A Predictive 3D Multi-Scale Model of Biliary Fluid Dynamics in the Liver Lobule.

CONTACT FOR REAGENT AND RESOURCE SHARING

Please contact Marino Zerial (Lead Contact, zerial@mpi-cbg.de ; Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstrasse 108, 01307 Dresden, Germany) for reagent and resource requests.

EXPERIMENTAL MODEL AND SUBJECT DETAILS Mouse Work

Animal experiments performed at the National

Institutes of Health (Bethesda, MD, USA) were approved by the National Institute of Dental and Craniofacial Research (NIDCR, National Institutes of Health, Bethesda, MD, USA) Animal Care and Use Committee.

Animal experiments performed a the Max Planck

Institute of Molecular Cell Biology and Genetics (MPI-CBG, Dresden, Germany) were conducted in accordance with German animal welfare legislation and in strict pathogen-free conditions in the animal facility of the MPI-CBG, Dresden, Germany. Protocols were approved by the Institutional Animal Welfare Officer (Tierschutzbeauftragter) and all necessary licenses were obtained from the regional Ethical Commission for Animal Experimentation of Dresden, Germany (Tierversuchskommission, Landesdirektion Dresden). Experiments were performed on 6–10 weeks old male C57BL/6JHsd mice (Harlan laboratories) and male or female Lifeact-EGFP mice (obtained from the laboratory of R. Wedlich-Soldner ( Riedl et al., 2010 )). For IVM of CF(DA) transport, animals were starved for 6 h (water ad libitum) prior experiments. For imaging of bile canaliculi contractility in Lifeact-EGFP mice, animals were not starved. Fasudil and APAP were dissolved in 0.9 % saline and administered at 20 mg/kg (Fasudil) or 150 mg/kg (APAP) by i.p. injection at 1.5 h (Fasudil) or 2 h (APAP) prior imaging or organ collection. As controls, mice were administered 0.9 % saline.

METHOD DETAILS Experimental Techniques Protein Extraction and Western Blot

Liver tissue was lysed in ice-cold 20 mM Tris-hydrochloride (Tris-HCl) pH 7.5, 150 mM sodium hydrochloride (NaCl), 1 mM ethylenediaminetetraacetic acid (EDTA), 1 mM ethylene glycol-bis(2-aminoethylether)-tetraacetic acid (EGTA), 1 % (w/v) sodium dodecyl sulfate (SDS), 1 % (w/v) NP-40 using a pestle. Cell debris were removed by centrifugation for 10 min at 12 000 × g at 4 °C and protein was denatured at 95 °C in presence of 100 mM dithiothreitol (DTT). A total of 10 mg protein was separated by sodium dodecyl sulfate polyacrylamide gel electrophoresis, and transferred onto a nitrocellulose membrane. Membranes were blocked and incubated with primary antibodies against glyceraldehyde 3-phosphate dehydrogenase (GAPDH, 1:2000) or phospho-myosin light chain (pMLC, 1:500) and HRP-conjugated secondary antibodies (1:10000) in 5 % dry-milk, 10 mM Tris-HCl pH 8.0, 200 mM NaCl, 0.1 % Tween20. Protein was detected using the enhanced chemiluminescence (ECL) detection kit (GE Healthcare, Buckinghamshire, UK) and chemiluminescence films (GE Healthcare, Buckinghamshire, UK) according to manufacturer’s instructions.

Liver Tissue Fixation and Immunofluorescence Staining

Liver tissue of WT and Fasudil-treated animals was fixed by trans-cardial perfusion (3.7 ml/min) with 4 % paraformaldehyde (PFA), 0.1 % Tween in phosphate buffered saline (PBS) and post fixed in 4 % PFA, 0.1 % Tween, PBS (for immunofluorescence microscopy, IF) or in 2 % glutaraldehyde, PBS (for electron microscopy, EM) at 4 °C overnight. Liver tissue of APAP-treated animals and controls were only immersion fixed in 4 % PFA, 0.1 % Tween20 in PBS for 48 h at 4 °C to avoid artefacts (trans-cardial perfusion caused bile canaliculi network blebbing). For IF stainings, fixed liver tissue was mounted in 4 % low melting agarose in PBS and sectioned into 100 μm thick slices using a vibratome (Leica VT1200S). Floating sections were permeabilized in 0.5 % Triton-X100 in PBS for 1 h, quenched by incubation with 10 mM ammonium chloride (NH 4 Cl) in PBS for 30 min and blocked by incubation with blocking buffer (0.2 % fish gelatin, 300 mM NaCl, 0.3 % Triton-X100 in PBS) 3 times for 5 min. Sections were incubated sequentially with a primary antibody against CD13 (1:500) in blocking buffer for 2 overnights, washed 5 times for 5 min with 0.3 % Triton-X100 in PBS, incubated with secondary antibody labelled with Alexa fluorophore 568 (1:1000), DAPI (1:2000) and Alexa fluorophore 488-conjugated Phalloidin (1:400) in blocking buffer for 2 overnights and washed again with 0.3 % Triton-X100 in PBS 5 times for 5 min. Sections were optically cleared with SeeDB (See Deep Brain) and imaged using 80 % (v/v) 2.2’-thiodiethanol as immersion medium as described previously ( Ke et al., 2013 ). All steps were performed at room temperature.

