeletal muscle in mdx mice relates to collagen architecture[END_REF] showed that the structural organization of the collagen fibers within the ECM impacts the mechanical properties of the tissue. Interestingly, we have previously demonstrated that loss of Klf10 expression results in a modification of the collagen network which may also contribute to altered mechanical properties [START_REF] Doucet | Modeling the lateral organization of collagen molecules in fibrils using the paracrystal concept[END_REF][START_REF] Gumez | Molecular structure of tail tendon fibers in TIEG1 knockout mice using synchrotron diffraction technology[END_REF]. In addition, [START_REF] Dimario | KLF10 gene expression modulates fibrosis in dystrophic skeletal muscle[END_REF] demonstrated an impact of Klf10 in the fibrosis process of the Duchenne myopathy disease. However, similar passive mechanical properties were observed between WT and Klf10 KO hindlimb muscles in the present study. It is possible that use of higher strains in these tests would allow for the detection of macroscopic differences that are not observed with lesser strains. In addition, it is of interest to analyze the role of Klf10 in mediating the composition and maintenance of extracellular matrix components such as collagens in soleus and EDL muscles. Moreover, the cytoskeleton and/or cytoplasm components and properties of muscle fiber cells could also be analyzed.

Recently, non-invasive imaging techniques such as elastography [START_REF] Kammoun | Development of a novel multiphysical approach for the characterization of mechanical properties of musculotendinous tissues[END_REF][START_REF] Qin | Combining MR elastography and diffusion tensor imaging for the assessment of anisotropic mechanical properties: a phantom study[END_REF]) make it possible to characterize such mechanical properties in vivo allowing for longitudinal assessment and ultimately non-invasive monitoring of pathological progression in the case of specific muscle diseases. In a previous study [START_REF] Ternifi | Ultrasound image processing to estimate the structural and functional properties of mouse skeletal muscle[END_REF], ultrasound shear wave (SWE) elastography was performed on Klf10 KO mice and the passive mechanical behaviors of a group of muscles were measured as it was not possible to independently analyze slow and fast twitch muscles. Nevertheless, non-invasive imaging techniques are promising tools for assessment of selected mechanical properties at the macroscopic scale, but at present, in vitro multiscale investigation is still required for comprehensive analysis of the mechanical properties at the different structural levels of muscle.

It has been shown that bones and tendons adapt their mechanical properties when muscles change their function, for example in disease, aging or disuse. Such adaptations also take place within the different structural levels of muscle, as reflected in the data presented here, thus, possibly providing a better understanding of the effects of Klf10 and the mechanisms by which such adaptations are initiated. This knowledge may serve in multiscale finite element models of muscles in general and Klf10 KO muscles specifically. Our results regarding the differential impact of Klf10 at the different structural levels may be useful in the modeling of other genetic muscle diseases (such as Duchenne myopathy [START_REF] Dimario | KLF10 gene expression modulates fibrosis in dystrophic skeletal muscle[END_REF]) when trying to identify mechanisms of action, treatment therapies, and the prediction of function through diseasespecific muscle models.

Figure Legends

Fig. 1. Representation of the mechanical tests realized on healthy mouse at the macroscopic (muscle), microscopic (fiber) and submicron (myofibril) scales. Fig. 2. Representative stress vs time curves for an exemplar ramp test (left side) and an exemplar relaxation test (middle side with a zoom of the initial stress on the right side), at the macroscopic (A), microscopic (B) and submicron (C) scales from wild type (WT) and Klf10 knockout (KO) soleus muscles. For the ramp test, the velocities were approximately 0.167 mm.s -1 , 66 µm.s -1 , 0.1 µm.s -1 for muscle, fiber and myofibril, respectively. For the relaxation test, the velocities were approximately 50 mm.s -1 and 6.6 mm.s -1 for muscle and fiber, respectively. Fig. 3. Boxplots of instantaneous stress (i_Ramp), static stress (s, s_Relax), dynamic stress (d), Young's modulus (E) and half relaxation time (t1/2) values of the soleus muscle components at the (A) macro and (B) micro scales, and for the ramp test and the relaxation test. ** : p < 0.01 (Mann-Whitney's test). Fig. 4. Representative stress vs time curves for an exemplar ramp test (left side) and an exemplar relaxation test (middle side with a zoom of the initial stress on the right side), at the macroscopic (A), microscopic (B) and submicron (C) scales from wild type (WT) and Klf10 knockout extensor digitorum longus (EDL) muscles. For the ramp test, the velocities were approximately 0.167 mm.s -1 , 66 µm.s -1 , 0.1 µm.s -1 for muscle, fiber and myofibril, respectively. For the relaxation test, the velocities were approximately 50 mm.s -1 and 6.6 mm.s -1 for muscle and fiber, respectively.

Table 3

For the (A) macroscopic, (B) microscopic and (C) submicron scales, instantaneous stress (i_Ramp), static stress (s, s_Relax), dynamic stress (d), Young's modulus (E) and half relaxation time (t1/2) values (mean ± sem) of the extensor digitorum longus (EDL) muscle components for wild-type (WT) and knockout (KO) mice obtained with the ramp and relaxation tests. ** : p < 0.01 (Mann-Whitney's test).

