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%  enslyonstage-exemple.tex — VISUAL DEMONSTRATION of a completed ENS internship report
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%     To write your own report, open  enslyonstage-gabarit.tex  instead.
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%  The text and figures are taken from a real M1 Biosciences internship report
%  (Zenodo: https://doi.org/10.5281/zenodo.21631816) solely to produce a
%  realistic-looking PDF.  Do not use the scientific content as a reference.
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%  Uses the enslyonstage.cls class
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%  Project structure:
%    enslyonstage-gabarit.tex ← YOUR blank template (start here)
%    enslyonstage-exemple.tex ← this file (full worked example)
%    enslyonstage.cls         ← class file (same directory or on TEXMFHOME)
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%      (exceptions: contact stages.biosciences@ens-lyon.fr)
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\hyphenation{hypo-gra-vi-ty quadru-pe-dal skip-re-la-ted light-wei-ght
             Shevt-sova me-ta-tar-sal hind-limb mul-ti-di-men-sio-nal}

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% ── TITLE ──────────────────────────────────────────────────────────────────
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%   \titre{First part:\texorpdfstring{\\}{ }Second part}
\titre{From Trot to Skip:\texorpdfstring{\\}{ }%
    Mice Adopt Human-like Hypogravity Gait in a Lunar Gravity Harness}

% ── AUTHOR ─────────────────────────────────────────────────────────────────
% Use \textsc{} for small caps on last name: Firstname \textsc{Lastname}
\auteur{Adama \textsc{Mbaye}}

% ── DEGREE LEVEL ───────────────────────────────────────────────────────────
% Enter "M1" or "M2" (without "Biosciences" — added automatically)
\master{M1}

% ── BIOLOGICAL DOMAIN ──────────────────────────────────────────────────────
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% Examples: Molecular and Cellular Biology, Neurosciences, Ecology, etc.
\domaine{Biomechanics}

% ── INTERNSHIP DATES ───────────────────────────────────────────────────────
% Format: DD Month YYYY (e.g., 02 February 2025)
\datedebut{09 February 2026}
\datefin{17 July 2026}

% ── LABORATORY ─────────────────────────────────────────────────────────────
% Laboratory name and/or institute
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\laboratoire{%
    \textsc{Max Delbrück Center for Molecular Medicine}, Berlin, Germany
    }

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% Lab supervisor (internship mentor) — name and email (email not shown on PDF)
\tuteurstage{Dr. N. \textsc{Zampieri}}{}
% ENS academic supervisor — name and email (email not shown on PDF)
\tuteurENS{Dr. J. \textsc{Derr}}{}

% ── ABSTRACT ───────────────────────────────────────────────────────────────
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\abstracts{%
Human astronauts on the lunar surface spontaneously skip rather than walk or
run, driven by the six-fold reduction in gravitational loading. Whether
quadrupeds display an analogous locomotor reorganisation under hypogravity is
unknown. Here we simulated lunar gravity ($\approx 16.5\%\,g$) in
treadmill-running mice using a custom elastic harness, and characterised the
resulting gait with markerless motion capture and comprehensive kinematic
analysis. We first located the center of mass at 50.8\% of body length,
providing a geometric basis for harness placement. Under simulated lunar
gravity, mice displayed several hallmarks of skipping: a 2.5-fold increase in
bilateral aerial time, a near-doubling of stride-to-stride cycle irregularity,
threefold increases in hindlimb paw lift and base of support, and a significant
elevation of the energy recovery ratio. Inter-limb phase coordination was
globally disrupted, with all three coupling directions showing significantly
reduced phase concentration under hypogravity. An unbiased multiple factor
analysis of 104 locomotor parameters confirmed fully distinct locomotor states
($R^2 = 0.638$, $p = 0.001$). These results provide the first evidence that a
skip-like gait is not unique to bipeds but is an emergent quadrupedal response
to reduced gravitational loading.%
}

% ── KEYWORDS ───────────────────────────────────────────────────────────────
% ENS guideline: 5 to 8 keywords
% Comma-separated list of key terms for your work
\keywords{hypogravity, locomotion, skipping, gait, mouse, spring-mass model,
    partial weight-bearing}

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\nombredemots{4676}

% ── PREVIOUS INTERNSHIPS ───────────────────────────────────────────────────
% Table of previous internships shown on cover page
% Use \stagerow{Year}{Lab, City, Country}{Supervisor}{Topic}
% Leave empty fields for levels not yet completed (e.g., M2 if you're in M1)
\stagesanterieurs{
    \stagerow{L3}{Institut Lumière-Matière, Lyon}{O. \textsc{Cochet-Escartin}}{Biophysics of Wnt Pathway}
    \stagerow{M1}{Max Delbrück Center, Berlin}{N. \textsc{Zampieri}}{Locomotion in Hypogravity Simulation in Mice}
    \stagerow{M2}{}{}{}
}

