\RequirePackage[2020-02-02]{latexrelease} \NeedsTeXFormat{LaTeX2e} % no hyphenation \LoadClass{extarticle} \renewcommand\familydefault{\sfdefault} \RequirePackage{lipsum} \parindent=0pt \onecolumn \sloppy \flushbottom \RequirePackage[none]{hyphenat} \RequirePackage{url} \RequirePackage{amsmath,amsfonts,amssymb} \RequirePackage{mathptmx} \RequirePackage{xcolor} \RequirePackage{authblk} \RequirePackage[latin1,utf8]{inputenc} \RequirePackage[english]{babel} \RequirePackage{lmodern} \RequirePackage[detect-all=true]{siunitx} \RequirePackage{textgreek} %\RequirePackage{cleveref} \RequirePackage{gensymb} \RequirePackage{textcomp} % this line causes a l3regex obsolete warning - problem seems Overleaf-side \RequirePackage[version=4]{mhchem} %% Units \DeclareSIUnit\molar{\mole\per\cubic\deci\metre} \DeclareSIUnit\Molar{\textsc{m}} \DeclareSIUnit\gee{\textit{g}} \DeclareSIUnit\Units{\textnormal{U}} \DeclareSIUnit\rpm{\textnormal{rpm}} \DeclareSIUnit\pixel{\textnormal{px}} \DeclareSIUnit\electron{\textnormal{e\textsuperscript{--}}} \RequirePackage[scaled]{helvet} \RequirePackage[T1]{fontenc} \RequirePackage[utf8]{inputenc} \RequirePackage{lettrine} % For dropped capitals \RequirePackage[rightcaption]{sidecap} % For sidecaptions %\sidecaptionvpos{figure}{t} \RequirePackage[misc]{ifsym} % For the \Letter symbol \RequirePackage{bbding} % For the \Envelope symbol \RequirePackage[a4paper, total={170mm,247mm}, left=20mm, top=25mm]{geometry} \RequirePackage[labelfont={bf,sf},% labelsep=period,% figurename=Figure]{caption} \begin{document} %TC:ignore \title{Interplay of actin nematodynamics and anisotropic tension controls endothelial mechanics} \author[*,1,2,\Letter]{Claire A. Dessalles } \author[*,3]{Nicolas Cuny } \author[4,5]{Arthur Boutillon } \author[6]{Paul F. Salipante} \author[1,\Letter]{Avin Babataheri} \author[1]{Abdul I. Barakat} \author[3,\Letter]{Guillaume Salbreux } \affil[*]{These authors contributed equally.} \affil[1]{Laboratoire d'Hydrodynamique (LadHyX), CNRS, Ecole polytechnique, Institut polytechnique de Paris, Palaiseau, France.} \affil[2]{Department of Biochemistry, University of Geneva, 1211 Geneva, Switzerland.} \affil[3]{Department of Genetics and Evolution, University of Geneva, 1205 Geneva, Switzerland.} \affil[4]{Laboratory for Optics and Biosciences, CNRS UMR7645, INSERM U1182, Institut Polytechnique de Paris, 91128 Palaiseau, France.} \affil[5]{Cluster of Excellence Physics of Life, Technische Universität Dresden, 01062 Dresden, Germany} \affil[6]{Polymers and Complex Fluids Group, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD, 20899 USA.} \date{} \maketitle \begin{abstract} Blood vessels expand and contract actively, while continuously experiencing dynamic external stresses from the blood flow. The mechanical response of the vessel wall is that of a composite material: its mechanical properties depend on its cellular components, which change dynamically as cells respond to external stress. Mapping the relationship between these underlying cellular processes and emergent tissue mechanics is an on-going challenge, in particular in endothelial cells. Here we assess the mechanics and cellular dynamics of an endothelial tube using a microstretcher that mimics the native environment of blood vessels. Characterization of the instantaneous monolayer elasticity reveals a strain-stiffening, actin-dependent and substrate-responsive behaviour. After a physiological pressure increase, the tissue displays a fluid-like expansion, with reorientation of cell shape and actin fibres. We introduce a mechanical model that considers the actin fibres as a network in the nematic phase and couples their dynamics with active and elastic fibre tension. The model accurately describes the response to pressure of endothelial tubes. \end{abstract} %TC:endignore \newpage \section*{Introduction}\label{s:introduction} The hierarchical structure of the cardiovascular system matures after the onset of the blood flow, starting from an initial microvascular meshwork in the embryo \cite{Udan2013, Hoefer2013, Lindsey2014}. In the adult, small vessels regulate the blood flow actively through changes in their diameter to optimize tissue oxygenation. The deformation of these microvessels depends on the mechanical properties of their walls \cite{Segal2005}. The endothelium, the main constituent of the thin wall of microvessels, is a composite material: a tubular assembly of connected cells, wherein each cell itself is an assembly of various biological components. Consequently, the overall mechanics of this living material emerges from both the properties and the interactions of its constituents. But neither are constant. Subcellular processes respond to external stresses such as changes in wall tension, and alter the individual cells, thereby inducing dynamic adaptation in tissues in both physiological and pathological cases \cite{Dessalles_2021_review}. While these changes initiate at the smallest scales, they propagate to the largest structures. In this adaptation process as well as in tissue mechanics, the primary actors are the cytoskeleton and adhesions complexes, physically connecting cells to the substrate and to neighboring cells \cite{Alert2020, Xi2018_review, Campas2023}. Tissues exhibit viscoelastic behavior, stemming from cytoskeletal elements, such as actin and intermediate filaments \cite{Bonakdar_2016, Latorre_2018, Needleman_Dogic_2017, Harris2014}, and from intercellular junctions \cite{Lang2018, Czirok2013,Campas2023} and adhesions to the substrate \cite{Vazquez2022, Pallares2022}. Besides passively resisting deformations, the actomyosin network creates contractile active stresses. Force transmission at adhesions propagates these subcellular stresses to the tissue level. On long time scales, cellular rearrangements such as intercalation, division and apoptosis influence the rheology of tissues \cite{oskar_2023, Trubuil_2021, Xi2018_review}. Deciphering how subcellular processes and their regulation by force sensing mechanisms are coupled across scales to give rise to active tissue mechanics is a current challenge. To that end, {\it in vitro} systems have become instrumental, with two main families : stretchers and mechanical testing platforms. Stretchers subject the substrate to controlled changes in length over time. Concomitant monitoring of the cellular response has led to the discovery of a host of mechanoadaptation mechanisms, such as remodeling of actin fibers and junctions or cell stiffening \cite{Constantinou2023, Dessalles_2021_review, krishnan2012, Pourati1998, Hatami2013}. In comparison, mechanical testing platforms, including systems such as micropipette aspiration or indentation, provide quantitative measurements of the material properties of cells and tissues \cite{Efremov2021, Narasimhan2020, Trubuil_2021, Xi2018_review}. Despite the remarkable advancements achieved with these systems, addressing the coupling between tissue mechanics and the multiscale dynamics of the mechanoresponsive components remains elusive, due to the difficulty of observing living tissue over the required spatial and temporal scales. %% ------------ FIGURE 1 ---------------- %% \section*{Results}\label{s:results} \subsection*{Endothelial tubes exhibit actin-dependent elasticity} \textbf{Anisotropic tension induced by luminal pressure.} Here, we use our previously developed microstretcher, mimicking the native environment of blood vessels \cite{Dessalles_2021}, to impose tension on a tubular endothelium templated within a soft collagen hydrogel through a physiological increase in luminal pressure (Fig. \ref{fig:fig1}A, Movie SV1). To assess tissue tension, we performed laser ablation in monolayers expressing the actin reporter lifeact, along the longitudinal (L) and circumferential (C) directions (Fig. 1Bi, Movie SV2), at the low pressure used for monolayer culture (150 Pa) and in the minutes following the pressure increase (650 Pa). The recoil velocity post-ablation is thought to increase with tissue tension and to decrease with tissue viscosity or elasticity \cite{Bonnet2012, Davis2022}. The recoil velocity is doubled when the pressure is increased to $\sim$650 Pa, but only in the circumferential direction (Fig. \ref{fig:fig1}Bii, Extended Data Fig. 1A), indicating an increase in circumferential tension. In addition, in monolayers on low concentration hydrogels the recoil velocities are higher (Extended Data Fig. 1A). As they are subjected to the same imposed tension, the viscoelastic properties of endothelia differ between soft and stiffer gels. Together, these results demonstrate a switch from an isotropic to an anisotropic tension upon pressure increase and a substrate-dependent monolayer viscoelasticity. \vspace{1mm} \textbf{Collagen gel mechanics.} We then investigated the mechanical properties of the collagen gel to evaluate its mechanical contribution to the tube dynamics. The response to strain steps ranging from 5 to 30 \% of bulk collagen gels of concentration 6mg/mL was measured using a plate rheometer (Extended Data Fig. 1Bi). The stress in the gel relaxes in time (Extended Data Fig. 1Bi, \cite{Nam2016, Ban2018}). For smaller strains of 5-10 \%, the Young's modulus relaxes to around 1 kPa after a minute of strain application. As the strain is increased, the gel exhibits initial strain stiffening, which turns into strain softening after $\sim$ 10 seconds, due to strain-enhanced stress relaxation \cite{Nam2016_2}. As a result, Young's moduli values drop below 1 kPa for strains of 20-30\% after $100s$ of strain application (Extended Data Fig. 1Bii).As a result, the contribution of the gel resisting pressure is small compared to the applied pressure in the lumen (SI section 2.1.2). We therefore neglect the mechanical contribution of the hydrogel from this point on. \textbf{Substrate-dependent stiffness of endothelial tubes.