Microscopy of Fixed Tissue

Fixed tissue was imaged with a Zeiss laser scanning microscope 780 NLO using a 63× 1.3 numerical aperture (NA) glycerol immersion objective (Zeiss), a Chameleon Ti-Sapphire 2-photon laser (780 nm), 488 and 561 laser lines and Gallium arsenide phosphide (GaAsp) detectors. Intravital Imaging of CFDA Transport Mouse anaesthesia was induced with 3–4 % isoflurane/ 0.3 % oxygen and maintained by i.p. injection of ketamine/xylazine throughout the experiment. Mice received 20 U of heparin dissolved in 0.9 % (w/v) NaCl by i.p. injection to prevent ischemia of the liver during the course of imaging. To visualize hepatocyte nuclei, Hoechst 33258 dissolved in 0.9 % (w/v) NaCl was administered retro-orbitally at a dose of 2 mg/kg and in a total volume of 50 μl. To expose the liver for imaging, the abdominal fur was removed using an electric shaver and a small transversal incision of 1 cm was made at the height of the sternum to expose the left lateral liver lobe using a surgical scissor and cauterizer. The mouse was positioned on the stage of an IX81 inverted confocal microscope equipped with a Fluoview 1000 scanning head (Olympus America) and a heat-adjustable UPLSAPO30X, 30× 1.05 NA silicon oil objective (Olympus). The objective was heated to 37 °C. To avoid compression of the liver lobe and to stabilize the tissue, the stage was designed with a small hole in the center into which the left lateral lobe was carefully placed. The residual volume of the hole was filled with a water-based and transparent 1 % carbomer gel (0.3 M Sorbitol, 1 % (w/v) Carbomer 940, polymerized by addition of triethanolamine and adjusted to pH 7) to immobilize the organ and prevent the organ from drying out. The bottom of the hole was designed with a cover-slide through which the organ was accessible for imaging. The animal body temperature was kept at 37 °C using a red lamp. Prior to imaging start, 18 mg/kg of 70 kDa Rhodamine-dextran or 20 ml of Qtracker 655 vascular label dissolved in 0.9 % (w/v) NaCl was injected retro-orbitally to identify the lobule orientation from the vascular flow pattern. To monitor the flux of CFDA in the liver, CFDA, dissolved in dimethyl sulfoxide (DMSO), was injected retro-orbitally at a dose of 0.2 mg/kg in a total volume of 50 μl. CFDA injection was performed slowly (approx. 30 sec) to avoid hydrodynamic effects and performed at 1 min after image acquisition start. The imaging field covered an entire CV-PV axis in the first cell layers below the liver capsule. Movies were acquired at temporal resolution of 1 min (WT, APAP and APAP control) or 2 min (Fasudil and Fasudil control) over a time course of 1 h. For each time point a 20 mm stack with an image size of 320 × 320 μm, a pixel size of 0.5–1 mm and 1 μm z-steps was acquired. Intravital Imaging of Bile Canaliculi Contractility For intravital imaging of bile canaliculi contractility the mouse preparation was the same as described for imaging of CFDA except of the following steps: Anaesthesia of Lifeact-EGFP mice was maintained using 3–4 % isoflurane/ 0.3 % oxygen throughout the entire experiment and imaging was performed using a Leica-DMI6000 inverted microscope with a heated stage (37 °C). Images were acquired using a 8 kHz resonant galvo-scanner and a Leica HC CS2 PL APO 63× 1.3 NA glycerol objective that was heated to 37 °C. Lifeact-EGFP was excited using a 488 laser and detected using a hybrid detector. Bile canaliculi were imaged within the first 1–2 cell layers below the liver capsule. Elastin fibres of the liver capsule were imaged by SHG microscopy using a tuneable 2-photon laser at 900 nm and a non-descanned photomultiplier tubes (PMT) detector. Movies were acquired with a pixel size of 0.09 mm and 0.020 or 0.025 sec frame rates. Electron Microscopy 1–2 mm 3 pieces of fixed liver tissue were processed for SBF-SEM pre-embedding staining, and flat embedding on glass slides in hard Durcupan resin