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\section{Introduction}
\label{sec:intro}
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\paragraph{}
\lettrine[lines=3]{O}{n} April 1, 2026, the Artemis~II mission carried four
astronauts on a ten-day journey around the Moon --- the first crewed flight
beyond low Earth orbit since Apollo~17 in 1972, and the opening act of a
planned era of sustained human presence on the lunar surface. As agencies
prepare for crews who will live and move under lunar gravity
($g_\text{Moon} \approx 0.16\,g_\text{Earth}$), a basic biological question
becomes urgent: how does the locomotor system reorganise in a gravitational
environment so different from the one in which it evolved?

The mechanics of legged locomotion are deeply governed by gravity. Two
fundamental mechanisms dominate. In walking, the body vaults over a relatively
stiff supporting limb --- an inverted-pendulum mechanism --- exchanging
gravitational potential energy (tied to height) and kinetic energy (tied to
speed) out of phase to minimise muscular
work\cite{lacquanitiHumanLocomotionHypogravity2017a}. In running and trotting,
the centre of mass bounces like a pogo-stick: potential and kinetic energy vary
in phase while elastic energy is transiently stored and returned by muscles and
tendons\cite{lacquanitiHumanLocomotionHypogravity2017a}. In both cases,
gravitational acceleration sets the characteristic timescales: it determines
preferred stride frequencies, optimal speeds, and ground reaction force
magnitudes. Reducing gravity does not simply make movement easier; it
fundamentally rescales every mechanical relationship that governs coordination
and stability.

This sensitivity is dramatically illustrated by the behaviour of Apollo
astronauts on the lunar surface. At low to moderate speeds, they spontaneously
adopted skipping rather than walking or
running\cite{minettiBiomechanicsSkippingGaits1998,paveiSkippingVsRunning2015}.
Skipping is a bilaterally asymmetric gait in which a walking-like
double-support phase alternates with a running-like aerial phase, and in which
one leading limb consistently produces a longer stride than the trailing limb,
resulting in a characteristic long-short cycle
alternation\cite{minettiBiomechanicsSkippingGaits1998}. The name is doubly
literal: one skips off the ground, and skips over the alternation --- each
limb taking two consecutive beats (\mbox{L--L--R--R}) rather than alternating
at every step (\mbox{L--R--L--R}). Crucially, skipping simultaneously exploits
both the pendulum-like and elastic energy-saving mechanisms, making it the
mechanically optimal gait in reduced
gravity\cite{minettiBiomechanicsSkippingGaits1998}. Whether an analogous gait
reorganisation occurs in quadrupeds under similar gravitational conditions is
entirely unknown.

In quadrupeds, gait is characterised by the inter-limb phase relationships
within a stride cycle\cite{dannerSpinalControlLocomotion2023} (the normalised
delay between two limbs' touchdowns: $0 =$ synchrony, $0.5 =$ perfect
alternation). The trot, the preferred attractor gait of mice at moderate
speeds, is defined by anti-phase coupling between left and right hindlimbs
($\phi_\text{HL} \approx 0.5$) and in-phase coupling between diagonal pairs
($\phi_\text{diag} \approx 0$)\cite{dannerSpinalControlLocomotion2023}. The
bound is equally well defined: both hindlimbs move in synchrony
($\phi_\text{HL} \approx 0$) and both forelimbs in synchrony, with a
half-cycle offset between fore and hind pairs.

To study hypogravity locomotion without access to space, researchers have
developed ground-based partial weight-bearing (PWB) systems. Early designs
relied on tail suspension, which restricts natural quadrupedal locomotion and
redistributes load toward the
forelimbs\cite{mortreuxApproachingGravityContinuum2020}. Subsequent
spring-based harnesses improved range of motion but suffered from daily drift
in unloading\cite{mortreuxApproachingGravityContinuum2020}. Chain-based pelvic
systems offer greater stability at the cost of bulk that may constrain joint
mobility\cite{mortreuxApproachingGravityContinuum2020}. Custom-fitted jacket
harnesses worn by rodents provide a naturalistic
option\cite{mortreuxApproachingGravityContinuum2020}, while the MARS
centrifuge aboard the ISS remains the only true partial-gravity platform but is
severely limited by cost and sample size\cite{shibaDevelopmentNewExperimental2017}.
Crucially, most of these systems were designed to study long-term
musculoskeletal outcomes (bone density, muscle atrophy) rather than
fine-grained locomotor kinematics, and none has been used to ask whether
quadrupeds adopt a skip-like gait under hypogravity.