} To measure tissue stiffness quantitatively, we recorded strain-stress curves in a physiological range of stress. We applied an external tension on the tissue by increasing the pressure continuously from 150 Pa to 1000 Pa in one minute, and measured the deformation of the channel, with live imaging (Fig. \ref{fig:fig1}C,E, Movie SV3) or at the beginning and end of pressure application (Fig. \ref{fig:fig1}F). The maximum pressure was chosen to approximate the pressure in native capillaries, where the vessel wall is composed of a single cell layer, around 1 kPa \cite{Shore2000}. We find the tissue stiffness to be around 0.13 N/m on the softer gel and 0.26 to 0.4 N/m on the stiffer gel, corresponding to Young’s moduli of 30 kPa and 50 to 120 kPa (Fig. \ref{fig:fig1}Cii), confirming the substrate-dependent tissue stiffening observed with the laser ablations and consistent with previous findings \cite{Salipante_Hudson_Alimperti_2022}. These Young's modulus values are similar to those reported for suspended epithelial tissues \cite{Harris_2012} and are an order of magnitude higher than the value of the collagen gels found above, confirming its negligible contribution. In addition, the deformation-pressure curves show a strain-stiffening behavior, with a threshold strain of approximately 20 \% separating a linear regime at low pressures and a saturating regime at large pressures, which can be captured using a Gent model (Fig. \ref{fig:fig1}Ci) \cite{Salipante_Hudson_Alimperti_2022, Pourati1998}. \vspace{1mm} \textbf{Subcellular determinants of endothelium elasticity.} To understand the biological origin of the substrate-dependent mechanics, we imaged the actin network and its anchoring points. More prominent actin filaments and larger focal adhesions are found on stiffer gels (Fig. \ref{fig:fig1}D). Actin stress fibers appear sensitive to substrate density or mechanical stiffness, and their reinforcement could underlie the substrate-dependent stiffening \cite{Harris_2012, Janmey_2020}. To further probe the mechanical contribution of actin and cell-cell junctions, we treated the monolayers with either cytochalasin D, an inhibitor of actin polymerization, or EDTA, a perturbator of adherens junctions (Extended Data Fig. 1C). Both treatments lead to a significant increase in monolayer deformation for both collagen concentrations (Fig. \ref{fig:fig1}Ei,Fi-ii), characteristic of tissue softening. The Young's modulus drops to 10 to 20 kPa upon actin depolymerization (Fig. \ref{fig:fig1}Eii,Fiv), consistent with previous reports \cite{Harris_2012, Pourati1998}, for both gel concentrations, confirming that actin underlies the adaptation to substrate properties. In addition, the maximal strains of actin-depleted monolayers are identical to untreated monolayers for the low collagen concentration (Fig. \ref{fig:fig1}Ei), suggesting that another cytoskeletal element controls the large deformation regime. We speculate that it could be intermediate filaments, intact in cells with depolymerized actin (Extended Data Fig. 1C), as was reported previously \cite{Latorre_2018, Liu2010, Hu_2019}. Perturbing adherens junctions decreases the effective Young’s modulus of the endothelium to 15 kPa and 50 kPa on the \SI{2}{\milli\gram \per \milli\liter} and \SI{6}{\milli\gram \per \milli\liter} collagen respectively (Fig. \ref{fig:fig1}Eii,Fiv). The tissue is likely to have some mechanical contribution despite being morcellated (Extended Data Fig. 1C), as these effective moduli are much higher than that of a bare gel (50 to 100 Pa for the \SI{2}{\milli\gram \per \milli\liter} collagen and 600 to 1000 Pa for the \SI{6}{\milli\gram \per \milli\liter} collagen) \cite{Jansen2018}. Individual cells may induce a local stiffening, due to their adhesions to the underlying matrix. The final strain is increased (Fig. \ref{fig:fig1}Ei,Fiii), likely due to stretching of the bare collagen between cells. %% ------------ FIGURE 2 ---------------- %% \subsection*{Cells and actin stress fibers align in the tension direction} We then sought to study endothelial tissue mechanics and long term adaptation to a change in luminal pressure, a phenomenon occurring in the native vasculature, for instance at the onset of blood flow in the embryo or due to pathologies in the adult \cite{Lindsey2014, Fegan2003, Williams1990}. We therefore subjected the endothelial tube, formed at $\simeq$150 Pa, to a fixed luminal pressure of $\simeq$650 Pa for several days and monitored tissue and cellular response. The order of magnitude of this pressure increase mimics the initial pressurisation of the native vascular network in embryos \cite{Lindsey2014} and the 400 to 900 Pa increase in capillary pressure found in hypertensive patients \cite{Fegan2003, Williams1990}. First, the diameter increases instantaneously due to the rapid pressure increase. Over the next 56 h, despite the fixed pressure, the diameter increases continuously, showing a fluid-like creeping behavior (Fig. \ref{fig:fig2}A). Decreasing the pressure back to 150Pa after 7 h of excess pressure application results in a diameter decrease, one minute after pressure release (Fig. \ref{fig:fig2}Bi), validating the presence of tension in the tissue. The diameter does not however recover its original value, consistent with dissipation of stresses in the tissue and the surrounding viscoplastic hydrogel. After cytochalasinD application at 7 h, the diameter increases abruptly (Fig. \ref{fig:fig2}Bii), likely due to softening of the endothelial tube induced by actin depolymerization (Fig. \ref{fig:fig1}E,F). This further supports the notion that tension in the tissue is resisting the applied pressure during the entire duration of the experiment. To link the dynamics of the subcellular elements to the observed tissue flow, we imaged the actin network, cell-cell junctions and nuclei, over time. During the assay, the actin cytoskeleton reorganizes from a longitudinal orientation to prominent stress fibers oriented in the circumferential direction (Fig. \ref{fig:fig2}Ci-iii, Extended Data Fig. 2Ai, Movies SV4, SV6,SV8). ECs and nuclei elongations follow the same dynamic pattern (Fig. \ref{fig:fig2}Di-iii, Extended Data Fig. 2Aii, Bi, Movies SV5, SV7). In addition, the orientation of cell divisions switches from longitudinal at $\Delta P \simeq 150$Pa to circumferential at $\Delta P \simeq650$ Pa, aligning with the cell elongation axis (Fig. \ref{fig:fig2}E). We introduce the order parameters $q$, $Q$ and $Q_n$ characterizing the circumferential order and orientation of actin stress fibers, cell shapes and nuclei, respectively (Methods, SI). Their sign indicates whether the elements are preferentially circumferential ($>0$) or longitudinal ($<0$), while their magnitude indicates the strength of this alignment. We find that $q$, $Q$ and $Q_n$ all show significant differences between successive time points at 0, 7 and 24 hours, as the actin stress fibers, the cells and the nuclei progressively reorient (Fig. \ref{fig:fig2}Civ,Div, Extended Data Fig. 2Bii). Nuclei elongation follows cell elongation (Extended Data Fig. 2Biii, C). \subsection*{Cell elongation and alignment are actin-dependent processes} To disentangle whether cell elongation results from direct deformation by anisotropic stretch or from an active process, we treated the cells prior to the pressure increase with CytochalasinD to depolymerize actin. Adherens junctions are still present right after the treatment and after 7 h of pressure application (Fig. \ref{fig:fig2}Fi, Extended Data Fig. 2D). CytoD-treated monolayers display round and randomly oriented cells (Fig. \ref{fig:fig2}Fi-iv) and randomly oriented nuclei (Extended Data Fig. 2E), showing that the cell elongation observed in this experiment is an active process, requiring an intact actin cytoskeleton. %% ------------ FIGURE 3 ---------------- %% \subsection*{Actin alignment requires cell-cell junctions and focal adhesions.} Stress fibers have to be anchored to transmit forces, usually at focal adhesions (FAs) and at adherens junctions (AJs) \cite{Han_de_Rooij_2016}. Here, in tissues under tension, two types of AJs are observed: classical linear adherens junctions and focal adherens junctions (Fig. \ref{fig:fig3}A, Extended Data Fig. 3A), known to form under tension \cite{Millan2010, Huveneers2012}, that enable actin anchoring and long transcellular actin cables (Extended Data Fig. 3B). Focal AJs are found mostly at longitudinal cell-cell interfaces (Fig. \ref{fig:fig3}A), while linear AJs with parallel stress fibers are found mostly at circumferential interfaces (Extended Data Fig. 3A), confirming that the tension needs to be orthogonal to the interface to trigger focal AJs formation. Interestingly, the stress fibers in focal AJs are spaced regularly (Fig. \ref{fig:fig3}A), suggestive of an optimization of the mechanical load distribution. A similar distribution is seen in anchoring at FAs, with FAs clustered together along a line, away from the cell periphery (Extended Data Fig. 3C).The lines along which FAs accumulate appear orthogonal to orientation of stress fibers, and both stress fibers and FAs appear to be regularly spaced (Fig. \ref{fig:fig3}B). To investigate possible tension sensing by AJs, we stained for vinculin, a known mechanosensor and actin regulator, that has been previously shown to be recruited to focal AJs under tension. Vinculin colocalizes with focal AJs but also with linear AJs (Fig. \ref{fig:fig3}C,F), contrary to what has been previously reported \cite{Huveneers2012}. In our system, linear AJs can be subjected to tension parallel to their axis. This is consistent with the hypothesis that vinculin is recruited by high tension in junctions \cite{Charras_Yap_2018, Huveneers2012}, but suggests that this effect can occur without the remodeling into focal AJs. To validate the putative role of junctions and FAs as mechanosensory hubs regulating actin, we first treated the monolayers prior to and during the pressure increase with EDTA to perturb AJs, while maintaining the presence of FAs (Fig. \ref{fig:fig3}D). The actin network in EDTA-treated tissues after stretch showed a weaker realignment (Fig. \ref{fig:fig3}D,E), indicating that AJs are involved in actin reorientation and/or tension sensing. EDTA-treated tissues continue to exhibit FAs, as shown by the vinculin dots (Fig. \ref{fig:fig3}D), that might be responsible for the weaker sensing. To probe the role of FAs, we used endothelial tissues cultured with DMEM, which have fewer and smaller FAs (Fig. \ref{fig:fig3}F). These tissues show intact response (Fig. \ref{fig:fig3}F, Extended Data Fig. 3F). When further treated with EDTA, they exhibit a complete loss of actin fibers circumferential orientation at 7 h (Fig. \ref{fig:fig3}G,E). In the DMEM+EDTA treatment, individual cells still possess ordered stress fibers which show some remodeling, with the formation of thick bundles (Fig. \ref{fig:fig3}G), consistent with a possible role for the remaining small FAs in tension sensing. Neither cells nor nuclei are collectively aligned in the tension direction (Fig. \ref{fig:fig3}G,E, Extended Data Fig. 3E). Cells are elongated in the direction of their internal stress fibers (Extended Data Fig. 3D), confirming that cell elongation is an active mechanism driven by actin. Taken together these results suggest that AJs are sufficient for tension sensing and actin reorientation, and that FAs can partially rescue the mechanosensing when AJs are perturbed with EDTA. \subsection*{A model for tissue mechanics and actin nematodynamics} To test our hypothesis linking actin dynamics to tissue mechanics, we developed an active surface description of the endothelial tube (Fig. \ref{fig:fig4}A). \vspace{2mm} \textbf{Actin nematodynamics.