as described previously ( Deerinck et al., 2010 ). Small pieces of embedded tissues were cut from the slides, remounted on SBF-SEM pins using conductive glue and carbon coated. SBF-SEM was performed on a Magellan 400 SEM (Fei, The Netherlands), equipped with a Gatan 3ViewXP2 (Gatan, Munich) at 1.5 kV, 100 pA beam current, using a 12.4 nm pixel size and 40 nm-thick sections. Mathematical and Computational Models 3D Reconstruction and Spatial Analysis of Bile Canaliculi Network Geometry 3D reconstructions of the bile canaliculi network were performed on high-resolution IF image stacks of fixed liver tissue stained for the apical marker CD13 (voxel size: 0.28 × 0.28 × 0.3 mm, 70–80 μm in depth). A tile of 2 × 1 image stacks was stitched to cover an entire CV-PV axis. Images were processed, analyzed and reconstructed using the software MotionTracking as described in ( Morales-Navarrete et al., 2015 ). In brief, images were segmented using a local thresholding algorithm (maximum entropy), segmented objects were corrected for artefacts using standard morphological operations (opening/closing) and the triangulation mesh of the segmented surfaces was generated by the cube marching algorithm. The active mesh was tuned to align the triangle mesh vertexes to the maximum gradient of fluorescence intensity in the original image. A representation of the skeletonized image was generated using a 3D graph describing the geometrical and topological features of the bile canaliculi network. For the spatial analysis of the bile canaliculi radius, porosity and network branch density, the CV-PV axis was computationally divided into 20 equidistant zones with relative coordinate x based on the two distances of each position from the CV ( d CV ) and PV ( d PV ): x = d C V d C V + d P V Then, the average radius and porosity was determined per zone. For the radius, the minimal distance of each node of the central line of the bile canaliculi network was quantified in the xy-plane. For the bile canaliculi network branch density, the network length per tissue volume was calculated. For the tissue porosity, the bile canaliculi network was computationally divided into cubes of 20 μm 3 that had a 5 μm grid spacing. For each cube, the porosity ε was calculated as the ratio of the void tissue volume of the bile canaliculi network V V to total tissue volume V T : ε = V V V T Then, the average porosity from all cubes within a zone was determined. To determine the shortest bile canaliculi network path between the PV and CV area, bile canaliculi network end-nodes were defined based on their distance to the CV and PV. For each end-node in the CV area the shortest distance through the bile canaliculi network to an end-node in the PV area was calculated using the Dijkstra’s algorithm. From the calculated paths, the shortest one was chosen. To determine the direct CV-PV axis distance, the distance from each point of the CV to the closest one of the PV was calculated. 3D Reconstruction of a Bile Canaliculus from EM Image Stacks SBF-SEM images were de-noised by applying a median filter and aligned using Matlab. The images were segmented by intensity thresholding and size filtering using the Imaris software and the bile canaliculi volume meshes were generated using the snappyHexMesh utility in openFoam ( http://www.openfoam.org ). Correction and Quantification of IVM Movie Shift Frames of CFDA transport movies were aligned by transitional image registration. The dextran or Hoechst channel was used as reference to align the frames of all other channels (target image) to it. The relative shift ([x,y] in 2D and [x,y,z] in 3D) of the target image stack was calculated using the phase correlation approach. The cross-correlation between stacks was computed using the Fast Fourier Transform. To determine the stability of the IVM setup, the same algorithms were applied to calculate the image shift in 2D on movies of elastin fibres.