Here we use a custom lightweight harness system to simulate lunar gravity in
freely running mice on a treadmill. We first determine the anteroposterior
center of mass position to validate harness placement, then characterise the
resulting locomotor phenotype using markerless motion capture and a
comprehensive kinematic analysis. We show that mice exposed to simulated lunar
gravity spontaneously display a gait reorganisation with multiple features of
human skipping: extended bilateral aerial phases, loss of hindlimb antiphase
coupling, increased stride irregularity, and greater hindlimb clearance. These
results provide the first evidence that a skip-like gait is not unique to
bipeds but is an emergent locomotor response to reduced gravity that also
manifests in quadrupeds.

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\section{Materials and Methods}
\label{sec:methods}
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\paragraph{Animals.}
All experiments were performed on adult mice of the
\textit{PV}\textsuperscript{\textit{cre}};\textit{Rx3}\textsuperscript{\textit{flpo}};\textit{Mapt}\textsuperscript{dsDTR};Ai65D
genotype. At the time of the locomotion recordings (day 0), no diphtheria toxin
had been administered and animals exhibited a fully wild-type locomotor
phenotype\cite{santuzWalkingMoonHypogravity2026}. Eight mice were used for the
center of mass determination experiment and seven mice for the treadmill
locomotion experiment, in which each animal was recorded in both the Earth and
Moon conditions (within-subject design). All procedures were conducted in
accordance with institutional animal care and use
guidelines\cite{santuzWalkingMoonHypogravity2026}.

\paragraph{Center of mass determination.}
Following euthanasia, animals were positioned in a standardised running posture
--- one diagonal limb pair extended, the contralateral pair flexed --- and
maintained in this configuration during rigor mortis. Specimens were stored at
\qty{-80}{\degreeCelsius} and handled in a cold room at \qty{4}{\degreeCelsius}
to limit tissue warming during analysis. Each frozen specimen was suspended from
a fixed overhead anchor via the tail-base strap of the harness, which was
clamped at successive positions along the dorsal strap at \qty{0.5}{\centi\metre}
intervals. At each position, the animal was allowed to reach static equilibrium
and a photograph was taken (\textit{Samsung Galaxy Z Flip 5};
\qty{50}{\centi\metre} fixed distance; 2× zoom to reduce peripheral
distortion). Images were analysed in \textit{Fiji} (\textit{ImageJ} v1.54p): a
reference segment was drawn along the body long axis and a perpendicular from
the suspension point onto this reference; the tilt angle and the normalised
suspension position were recorded. The anteroposterior CoM was estimated by
linear regression restricted to the central portion of the curve
($0.35 \leqslant x \leqslant 0.70$ of normalised body length), and the
zero-crossing of the fitted line was taken as the CoM position. A mass-based
lookup table was derived by regressing body length against body mass.

\paragraph{Locomotion experiment.}
Mice ran on a motorised treadmill at \qty{30}{\centi\metre\per\second} wearing
a custom suspension harness consisting of a commercially available soft Velcro
jacket (\textit{Butterfly Mouse Harness}, Lomir Biomedical Inc.,
Notre-Dame-de-l'Île-Perrot, QC, Canada) connected via a dorsal midline strap
to a tail-base wrap, with a solid silicone elastic cord
(\textit{HokoFLEX}\textsuperscript{\textregistered}, \qty{1}{\milli\metre}
nominal diameter, \qty{60}{Shore~A}; HOKOSIL\textsuperscript{\textregistered}
Elastomertechnik GmbH, Bredenbek, Germany) providing vertical
suspension\cite{santuzWalkingMoonHypogravity2026}. In the Earth condition, the
elastic element was slack. In the Moon condition, the cord was pre-tensioned to
exert an upward force equal to 83.5\% of body weight, reducing effective
gravity to approximately $g_\text{Moon} = 16.5\%\,g_\text{Earth}$. Full-body
kinematics were captured at \qty{250}{\hertz} using lateral high-speed cameras
and processed with \textit{DeepLabCut~v2.3.9}\cite{mathisDeepLabCutMarkerlessPose2018}
to extract anatomical landmarks including toe tips, metatarsal joints, knee,
hip, iliac crest, scapula, and tail base.