} We first investigated actin reorientation dynamics during tube expansion. We asked if the reorientation of actin stress fibers was a direct consequence of the anisotropic deformation induced by the circumferential elongation of the tube (Fig. \ref{fig:fig4}B). However, we found that actin stress fibers are not simply following the tube deformation (Fig. \ref{fig:fig4}B, SI, section 1.1.2). We then asked if the $q$ dynamics could be explained by a generic nematodynamics description (Fig. \ref{fig:fig4}C). Upon the application of additional pressure, $q$ switches sign but eventually recovers a similar magnitude than prior to pressure application, suggesting that the net effect of pressure application is for actin stress fibers to maintain a similar level of organisation, while strongly reorienting. Therefore, we assumed that the actin fibers form a network in the nematic phase. We then write the following equation for the nematic tensor $q_{ij}$: \begin{align} \label{eq:nematodynamics} D_t q_{ij}=-\gamma \left(\frac{1}{2}q_{kl} q^{kl} - q_0^2\right) q_{ij} + \beta \tilde{t}_{ij}^r \end{align} Here, $D_t$ is the corotational time derivative (SI section 1.1.2), $1/\gamma$ a time scale of relaxation of the order parameter $q_{ij}$, $q_0$ a magnitude of nematic order, and $\beta$ a mechanosensitive coupling term between the actin order and $\tilde{t}_{ij}^r$ the traceless part of the residual tension $t_{ij}^r$, defined in (Eqs. \ref{eq:total_tension}-\ref{eq:tij_t}). We envision that this residual tension corresponds to the tension supported by cell-cell junctions. In such a picture, anisotropic junctional tension, giving rise to the coarse-grained tissue-level residual tension $t_{ij}^r,$ could trigger differential actin network assembly and anchorage to the membrane, leading to anisotropic remodelling of actin stress fibers. Indeed, cell-cell junctions appear to be differently organised depending on their direction relative to the direction of tissue stretch (Extended Data Fig. 3) and actin reorientation relies on intact cell-cell junctions (Fig. \ref{fig:fig3}). \vspace{2mm} \textbf{Active viscoelastic model of tissue tension.} The luminal pressure in the tube $\Delta P$, its radius $R$ and circumferential tension $t_{\theta}^{\theta}$ are related by Laplace's law: \begin{align} \label{eq:force_balance} \Delta P R = t_{\theta}^{\theta}~, \end{align} such that at constant pressure and for an increasing tube radius, the circumferential tension must increase. To account for this increase, we assumed that the tissue tension $t_{ij}$ stems from an elastic tension from the actomyosin network $t_{ij}^a$, acting along actin stress fibers, and a residual viscoelastic tension from the other tissue components, $t_{ij}^r$, such that: \begin{align} \label{eq:total_tension} t_{ij}=&t_{ij}^a+t_{ij}^r\\ \label{eq:tij_a} t_{ij}^a=&(\zeta_0+K_a s) n_{ij}, D_t s= v_{kl} n^{kl}\\ \label{eq:tij_t} (1+\tau D_t)t_{ij}^r=&\mu v_{ij} ~. \end{align} The tension in the actin network is taken to be proportional to the mean orientation tensor $n_{ij}=g_{ij}/2+q_{ij}$, with $g_{ij}$ the surface metric tensor. Our rationale is that the tension in the actin network is generated by a set of actin fibers under tension (Fig. \ref{fig:fig4}C). The actin network tension magnitude has a constant active contribution, $\zeta_0$, and an additional contribution proportional to the elongational strain of actin stress fibers $s$, with $K_a$ a two dimensional elastic modulus. The dynamics of elongational strain depends on the tissue shear $v_{ij}$. Laser ablation experiments indicate that the tension is not simply acting along actin stress fibers, as the circumferential tension is larger than the longitudinal tension following pressure application, before actin fibers have reoriented (Figs. \ref{fig:fig1}Bii, \ref{fig:fig2}C, Extended Data Fig. 1A). This observation is consistent with a contribution to the total tension of the additional residual tension $t_{ij}^r$, which we simply describe by a viscoelastic Maxwell model with $\mu$ a viscosity and $\tau$ a viscoelastic relaxation timescale (Eq. \ref{eq:tij_t}). At short time scales, the response of the material is that of a linear elastic material, in line with the linear deformation observed at high collagen concentration in the range of pressure considered here (Fig. \ref{fig:fig1}Ci). \vspace{2mm} \textbf{Dynamics of tube expansion and fiber reorientation.} We found that Eqs. \ref{eq:nematodynamics}-\ref{eq:tij_a} account for the dynamics of the actin nematic order (Fig. \ref{fig:fig4}Di). The increase of circumferential tension after application of additional tube pressure leads to reorientation of actin stress fibers from longitudinal to circumferential on a timescale of $\sim 1$ h ($\gamma=1.3\pm 1.3$ h$^{-1}$, here and for other parameters, mean and standard deviation of uncertainty analysis, see Supplementary Section 1.2 for details). This timescale is comparable in magnitude to previously reported values of actin reorientation in endothelial cells under cyclic stretch \cite{krishnan2012, Takemasa1997, Iba1991, Hayakawa2001}. We also note that in line with the model prediction, we did not observe significant deviation of the fiber orientations from the longitudinal or circumferential directions (Extended Data Fig. 4A,B). The model also accounts quantitatively for the dynamics of tube expansion (Fig. \ref{fig:fig4}Dii). In the model, the initial jump in tube radius is limited by the initial elastic response of the tissue (Fig.\ref{fig:fig4}C, Diii, Extended Data Fig. 4E). The order of magnitude of fitted values of the elastic coefficients, $K_a=0.22$ N/m ($0.22\pm 0.03$ N/m) and $K=\mu/\tau=0.29$ N/m ($0.31\pm 0.03$ N/m), match well with values extracted from pressure ramp application, of the order of $0.26-0.4$ N/m (Fig. \ref{fig:fig1}C). Elastic residual tension in the tissue then relaxes, leading to further tube expansion (Fig.\ref{fig:fig4}C, Dii,iv). The reorientation and strain of elastic fibers however allows limiting and eventually fully opposing expansion of the tube (Fig. \ref{fig:fig4}Di, ii, blue and green curves, Extended Data Fig. 4F). Alternative models did not account as well for experimental data, except for a model with mechanosensitive coupling of the nematic order to the full tension tensor $t_{ij}$ (SI, section 1.3.6, Extended Data Fig. 5E), and a model with active tension along actin fibers, but where the long-time scale elastic response does not arise from actin fibers but from the rest of the tissue (SI, section 1.3.8, Extended Data Fig. 5F). The total tension values (Fig. \ref{fig:fig4}Diii) are anisotropic with a larger circumferential tension after pressure increase, in qualitative agreement with laser ablation experiments (Fig. \ref{fig:fig1}Bii, Extended Data Fig. 1A). The model also predicts a larger longitudinal tension prior to pressure application (Fig. \ref{fig:fig4}Diii), detected by laser ablation only on soft collagen (Fig. \ref{fig:fig1}Bii, Extended Data Fig. 1A), possibly due to the weak longitudinal anisotropy of the high-density monolayers used for these experiments. Overall, we propose that actin stress fibers reorient along the direction of highest residual tissue tension, allowing the tissue to resist anisotropic deformation (Fig. \ref{fig:fig4}Di,ii). \vspace{2mm} \textbf{Dynamics of cell area.} We then investigated the dynamics of the cell area, which increases transiently after pressure application before decreasing over $56$ h (Fig. \ref{fig:fig5}A). The nuclei area mirrors this trend, suggesting that nuclei are also stretched transiently (Extended Data Fig. 4G). In the absence of cell apoptosis, the cell area $a$ follows an isotropic shear decomposition \cite{etournay2015interplay, popovic2017active} (Fig. \ref{fig:fig4}Ei): \begin{align} \frac{1}{a}\frac{da}{dt}=\frac{1}{R}\frac{dR}{dt}-k_d~. \end{align} This relationship indeed accounts well for the observed dynamics of the cell area, for a constant cell division rate $k_d=0.27\pm 0.07 d^{-1}$ (Fig. \ref{fig:fig5}Aii). After pressure increase, the cell area increases due to fast tissue expansion, and then relaxes due to continued cell division (Fig. \ref{fig:fig5}Ai,ii). We then measured directly the cell division rate under both $150$Pa and $650$Pa pressures with a proliferation assay (Fig. \ref{fig:fig5}Aiii). To avoid confounding effects of changes in cell density brought by tissue expansion, we measured cell division rates in endothelial tubes seeded with different initial cell densities. The cell division rate sharply decreases with cell density, with a dependency well fitted by an exponential function (Fig. \ref{fig:fig5}Aiii). One may then expect that increasing tissue tension leads to larger cell area and therefore higher proliferation. Surprisingly however, the cell division rate is lower for larger pressure, implying that increased tissue tension slows down proliferation (Fig. \ref{fig:fig5}Aiii). Therefore, tissue tension influences cell proliferation beyond changing cell area. The predicted cell division rate obtained from isotropic shear analysis (Fig. \ref{fig:fig5}Aii) matches very well with its measured value under high pressure, at the average density of the experiment (Fig. \ref{fig:fig5}Aiii), consistent with cell proliferation being responsible for the decrease in cell area after $7$ h and the absence of apoptosis. \textbf{Dynamics of cell elongation.