Quantification of CF Intensities from Intravital Movies

Quantification of the CF intensity in the hepatocyte cytoplasm and bile canaliculi from IVM movies was performed using the image analysis software MotionTracking. Following correction for shift, IVM movies contained 16–21 frames per stack, covering 15–20 μm in z. To avoid liver damage from photo-toxicity, IVM movies were acquired with minimum laser intensities resulting in low signal-to-noise ratio. The resulting difference of intensity between the background and the CF fluorescence in the hepatocyte cytosol was in the range of 5–20 intensity units and varied with depth. Therefore, we used the modified Mean-Shift algorithm to separate the CF fluorescence from the background. The result of the background/foreground discrimination was checked manually ( Figure S1C ). The bile canaliculi were detected in three steps. First, the image was convolved with Laplacian of Gaussian. Second, pixels with an intensity > 2 standard deviations of the local noise were defined as potential bile canaliculi. The local noise was determined from the local intensity minimums in at least one of 4 discrete directions. Third, along the line of the local maximum intensity direction of a bile canaliculus, pixels that co-localized with sharp intensity transitions between the cytoplasm and sinusoids were excluded from the bile canaliculi compartment. For all compartments (cytoplasm, bile canaliculi and background), the mean intensity was calculated. To avoid mixing of compartments from light scattering of bright objects (bile canaliculi to cytoplasm and cytoplasm to background), the area within the radius of 2 pixels from the object border was excluded from the calculation. Following segmentation, the mean intensity of the bile canaliculi and cytoplasm was corrected for the intensity of the background. Due to the low signal-to-noise ratio, the direct subtraction of background intensities from the cytosolic intensities sometimes resulted in negative values and consequently created artefacts. To avoid these artefacts, we developed a Bayesian estimation of the most probable value of the foreground intensity by considering the noise of the background and foreground intensity measurements. In short, we denoted f and b to be the foreground and background intensities which we want to estimate and m and n to be the foreground and background intensities we have measured. Then the probability of f , b given m , n is p ( f , b ∣ m , n ) = 1 Z ( m , n ) p ( m , n ∣ f , b ) p ( f ) p ( b ) where p ( f ) and p ( b ) are prior distributions of the foreground and background. We assumed that m , n are independent and normally distributed. This assumption is reasonable, because the intensities were estimated by the summation of thousands of pixels (see above) and according to the Central Limit Theorem these distributions have to converge to a normal one. Therefore: p ( m , n ∣ f , b ) = 1 2 π σ 1 σ 2 m n e x p ( − 1 2 ∗ ( l n 2 ( f + b m ) σ 1 2 + l n 2 ( b n ) σ 2 2 ) ) Since we were not interested in the background value, we marginalized it: p ( f ∣ m , n ) = p ( f ) Z ( m , n ) ∫ 0 ∞ e x p ( − 1 2 ∗ ( l n 2 ( t + b m ) σ 1 2 + l n 2 ( b n ) σ 2 2 ) ) p ( b ) d b We assumed uniform improper prior for f and b : p ( b ) = c o n s t and p ( f ) = c o n s t that resulted in: p ( f ∣ m , n ) = 1 Z ( m , n ) e x p − 1 2 ( m − n − f ) 2 σ 1 2 + σ 2 2 ) ( 1 + e r f ( m − f ) σ 2 2 + n σ 1 2 2 ( σ 1 2 + σ 2 2 ) S ) ) where S 2 = ( 1 σ 1 2 + 1 σ 2 2 ) − 1 and Z ( m,n ) is normalization constant. The planes in a 3D stack were split on 16 sub-images and the values σ 1 and σ 2 were estimated from the variation of the intensity measurements between the sub-images within z-planes and across z-planes in a 3D image stack. The most probable value of f was found numerically as f = max f ∈ [ 0 , ∞ ] { e x p − 1 2 ( m − n − f ) 2 σ 1 2 + σ 2 2 ) ( 1 + e r f ( m − f ) σ 2 2 + n σ 1 2 2 ( σ 1 2 + σ 2 2 ) S ) ) } Then, the resulting estimations of the compartment intensities were multiplied by their total pixel number to calculate the final integral intensity of the compartment. Within an experimental condition (WT, controls, Fasudil or APAP-treated mice) intensities from each movie were scaled to the mean value of the condition by applying a scaling factor that was calculated as: f i = ∑ j = 1 N y i , j y j ∑ j = 1 N y i , j 2 Where y i , j is an intensity of i -th curve in j -th time point, y j is a mean intensity in j -th time point and f i is a scaling factor for i -th curve. For each experimental condition, the mean intensity curve was calculated from 4–5 IVM movies and later used for further mathematical modelling. IVM movies of Lifeact-EGFP were de-noised by applying a mean filter using the Fiji software. All other IF images and movies were intensity threshold adjusted but not processed otherwise. Mathematical 