\paragraph{Center of mass reconstruction and energy analysis.}
The whole-body CoM was approximated as the centroid of three landmarks (tail
base, right iliac crest, and scapula), low-pass filtered at \qty{10}{\hertz}
(zero-phase Butterworth, order 4)\cite{signaldevelopersSignalSignalProcessing2023}.
All other kinematic signals (joint angles, toetip and metatarsal trajectories)
were filtered at \qty{20}{\hertz} with the same filter design. Velocity and
acceleration were obtained by numerical
differentiation\cite{borchersPracmaPracticalNumerical2011}. The dominant
oscillation frequency was identified as the spectral peak in the
\qtyrange{1.5}{20}{\hertz} band of the Welch power spectral density of the
vertical CoM position. Effective gravity was estimated as the mean absolute
vertical acceleration of the CoM during aerial phases (all four paws
simultaneously off the ground), retaining only phases that contained at least
one acceleration minimum to exclude spuriously brief events.
The energy recovery ratio $ER$ was computed following
\citeauthor{cavagnaSourcesExternalWork1976}\cite{cavagnaSourcesExternalWork1976}
as

\begin{equation}
    ER = \frac{\Delta E_p + \Delta E_k - \Delta E_\text{tot}}{\Delta E_p + \Delta E_k}
    \label{eq:er}
\end{equation}

\noindent where $E_p = mgy_\text{CoM}$ is the gravitational potential energy,
$E_k = \tfrac{1}{2}m(v_x^2 + v_y^2)$ the kinetic energy of the CoM,
$E_\text{tot} = E_p + E_k$ the total mechanical energy, and
$\Delta X = \sum \max(\Delta X_i, 0)$ denotes the sum of positive increments of
quantity $X$ over one stride.

\paragraph{Gait cycle analysis.}
Touchdown and liftoff events were extracted from the vertical toetip
trajectories. The right hindlimb served as the gait-cycle reference; inter-limb
phases were defined as the normalised timing of each limb's first touchdown
within the reference cycle window. Circular statistics (mean direction and
Rayleigh concentration $\bar r$) were computed
analytically\cite{mardiaDirectionalStatistics1999}.
The Consecutive Cycle Irregularity was computed as

\begin{equation}
    \text{CCI} = \frac{\langle\, |T_{n+1} - T_n| \,\rangle}{\langle T \rangle}
    \label{eq:cci}
\end{equation}

\noindent where $T_n$ is the duration of the $n$-th stride cycle,
$\langle \cdot \rangle$ denotes the mean over all strides, and $|\cdot|$ the
absolute value. A high CCI indicates strongly alternating long and short
strides, as expected during skipping.

Paw lift was computed as the time-integral of hindlimb toetip clearance above
its swing-phase minimum, normalised by hindlimb length:

\begin{equation}
    \mathrm{Paw\, Lift} = \frac{1}{L_\text{leg}}
    \int_{t_\text{lo}}^{t_\text{td}}
    \bigl(y_\text{toe}(t) - y_\text{min}^\text{sw}\bigr)\, dt
    \label{eq:pl}
\end{equation}

\noindent where $t_\text{lo}$ and $t_\text{td}$ are the liftoff and subsequent
touchdown times of the hindlimb, $y_\text{toe}(t)$ is the vertical toetip
position, $y_\text{min}^\text{sw} = \min_t y_\text{toe}(t)$ its minimum during
the swing phase, and $L_\text{leg} = L_\text{femur} + L_\text{tibia}$.

\paragraph{Multivariate analysis.}
For each lower-limb joint (hip, knee, ankle, MTP), the joint angle per stride
was normalised to $[0, 1]$ within each recording; four statistics were
extracted from the resulting Poincaré return map: short-axis SD
$\mathrm{SD}_1$ (consecutive-cycle angle variability), long-axis SD
$\mathrm{SD}_2$ (overall angle variability), and the mean current-cycle and
next-cycle normalised angles, yielding 16 stride-regularity parameters in
total\cite{brennanExistingMeasuresPoincare2001}.
104 locomotor parameters grouped into eight variable families were submitted to
Multiple Factor Analysis\cite{escofierMultipleFactorAnalysis1994,leFactoMineRPackageMultivariate2008}.
The significance of condition separation was assessed by
PERMANOVA\cite{andersonNewMethodNonparametric2001,oksanenVeganCommunityEcology2001}
on Euclidean distances in MFA space (999 permutations). Univariate comparisons
used linear mixed models with mouse as a random intercept; $p$-values were
corrected by the Benjamini–Hochberg procedure.