Figure 2

 2 Figure 2 depicts the comparison of the stress curves between WT and Klf10 KO soleus at

Figure 4

 4 Figure 4 depicts the comparison of the stress curves between WT and Klf10 KO EDL at each

Fig. 5 .

 5 Fig. 5. Boxplots of instantaneous stress (i_Ramp), static stress (s, s_Relax), dynamic stress (d), Young's modulus (E) and half relaxation time (t1/2) values of the extensor digitorum longus (EDL) muscle components at the (A) macro and (B) micro scales, and for the ramp test and the relaxation test. * : p < 0.05 ; ** : p < 0.01 (Mann-Whitney's test).

Table 1

 1 For the (A) macroscopic, (B) microscopic and (C) submicron scales, instantaneous stress (i_Ramp), static stress (s, s_Relax), dynamic stress (d), Young's modulus (E) and half relaxation time (t1/2) values (mean ± sem) of the soleus muscle components for wild-type (WT) and knockout (KO) mice obtained with the ramp and relaxation tests. ** : p < 0.01 (Mann-Whitney's test).

	(A) Macroscopic scale
		 i_Ramp (kPa)	 (kPa)	 s_Relax (kPa)	 d (kPa)	t1/2 (ms)
	WT (n = 8)	256.8 ± 8.1	1.52 ± 0.06	146.8 ± 4.2	368.3 ± 10.5	104.6 ± 4.0
	KO (n = 9)	249.7 ± 14.7	1.52 ± 0.10	140.0 ± 7.3	361.0 ± 19.1	97.1 ± 3.0
	(B) Microscopic scale
		 i_Ramp (kPa)	 (kPa)	 s_Relax	(kPa)	 d (kPa)	t1/2 (ms)
	WT (n = 17)	212.6 ± 20.4	0.60 ± 0.06	108.9 ± 11.0	305.6 ± 26.1	64.9 ± 2.2
	KO (n = 16)	321.3 ± 28.0 **	0.97 ± 0.10**	174.4 ± 15.7**	444.7 ± 40.2**	68.4 ± 2.4
	(C) Submicron scale
		 s (kPa)
	WT (n = 11)	51.8 ± 6.4
	KO (n = 11)	47.8 ± 7.7

Table 2

 2 For the macroscopic, microscopic and submicron scales, p-value of Mann-Whitney test for the comparison, between wild-type (WT) and knockout (KO) soleus muscle components of the instantaneous stress (i_Ramp), static stress (s_Relax), dynamic stress (d), Young's modulus (E) and half relaxation time (t1/2) values (mean ± sem) obtained with the ramp and relaxation tests. ** : p < 0.01 (Mann-Whitney's test).

		 i_Ramp		 s_Relax	 d	t1/2
	Macroscopic
	scale	0.773	0.847	0.700	1.000	0.200
	(WT vs KO)
	Microscopic
	scale	0.008	0.004	0.002	0.009	0.364
	(WT vs KO)
		 s
	Submicron
	scale	0.526
	(WT vs KO)

Table 4

 4 For the macroscopic, microscopic and submicron scales, p-value of Mann-Whitney test for the comparison, between wild-type (WT) and knockout (KO) extensor digitorum longus (EDL) muscle components of the instantaneous stress (i_Ramp), static stress (s_Relax), dynamic stress (d), Young's modulus (E) and half relaxation time (t1/2) valuesinstantaneous stress (i_Ramp), static stress (s, s_Relax), dynamic stress (d), Young's modulus (E) and half relaxation time (t1/2) values (mean ± sem) obtained with the ramp and relaxation tests. ** : p < 0.01 (Mann-Whitney's test).

	(A) Macroscopic scale
		 i_Ramp (kPa)	 (kPa)	 s_Relax (kPa)	 d (kPa)	t1/2 (ms)
	WT (n = 8)	193.1 ± 14.7	1.16 ± 0.10	110.3 ± 7.0	295.4 ± 18.2	98.4 ± 4.4
	KO (n = 10)	171.0 ± 13.9	1.01 ± 0.08	96.7 ± 7.3	269.2 ± 17.2	108.6 ± 4.8
	(B) Microscopic scale
		 i_Ramp (kPa)	 (kPa)	 s_Relax	(kPa)	 d (kPa)	t1/2 (ms)
	WT (n = 16)	286.7 ± 34.0	0.86 ± 0.13	. 147.8 ± 19.9	396.9 ± 47.1	74.2 ± 7.6
	KO (n = 15)	154.3 ± 10.8**	0.45 ± 0.04**	81.2 ± 5.8**	219.0 ± 15.4**	73.8 ± 5.4
	(C) Submicron scale
		 s (kPa)
	WT (n = 11)	42.5 ± 4.7
	KO (n = 11)	41.6 ± 7.2

Acknowledgements

This work was supported by Idex Sorbonne University SU-19-3-EMRG-12 (S.F.B), the Research Department of UTC within the framework of AMI International (S.F.B) and the National Institutes of Health (USA), Grant No. R01 DE14036 (J.R.H.). This work was also supported by the Interdisciplinary Thematic Institute ITI HealthTech, as part of the ITI 2021-2028 program of the University of Strasbourg, CNRS and Inserm, through IdEx Unistra (ANR-10-IDEX-0002) (S.C) and SFRI (STRAT'US project, ANR-20-SFRI-0012 (S.C). We would also like to thank Frank Corl of the Mayo Clinic for the artistic rendering provided in Fig. 1.