3-Compartment Model of CF(DA) Transport in the Liver The transport of CF(DA) from the blood into and through the biliary network was described in a mathematical model that considers 3 hepatic compartments: the blood (s), hepatocyte cytoplasm (c) and bile canaliculi (b) (see Figure 2F ). Dye propagation through these three compartments was modelled for three spatially distinct zones within the liver lobule: The CV, MD and PV zone as defined in Figure 2C (see also Figure S2B ). The different zone geometries of the kite-shaped CV-PV axis were accounted for by introducing respective geometry factors ( Figure S2C ). The model considers that only a fraction of the injected CFDA is delivered to the liver, whereas the rest is cleared by other tissues at rate k clear . The injection of CFDA into the blood circulation is described by Pulse ( t ). It is defined by the time point of injection start ( τ 1 ) and the injection duration ( τ 2 ) assuming that CFDA is injected with constant rate in time t > τ 1 and t < τ 1 + τ 2 . Both τ 1 and τ 2 were fitted by the model with boundary intervals 40–80 sec ( τ 1 ) and 20–60 sec ( τ 2 ) . In the liver, the model considers that CFDA is taken up from the blood with a permeability coefficient Perm = 3 sec −1 (according to ( Breeuwer et al., 1995 ), considering a mammalian plasma membrane thickness of 4 nm), converted into CF by cytoplasmic esterases with cleavage rate k cleav and secreted by apical transporters with transporter activity k pump . To account for the spatial heterogeneity of esterase and transporter levels within the CV-PV axis, the amounts of both esterases ( q i ) and apical transporters ( q 1 i ) were determined for each zone ( i = cv, md, pv). The model further considers passive back flux of CF from the bile canaliculi into the hepatocyte cytoplasm at rate k l i . The bile canaliculi compartment of the three zones is connected, occurs unidirectional and sequential from the CV to the MD with transport rate k t c v m d and form the MD to the PV zone with rate k t m d p v and exits the network from the PV zone into the bile duct with transport rate k t p v out . The dynamics of CF(DA) were described by a set of ODEs. In the blood compartment ( C s ), the flux of the tracer was described as: d C s d t = P e r m ∗ P u l s e ( t ) − k c l e a r ∗ C s The flux of the tracer was described separately for the cytoplasmic compartment ( C c i ) as: d C c c v d t = v c v ∗ k c l e a v ∗ q c v ( q c v + C s ) ∗ C s + k l c v ∗ C b c v − k p u m p ∗ q 1 c v ( q 1 c v + C c c v ) ∗ C c c v d C c m d d t = v m d ∗ k c l e a v ∗ q m d ( q m d + C s ) ∗ C s + k l m d ∗ C b m d − k p u m p ∗ q 1 m d ( q 1 m d + C c m d ) ∗ C c m d d C c p v d t = v p v ∗ k c l e a v ∗ q p v ( q p v + C s ) ∗ C s + k l p v ∗ C b p v − k p u m p ∗ q 1 p v ( q 1 p v + C c p v ) ∗ C c p v And for the bile canaliculi compartment ( C b i ) as: d C b c v d t = k p u m p ∗ q 1 c v ( q 1 c v + C c c v ) ∗ C c c v − k l c v ∗ C b c v − k t c v m d ∗ C b c v d C b m d d t = k p u m p ∗ q 1 m d ( q 1 m d + C c m d ) ∗ C c m d − k l m d ∗ C b m d + k t c v m d ∗ C b c v − k t m d p v ∗ C b m d d C b p v d t = k p u m p ∗ q 1 p v ( q 1 p v + C c p v ) ∗ C c p v − k l p v ∗ C b p v + k t m d p v ∗ C b m d − k t p v out ∗ C b p v All parameters were fitted to the experimental data by maximizing the Gaussian likelihood function using the simulation software FitModel ( Zeigerer et al., 2012 ). Since the rate parameters could vary by orders of magnitude the logarithms of the rates were used as fitting parameters. The confidence intervals for parameters were estimated by numerical calculation of the inverse Hessian matrix of the Gaussian likelihood function ( Sivia and Skilling, 2006 ). Apical secretion rates sq i were calculated relative to the MD zone as follows: s q i = q 1 i ∗ v m d q 1 m d ∗ v i Bile flow velocity v i at the interfaces of the lobule zones was estimated from the volume flux rates k t c v m d , k t m d p v and k t p v out considering the size of the zone volumes V i and zone boundaries A i ( i = cv , md , pv ) as well as a CV-PV axis distance L of 229 μm (see Figure S2E ): v c v = k t c v m d ∗ V c v A c v ∗ L v m d = k t m d p v ∗ V m d A m d ∗ L v p v = k t p v o u t ∗ V p v A p v ∗ L Computational Fluid Dynamics Simulation of Bile Flow in a 3D EM-Reconstructed Bile Canaliculus The simulation of bile flow in a 3D reconstructed bile canaliculus from EM was carried out in the laminar regime as an incompressible and Newtonian fluid for physiologically relevant bile pressure conditions (10 −3 –10 5 Pa) and in steady state mode using the open-source software openFoam ( http://www.openfoam.org ) and, specifically, the simpleFoam laminar solver therein. Grid convergence studies were conducted in the standard way in order to ascertain robustness and accuracy of the numerical simulation. To verify