} We then asked if the dynamics of cell elongation could be understood with an anisotropic shear decomposition, where the average cell elongation changes due to tissue anisotropic shear and cellular rearrangements \cite{etournay2015interplay, popovic2017active}. We postulated that cellular rearrangements are driven by the difference between the actin nematic order and the cell elongation, based on the observed empirical linear correlation between $Q$ and $q$ (Fig. \ref{fig:fig5}Bi,ii) and on the absence of cell elongation when actin is depolymerized (Fig. \ref{fig:fig2}F), leading to the following dynamics: \begin{align} D_t Q_{ij}=\tilde{v}_{ij} -\lambda(Q_{ij}-\alpha q_{ij})~, \end{align} where $\tilde{v}_{ij}$ is the traceless part of the tissue shear $v_{ij}$, $1/\lambda$ a relaxation timescale of the cell elongation $Q_{ij}$ to a preferred value $\alpha q_{ij}$. This hypothesis accounts well for the dynamics of cell elongation (Fig. \ref{fig:fig5}Biii) for a timescale $1/\lambda \simeq 45$ min ($1\pm 1.1$ h), indicating that cell elongation is largely slaved to the orientation of actin fibers over the experiment duration. Indeed, large values of $\lambda$, corresponding to faster relaxation to the actin fiber nematic order, can still account for the elongation dynamics (Extended Data Fig. 4D). The final decrease of cell elongation at $56$ h however is not predicted by the theory and could arise from cell divisions, which are oriented circumferentially (Fig. \ref{fig:fig2}E), indicating a possible decoupling between the actin stress fibers and cell elongation nematics on longer time scales. \textbf{Effect of pressure magnitude.} To further verify that the proposed physical description indeed accounts for endothelial tube dynamics under pressure, we obtained the predicted tube radius $R$, actin order $q$, cell elongation order $Q$ and the cell area $a$ for a range of pressures. The model predicts that for larger pressures, both the tube radius and the mean cell area expands more and that actin fibers and cell elongation reorient more strongly along the circumferential direction (Fig. \ref{fig:fig5}C, Extended Data Fig. 4H). To test these predictions, we measured the response of the tissue at $7$ h for different imposed pressures ($\Delta P\simeq$ 450 Pa and $\Delta P \simeq$ 850 Pa). The tube radius, mean cell area, actin orientation and cell orientation at $7$ h all scale roughly linearly with the applied pressure, in good agreement with the theoretical predictions (Fig. \ref{fig:fig5}C, Extended Data Fig. 4H). Overall, we conclude that actin fibers orientation is sensitive to the physiologically relevant range of pressure variations $0$ to $850$ Pa, thanks to the mechanosensitivity of the nematic order of actin stress fibers, encoded by the parameter $\beta$ in Eq. \ref{eq:nematodynamics}. \section*{Discussion}\label{s:discussion} Here we demonstrate that pressure application on a reconstituted endothelial tube leads to actin stress fiber circumferential alignment, parallel to the direction of applied stretch and maximum tension. This response is consistent with the alignment of fibers along the direction of maximal tension reported in epithelia {\it in vivo} \cite{lopez-gay_2020}, but contrasts with actin fibers in ECs reorienting perpendicularly to the direction of stretch under imposed cyclic deformation \cite{Dessalles_2021_review}. Tubes under tension famously tend to be unstable \cite{plateau1873statique, Gennes2004}. Indeed, Laplace's law (Eq. \ref{eq:force_balance}) implies that the circumferential tension must increase in a pressurised expanding tube. This indicates that the endothelial tube should respond elastically to resist expansion. However, the average cell area and circumferential cell elongation decrease. This led us to propose that the endothelial tube expansion is instead limited by actin fibers reorientation and elongational strain. In addition to the actin stress fiber nematic, we have examined simultaneously the dynamics of cell elongation. Although these two nematic fields have been proposed to be decoupled in epithelial layers \cite{nejad2023stressshape}, here we find that they follow each other for most of the tube expansion. Our microstretcher allows to set a fixed value of pressure magnitude, thus preventing tension relaxation in the tissue. It mimics a key \textit{in vivo} scenario, modeling pressure increases due to the onset of the heart beat or hypertension, with physiologically relevant pressure differences \cite{Lindsey2014, Fegan2003, Williams1990}. The cellular dynamics we report here could underlie vessel remodeling and pathological mechanoadaptation of vessels. Tension-induced remodeling of adherens junctions is evident by shape change and actin and vinculin association, a mechanism previously linked to the protection of tissue integrity and barrier function \cite{Millan2010, Huveneers2012, stoel_2023, Oldenburg2014}. {\it In vivo}, an increase in luminal pressure has been reported to trigger radial growth of vessels and junction remodeling along the tension direction in the zebrafish, mirroring our observations \cite{kotini_2022}. Pressure induced remodeling is believed to underlie other fluid transporting tubular networks, such as the mammary glands, the bronchial tree or the lymphatic network, potentially presenting a mechanism extending beyond the cardiovascular network \cite{Torres-Sanchez_2021, Breslin2014}. Thereby, luminal pressure induced wall tension may serve as a universal regulator in vessels in vivo, governing the adaptation of their properties and shape and optimizing them for their specific function. By linking the behavior of biological components to the emergent tissue mechanics, we present a key step towards understanding the process of mechanoadaptation in vessels. It would be interesting in further studies to use our microstretcher set-up to further dissect the role of cytoskeletal components and different types of endothelial cells in endothelial tube mechanics, to study the role of chirality, which was recently reported in microvessels both in vivo and in vitro \cite{Zhang2024}, or to apply oscillatory pressures to mimic the pulsatility of the blood flow. In addition, interactions with other cell types such as smooth muscle cells and fibroblasts could play a role in mechanoadaptation in larger vessels. %TC:ignore \section*{Acknowledgments} We thank Philippe Bourrianne for assistance with the rheometry experiments. We thank Pierre Mahou and the Polytechnique Bioimaging Facility for assistance with live imaging on their equipment partly supported by Région Ile-de-France (interDIM) and Agence Nationale de la Recherche (ANR-11-EQPX-0029 Morphoscope2, ANR-10-INBS-04 France BioImaging). We also thank Michael Riedl and Mathieu Dedenon for constructive inputs on the manuscript. This work was funded in part by an endowment in Cardiovascular Bioengineering from the AXA Research Fund to AIB, an AMX doctoral fellowship from Ecole Polytechnique and an EMBO fellowship ALT 886-2022 to CAD. NC was supported by a SNSF project grant 200021\_197068 to GS. \section*{Author contributions} CAD and GS conceived the project and ABa, AIB and GS supervised the project. CAD performed experiments and analysed the data, with ABo for the laser ablation experiments and PS for the Gent model analysis. NC and GS developed the theoretical model and NC performed numeric simulations and ran fitting procedures. AIB contributed resources to the project. CAD, NC, ABa and GS wrote the manuscript, with feedback from all authors. \section*{Conflict of interest} The authors declare no competing or financial interests. \section*{Declarations} Certain instruments and materials are identified in this paper to adequately specify the experimental details. Such identification does not imply recommendation by the National Institute of Standards and Technology; nor does it imply that the materials are necessarily the best available for the purpose. \newpage \section*{} % full size figure is figure* \begin{figure*} \centering %\includegraphics[width=1\linewidth]{Figures/Fig1.pdf} \caption{\textbf{Endothelial tubes exhibit actin-dependent elasticity under luminal pressure.}\\ \textbf{A} Optical coherence tomography images of the vessel cross section showing the increase in radius during the increase of pressure. Scale bar, \SI{50}{\micro\meter}. \textbf{Bi} Schematics of the laser ablation showing the two directions of ablation: longitudinal (L) and circumferential (C). Fluorescence images of LifeAct-Endothelial cells showing the endothelial actin network prior and post longitudinal ablation, with the area of ablation denoted in yellow, showing a rapid opening of the wound, characteristic of high tissue tension in the circumferential direction. Scale bar, \SI{20}{\micro\meter}. \textbf{Bii} Initial recoil velocity post ablation for monolayers cultured on a \SI{6}{\milli\gram \per \milli\liter} collagen gel, showing an increase between the control (150 Pa) and stretched (650 Pa) channels, but only in the circumferential direction. Ablations were performed in the minutes following the pressure increase for the stretched condition (n=3). \textbf{Ci} Channel diameter as a function of the luminal pressure (points) for monolayers cultured on a \SI{2}{\milli\gram \per \milli\liter} (yellow, n=3) and \SI{6}{\milli\gram \per \milli\liter} (red) collagen gel, obtained either continuously with live imaging (chain of dots, n=3), or at the beginning and the end of the pressure application (paired dots, n=18), with the fitted analytical curves obtained from the strain-stiffening model (solid lines). \textbf{Cii} Inferred Young’s moduli of the endothelial tissue for the two collagen concentrations. For the \SI{6}{\milli\gram \per \milli\liter} concentration (red), data from the continuous measurement (right, n=3) and the discrete two-points measurement (left, n=18), matching the curves of panel ii, are separated for clarity. \textbf{Di} Endothelium stained for VE-cadherin, phalloidin and vinculin for the two collagen concentrations: \SI{2}{\milli\gram \per \milli\liter} (top) and \SI{6}{\milli\gram \per \milli\liter} (bottom). \textbf{Dii} Fluorescence intensity of the actin stress fibers (normalized by the mean cell intensity) as a function of collagen concentration (n=5 (2mg/mL), n=6 (6mg/mL)). \textbf{Ei} Channel diameter as a function of the luminal pressure for control monolayers (yellow, n=3) and monolayers treated with cytochalasinD (green, n=3) and EDTA (blue, n=2), cultured on a \SI{2}{\milli\gram \per \milli\liter} collagen gel. \textbf{Eii} Inferred Young’s moduli of control (n=3), cytochalasinD-treated (n=3) and EDTA-treated endothelia (n=2), cultured on a \SI{2}{\milli\gram \per \milli\liter} collagen gel. \textbf{Fi} Channel diameter as a function of time just after treatment with cytochalasinD (at t=0), for monolayers cultured on a \SI{6}{\milli\gram \per \milli\liter} collagen gel (n=7). \textbf{Fii,iii} Channel diameter as a function of the luminal pressure for control monolayers (red, n=18) and monolayers treated with cytochalasinD (green, n=9) and EDTA (blue, n=12), cultured on a \SI{6}{\milli\gram \per \milli\liter} collagen gel. \textbf{Fiv} Inferred Young’s moduli of control (n=18), cytochalasinD-treated (n=9) and EDTA-treated (n=12) endothelia, cultured on a \SI{6}{\milli\gram \per \milli\liter} collagen gel.