\paragraph{Statistics.}
Unless otherwise stated, group comparisons used linear mixed-effects models
with mouse identity as a random intercept, fitted by maximum
likelihood\cite{batesFittingLinearMixedEffects2015}, with Holm-corrected
post-hoc pairwise contrasts\cite{lenthEmmeansEstimatedMarginal2017}. Circular
data were compared with the Watson-Williams
test\cite{mardiaDirectionalStatistics1999} applied to per-mouse mean phases.
Bounded variables were logit-transformed prior to modelling. Effect sizes are
reported as Cohen's~$d$. All analyses were conducted in \textit{R~(v4.6.0)}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Results}
\label{sec:results}
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\subsection{The center of mass of mice falls at mid-body and is insensitive to body mass}

Effective hypogravity simulation requires that the elastic restoring force be
applied directly above the animal's center of mass (CoM): any anteroposterior
offset introduces a torque that tilts the body during locomotion. The harness
used in this study (\autoref{fig:fig1}A) consists of a Velcro thoracic vest
securing the forelimbs, linked by a dorsal midline strap to a tail-base wrap;
the elastic element attaches to this strap at an adjustable anteroposterior
position, providing a practical degree of freedom for CoM targeting.

To locate the CoM experimentally, we suspended frozen mice postured in a
standardised running configuration from successive positions along the dorsal
strap (\autoref{fig:fig1}B) and recorded the equilibrium tilt angle at each
point. The zero-crossing, which locates the CoM, was remarkably consistent
across animals and fell at $50.8\%$ of total body length from the tail base
(\autoref{fig:fig1}C). Body length scaled significantly with mass
(\autoref{fig:fig1}D), allowing us to derive a lookup table that maps mass to
expected CoM position (\autoref{fig:fig1}E). Over the full range of body masses
encountered in the colony (18--30\,g), the absolute CoM position changes by
only \qty{5}{\milli\metre} --- confirming that a single standardised attachment
suffices across animals.

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\textbf{The center of mass of mice falls reproducibly at mid-body.}
(\textbf{A})~The custom suspension harness, consisting of a Velcro thoracic
vest attached to a tail-base wrap by a dorsal midline strap.
(\textbf{B})~Sagittal view of a mouse in a running posture suspended from the
dorsal strap; the tilt angle and normalised pickup position are indicated.
(\textbf{C})~Equilibrium tilt angle \textit{vs.}\ normalised pickup-point
position ($n = 8$ animals); the zero-crossing at $\overline{\mathrm{CoM}}
= 50.8\%$ of body length identifies the center of mass.
(\textbf{D})~Body length \textit{vs.}\ body mass (linear regression:
$R^2 = 0.461$, $p < 0.001$; $n = 24$ animals).
(\textbf{E})~Lookup table relating body mass to predicted CoM distance from
the tail base (mean~$\pm$~SD). Over the full mass range, the CoM position
shifts by only \qty{5}{\milli\metre}.%
}{fig:fig1}

\subsection{The elastic harness produces a genuine hypogravity perturbation without perturbing stride mechanics}

Seven mice were recorded on a treadmill at \qty{30}{\centi\metre\per\second}
in two within-subject conditions: unsuspended (\textit{Earth}) and suspended at
83.5\% of body weight to simulate lunar gravity (\textit{Moon},
$g_\text{Moon} \approx 16.5\%\,g_\text{Earth}$). The vertical CoM oscillated
rhythmically at the stride frequency in both conditions (\autoref{fig:fig2}A);
neither the peak-to-peak excursion, positional variability, nor dominant
oscillation frequency differed significantly between conditions
(\autoref{fig:fig2}B--D). The oscillation frequency was approximately
\qty{3.5}{\hertz} in both conditions, consistent with the expected trot stride
rate at this speed, and well above the theoretical resonance frequency of the
suspension system
($f_0 = \tfrac{1}{2\pi}\sqrt{k/m} \approx \qty{2.1}{\hertz}$, with cord
stiffness $k \approx \qty{4.3}{\newton\per\metre}$ and mouse mass
$m \approx \qty{25}{\gram}$). Moon-suspended mice showed a significantly higher
energy recovery ratio $ER$ than Earth controls (\autoref{fig:fig2}G,H) ---
about two-thirds higher --- indicating a shift toward pendular energy exchange
under hypogravity\cite{lacquanitiHumanLocomotionHypogravity2017a}.