Declaration of competing interest

The authors declare that they have no competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Victor Gysembergh

Babylonian Astral Sciences and Mathematics in Uruk After 47 CE

Keywords: Babylonian Astronomy, History of Science, Uruk

This paper argues that the cuneiform tablet TU 11 can be dated to after 47 CE based on a parallel with Greco-Roman sources; that tablet TU 31 can be dated similarly, because it was written by the brother of the scribe of TU 11; and that the new datings of TU 11 and 31 lend further weight to the astronomical dating of tablet W 22340a to 79/80 CE. Some historical consequences of these datings are then examined: Akkadophone scribes appear to have continued after 47 CE to maintain and develop the astral sciences and mathematics of the cuneiform tradition.

Introduction

Greek and Latin sources from the 1 st and 2 nd centuries CE express a notion that the ancient Mesopotamian city of Uruk was still very much an active center of astral science in their time. 1 Strabo of Amasea, the Greek-language historian and geographer of the Augustan period (d. after 25 CE), mentions its inhabitants, the Ὀρχηνοί, in the present tense as one of the "clans" (γένη) of "Chaldean" astronomers (Geography, XVI, 1, 6). Pliny the Elder (23/24 -79 CE) calls them Orcheni and notes their "Chaldean" doctrine (Natural History, VI, 123). An astrological papyrus from Oxyrhyhnchus dated on paleographical grounds to the 2 nd century CE, P. Oxy astr. 4139, ascribes certain astronomical parameters to the Ὀρχη [νοί]. It is often assumed that these references to Uruk reflect an earlier state of affairs because, despite continued occupation of the city, the latest securely dated cuneiform tablet from Uruk (W 18568) is from 108 BCE -a time at which the temples "Irigal, Bīt rēš, and all the god's houses" are said to still be operating. 2 An astronomical almanac from Uruk (W 22340a) can arguably be dated to 79/80 CE, but this date does not allow us to account for all the phenomena described in the diary, and skepticism has therefore been expressed regarding such a date 3 . This paper will present evidence that the cuneiform tablet from Uruk known as TU 11 = TCL VI, 11 (Paris, Musée du Louvre, inventory number AO 6455) dates from after -arguably, long after -the year 47 CE. A hand-copy of TU 11 was published in 1922 by François Thureau-Dangin. 4 The tablet was edited for the first time, with a translation and commentary, in 2002 by Lis Brack-Bernsen and Hermann Hunger. 5 It "contains a mixture of … astrological, meteorological and astronomical prediction rules". 6 Visual inspection of the tablet at the Musée du Louvre in November 2022 revealed that the tablet measures 133mm in length by 178 mm in height by 14 mm in thickness, and is unusually flat on both sides. Its single-column layout seems unusual for such a wide tablet, as if reflecting a writing board. Its color is ivory white, like a wax tablet. The tablet's surface exhibits numerous firing-holes (not noted by Thureau-Dangin) and it seems to have been baked. It is written in the regular and aesthetically pleasing hand of a highly proficient scribe. Collation of the tablet further yielded the following observations about unusual features and difficult passages in the text: -obv. 9: the line runs over as in Thureau-Dangin's hand-copy, the overrunning characters being preceded by a double Trennungszeichen (i.e. MesZL sign n° 577, duplicated). This feature, which is not reflected in Brack-Bernsen and Hunger's edition, suggests that the lines in the exemplar were very long.

-obv. 22: MIN is certain.

-obv. 23: PA is certain.

-obv. 35: as on obv. 9, the line runs over and the overrunning characters are preceded by a double Trennungszeichen.

-rev. 19: the first sign is clearly šá (not 4), written with two verticals atop one vertical. It is tempting to read šá-niš. The second 4 is confirmed, but it is also tempting to read šá ! -niš.

-rev. 20: the LA sign in al-la is a supralinear addition, as suggested by Thureau-Dangin's handcopy (this is not reflected in Brack-Bernsen and Hunger's edition).

-rev. 32: itu DU6 4 (not 5).

-rev. 33: TAR TAR TI (not UB UB TI).

-rev. 34: 30 GI is confirmed.