} \label{fig:fig1} \end{figure*} % full size figure is figure* \begin{figure*} \centering %\includegraphics[width=0.9\linewidth]{Figures/Fig2.pdf} \caption{\textbf{Cells dynamically align in the tension direction via an active actin-dependent process.}\\ \textbf{A} Channel diameter as a function of time after the pressure increase (t=0), color coded for time (n=6). \textbf{Bi} Relative diameter change when increasing pressure from $150$ Pa to $650$ Pa (yellow, n=21) and when decreasing pressure back to $150$ Pa $7$ h later (orange, n=21). The diameter fluctuations at $150$ Pa are shown in grey as a reference (Ctr). \textbf{Bii} Evolution of the channel diameter between $6$ and $8.5$ h for control monolayers (orange, n=3) and for monolayers treated with cytochalasin at $t=7$ h (green, n=3) under a pressure of $\simeq 650$ Pa, showing a sudden diameter increase due to actin depolymerization. \textbf{Ci,ii} Endothelium stained for phalloidin at $t=0$ h under $\simeq$ 150 Pa (\textbf{i}) and after $t=7$ h under $\simeq$ 650 Pa (\textbf{ii}), with the orientation of the actin stress fibers color coded. \textbf{Ciii,iv} Evolution of the probability distribution of the actin stress fibers orientation (\textbf{iii}) and the associated nematic order parameter q (\textbf{iv}) at 0 h (yellow, n=8), 7 h (orange, n=9), 24 h (red, n=5) and 56 h (purple, n=2). \textbf{Di,ii} Endothelium stained for VE-cadherin at $t=0$ h under $\simeq$ 150 Pa (\textbf{i}) and after $t=7$ h under $\simeq$ 650 Pa (\textbf{ii}), with the orientation of the junctions color coded. Nuclei are overlaid in white. \textbf{Diii,iv} Evolution of the probability distribution of the cells orientation (\textbf{iii}) and the associated nematic order parameter Q (\textbf{iv}) at 0 h (yellow, n=8), 7 h (orange, n=7), 24 h (red, n=5) and 56 h (purple, n=2). \textbf{E} Probability distribution of the division orientation for monolayers, measured at $t=7$ h, under low pressure $\Delta P\simeq 150$ Pa (yellow) and high pressure $\Delta P\simeq 650$ Pa (orange). \textbf{Fi} Cytochalasin-treated monolayer stained for VE-cadherin after 7 h of pressure showing round cells. \textbf{Fii,iii} Evolution of the probability distribution of the cells orientation (\textbf{ii}) and the associated nematic order parameter Q (\textbf{iii}) before the pressure increase ($\simeq150$ Pa, n=8), and after 7 h of high pressure for the control ($\simeq650$ Pa, n=7) and cytochalasin-treated (CytoD, n=3) monolayers. \textbf{Fiv} Schematics showing round cells after actin depolymerization by the cytochalasinD treatment, despite the circumferential stretching force. Scale bar, \SI{50}{\micro\meter}. } \label{fig:fig2} \end{figure*} % full size figure is figure* \begin{figure*} \centering %\includegraphics[width=0.9\linewidth]{Figures/Fig3.pdf} \caption{\textbf{Cell-cell junctions and focal adhesions are necessary for actin alignment.}\\ \textbf{A} Endothelium stained for VE-cadherin (yellow) and phalloidin (cyan) after 7 h of stretch, showing a focal adherens junction with transendothelial actin fibers association (arrows). \textbf{B} Endothelium stained for phalloidin (cyan) and vinculin (magenta) after 7 h of stretch at $\Delta P \simeq650$ Pa, showing a line of clustered focal adhesion with actin fibers anchoring (arrowhead). Scale bar A-B, \SI{20}{\micro\meter}. \textbf{C} Control endothelium stained for VE-cadherin (yellow), phalloidin and vinculin (magenta) after 7 h of stretch, showing vinculin association to focal adhesions at the end of actin stress fibers (arrowheads) and to adherens junctions with parallel actin stress fibers (double arrowheads). \textbf{D} EDTA-treated endothelium stained for VE-cadherin, phalloidin (cyan) and vinculin (magenta) after 7 h of stretch, showing vinculin association to focal adhesions at the ends of actin stress fibers (arrowheads). \textbf{E} Probability distribution of the actin stress fibers at 7 h (\textbf{i}) and 24 h (\textbf{ii}) for control (orange, n=7 (7h); red, n=5 (24h)) and EDTA-treated in control medium (blue, n=5 (7h), n=6 (24h)) or DMEM (teal, n=3 (7h)) endothelia. \textbf{Eiii} Nematic order parameter q of the actin stress fibers for control (orange-red), either in standard medium (label C) or DMEM medium (label D), and EDTA-treated (label +e) endothelia, with the nematic order parater q at 0 h (yellow, n=8). \textbf{Eiv} Schematic of a cell before and after treatment with EDTA, with actin anchoring switching from junctions to focal adhesions. \textbf{F} DMEM-cultured endothelium stained for VE-cadherin (yellow), phalloidin and vinculin (magenta) after 7 h of stretch, showing vinculin association to adherens junctions with parallel actin stress fibers (double arrowheads). \textbf{G} DMEM-cultured and EDTA-treated endothelium stained for VE-cadherin, phalloidin (cyan) and vinculin (magenta) after 7 h of stretch. Scale bar C,D,F,G, \SI{50}{\micro\meter}. } \label{fig:fig3} \end{figure*} \begin{figure*} \centering %\includegraphics[width=0.9\linewidth]{Figures/Fig4.pdf} \caption{\textbf{A model for tissue mechanics and actin nematodynamics recapitulates the response of endothelial tubes.}\\ \textbf{Ai} Schematic of cylindrical tube or radius $R$ subjected to the pressure difference $\Delta P$, balanced by the circumferential tension $t_{\theta}^{\theta}$. \textbf{Aii} The change of orientation of actin fibers from longitudinal to circumferential corresponds to a change of sign of the order parameter $q$. \textbf{B} Circumferential actin nematic order $q$, as a function of the normalized tube radius $R/R_0$. Dots: experimental data, corresponding to panels Di, ii. Grey lines: numerically computed contribution of deformation by the tissue shear, starting with 6 sample images at $R/R_0=1$. Insets: actin fibers color-coded for their orientation, before tube stretching (yellow), after $7$ hours of 650 Pa pressure application (red) and for an artificial deformation of the initial image by an amount corresponding to the observed deformation $R/R_0$ at $7$ hours (blue). \textbf{C} Schematic of tube expansion dynamics and nematic reorientation induced by the tube expansion. A sudden increase in the luminal pressure from $\Delta P \simeq 150$ Pa to $\Delta P \simeq 650$ Pa results in an instantaneous deformation, followed by a reorientation of actin fibers and an increase of the tension generated in actin stress fibers, ${t^a}_{\theta}^{\theta}$, that slows down tube expansion. \textbf{D} Actin order parameter $q$ (\textbf{i}) and normalized tube radius $R/R_0$ (\textbf{ii}) as a function of time, comparing the experimental data (dots) and the model prediction (solid lines), for a constant pressure $\Delta P\simeq 150$ Pa (yellow) and with a pressure increase $\Delta P\simeq 650$ Pa (red), with experimental data as in Fig. 2A (with radius normalised by R0 for each experiment) and Fig. 2Civ. Model predictions without the elastic component of the actin tension (green line, $K_a=0$) and without the tension coupling inducing actin reorientation (blue line, $\beta=0$) are also shown. \textbf{Diii} Normalized total circumferential tension $t_{\theta}^{\theta}/\zeta_0$ (solid red line), and total longitudinal tension $t_z^z/\zeta_0$ (solid blue line), as a function of time. \textbf{Div} Normalized total circumferential tension $t_{\theta}^{\theta}/\zeta_0$ (solid red line), circumferential tension in the actin stress fiber network ${t^a}_{\theta}^{\theta}/\zeta_0$ (dashed green line)and residual tension ${t^r}_{\theta}^{\theta}/\zeta_0$ (dotted red line). } \label{fig:fig4} \end{figure*} \begin{figure*} \centering %\includegraphics[width=0.9\linewidth]{Figures/Fig5.pdf} \caption{\textbf{Dynamics of cell area, elongation, and response to a range of pressures.}\\ \textbf{Ai} Schematic of the mean cell area dynamics. \textbf{Aii} Normalised cell area as a function of time, comparing the experimental data (dots) and the model prediction (solid lines), for a constant pressure $\Delta P\simeq 150$ Pa (yellow, n=8) and after the pressure increase $\Delta P\simeq 650$ Pa (red, n=7 (7h), n=3 (24h), n=2 (56h)). \textbf{Aiii} Proliferation rate $k_d$ as a function of cell density, measured between $t=0$ and $t=7$ h, for monolayers under low pressure $\Delta P_0\simeq 150$Pa (yellow dots) and high pressure $\Delta P_m\simeq 650$Pa (red dots). Lines: exponential fit. Grey square: prediction from isotropic shear decomposition. \textbf{Bi} Schematic of the cell elongation dynamics. \textbf{Bii} Cell circumferential elongation $Q$ as a function of the actin nematic order parameter $q$, showing a linear empirical correlation, color coded for time (0h yellow, 7h orange, 24h red and 56h purple), with experimental data as in Fig. 2Div. \textbf{Biii} Cell circumferential elongation $Q$ as a function of time, comparing the experimental data (dots) and the model prediction (solid lines), for a constant pressure $\Delta P\simeq 150$ Pa (yellow, n=8) and with a pressure increase $\Delta P\simeq 650$ Pa (red, , n=7 (7h), n=3 (24h), n=2 (56h)), with experimental data as in Fig. 2Civ, Div. Blue line: model prediction for the case where the cell elongation follows tissue deformation. \textbf{Ci} Schematic of the different pressures applied to the endothelial tube. \textbf{Cii-v} Normalized tube radius $R/R_0$ (\textbf{ii}), actin nematic order parameter $q$ (\textbf{iii}), cell area $a/a_0$ (\textbf{iv}) and cell elongation $Q$ (\textbf{v}) as a function of pressure, measured 7 h after pressure step application, comparing the experimental data (circles) and the model prediction (squares). (\textbf{ii}) n=30 (150Pa), n=4 (450Pa), n=18 (650Pa), n=7 (850Pa). (\textbf{iii-iv}) n=8 (150Pa), n=4 (450Pa), n=9 (650Pa), n=7 (850Pa). (\textbf{v}) n=8 (150Pa), n=4 (450Pa), n=7 (650Pa), n=7 (850Pa). } \label{fig:fig5} \end{figure*} \newpage \section*{Extended Data Figure Legends} \begin{figure*}[!ht] \centering \captionsetup{labelformat=empty} \caption{\textbf{Extended Data Fig. 1. Endothelial tubes exhibit actin-dependent elasticity under luminal pressure.