% Figure 2 — full page, custom width
\insererfigure[p, w=0.95\linewidth]{figures/fig2.pdf}%
{%
\textbf{The elastic harness does not contaminate stride dynamics, yet reliably
induces a hypogravity perturbation.}
(\textbf{A})~Representative vertical CoM position trace from a Moon-suspended
mouse. (\textbf{B}--\textbf{D})~Group statistics for peak-to-peak excursion,
positional variability, and dominant CoM frequency ($n = 7$); none differed
significantly. In all group-comparison panels: right half shows a kernel-density
estimate (violin); left half shows a boxplot (median, IQR, whiskers); open
circles are individual mice; filled circle and error bar are mean~$\pm$~SE.
(\textbf{E})~Vertical CoM acceleration trace; yellow shading marks aerial
phases.
(\textbf{F})~Effective gravity $g_\text{eff}/g_\text{Earth}$ during aerial
phases ($n = 7$); Moon-suspended mice experienced significantly lower effective
gravity (linear mixed-effects model, Holm-corrected; $p < 0.05$).
(\textbf{G})~Representative energy exchange trace.
(\textbf{H})~Energy recovery ratio $ER$ ($n = 7$); Moon-suspended mice showed
significantly higher $ER$ (linear mixed-effects model, logit-transformed,
Holm-corrected; $p < 0.05$). Different letters: significant post-hoc
differences ($\alpha = 0.05$).%
}{fig:fig2}

\subsection{Simulated lunar gravity disrupts inter-limb coordination}

To characterise gait at the level of individual limb timing, we tracked all
four paws during locomotion (\autoref{fig:fig3}A) and quantified inter-limb
phases using the right hindlimb (RH) as the reference. Under simulated lunar
gravity, the mean inter-limb phase shifted significantly for all three couplings
relative to Earth controls, as assessed by the Watson-Williams circular test
applied per mouse (\autoref{fig:fig3}D). Phase consistency, measured by the
Rayleigh concentration $\bar r$, was significantly reduced for all three
couplings under hypogravity (\autoref{fig:fig3}E). The hindlimb coupling
dropped most severely --- falling to less than half its Earth value under Moon
conditions --- indicating a profound loss of left-right hindlimb synchrony.

% Figure 3 — full page, narrower (portrait)
\insererfigure[p, w=0.6\linewidth]{figures/fig3.pdf}%
{%
\textbf{Simulated lunar gravity disrupts inter-limb coordination.}
(\textbf{A})~Experimental setup: mice ran at \qty{30}{\centi\metre\per\second}
under Earth or Moon gravity while high-speed cameras recorded full-body
kinematics\cite{santuzWalkingMoonHypogravity2026}.
(\textbf{B})~Schematic illustrating the skip-like gait pattern: a regular trot
(top) is replaced by a long-short stride alternation (bottom) when hindlimb
phase coupling is disrupted\cite{santuzWalkingMoonHypogravity2026}.
(\textbf{C})~Temporal stance diagrams for trot and bound reference gaits.
(\textbf{D})~Inter-limb phase polar plots for three pairwise couplings under
Earth (top) and Moon (bottom) ($n = 7$).
(\textbf{E})~Rayleigh concentration $\bar r$ for all three couplings ($n = 7$).
All three were significantly reduced under hypogravity (linear mixed-effects
model, logit-transformed, Holm-corrected). Different letters: significant
post-hoc differences ($\alpha = 0.05$).%
}{fig:fig3}

\subsection{Skip-like kinematic signatures are significantly elevated under hypogravity}

Five independent kinematic metrics were elevated under hypogravity
(\autoref{fig:fig4}). The bilateral aerial time was 2.5-fold greater in
Moon-suspended mice ($7.0\%$ of stride cycle; \autoref{fig:fig4}A). The
Consecutive Cycle Irregularity (CCI; \autoref{eq:cci}) was nearly twice as
high in Moon-suspended mice ($32.4\%$; \autoref{fig:fig4}D). Normalised paw
lift (\autoref{fig:fig4}E) was threefold greater under hypogravity, and base
of support (\autoref{fig:fig4}F) was also threefold larger. A composite skip
score aggregating nine kinematic variables drawn from
\crefcolor{fig:fig2,fig:fig3,fig:fig4} --- each min-max normalised to $[0, 1]$
across all animals and conditions --- was significantly higher in Moon-suspended
mice (\autoref{fig:fig4}G).

% Figure 4 — full page (portrait)
\insererfigure[p, w=0.85\linewidth]{figures/fig4.pdf}%
{%
\textbf{Skip-like kinematic metrics are all significantly elevated under
hypogravity.}
(\textbf{A})~Bilateral aerial time ($n = 7$). Individual mouse values are
shown as dots; the donut chart arc represents the group mean. Significantly
elevated under hypogravity (linear mixed-effects model, Holm-corrected;
$p < 0.001$).
(\textbf{B})~Left-right hindlimb swing asymmetry ($n = 7$); not significantly
different between conditions.
(\textbf{C})~Schematic illustrating CCI, paw lift, and base of support (BoS).
(\textbf{D})~CCI, (\textbf{E})~paw lift, and (\textbf{F})~BoS ($n = 7$); all
significantly elevated under hypogravity (Holm-corrected; $p < 0.05$).
(\textbf{G})~Composite skip score ($n = 7$); significantly higher in
Moon-suspended mice (logit-transformed, Holm-corrected). Different letters:
significant post-hoc differences ($\alpha = 0.05$).%
}{fig:fig4}