The chronological significance of the 654-year cycle mentioned in TU 11

The colophon of TU 11 states that it is a "tablet of Nidinti-Ani, son of Ina-qibīt-Ani, descendant of Hunzû, incantation priest of Anu and Antu, from Uruk. Hand of Anu-uballiṭ, his son" (TU 11, rev. 38; transl. Brack-Bernsen and Hunger). In other words, the scribe is referred to as Anuuballiṭ, son of Nidinti-Ani and grandson of Ina-qibīt-Ani, descendant of Hunzû. Based on this colophon, the editors (following Thureau-Dangin's opinion) dated the tablet "towards the end of the 3rd century B.C.", because they believed the scribe to be identical with the Anu-uballiṭ, son of Nidinti-Ani, who wrote the tablets TU 16 and BRM 4,12. 7 However, in the colophon of TU 16, the scribe is referred to as Anu-uballiṭ, son of Nidinti-Ani and grandson of Anu-bēlšunu (not Ina-qibīt-Ani), descendant of Hunzû; in the colophon of BRM 4, 12, the scribe is referred to as Anu-uballiṭ, son of Nidinti-Ani and grandson of Anu-bēlšunu (not Ina-qibīt-Ani), descendant of Ekur-zākir (not Hunzû)8 . Thus, the dating of TU 11 to the 3rd century BCE based on the identification of its scribe cannot stand. On the other hand, the scribe of TU 11 seems to have been the brother of the scribe of TU 31, who is referred to as Ina-qibīt-Ani, son of Nidinti-Ani and grandson of Ina-qibīt-Ani, descendant of Hunzû9 . In this respect, it should also be emphasized that the inventory number of TU 31 (AO 6456) follows immediately upon that of TU 11 (AO 6455).10 These two tablets share the same unusual flatness on both sides. The dimensions of TU 31 are 12.5 cm in length by 20.5 cm in height by 2.1 cm in thickness. 11 Its handwriting is also that of a highly proficient scribe, and it is the same color as TU 11. It has been argued that tablets AO 6448-6496 from the Louvre Museum in Paris all stem from one specific site within the Rēš temple of Uruk, because of links between some of these tablets and others kept in Berlin, Chicago and Istanbul 12 . Because many of these tablets date to the first half of the 2 nd c. BCE, the recognition of one homogeneously provenanced group would provide a strong chronological indication that TU 11 and 31 also date from ca. 200-150 BCE. However, this argument is inconclusive: indeed, the Paris tablets linked with the Berlin, Chicago and Istanbul collections are all contained within the subset AO 6470-6486, except for AO 6448 13 ; and while AO 6449-6486 were all purchased in one lot from the Dumani brothers, AO 6448 was purchased separately, from Elias Géjou. 14 Hence there is no reason to believe that tablets AO 6449-6469 were found near AO 6470-6486, nor indeed that they all have the same provenance -the Dumani brothers may just as well have sold tablets recovered in various parts of the Rēš temple and elsewhere in Uruk/Warka. Unfortunately, therefore, the limited information available about the provenance of TU 11 and 31 does not provide any means of dating these two tablets. Fortunately, it is possible nevertheless to establish a terminus post quem for TU 11 (and as a corollary, for TU 31) based on a hitherto unnoticed parallel with Greco-Roman sources. In a section dealing with cyclical meteorological phenomena of ominous significance, the text indicates that:

"In 72 years a comet which had appeared in the Tails, will appear (again) in the Tails, (and) in 36 years it will correspond (Akk. ip-pal, lit. 'answer'). In 21 years rain will correspond to rain, flood to flood. In 21 years an earthquake will correspond to an earthquake. In 654 years -broken (Akk. he-pí)." (TU 11, rev. 27-28; transl. Brack-Bernsen and Hunger, slightly modified) 15 Before proceeding with the chronological argument, it should be noted that the unpublished tablet BM 36665+37056+37074 from Babylon contains a quasi-duplicate of this passage on Rev. 7-10. 16 While the rest of the section mostly agrees with the Uruk tablet, Rev. 10 reads: ina 10,⸢48 MU.MEŠ⸣ ana 1-en GUR šá ⸢MU ? ⸣ […]. 17 Regardless of whether the time-period on the Babylon tablet should be read "in 648 years" or "in 658 years", two alternative interpretations of the difference with the Uruk tablet offer themselves: either the discrepancy is due to a scribal error, in which case there is no basis on which to decide which tablet has the correct number; or the number, and perhaps the text after it, were altered intentionally to 654 in a precursor of the Uruk text to reflect a difference in world-view, as often happens in scholarly texts. The present author inclines towards the second interpretation, but whatever the case may be, the textual variant 648 (or 658) in BM 36665+ does not significantly weaken the argument that will now be presented for dating TU 11 based on the 654-year period.

At first glance, it may seem hopeless to try to explain this 654-year period, considering that the remainder of the sentence was broken in the tablet from which TU 11 was copied (or in an earlier exemplar). Furthermore, no explanation has been put forward of this number in the context of Mesopotamian astral sciences, which suggests that the number may have a foreign background. And indeed, a similarly cyclical and ominous 654-year period is known from ancient Greek and Roman texts (this parallel does not seem to have been pointed out in previous literature). 18 The Byzantine encyclopedia known as the Souda, which compiles valuable ancient sources, indicates the following in its entry on the phoenix: "During the reign of emperor Claudius (viz. 41-54 CE), they say that it (i.e. the phoenixbird) came unto the Egyptians after a period of 654 years." (Souda, φ 798; my translation) 19 Similar information is given by the historian Publius Herennius Dexippus (3 rd c. CE), as quoted by the Byzantine Chronographer George Syncellus (8 th -9 th c. CE):

"At this time (viz. during the reign of emperor Claudius), the phoenix-bird appeared, according to the Egyptians' reports, having appeared 654 years earlier, as Dexippus also agrees." (P. Herennius Dexippus apud George Syncellus, p. 407, ll. 3-4 Mosshammer; my translation) 20 ina 6 ME 54 MU.MEŠ he-pí. Collation of the original tablet confirmed Thureau-Dangin's handcopy and Brack-Bernsen and Hunger's edition for this passage, including the number 654. 16 The three fragments in the British Museum were joined by John Steele, who generously permitted me to quote from his forthcoming edition. 17 According to Prof. Steele, the traces he reads as 48 are also consistent with 58, although he finds this less plausible. The meaning of ana 1-en GUR, literally "(they) return to one", remains unclear to the present author. 18 On the complex cosmic symbolism of the phoenix in the Greco-Roman world and its relation to the Egyptian benu, see Van den Broek, 1972. 19 22 See Rackham, 1940: 295. 23 See Van den Broek, 1972: 116. 24 See Jackson, 1937: 201.