}\\ \textbf{A} Initial recoil velocity post ablation for monolayers cultured on a \SI{2}{\milli\gram \per \milli\liter} collagen gel, showing an increase between the control (150Pa, n=3) and stretched (650Pa, n=5) channels, but only in the circumferential direction. \textbf{Bi} Shear stress in collagen gels, measured in a rheometer, as a function of time (dots), after a strain step of varying amplitude, ranging from 5 (yellow) to 30\% (purple). n=3 in each strain condition. Stress curves show a decay, indicating stress relaxation, enhanced for higher strains. The stress relaxation curves are fitted with an exponential, stemming from a Maxwell viscoelastic model with a residual stress. One example is shown for a strain of 30 \% (dashed line). \textbf{Bii} Young's moduli extracted from the stress relaxation curves as a function of the applied strain at different timepoints after the strain step, from 0.1 s (yellow) to 100 s (purple), showing a switch from strain-stiffening to strain-softening as a function of time. \textbf{C} Endothelium stained for DAPI, VE-cadherin, phalloidin and vimentin one minute after the application of the 1000 Pa pressure, for the two collagen concentrations: \SI{2}{\milli\gram \per \milli\liter} (n=3) and \SI{6}{\milli\gram \per \milli\liter} (n=3), and with the cytochalasinD (n=3) or EDTA (n=2) treatment, on the soft gel. Scale bar \SI{50}{\micro\meter}. } \label{suppfig:1} \end{figure*} \vspace{1cm} \begin{figure*}[!ht] \centering \captionsetup{labelformat=empty} \caption{\textbf{Extended Data Fig. Extended Data Fig. 2. Cells dynamically align in the tension direction via an active actin-dependent process.}\\ \textbf{A} Endothelium stained for phalloidin (\textbf{i}) and VE-cadherin (\textbf{ii}) at $t=24$ h under $\simeq$ 650 Pa, with the orientation of the actin stress fibers and junctions color coded. Nuclei are overlaid in white (\textbf{ii}). \textbf{B} Evolution of the probability distribution of the nuclei orientation (\textbf{i}) and the associated nematic order parameter $Q_n$ (\textbf{ii}) at 0 (yellow, n=8), 7 (orange, n=9), 24 (red, n=5) and 56 (purple, n=2) hours. The sign of $Q_n$ denotes the direction of the orientation and the absolute value its strength. \textbf{Biii} $Q_n$ as a function of the cell elongation order parameter $Q$, showing a linear empirical correlation, color coded for time (0h yellow, 7h orange, 24h red and 56h purple, same data as in Fig. 2Div, Extended Data Fig. 2Bii). \textbf{C} Mean nucleus aspect ratio as a function of time. \textbf{D} Cytochalasin-treated monolayer stained for nuclei, VE-cadherin and phalloidin after 7h of pressure showing round cells, the presence of cell-cell junctions and the absence of actin fibers. Scale bar \SI{50}{\micro\meter}. \textbf{E} Evolution of the probability distribution of the nuclei orientation before the pressure increase ($\Delta P \simeq150$Pa, yellow, n=8), and after 7h of high pressure for the control ($\Delta P\simeq650$Pa, orange, n=7) and cytochalasin-treated (green, n=3) monolayers. } \label{suppfig:2} \end{figure*} \begin{figure*}[!ht] \centering \captionsetup{labelformat=empty} \caption{\textbf{Extended Data Fig. 3. Cell-cell junctions and focal adhesions are necessary for actin alignment.}\\ \textbf{A} Schematics of the cell-cell junctions and associated actin fibers, showing a linear AJ (left) and a focal AJ (right), observed in monolayers under $\Delta P\simeq150$Pa. \textbf{B} Endothelium stained for VE-cadherin (pink) and phalloidin (white) after 7h of stretch at $\Delta P\simeq650$Pa, with long transcellular actin cables manually traced (white and green triangles). \textbf{C} Endothelium stained for nuclei, vinculin (magenta), VE-cadherin (yellow) and phalloidin (cyan) after 7h of stretch at $\Delta P\simeq650$Pa, showing a line of clustered focal adhesion (white arrowhead) with actin fibers anchoring (cyan), away from cell-cell junctions (yellow). Scale bar \SI{20}{\micro\meter}. \textbf{D} EDTA-treated endothelium stained for nuclei (cyan) and phalloidin (white) after 7h of stretch at $\Delta P\simeq650$Pa, with cell border outlined (magenta, bottom), showing elongated cells whose orientation follows stress fiber orientation. \textbf{E} Probability distribution of the nuclei long axis orientation at 7 h (\textbf{i}) and 24 h (\textbf{ii}) for control (orange, n=7 (7h); red, n=5 (24h)) and EDTA-treated in control medium (blue, n=5 (7h), n=6 (24h)) or DMEM (teal, n=3 (7h)) endothelia. \textbf{F} Nematic order parameter q as a function of time for EGM2-cultured (light orange, n=5 (7h); red, n=3 (24h)) and DMEM-cultured monolayers (dark orange, n=3 (7h); purple, n=2 (24h)), same data as in Fig. 2Civ. } \label{suppfig:3} \end{figure*} \begin{figure*}[!ht] \centering \captionsetup{labelformat=empty} \caption{\textbf{Extended Data Fig. 4. A model for tissue mechanics and nematodynamics recapitulates the response of endothelial tubes.}\\ \textbf{A,B} Value of normalized off-diagonal component $q_{z \theta}/R$ of actin orientation tensor (\textbf{Ai},\textbf{Bi}) and $Q_{z \theta}/R$ of cell elongation tensor (\textbf{Aii},\textbf{Bii}) at different time after pressure increase from $150$Pa (yellow) to $650$Pa (red) (\textbf{A}) and $7$ hours after different pressure increases (\textbf{B}). \textbf{Ai} n=8 (0h), n=9 (7h), n=5 (24h), n=2 (56h). \textbf{Aii} n=8 (0h), n=7 (7h), n=5 (24h), n=2 (56h). \textbf{Bi}) n=8 (150Pa), n=4 (450Pa), n=9 (650Pa), n=7 (850Pa). \textbf{Bii} n=8 (150Pa), n=4 (450Pa), n=7 (650Pa), n=7 (850Pa). \textbf{C} Time evolution of normalized radius $R/R_0$ (\textbf{i}) and actin order parameter $q$ (\textbf{ii}) for $\gamma=10.8h^{-1}$ and $\beta=8 N^{-1}.m.h^{-1}$, other parameters being the same as in optimal fit (dotted line) and for best fit with $\gamma=0 h^{-1}$ (small dotted line) compared to the optimal fit (solid line). The experimental data are the same as in Fig.2A,Civ. \textbf{D} Time evolution of cell elongation $Q$ for $\lambda=0$ (small dotted line) and $\lambda=30.2h^{-1}$ (dotted line) with all other parameters being the same as in optimal fit, compared to the optimal fit result (solid line). The experimental data are the same as in Fig.2Div. \textbf{E} Absolute relative radius change when increasing pressure from $150$Pa to $650$Pa (yellow) and when decreasing pressure back to $150$Pa $7$ hours later (orange), comparing the experimental data (dots, same data as in Fig.2Bi) to the theoretical prediction (squares, SI, section 2.5). \textbf{F} Tissue strain $\ln(R/R_0)$ (red) and actin strain $s$ (green) as a function of time, in the model. \textbf{Gi} Mean nucleus area as a function of time (experimental data). \textbf{Gii} Nucleus area as a function of cell area after 0 (yellow), 7 (orange), 24 (red) and 56 (purple) hours, showing a linear correlation. Data are the same as in Fig.5Aii, Extended Data Fig. 4Gi. \textbf{H} Time evolution of normalized radius $R/R_0$ (\textbf{i}), actin order parameter $q$ (\textbf{ii}), mean cell area (\textbf{iii}) and cell elongation (\textbf{iv}) for $\Delta P=150$Pa (yellow, n=8), $450$Pa (orange, n=7), $650$Pa (red, n=3) and $850$Pa (purple, n=2) (lines: model, same curve as in Figs.4Di-ii,5Aii,5Bii for $\Delta P=150$ and $650$Pa, dots: experiment, same as in Fig. 5C) } \label{suppfig:4} \end{figure*} \begin{figure*}[!ht] \centering \captionsetup{labelformat=empty} \caption{\textbf{Extended Data Fig. 5. Exploring alternative models of endothelial tube mechanics.}\\ \textbf{A} Time evolution of normalized radius $R/R_0$ (\textbf{i}) and actin order parameter $q$ (\textbf{ii}), in a model with viscoelastic actin accounting for actin strain memory loss (solid line, SI section 1.3.2) compared to experimental data (shadow, dots, same data as in Fig.2A,Civ). \textbf{B} Endothelium stained for DAPI (blue), VE-cadherin (magenta) and phalloidin (white) under low pressure (\textbf{i}) and high pressure (\textbf{ii}), showing a mitotic cell (arrowhead) with condensed chromatin and no stress fibers. Scale bar \SI{20}{\micro\meter}. \textbf{C} Time evolution of normalized radius $R/R_0$ (\textbf{i}) and actin order parameter $q$ (\textbf{ii}) taking into account the contribution of the surrounding gel (green lines, SI Sec.1.3.3) or not (red lines, same data as in Fig.4Di,ii), removing actin elasticity (continuous lines) or not (dashed lines), based on the values for the relaxation time constant $\tau_g$ (\textbf{iii}) obtained by fitting with an exponential the time evolution of the stress after a strain step of varying amplitude (Extended Data Fig. 1Bi). \textbf{D} Time evolution of normalized radius $R/R_0$ (\textbf{i}) obtained for a model where the total tension is the sum of a purely elastic tension $t^r_{ij}$ and a tension $t^a_{ij}$ oriented along actin stress fibers, either purely elastic (green line, SI section 1.3.4) or viscoelastic (red line, SI section 1.3.4), fitted to experimental data. Red shadow indicates experimental data as in Fig.2A. Here the actin stress fibers order parameter has been fitted by $q(t)=-0.25+0.57\times(1-\exp(-0.17t))$ (\textbf{ii}, dots show experimental data as in Fig.2Civ). \textbf{Ciii} Time evolution of normalized circumferential tension $t_{\theta}^{\theta}/K$ (red) and longitudinal tension $t_z^z/K$ (blue), computed from the model in (i), with viscoelastic actin oriented tension. \textbf{E} Time evolution of normalized radius $R/R_0$ (\textbf{i}) and actin order parameter $q$ (\textbf{ii}) after a pressure increase from $150$Pa to $350$Pa (orange) and $650$Pa (red), obtained from a model where actin fibers mean orientation dynamics is coupled to total tension (solid lines, SI Sec. 1.3.6), fitted to experimental data. Shadow and dots indicate experimental data as in Fig.2A,Civ. \textbf{Eiii} Time evolution of normalized circumferential tension $t_{\theta}^{\theta}/\zeta_0$ (red and orange) and longitudinal tension $t_z^z/\zeta_0$ (blue and cyan) for a pressure increase from $150$Pa to $350$Pa (red and blue) and $650$Pa (orange and cyan), computed from the model in (i). \textbf{Eiv} Time evolution of actin strain $s$ after a pressure increase from $150$Pa to $350$Pa (orange) and $650$Pa (red), computed from this model. \textbf{Fi} Time evolution of normalized radius $R/R_0$ obtained from the following models: tissue described as an isotropic material following a Zener rheology, without (green, SI section 1.3.7), or with isotropic active tension (red dashed line, SI section 1.3.7), and tissue described as an elastic material with Zener rheology, together with an active tension contribution oriented along actin stress fibers (red solid line, SI section 1.3.8). Shadow indicates experimental data as in Fig.2A. \textbf{Fii} Time evolution of actin order parameter $q$ obtained from the model describing the tissue as an elastic material with Zener rheology together with actin oriented active tension (red), fitted to experimental data (dots, same data as in Fig.2Civ). \textbf{Fiii} Time evolution of normalized circumferential tension $t_{\theta}^{\theta}/K$ (red) and longitudinal tension $t_z^z/K$ (blue), computed from either a model describing the tissue as an elastic material with Zener rheology and subjected to actin oriented active tension (solid line) or a model describing the tissue as an isotropic material following a Zener rheology, together with isotropic active tension (dashed lines). \textbf{Fiv} Schematics of the Zener rheology, consisting of a spring of elastic modulus $K$, in parallel with a serial association of a dashpot of viscosity $\mu$ and a spring of elastic modulus $\mu/\tau$, with $\tau$ a characteristic time. } \label{suppfig:5} \end{figure*} \begin{figure*}[!ht] \centering \captionsetup{labelformat=empty} \caption{\textbf{Extended Data Fig. 6. Schematics of the system and determination of the coefficient in the cell elongation nematic parameter Q.