\subsection{An unbiased multivariate analysis reveals a global locomotor reorganisation}

All preceding analyses targeted pre-selected variables. To ask without prior
hypothesis whether the Earth-Moon difference was confined to these variables or
reflected a global reorganisation, we performed a Multiple Factor Analysis
(MFA\cite{escofierMultipleFactorAnalysis1994}) on 104 locomotor parameters
grouped into eight families (\autoref{tab:mfa_families}).

\begin{table*}[!ht]
\footnotesize
\centering
\caption{\bf The eight variable families submitted to MFA ($n$ = number of
    parameters per family).}
\label{tab:mfa_families}
\begin{tabular}{lrp{0.72\textwidth}}
\toprule
\textbf{Family} & $n$ & \textbf{Parameters} \\
\midrule
\textsc{Temporal}        & 28 & Per-limb cadence, stance and swing duration
  (mean, SD, CV), and duty factor for all four limbs (\autoref{fig:fig5}) \\
\midrule
\textsc{Coordination}    &  7 & Inter-limb phases $\bar\phi$, Rayleigh
  concentration $\bar r$, bilateral aerial time, and swing asymmetry
  (\autoref{fig:fig3}, \autoref{fig:fig4}) \\
\midrule
\textsc{Trajectories}    & 30 & Per-limb step height, stride length, and paw
  lift (mean and SD); stride-length ataxia coefficient; tail-base height
  (\autoref{fig:fig4}, \autoref{fig:fig5}) \\
\midrule
\textsc{Poincaré}        & 16 & Stride-to-stride joint angle consistency via
  Poincaré return maps for each lower-limb segment (\autoref{fig:fig5}) \\
\midrule
\textsc{Kinematics}      & 12 & Minimum, maximum, and range of motion of the
  hip, knee, ankle, and MTP joints (\autoref{fig:fig5}) \\
\midrule
\textsc{Base of support} &  3 & Maximum, minimum, and range of convex-hull
  stance area across stride cycles (\autoref{fig:fig4}) \\
\midrule
\textsc{CoM dynamics}    &  5 & $\Delta Y$, $\sigma(y_\text{CoM})$,
  $f_\text{CoM}$, $g_\text{eff}$, and $ER$ (\autoref{fig:fig2}) \\
\midrule
\textsc{Morphometry}     &  3 & Body mass, femur length, and tibia length \\
\bottomrule
\end{tabular}
\end{table*}

Dimension~1 captured 46.2\% of total variance and Dimension~2 an additional
17\%, together accounting for 63.2\% of all locomotor variability.
PERMANOVA confirmed significant overall separation between groups
($R^2 = 0.638$, $p = 0.001$), indicating that 63.8\% of all locomotor
variability is attributable to whether the mouse ran on Earth or the Moon.
Unbiased $k$-means clustering ($k = 2$) perfectly recovered the Earth and Moon
groups without access to experimental labels. Of the 104 parameters tested, 75
were significantly different between conditions (\autoref{fig:fig5}C).

% Figure 5 — full page, custom width
\insererfigure[p, w=0.95\linewidth]{figures/fig5.pdf}%
{%
\textbf{An unbiased multivariate approach shows that locomotion under simulated
hypogravity is globally and specifically altered.}
(\textbf{A})~MFA of 104 locomotor parameters projected onto Dimensions~1 and
2; individual recordings are coloured by condition (Earth, blue; Moon, grey).
Ellipses delineate the two $k$-means clusters. PERMANOVA:
$R^2 = 0.638$, $F_{1,12} = 21.16$, $p = 0.001$.
(\textbf{B})~Contribution of each variable family to Dimension~1; all
locomotor families contributed equally (11--16\%), while morphometry
contributed only 0.2\% (negative control).
(\textbf{C})~Volcano plot of effect size (Moon $-$ Earth, Cohen's $d$)
against corrected $-\log_{10}(p)$ for all 104 parameters. Points in red are
significant after Benjamini–Hochberg correction; 75 out of 104 parameters
were significantly different.
(\textbf{D})~Hindlimb joint schematic.
(\textbf{E})~Group comparison plots ($n = 7$) for the eight parameters with
the largest significant effect sizes. Different letters: significant post-hoc
differences ($\alpha = 0.05$, linear mixed-effects model, Holm-corrected).%
}{fig:fig5}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Discussion}
\label{sec:discussion}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ENS requirements for Discussion:
%   - Explain significance of results (broad biological context)
%   - Critical evaluation of results — do NOT oversell
%   - Discuss shortcomings and how they could be addressed
%   - Propose 2–3 concrete follow-up experiments
%
% This is NOT a journal manuscript — show your capacity to discuss and
% defend your work, including negative results and limitations