Ptolemaeum ac Tiberium minus ducenti quinquaginta anni fuerunt. Unde nonnulli falsum hunc phoenicem. "As to its term of years, the tradition varies. The generally received number is five hundred; but there are some who assert that its visits fall at intervals of 1461 years, and that it was in the reigns, first of Sesosis, then of Amasis, and finally of Ptolemy (third of the Macedonian dynasty), that the three earlier phoenixes flew to the city called Heliopolis with a great escort of common birds amazed at the novelty of their appearance. But while antiquity is obscure, between Ptolemy and Tiberius there were less than two hundred and fifty years: whence the belief has been held that this was a spurious phoenix." (Tacitus, Annals VI, 28; transl. J. Jackson 25 )

This passage further illustrates that the duration of the phoenix cycle was a matter of debate among Roman scholars, as was the exact moment of its appearance. Nonetheless, the appearance of a phoenix towards the end of Tiberius' reign was clearly understood in the Roman empire as a potential sign of epochal change. 26 An appearance of the phoenix towards the end of Tiberius' reign should have announced prosperity under the next emperor, but this did not ensue as Caligula (r. 37-41) proved to be a mad and cruel ruler. It is in this context that Caligula's successor Claudius exhibited the phoenix on the Roman Forum, hoping to usher in a new Golden Age. Considering the scholarly debates about the date and authenticity of the phoenix's appearance under Tiberius, it is understandable that later tradition focused on the event of the Roman exhibition during the city of Rome's 800 th anniversary, rather than on the bird's doubtful appearance.

Although the number 654 has defied explanation until now 27 , it appears to have been derived by Greco-Roman scholars who calculated the interval between the reign of pharaoh Amasis II, when a previous appearance of the phoenix was supposed to have taken place, and the 6 th year of Claudius' reign. To perform this calculation, they demonstrably used a list of regnal durations that was related to the regnal years in Eusebius' Chronicles: the first year of Claudius' reign is supposed to have been in anno Abrahami 2057 (according to both Jerome's Latin translation and to the anonymous Armenian translation), and the first year of Amasis II's reign in anno Abrahami 1451 (also according to both translations). 28 Now, the subtraction of 1451 from 2057 yields a period of 606 years, to which adding 6 (for the sixth regnal year of Claudius) yields a result of 612 years. This is still 42 years short of the phoenix period, which is exactly the length of Amasis' reign according to Eusebius. For whatever reason, the authors of the calculation must have assumed that a.A. 2057 was not the beginning but the end of Amasis'

25 See Jackson, 1937: 201. 26 See Van den Broek, 1972: 113 ff. 27 See Van den Broek, 1972: 69. 28 The original Greek text of Eusebius' chronicle is mostly lost and must be reconstructed by comparing Jerome's Latin translation and the anonymous Armenian translation. When both agree with each other, this generally indicates that they reflect Eusebius' original text faithfully. The reference edition of Jerome's Latin translation is by Helm, 1956; the reference edition of the anonymous Armenian translation is by Karst, 1911. Useful information on how to use Eusebius' Chronicle is given by Mosshammer, 1979; and in Cohen-Skalli, 2020. reign, and therefore added another 42 years to the 612 years. These arithmetical operations can be conveniently summed up as: 2057 (beginning of Claudius' reign) -1451 ((beginning of) Amasis' reign) + 42 (length of Amasis' reign) + 6 (for the sixth year of Claudius' reign) = 654 years. This calculation can be described as an attempt by ancient scholars to determine, based on the chronographical evidence available to them, the exact duration of the period between two successive appearances of the phoenix (this attempt contrasts with the vague figure of 500 years that was 'generally received' according to Tacitus, and with a different attempt at an exact assessment by reinterpreting the so-called Sothis period of 1461 years, which is important in calendar theory, as the Phoenix period). Although it is not possible to divine just how the calculations were conducted and combined, the above reconstruction implies that the 654-year period, explicitly associated in Greco-Roman sources with appearances of the phoenix, cannot have been calculated before the sixth year of Claudius' reign, i.e. in 47 CE. In and of itself, it is unlikely that such a large number as 654 would appear in a Late Babylonian tablet, independently from the Greco-Roman tradition, as the period between two instances of an ominous event. It was likely to travel far in as much as it was connected with an event of worldwide significance: the 800 th anniversary of the Roman empire. Furthermore, the reference in George Syncellus, by mentioning a local Egyptian tradition in this connection, may bear witness to the intercultural circulation of a 654-year phoenix cycle all around the Mediterranean, although we should be wary of the possibility that this local tradition may have existed only in George's or Dexippus' mind. A similar instance of long-distance exchange arguably underlies the comet period of 72 years mentioned by TU 11, which is close to the 70year comet period referred to in the Babylonian Talmud, Horayoth 10a 29 . Finally, the notion of a phoenix-bird had an analogue in Mesopotamian mythology in the guise of the monstruous storm-bird Anzû, who shares the phoenix's eagle-like features, mountain origins and connection to flooding 30 , and has obvious cosmic significance although he does not seem to be otherwise associated with periodic returns. 31 Under these circumstances, it is reasonable to assume that the 654-year period made its way from Rome to scholars of the cuneiform tradition, perhaps through intermediaries.