that bile flow inside bile canaliculi is laminar, we calculated the Reynolds number (Re) from the orders of magnitude of our measured bile velocity and bile canaliculi diameter as well as bile density and bile viscosity ( Luo et al., 2007 ) and obtained R e ∼ 1 μ m s e c ∗ 10 3 k g m 3 ∗ 1 μ m 1 m P a ∗ sec = 10 − 6 which lies 9 orders of magnitude below the threshold to turbulent flow. Mechanistic Model of Osmotic Fluid Secretion and Bile Flow We developed a mechanistic model of osmotically driven secretion of biliary fluid to predict the spatial water influx profile j ( x ) into the bile canaliculi network and the bile flow velocity v i at the borders of zones i = cv, md, pv along the CV-PV axis (see Figure 2C , S2B , and S2C for the definition of the zones). The model takes into account previously reported fluid mechanic properties of bile ( Luo et al., 2007 ) and the measured geometrical parameters, including the canaliculus radius profile a ( x ) = a a ( x ) * r corr with apparent radius a a ( x ) (e.g. shown in Figure 3C for WT mice) and correction factor r corr = 0.344 for the hydraulic diameter or radius, a mean cumulative bile canaliculi path length L between the CV and PV of 344 μm ( Figure S2D ) and a linear coordinate x along a shortest path of bile canaliculi branches from a tip of the bile canaliculi network near the CV ( x = 0) to a junction with a draining bile duct in the PV area ( x = L ), neglecting potential effects of branch points ( Figure 4B ). The osmotic driving due to osmolites with concentration c in the bile canaliculi lumen is considered spatially uniform (see justification below) and static (independent of the CF pulse) p osm = RTc , causing bile canaliculi water influx j ( x ) to be proportional to the pressure surplus of p osm over the local fluid pressure p ( x ). The local fluid pressure p ( x ) is monotonously decreasing from a self-organising pressure maximum at the closed central tip to zero at the open outlet, hence also j ( x ) is non-uniform in the general case. This feedback mechanism ( Figure 4B ) was modelled by a first order ODE for the fluid velocity profile v ( x ) at steady state according to ( Mathias, 1985 ): d v ( x ) d x = 2 κ a ( p o s m − p ( x ) ) where κ is the water permeability of the apical membrane of hepatocytes, the factor 2/a accounts for the surface to volume ratio and v ( x ) is the cross-section average of the local fluid velocity. We assumed Poiseuille flow with v ( x ) = − a 2 8 μ d p d x where μ is the fluid viscosity of bile and applied mixed boundary conditions with zero inflow v ( x = 0 ) = 0 at the closed central tip (corresponding to the Neumann boundary condition dp / dx = 0 for pressure as a ( x =0) is finite) and the Dirichlet condition p ( x = L ) = 0 at the open outlet. The solution is v ( x ) = v 0 M sinh ( M × / L ) cosh M with two parameters, a velocity amplitude V 0 = a 2 R T c 8 μ L and the dimensionless Münch number M = 16 κ μ L 2 a 3 . To factor out the measured geometrical parameters, we rewrote V 0 ( x ) = a ( x ) 2 p 1 L and M ( x ) = p 2 L 2 a ( x ) 3 with fit parameters p 1 and p 2 . The heterogeneous radius profile a ( x ) = a a ( x ) * r c o r r weakly modulated both terms such that the analytical solution remained a valid approximation of the heterogeneous problem. Matlab was used to fit p 1 and p 2 such that the analytical solution reproduced the measured bile flow velocity values at the border of each of the three zones (CV, MD, PV) and to determine the full spatial profile of the flow velocity v ( x ). The used approximation of a spatially uniform osmolite concentration profile is valid for the contributing small molecules and ions. These typically have diffusion constants of the order of D = 100 μm 2 /sec. Even if continuously secreted only at one location, decay with a half-life of τ = 20 min results in a steady state concentration profile with a decay length of D τ > L . From the continuity equation we further calculated j ( x ) = j 0 ( x ) c o s h ( M ( x ) x / L ) c o s h M ( x ) with j 0 ( x ) = 2 π a ( x ) κ p osm . The resulting water influx profile was monotonously ffiincreasing ( Figure 4C ). Using the equation for v 0 ( x ) from above to replace p osm , we could express j 0 purely as a function of the geometrical parameters of the canaliculus and the parameters v 0 ( x ) and M ( x ) of the velocity solution above and obtained: j 0 ( x ) = π a ( x ) 2 v 0 ( x ) M ( x ) L Given the measured fluid velocities v i , we could predict the complete fluid source density profile j ( x ) independent of the exact parameter values for membrane permeability κ , fluid viscosity μ or osmotic driving p osm . Inference of Osmolite Concentration Changes and Prediction of Parameter Changes We considered the steady state balance of osmolites for the kite-shaped part of the lobule as a whole. Then the sum of sources