\paragraph{}
The central finding of this study is that mice exposed to simulated lunar
gravity spontaneously express a gait reorganisation with multiple features of
the skipping observed in human astronauts under the same gravitational
condition. Under hypogravity, mice displayed doubled stride irregularity,
threefold increases in paw lift and base of support, elevated energy recovery,
and a global loss of inter-limb phase coordination --- changes captured without
prior hypothesis by an unbiased multivariate analysis separating the two
conditions with an $R^2$ of 0.638. To our knowledge, this is the first
demonstration that a skip-like gait emerges in a quadrupedal species under
reduced gravity.

\paragraph{Similarities and differences with human lunar skipping.}
In humans, skipping under hypogravity is characterised by a persistent
leading-limb asymmetry alongside increased stride irregularity and greater foot
clearance\cite{minettiBiomechanicsSkippingGaits1998,paveiSkippingVsRunning2015}.
Our data reproduce the irregular stride timing and increased paw clearance
faithfully, but left-right hindlimb swing asymmetry did not reach significance
in mice. This likely reflects a fundamental difference between bipedal and
quadrupedal locomotion: in a biped, skipping requires a committed choice of
leading limb, whereas a quadruped may distribute the asymmetry across both
sides, diluting the signal at the group level.

More broadly, the gravitational reduction renders energetics a poor predictor
of gait choice: on the Moon, the metabolic costs of running, skipping, and
hopping converge to near-Earth-walking
values\cite{paveiSkippingVsRunning2015,paveiHoppingLocomotionDifferent2016},
even though hopping is prohibitively expensive on Earth. This metabolic
equivalence implies that the gait repertoire in hypogravity is shaped primarily
by biomechanical constraints and neuromechanical timescales.

%\newpage

\paragraph{Comparison of hypogravity simulation modalities.}
The elastic suspension system used here belongs to a family of partial
weight-bearing (PWB) devices, each presenting a distinct trade-off between
mechanical fidelity, practicality, and impact on natural
movement\cite{mortreuxApproachingGravityContinuum2020}. The custom
Velcro-and-elastic harness used here is lightweight, minimally obstructive,
and allows unrestricted quadrupedal locomotion without daily recalibration. Its
main drawbacks are: Velcro degrades after approximately five to six
experimental sessions; and the single-point overhead attachment provides no
lateral stability. A neoprene construction and a triangular suspension geometry
would address both limitations.

\paragraph{Limitations.}
A systematic underestimation of $g_\text{eff}$ relative to theoretical
predictions was observed in both conditions, a recognised limitation of
reconstructing CoM dynamics from surface-landmark tracking during fast
locomotion\cite{paveiEstimationAccuracy3D2017}. Because this bias affects
both conditions equally, the statistically robust Earth-Moon difference in
$g_\text{eff}$ remains a valid indicator of the relative change in
gravitational loading.

\paragraph{Perspectives.}
The present dataset characterises the immediate, neuromechanically intact
response to hypogravity at day~0. The animals used here carry genetic tools for
inducible selective ablation of specific neuronal populations, making it
possible to ask which spinal circuits are required for the gravity-dependent
gait reorganisation\cite{santuzWalkingMoonHypogravity2026}. A longitudinal
design would also reveal whether the skip-like pattern is a stable attractor
or a transient response --- a question with direct implications for predicting
long-term locomotor adaptation during future lunar surface missions.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Author Contributions}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ENS requirement (mandatory):
%   - State YOUR personal contribution (which experiments/analyses you performed)
%   - Describe the role of EVERY person who participated in your mentoring
%     or helped in the study
%
% Use initials matching those in author names above.

\paragraph{}
A.M.\ performed all data analysis and statistical analyses, prepared all
figures, and collected and analysed the center-of-mass suspension data.
N.Z.\ supervised the project and reviewed and edited the manuscript.
A.S.\ recorded the treadmill videos, performed markerless pose estimation, and
assembled the landmark coordinate
dataset\cite{santuzWalkingMoonHypogravity2026}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgements}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Optional section to thank people who helped but are not listed in
% Author Contributions (technical staff, facility managers, etc.)

This report was typeset using a custom \LaTeX{} class developed for ENS de
Lyon Biosciences internship reports. The original version of this report is
archived on Zenodo: \url{https://doi.org/10.5281/zenodo.21631816}.

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\end{document}