Some consequences of dating TU 11 based on the 654-year cycle

29 For a detailed discussion of this parallel, see V. Gysembergh, in press. The story of Gamaliel's voyage to Rome is generally dated towards the end of the reign of Roman emperor Domitian (r. 81-96). This passage and TU 11 contain the only two quantitative assessments of a comet period known from Antiquity. 30 On the mythology of Anzû see esp. Hruška, 1975. On Anzû and the phoenix's eagle-like features, compare Hruška, 1975: 251-253 and Van den Broek, 1972: 251-253; on their mountain origins, compare Hruška, 1975: 48-51 Van den Broek, 1972: 166-168 and passim; on their connection to flooding, compare SB Anzû, Tablet 1, ll. 50-51 (with Foster, 2003: 555), and van den Broek, 1972: 71-74 and passim. 31 Indeed, it is possible that a reference to Anzû was made in the Vorlage of TU 11 before it was broken (an unfortunate break in the Vorlage just after the indication of "654 years" by the he-pí notation at the end of TU 11, rev. 28) -but this is a mere guess.

Having made the case for dating TU 11 based on the parallel with the 654-year phoenix cycle known from Greco-Roman sources, let us now move on to considering some consequences of such a dating. Not only does it put the date of TU 11 in or after 47 CE: since the tablet is a copy of a broken Vorlage, decades (if not centuries!) likely separate it from its original exemplar, so that the Louvre tablet may have been copied at any time during the second half of the 1 st century CE, or even during the 2 nd or 3 rd century32 . Indeed, it is perhaps more likely, on the whole, that the 654-year cycle was borrowed after Roman emperor Trajan's campaign to the East of the Euphrates (115-117 CE). 33 However, it should also be noted that Mediterranean influences were present in Uruk even before Trajan's attempted conquest, as evidenced most clearly by the Greek language and formulary of the inscription from Uruk commemorating the erection of a statue of Artemidoros, son of Diogenes, also called Minnanaios, son of Touphaios, in the temple of the otherwise unknown god Gareus -which inscription dates from 110/111 CE (= 422 SE). 34 In any case, a date after 47 CE makes it all the more remarkable that the tablet is well shaped despite its large format, and that it exhibits firing-holes and was probably baked (as noted above), which indicates a deep familiarity with clay as a writing medium. The tablet's wellformed, non-cursive style of writing is also striking, as the latest cuneiform tablets are often characterized by very cursive script. 35 Finally, the indentation of overflowing lines (as noted above) may provide further support for a very late date, as in astronomical almanacs where this feature appears only in the latest tablets. 36 As a corollary, tablet TU 31 (mentioned above), seemingly written by the brother of the scribe of TU 11, must also be dated to the 1 st c. CE or later. These two tablets taken together point to intense activity in the astral sciences and mathematics in Uruk at the time when they were written. Indeed, TU 31 is a highly unusual table of reciprocals that contains entries not usually included in tables of reciprocals 37 ; and TU 11 presents many features in content and language that are unparalleled in extant cuneiform literature 38 . This suggests that Babylonian science was still alive and continuing to evolve at the time when TU 11 and TU 31 were written. Evidence for such scientific activity also casts a different light on the almanac tablet W 22340a (mentioned above): although the difficulties with its astronomical dating remain, they can of course be due to recording errors and/or scribal mistakes. In a context where Babylonian astral sciences were still in practice in Uruk, Hunger and De Jong's dating of the tablet to 79-80 CE becomes much more likely. 39 The latest currently datable cuneiform tablet from Babylon is an almanac for the years 74/75 CE, and almanacs are also extant for the years 31/32, 36/37, 44/45 and 61/62 CE. 40 The addition of two or three cuneiform tablets from Uruk datable to the 2 nd half of the 1 st century CE or later invites the possibility that other undated Late Babylonian cuneiform tablets, especially of astral and mathematical content, were also written later than commonly assumed. The scribes in these times may have had no reason to refer to the Seleucid or Arsacid era or other dating conventions, and they may conceivably have had reason not to. The vast majority of Late Babylonian tablets not being explicitly dated, it is at least theoretically possible that a significant fraction of this material was in fact written in the 1 st century CE or later. Next to Babylon and Uruk, other possible sources of tablets from such a late time are Nippur and Sippar, both of which may lie behind the mention of a city called 'Hipparenum' quoted by Pliny the Elder (Natural History VI, 123) next to Babylon and Uruk as one of the three centers of "Chaldean" learning in his time. [START_REF]On the identification of the city called 'Hipparenum' by Pliny see Oelsner[END_REF] The survival, and indeed continuing development, of at least some strands of cuneiform culture sheds new light on the so-called 'Graeco-Babyloniaca', a corpus of sixteen clay tablets each bearing an Akkadian text written in both cuneiform and Greek script, and two clay tablets each bearing an Akkadian or Aramaic text written in Greek script. [START_REF]On the Graeco-Babyloniaca see esp[END_REF] The date and purpose of these tablets has been the object of much debate. The evidence presented here is consistent with the idea that they were experiments by advanced cuneiform scholars in using a more generally accepted graphic system to couch their ideas in writing. It also supports the possibility that at least some of the 'Graeco-Babyloniaca' were written in the first centuries CE, as is also suggested by paleographic datings (although paleographic parallels with other Greek texts must be considered with caution because these other texts were not written on clay). [START_REF]A paleographical dating of the Greek script of HSM 1137[END_REF] Finally, this opens up the possibility that traces of Mesopotamian influence in texts from other cultures from the first centuries CE may be due to contemporary instances of cultural interaction, and not to the use of older sources. The latest datable instance known to the present author is a report by the Neoplatonist philosopher Damascius of Athens (ca. 460 -after 538 CE) on "Babylonian" theology that gives an interesting variant of the theogony presented at the beginning of Enūma Eliš: 44 Among the Barbarians, the Babylonians seem, on the one hand, to keep silent about the one principle of all things, and on the other hand, to produce two, Tauthe and Apasōn; they make Apasōn the husband of Tauthe and call her the "Mother of gods".