from apical secretion, J = j C V + j M D + j P V equals the sum of sinks from portal outflow J = c * A d u c t * v ( x = L ) where A duct is a fixed geometrical property related to the cumulative cross section area of all bile canaliculi junctions with bile ducts. We considered the ratio of this equality for two conditions, denoted by subscripts control and treated for all quantities J t J c = c t ∗ v t ( L ) c c ∗ v c ( L ) We approximated the apical secretion fluxes of osmolites by the measured apical secretion fluxes of CF and obtained flux ratios J t J c at t = 500 sec when image segmentation had the highest accuracy due to near-maximum CF intensities in all compartments, J F a s u d i l J c o n t r o l = 0.464 and J A P A P J c o n t r o l = 0.798 . Next, we considered the ratio of the analytical solutions v ( x ) at x = L , that are proportional to p o s m = R T c , for each pair of conditions and calculated their ratio. From the two equations for J t J c and v t ( L ) v c ( L ) we then eliminated the velocity ratio V t V c and obtained the osmolite concentration ratio α = c t c c = J t J c ∗ a c ( L ) 2 M c ( L ) tanh M c ( L ) a t ( L ) 2 M t ( L ) tanh M t ( L ) as a dimensionless number α . Note that osmolite concentration only grows with the square root of the osmolite secretion flux as a result of the negative feedback by induced water secretion and resulting osmolite washout (see Figure 4B ). Therewith the alteration of parameter p 1 due to osmolite secretion changes compared to a control condition could be calculated p 1 t = R T c t 8 μ = p 1 c ∗ α to then predict corresponding alterations in the velocity profile. Parameter p 2t = p 2c remained unchanged as it is independent of geometric properties and the osmolite concentration. To demonstrate the use of directly measured geometric parameters (apparent bile canaliculi radii a a ( x ) for c(ontrol) and t(reated) conditions: a c ( x ) , a t ( x ) ) and apical secretion fluxes J c , J t for determining parameter values and model predictions upon a change of treatment condition, we here explicitly consider the prediction of v t ( x ) upon Fasudil treatment given velocity measurements v i for the control condition ( i = cv, md, pv). First, the parameter values p 1c and p 2c for the control condition were determined by fitting the curve (just inserted the substitutions v 0 and M into the analytical model solution, see above) v c ( x ) = p 1 c p 2 c r c o r r a c ( x ) sinh ( p 2 c r c o r r 3 a c ( x ) 3 x ) cosh p 2 c L 2 r c o r r 3 a c ( x ) 3 to the experimental data points v i in relative units. This yielded p 1 c = 566.9 μ m − 1 and p 2 c = 6.656 * 10 − 6 μ m which were confirmed by solving the initial ODE numerically using the software Morpheus ( Starruss et al., 2014 ). Second, the apical secretion fluxes (in arbitrary intensity units per time) at t = 500 sec from data shown in Figure S4F were summed over the entire CV-PV axis: J c = 0.0041 + 0.0592 + 0.0209 = 0.0842 and J t = 0.0019 + 0.0312 + 0.0059 = 0.0390. Third, using p 2 t = p 2 c = 6.656 * 10 − 6 μ m and the extrapolated bile canaliculi radii at x = L , a c ( L ) = 1.320 μ m and a t ( L ) = 1.422 μ m , we calculated the osmolite concentration ratio (see above, after cancelling common factors) α = J t J c ∗ a c ( L ) tanh p 2 c L 2 r c o r r 3 a c ( L ) 3 a t ( L ) tanh p 2 t L 2 r c o r r 3 a t ( L ) 3 = 0.6697 . Fourth, the final parameter p 1 t = p 1 c * α = 379.7 μ m − 1 was determined. The parameter values for all conditions are given in Table S2 . Inference of Peristaltic Contribution We defined the contribution of peristalsis v p ( x ) to bile flow velocity as the difference between the measured velocity profile v c ( x ) under control conditions (where osmosis and peristalsis coexist) and the velocity profile of osmotic driving alone v o ( x ) under the same condition. We obtained the velocity profile of sole osmotic driving under control conditions from the different condition of Fasudil treatment by first fitting our mechanistic model to the measured velocity profile v f ( x ) upon Fasudil treatment and then calculating the corresponding velocity profile v o ( x ) under control conditions by inserting the measured radius profile a c ( x ) and the predicted osmolite concentration, see also Figure 5E , Table S2 . The resulting function v p ( x ) = v c ( x ) − v o ( x ) is displayed as solid black curve in Figure 5F . Next we computed the ratio β ( X ) = V p ( x ) V c ( x ) to quantify the relative local contribution of peristalsis to total bile flow velocity, shown by the dashed black curve in Figure 5F . For different experimental conditions with measured total bile flow velocity v t ( x ), we could then estimate the contribution of peristalsis as v t p ( x ) = β ( x ) * v t ( x ) and that of sole osmotic driving as v t o ( x ) = ( 1 − β ( x ) ) * v t ( x ) . Fitting the