}\\ \textbf{A} Schematics of the microfluidic set up showing the imposed flow rate at the channel inlet and the imposed pressure at the channel outlet. \textbf{Bi} Cell order parameter extracted from immunostaining of VE-cadherin $Q_{Cadh}$ as a function of the cell order parameter extracted from phase contrast brightfield $Q_{BF}$ showing a linear correlation with a 0.5 coefficient. \textbf{Bii} Jump in the cell order parameter, extracted from phase contrast brightfield $Q_{BF}$ as a function of the logarithm of the jump in radius, showing a linear correlation with a 5/2 coefficient. $Q_{BF}^+$ and $Q_{BF}^-$ (resp. $R^+$ and $R^-$) are respectively the value of $Q_{BF}$ (resp. $R$) just before and just after the pressure increase.} \label{suppfig:methode} \end{figure*} \newpage \bibliographystyle{ieeetr} \bibliography{refs.bib} \newpage \section*{Methods}\label{s:methods} \subsection*{Microvessel-on-chip fabrication} The microvessel-on-chip system consists of a chamber that houses a \SI{120}{\micro \meter}-diameter endothelium-lined channel embedded in a soft collagen hydrogel \cite{Dessalles_2021}. After fabricating the PDMS housing with its inlet and outlet ports, a \SI{120}{\micro \meter} diameter acupuncture needle (Seirin) was introduced into the chamber and the housing was bound to a coverslip through plasma activation. Two PDMS reservoirs were sealed with liquid PDMS to the inlet and outlet ports, their inner diameter matching the diameter of standard plastic straws. The chamber was sterilized with 70 \% ethanol and 20 min of UV light. To improve collagen adhesion to the PDMS walls, the chamber was coated with 1 \% polyethylenimine (PEI,an attachment promoter; Sigma-Aldrich) for 10 min followed by 0.1 \% glutaraldehyde (GTA, a collagen crosslinker; Polysciences, Inc.) for 20 min. Collagen I was isolated from rat tail tendon as described previously \cite{Antoine_Vlachos_Rylander_2015}, to obtain a stock solution of \SI{12}{\milli\gram \per \milli\liter} . Type I collagen solution was then prepared by diluting the acid collagen solution in a neutralizing buffer at a 1-to-1 ratio, pipetted into the housing chamber, and allowed to polymerize in a tissue culture incubator for 15 min for the baseline \SI{6}{\milli\gram \per \milli\liter} collagen concentration and for up to 4 h for lower collagen concentrations. The acupuncture needle was then carefully removed, and the needle holes were sealed with vacuum grease (Bluestar Silicones) to avoid leakage. \subsection*{Cell culture, seeding and inhibition} Human umbilical vein ECs (Lonza) were cultured using standard protocols in Endothelial Growth Medium (EGM2; Lonza) and used up to passage 7. Medium was changed every other day and cells were passed upon confluence, on average every four days. For the channel seeding, upon confluence, ECs were detached from the flask using trypsin (Gibco, Life Technologies) and concentrated to 10\textsuperscript{7} cells.ml\textsuperscript{-1}. \SI{1}{\micro\liter} of the concentrated cell suspension was pipetted through the inlet port of the device. After a 5 min incubation, non-adhering cells were gently flushed out. After 1 h, a flow rate of \SI{2}{\micro \liter \per \minute} was applied via a syringe pump (PhD Ultra, Harvard apparatus). A confluent monolayer was obtained in 24 hours. For the pharmacological experiments, cells were cultured for one hour prior to the experiment in the presence of 100 nmol/L cytochalasinD in EGM2 for actin disruption, and 5 mmol/L EDTA in EGM2 or 2 mmol/L EDTA in DMEM for cell-cell junction perturbation. \subsection*{Monolayer stretch} A hydrostatic pressure head was used to impose both the luminal pressure while the flow rate was imposed using a syringe pump (PhD Ultra, Harvard apparatus). The hydrostatic pressure head was created by the medium filling a plastic straw of a specific length attached to the channel outlet (Extended Data Fig. 6A). A PDMS base was created by puncturing a 5 mm-diameter hole in a PDMS cubic block (1 cm on a side) and gluing the block to the inlet and outlet. The straws were them inserted into the PDMS base. The inlet straw was continuously replenished using the syringe pump at a fixed flow rate. The pressure within the channel is therefore set by the height of the outlet straw while the luminal flow rate (and the ensuing pressure gradient) is set by the syringe pump flow rate. The height of medium in the inlet straw is equal to that in the outlet straw height plus the pressure gradient due to the luminal flow and the channel hydraulic resistance. During the monolayer growth the flow rate was set to \SI{2}{\micro \liter \per \minute} and the outlet pressure to 100 Pa, which was maintained for the control channels. A pressure gradient of $~$100 Pa is established between the inlet and the outlet. For the stretch experiments, at t=0, both inlet and outlet reservoirs were filled with a syringe in less than a minute to impose a hydrostatic pressure at the outlet of 400, 600 or 800 Pa, defined by the height of the reservoir. The outlet pressure was maintained constant for the duration of the experiments (7 h, 24 h or 56 h), while the inlet pressure was maintained by the flow rate imposed with a syringe pump. The flow rate was increased during the course of the experiments, to \SI{3 }{\micro \liter \per \minute} at t = 0 h and to \SI{4 }{\micro \liter \per \minute} after 24 h, to account for the increased diameter and to maintain the pressure gradient roughly constant, $~100Pa$. We neglected the effect of the pressure gradient, in both experimental quantifications and theoretical modeling, and considered the average pressure of the channel to be around 150, 450, 650 and 850 Pa for the outlet pressures of 100, 400, 600 and 800 Pa respectively. \subsection*{Measurement of the channel deformation} An increase in the luminal pressure leads to a pressure difference across the vessel wall and subsequent channel dilation and circumferential stretch (Movie SV1). The circumferential strain, defined as the ratio of the increase in perimeter of the cross section of the channel to the initial perimeter, was obtained from the vessel diameter. Channel diameters were automatically measured, as previously described \cite{Salipante_Hudson_Alimperti_2022}. Briefly, channels edges are detected by identifying the position of the peaks in the intensity gradient along the vertical direction. The diameter is then the mean distance between the two peaks. \subsection*{Laser ablation} Laser ablation experiments were performed as described in \cite{Boutillon_2021, Boutillon_2022}. The chip was placed on a TriM Scope II microscope (La Vision Biotech) equipped with a femtosecond Mai Tai HP DeepSee laser (Spectra Physics), an Insight DeepSee (Spectra Physics) laser and a XLPLN25XWMP2 (Olympus) 25x water immersion objective. Lifeact mCherry was excited through 2-photon excitation using the Inshight laser set to 1160 nm and ablation was performed using the Mai Tai laser set to 820 nm and exit power at 0.45 mW. Using an electro-optic modulator, the region to be ablated was defined as an XY ROI of 4.5x76 µm located at the level of actin cytoskeleton and oriented either longitudinally or circumferentially. Endothelial cells were imaged with a frame every 130 ms, for 5 time-frames prior to ablation, then ablated for two frames and, finally, imaged for 53 time-frames (Movie SV2). The same channel served for six ablations, three in each directions and alternating, starting from 1.5 mm away from the channel border and separated by 1.5 to 2 mm in order to avoid the influence of one cut on the adjacent cuts. To compute the initial recoil velocity, data were analyzed by manually measuring the distance traveled by the edge of the cut in the first frame relative to its initial position. \subsection*{Rheology measurement of the collagen gel} Rheology measurements of the collagen gels were performed following a previously published protocol \cite{Nam2016_2}. We measured stress relaxation using a stress controlled rheometer (Anton Paar MCR 301) equipped with measuring plates of 25mm in diameter with stainless-steel surfaces. To prevent slipping of the collagen gel, a profiled surfaced top plate was used. The collagen hydrogel with a concentration of 6mg/ml, prepared following the same protocol as the one used for microvessel fabrication, was deposited on the bottom plate cooled at 4°C. The top plate was lowered quickly, before the gelation of the collagen was initiated by heating the plate to 37°C. Gelation was monitored with continuous oscillations at a strain rate of 0.01 and frequency of 1rad/s. The mechanical measurements were performed after the storage modulus reached a stable value. Different strains ranging from 5 to 30 \% were applied with a rise time of 0.1s, then maintained for 5 minutes to observe stress relaxation. The Young's modulus $E_g$ was extracted from the shear modulus $G$ using the relationship $E_g=2G(1+\nu_g)$, with $\nu_G=0.3$ \cite{Knapp2014,LANE2018}. \subsection*{Measurement of the monolayer stiffness} For instantaneous deformations of linear elastic materials, the relationship between tension and strain is dictated by the Young’s modulus. We therefore used the present system to measure the Young’s modulus of the endothelium, as previously described \cite{Salipante_Hudson_Alimperti_2022} (see SI, section 2). \subsubsection*{Measurement of the stress-strain relationship} Briefly, channels were subjected to a one minute long pressure ramp, from 150 Pa to 1000 Pa and the circumferential strain was recorded (Movie SV3). The Young's modulus is then extracted from the slope of the stress-strain curve, assuming that dissipative stresses are negligible. The pressure was increased at a constant speed by filling simultaneously the inlet and outlet reservoirs with a syringe pump at a \SI{2 }{\milli \liter \per \minute } rate, which corresponds to \SI{1000 }{\pascal \per \minute }. Channels were imaged every second in phase contrast with a 10x objective. The increase in diameter was then measured automatically with the same method as for still snapshots (see above). A second method was used, where a similar one minute long pressure ramp was applied, starting at 150 Pa but stopping at 650 Pa. Here there was no continuous imaging, a brightfield image was taken only at the beginning (150 Pa) and the end of the pressure application (650 Pa), from which the diameters were measured. \subsubsection*{Fitting procedures for parameter inference} The stress-strain curves of control and pharmacologically-perturbed monolayers on \SI{2}{\milli\gram \per \milli\liter} collagen, measured continuously, displayed a typical strain-stiffening behavior (Fig 1C,E). The cell monolayer was then modeled as a $3.6 \pm 0.5 \micro m$ thick shell, composed of a nonlinear elastic Gent material; while the hydrogel was modeled as a linear elastic material that decreases the pressure drop across the cell layer. The monolayer thickness was measured from fluorescent images of the actin cytoskeleton obtained at the tube mid-plane. By fitting the model to the experimental curves, we inferred the Young’s modulus of the endothelium (see SI, section 2.2). The stress-strain curves of control monolayers on \SI{6}{\milli\gram \per \milli\liter} collagen, measured continuously, displayed a linear relationship (Fig. \ref{fig:fig1}C) up to 900 Pa. The paired-values of the control monolayers on \SI{6}{\milli\gram \per \milli\liter} collagen also showed a linear behavior when connected to the reference state $D_0 = 125 \mu m$ at $\Delta P = 0$ Pa. This reference state was determined with the Gent model (see SI, section 2.1.1) and consistent with previous measurement of bare channel diameter \cite{Dessalles_2021}. We therefore used the value of the radial strain at 650 Pa to estimate the Young's modulus of these control monolayers (Fig. \ref{fig:fig1}C, F). The paired-values of the pharmacologically-treated monolayers showed a strain-stiffening behavior when connected to the reference state (Fig. \ref{fig:fig1}F), consistent with the diameter at 650 Pa being above the threshold diameter for stiffening, estimated to be around 150 $\mu$m (Fig. \ref{fig:fig1}Ei). We therefore used the value of the radial strain at 150 Pa, still in the linear regime, to estimate the Young's modulus of the cytoD and EDTA treated monolayers (Fig. \ref{fig:fig1}F). \subsection*{Immunostaining} Cell-cell junctions were stained using a rabbit anti-VE-cadherin primary antibody (Abcam, 33168). Actin filaments and nuclei were stained using Alexa Fluor phalloidin (Invitrogen, Thermo Fisher Scientific, A12379) and DAPI (Invitrogen, Thermo Fisher Scientific D3571), respectively. In addition, a mouse anti-vinculin (Sigma Aldrich, Merck V9264) and a mouse anti-vimentin (Abcam, 92547) primary antibodies were used to stain for focal adhesions and intermediate filaments. Immunostaining was performed by slow infusion of reagents into the microchannel. Cells were fixed in 4 \% paraformaldehyde (PFA; Thermo Fisher Scientific) for 15 min, rinsed with phosphate-bufered saline (PBS), and then permeabilized with 0.1 \% Triton in PBS for another 15 min. The channel was then perfused with a 3 \% bovine serum albumin (BSA) solution in PBS for 1 h to block non-specific binding. Cells were incubated with the primary antibodies (1:400) in PBS for 1 h at room temperature and then rinsed with PBS for an additional 1 h. The channel was then perfused with the secondary antibodies (1:400), phalloidin (1:200), and DAPI (1:1,000,000) in PBS. Finally, the cells were incubated overnight in PBS at 4\degree C. Samples were imaged using the NIS-Elements software (5.02.03, Build 1273) on an epifluorescence inverted microscope (Nikon Eclipse Ti) and/or a Crest X-Light confocal system mounted on an inverted microscope (Nikon Eclipse Ti). \subsection*{Analysis of orientation} For statistical analysis of orientations, at least 15 images along the bottom half and the top half of the channel were acquired with a 10x objective. A region of interest was then selected to match the area in focus. Angles were defined relative to the channel longitudinal axis, aligned to the horizontal axis. To be coherent with the tangential basis we chose in the model (Fig. \ref{fig:fig4}Ai), angles were defined positive in the bottom half of trigonometric circle and negative in its bottom half. \subsubsection*{Actin and cell orientation} Actin fiber orientation was obtained from images of phalloidin stainings using the plugin OrientationJ in ImageJ \cite{Rezakhaniha}. The window size was set to 5 pixels and the method to cubic spline. The probability distributions of the angles generated by the plugin for each longitudinal position within one channel were then averaged together. The same pipeline was applied to the VE-cadherin immunostaining and to the brightfield images to estimate the cell elongation and orientation. \subsubsection*{Nuclei orientation} Nuclei were segmented using a custom-made Matlab code. Each nucleus was fitted with an ellipse and the angle of the long axis of the ellipse was used as the nucleus angle. Angles were then binned to create a probability distribution. \subsubsection*{Division orientation} Mitotic angles were manually measured from nuclear (DAPI) immunostainings. Dividing cells were identified by their condensed chromosomes and the angle between the segment connecting the two daughter nuclei and the longitudinal axis was measured using ImageJ. Angles were grouped and then binned to create a probability distribution. \subsubsection*{Nematic order parameter calculation} The tensors $q_{ij}$, $Q_{ij}$ and ${Q_n}_{ij}$ are defined as: \begin{align} \label{nematic_tensor} q_{ij}=&\frac{1}{2} \begin{pmatrix} -R^2\left<\cos 2\theta_q\right> & R\left<\sin 2\theta_q\right> \\ R \left<\sin 2\theta_q\right> & \left<\cos 2\theta_q\right> \end{pmatrix},\\ Q_{ij}=&\frac{\alpha_Q}{2} \begin{pmatrix} -R^2\left<\cos 2\theta_Q\right> & R\left<\sin 2\theta_Q\right> \\ R \left<\sin 2\theta_Q\right> & \left<\cos 2\theta_Q\right> \end{pmatrix},\\ {Q_n}_{ij}=&\frac{1}{2} \begin{pmatrix} -R^2\left<\cos 2\theta_n\right> & R\left<\sin 2\theta_n\right> \\ R \left<\sin 2\theta_n\right> & \left<\cos 2\theta_n\right> \end{pmatrix} \end{align} where $\theta_q$, $\theta_Q$ and $\theta_n$ are a set of angles obtained by the image analysis, as described above. In the case of symmetric distribution of angles $\theta_q$, $\theta_Q$ and $\theta_n$around $0$, off-diagonal terms of the tensors $q_{ij}$, $Q_{ij}$ and ${Q_n}_{ij}$ vanish and actin orientation, cell elongation and nucleus elongation can be described by the order parameters $q=q_{\theta}^{\theta}=-\left<\cos 2\theta_q\right>/2$, $Q=Q_{\theta}^{\theta}=-\alpha_Q\left<\cos 2\theta_Q\right>/2$ and $Q_n=-{Q_n}_{\theta}^{\theta}=\left<\cos 2\theta_n\right>/2$. We chose the convention where a positive value of $q$, $Q$ or $Q_n$ indicates that the orientation is preferentially circumferential. Conversely a negative value of $q$, $Q$ or $Q_n$ indicates a preferentially longitudinal orientation. The magnitude of $q$, $Q$ or $Q_n$ corresponds to the strength of the alignment along the circumferential or longitudinal direction. \subsubsection*{Calculation of the coefficient $\alpha_Q$} Because the orientation of junctions does not necessarily exactly reflect cell elongation, we introduce a correction factor $\alpha_Q$ as follows. For a uniform shear flow $\tilde{v}_{ij}$ (traceless part of the gradient of flow $v_{ij}$) and in the absence of cellular rearrangements, we expect $D_t Q_{ij}=\tilde{v}_{ij}$. In the context of a cylindrical tube, this implies that the variation of cell elongation following a change of radius and for a homogeneous material deformation should be $\Delta Q=\frac{1}{2}\ln(R^+/R^-)$, with $R^-$ (resp. $R^+$) the radius of the tube before (resp. after) the deformation. We tested this relation by imposing a fast change of pressure on tubes of different radii, and by measuring the resulting change of tube radius and change in measured average cell elongation $\Delta Q$. For measurement of $\Delta Q$ with a fast change of pressure the junction angle distribution was obtained from brightfield images, instead of VE-cadherin stainings in the general case. Using images with both VE-cadherin staining and brightfield pictures, we find that the measured value of $Q$ using VE-cadherin staining corresponds to approximately half its measured value using brightfield picture (Extended Data Fig. 6Bi). Converting the value of $Q$ compute from brightfield to its VE-cadherin staining based value, we finally found that the linear relation $\Delta Q=\frac{1}{2}\ln(R^+/R^-)$ was satisfied for a correction factor $\alpha_Q=0.8$ (Extended Data Fig. 6Bii). \subsection*{Nuclei metrics and density measurements} Nuclei were segmented using the StarDist ImageJ pluggin \cite{Schmidt_Weigert_Broaddus_Myers_2018}. Nuclei area and aspect ratio were extracted from each segmented object in ImageJ. Cell density was calculated by dividing the number of cells in a field of view by the area (accounting for channel curvature), for each position along the channel length. The mean cell area was calculated as the inverse of cell density. \subsection*{Proliferation assay} To assess EC proliferation, EdU was added to the cell culture medium at a concentration of 10 \textmu M. Cells were maintained in EdU-containing culture medium for 8h, either at 150 Pa or at 650 Pa, after which they were fixed and stained for DAPI and EdU-positive nuclei. The fraction of EdU-positive to EdU-negative nuclei provides a measure of the proliferation rate. \subsection*{Statistical analysis} The statistical unit corresponds to an experimental replicate, i.e. a single microvessel. For all Figures and Extended Data Fig., all data are plotted as mean ± standard deviation, except for the probability distribution plots where the line corresponds to the mean curve and the shadowed area corresponds to the standard error of the mean. All significance testing are based on an unpaired Student t-test, performed using Matlab. *** denotes p \textless{} 0.001, ** denotes p \textless{} 0.01, and * denotes p \textless{} 0.05. \section*{Data availability} Data for each plot are available in supplementary information in table format, raw data is available from authors upon reasonable request. \section*{Code availability} Codes are available at \url{https://gitlab.unige.ch/salbreux-group/nicolas-cuny/endothelialtubemodel} %TC:endignore \end{document}