From them was begotten, as an only son, Mōumin, who is, I think, the intelligible cosmos itself, made from the two principles. From these same (viz. gods) came forth another generation, Lachê and Lachos; and again, from the same (viz. Apasōn and Tauthe), a third (viz. generation), Kissarê and Assēros, from whom are born three (viz. gods), Anos, Illilos and Aos. From Aos and Dauchē is born a son, Bēlos, who according to them is the demiurge. (Damascius, De principiis 3, 165, 6-16 Westerink; my translation). 45 Differences with the Enūma eliš, such as the mention of Enlil, show that Damascius' source(s) cannot have been the standard Babylonian text (nor does it match any other known cuneiform text relating to the myth). The Babylonian theonyms in Damascius' report are remarkably accurate -more so than the often Hellenized Babylonian theonyms introduced in the Greekspeaking world by Berossus (e.g. Ταλάτθ for Tiāmtu). This level of accuracy shows that Damascius cannot be relying on his acknowledged source Eudemus of Rhodes (4 th c. BCE) for the theonyms: in the centuries separating Damascius from Eudemus, these foreign names would have been corrupted beyond recognition by scribal mistakes, in accordance with a phenomenon that can be observed in the manuscript tradition of countless classical texts. Moreover, Damascius was able to explain the difficult word mummu from the Akkadian text by equating it with the Neoplatonic notion of the 'intelligible cosmos', echoing one of the possible Akkadian meanings of the word (viz. 'intelligence, wisdom' 46 ). Since he had occasion to travel in the Near East and is known to have actively researched foreign theologies, it is plausible that he combined general information from Eudemus with specific details such as theonyms collected during his travels. This implies that traditions pertaining to Babylonian theology were still maintained in the Near East in the sixth century CE. In summary, the dating of TU 11 to after 47 CE, the similar dating of TU 31, and the astronomical dating of W 22340a, establish that there was a lively community of practicians of the astral sciences and mathematics in the cuneiform tradition in the second half of the first century CE, and possibly later. This in turn makes it plausible that the culture embedded in cuneiform texts survived and continued to evolve in contact with other cultures during the first 44 For an in-depth study of this report, see Gysembergh and Lecerf, 2016. 45 Greek text: Τῶν δὲ βαρβάρων ἐοίκασι Βαβυλώνιοι μὲν τὴν μίαν τῶν ὅλων ἀρχὴν σιγῇ παριέναι, δύο δὲ ποιεῖν Ταυθὲ καὶ Ἀπασών, τὸν μὲν Ἀπασὼν ἄνδρα τῆς Ταυθὲ ποιοῦντες, ταύτην δὲ μητέρα θεῶν ὀνομάζοντες, ἐξ ὧν μονογενῆ παῖδα γεννηθῆναι τὸν Μωϋμίν, αὐτόν, οἶμαι, τὸν νοητὸν κόσμον ἐκ τῶν δυεῖν ἀρχῶν παραγόμενον• ἐκ δὲ τῶν αὐτῶν ἄλλην γενεὰν προελθεῖν, Λαχην καὶ Λαχον, εἶτα αὖ τρίτην ἐκ τῶν αὐτῶν, Κισσαρη καὶ Ασσωρον, ἐξ ὧν γενέσθαι τρεῖς, Ανον καὶ Ιλλιλον καὶ Αον• τοῦ δὲ Αου καὶ Δαυκης υἱὸν γενέσθαι τὸν Βῆλον, ὃν δημιουργὸν εἶναί φασι. 46 On this possible meaning of mummu see Lambert, 2013: 219. According to Lambert, the equation of mummu with νοητός κόσμος ('intelligible cosmos') stems from Eudemus, but this is implausible because the concept is typically Neoplatonic, not Peripatetic. centuries CE. This makes it highly desirable to continue in future both the search for other tablets datable to the first century CE or later, and the investigation of cultural exchange between the cuneiform and other traditions that may have taken place after the first century CE.

  The cyclical character of the Phoenix period is implicitly grounded in the most fundamental aspect of the Phoenix myth, viz. the bird's periodic death and rebirth.21 Underlying the terse chronographical reports by Dexippus and the Souda is a well attested event of Claudius' reign. Pliny the Elder (Natural History X, 5; see also Caius Iulius Solinus, 33, 14, who depends on Pliny) tells us that during the celebrations for the 800 th anniversary of the founding of Rome, which took place during the sixth year of Claudius' reign, the emperor had the "phoenix" brought to Rome and put on display on the Comitium (the open-air assembly space) of the Forum Romanum:Cornelius Valerianus phoenicem devolavisse in Aegyptum tradit Q. Plautio Sexto Papinio coss.; allatus est et in urbem Claudii principis censura anno urbis dccc et in comitio propositus, quod actis testatum est, sed quem falsum esse nemo dubitaret. "Cornelius Valerianus reports that a phoenix flew down into Egypt in the consulship of Quintus Plautius and Sextus Papinius (viz. 36 CE); it was even brought to Rome in the Censorship of the Emperor Claudius eight hundred years after the founding of the City and displayed in the Comitium -a fact attested by the Records, although nobody would doubt that this phoenix was a fabrication." (Pliny the Elder, Natural History, X, 5; transl. H. Rackham, slightly modified 22 ) Although, according to Pliny, no one at the time believed this phoenix to be real, its existence appears to have been taken for granted by later authors. 23 Tacitus reports that the phoenix had appeared under pharaohs Sesosis (probably meaning Sethos I), Amasis II, and Ptolemy III Euergetes, and more recently under Tiberius in 34 CE: Paulo Fabio L. Vitellio consulibus post longum saeculorum ambitum avis phoenix in Aegyptum venit praebuitque materiem doctissimis indigenarum et Graecorum multa super eo miraculo disserendi. "In the consulate of Paulus Fabius and Lucius Vitellius (viz. 34 CE), after a long period of ages, the bird known as the phoenix visited Egypt, and supplied the learned of that country and of Greece with the material for long disquisitions on the miracle." (Tacitus, Annals VI, 28; transl. J. Jackson 24 ) Tacitus adds that the authenticity of this appearance was debated because the time interval from its latest purported appearance under Ptolemy III Euergetes was considered too short: De numero annorum varia traduntur. Maxime vulgatum quingentorum spatium: sunt qui adseverent mille quadringentos sexaginta unum interici, prioresque alios tres Sesoside primum, post Amaside dominantibus, dein Ptolemaeo, qui ex Macedonibus tertius regnavit, in civitatem, cui Heliopolis nomen, advolavisse, multo ceterarum volucrum comitatu novam faciem mirantium. Sed antiquitas quidem obscura: inter This is F 15 in Martin, 2006; and F 16 in Mecella, 2013. Notably, neither Mosshammer nor Martin and Mecella accept Dindorf's correction of the number of years, which according to the text of the manuscripts is indicated as 650, but they appear to have been unaware of the parallel with the Souda, which strongly supports Dindorf's correction to 654.

See Souda, φ 798 Adler, s.v. Φοῖνιξ: Ἐπὶ Κλαυδίου Καίσαρος ἐλθεῖν φασι τοῦτο τοῖς Αἰγυπτίοις διὰ τεττάρων καὶ ν´ καὶ χ´ ἐτῶν.

20

See George Syncellus, Ecloga chronographica, p. 407, ll. 3-4 Mosshammer : Ἐν τούτοις τοῖς χρόνοις ἐφάνη τὸ ὄρνεον ὁ φοίνιξ, καθὼς ἱστοροῦσιν Αἰγύπτιοι, πρὸ χνδ´ (corr. Dindorf : χν´ δὲ codd.) ἐτῶν φανείς, ὡς καὶ Δέξιππος συμφωνεῖ. Dindorf's correction assumes the common scribal error of mistaking the numeral δ´ (4) for the particle δέ (especially in its elided form δ᾽).

21

See

Van den Broek, 1972 (especially p. 146-232)

.

See Brack-Bernsen and Hunger, 2002.

See Brack-Bernsen and Hunger, 2002: 24.

"Vers la fin du premier siècle des Séleucides" according to Thureau-Dangin, 1922: unpaginated ("Description des tablettes"); "towards the end of the 3 rd century B.C." according toBrack-Bernsen and Hunger, 2002: 6.

See TU 16, rev. 55; BRM 4, 12, 84.

See TU 31 rev., col. 2,[33][34][35]

On the mathematical contents of TU 31, an unusual table of reciprocals, seeOssendrijver, 2019: 191-201.

On the first and second centuries CE as the period when Uruk was most populated according to the archeological record, see[START_REF] Oppenheimer | Babylonia Judaica in the Talmudic Period[END_REF]

 33 It is possible that Uruk was part of the province of Assyria reportedly created by Trajan, as implied byMaricq, 1959 (esp. pp. 257-262). An undated Greek inscription from Uruk may be evidence of support for the Roman empire, on its reading as Κῖσαρ νικᾷ ("hail to the emperor", with iotacistic form of), proposed by Canale di Rossi, 2004: 85, n° 141. However, the existence of this province is disputed, see e.g.Lightfoot, 1990: 121-124. 34 The text of the inscription is given byOppenheimer, 1983: 335-336; and by Canale di Rossi, 2004: 84-85, n° 140. Both authors consider it unlikely that the "year 422" in the text refers to the Arsacid era, which would make its date 175 CE.35 For this claim see e.g.Walker, 1987: 18. 36 On indentation as a characteristic of the latest cuneiform tablets from Babylon seeSachs, 1976: 380 and 395. 37 See Ossendrijver, 2019: 191-201. 38 See the comments byBrack-Bernsen and Hunger, 2002 (esp. pp. 17-23).