latter with our mechanistic model, we could predict the corresponding water influx density j t o ( x ) . We applied this workflow independently to the control of APAP treatment and the WT velocity profile. From the latter, we used the predicted fluid source profile in the 3D porous medium model. From V A P A P c o n t r o l o ( X ) we predicted V A P A P t r e a t e d o ( X ) using the measured radius profile and then the peristalsis contribution by v A P A P t r e a t e d p ( x ) = β ( x ) ( 1 − β ( x ) ) ∗ v A P A P t r e a t e d o ( x ) such that V A P A P t r e a t e d ( x ) = V A P A P t r e a t e d o ( x ) + V A P A P t r e a t e d p ( x ) = 1 ( 1 − β ( x ) ) ∗ V A P A P t r e a t e d o ( x ) A 3D Anisotropic Porous Medium Model of Biliary Fluid Dynamics The liver lobule was considered as a regular hexagonal prism, with the z-axis along its center. The top and bottom hexagonal planes were characterized by a translational periodic boundary condition. The bile canaliculi network was considered to transport bile from the center radially to the bile ducts located at the six corners of the hexagon. The network is closed at the central tips surrounding the CV (CV diameter = 90 μm), but has open outlets at the portal triad (portal triad diameter = 60 μm). Based on measurements from the 3D geometric model of the bile canaliculi network, the distance from the surface of the CV to the portal triad is 229 μm (see Figure S2E ). The hexagonal edges (representing the interfaces between lobules) and the center of the lobule (surrounding the central vein) were treated as bile-impermeable solid walls. The length of the z-axis was 269 μm. The lobule was considered as porous medium with a location-dependent porosity ε( x ) along the CV-PV axis as determined by our geometric measurements ( Figure 3C , right y-axis). The porosity profile was described by a 10 th order polynomial fit of the experimental measurements. From the porosity profile, the location-dependent tissue permeability k ( x ) was estimated using the Kozeny-Carman model k = ( r * r c o r r ) 2 * ε 3 where r is the mean bile canaliculi network radius of 1.143 μm ( r = a a ( x ) determined from the geometric model (see also Figure 3C ) and r corr is the correction factor to account for the hydraulic diameter of bile canaliculi (see above). The spatial heterogeneity of the bile canaliculi radius does not enter here since the heterogeneous geometry of the network was already accounted for by considering an anisotropic location-dependent porosity. For the simulation, an average bile pressure of 100 Pa was applied at the bile duct (estimated according to measurements reported in ( Wiener et al., 2000 )) and bile was assumed to have a viscosity of 1 mPa*sec ( Luo et al., 2007 ). Bile flow was considered to be driven by the osmotic effects of bile secretion and peristalsis. To simulate the osmotic effect, the local bile mass production rate (in units k g m 3 * s e c ) was determined. Therefore, an empirical fit of the heterogeneous fluid source profile j t o ( x ) ( in units μ m 3 μ m * s e c ) , predicted from the combined model of osmotic fluid secretion and peristalsis, was multiplied by the spatial bile canaliculi branch density profile (in units μ m μ m 3 , see Figure S2F ) and the bile density (928 kg/m 3 ( Mcintosh and Anderson, 2010 )). To simulate fluid dynamics, the laminar Navier-Stokes equations at steady-state were numerically solved using the software ANSYS CFX (Ansys, Canonsburg, PA, USA). The liver lobule geometry was meshed using the ICEM CFD software (Ansys, Canonsburg, PA, USA). A mesh sensitivity study was carried out in order to define a mesh independent numerical solution. For that reason several grid configurations were used, resulting in 4.2 million tetrahedral elements. The total bile mass source in the liver lobule was estimated to be 9.784*10 −11 kg/sec. To account for the additional contribution to bile flow velocity from bile canaliculi network peristalsis, the bile velocity profile predicted by the porous medium model from the osmotic effects was multiplied by the space dependent factor 1 1 − β ( x ) , with β ( x ) representing the inferred relative contribution of peristalsis (see above). Bile velocity and pressure were normalized to the maximum values.

QUANTIFICATION AND STATISTICAL ANALYSIS Statistical Analysis

In all experiments, n represents the number of mice used (see Figure legends for explicit n used per experiment). Intensity measurements of CF in the bile canaliculi and hepatocyte cytoplasm from IVM movies of CFDA ( Figures 2D , 2E , S4B – S4E , and S5B – S5E ) are given as mean ± 68 % confidence interval (CI). The uncertainty of transport parameters from the 3-compartment model are represented as 95 % CI ( Figures 2G , 4C , 5E , 7D , S5G , and Table S1 ). It was estimated by calculation of the inverse Hessian matrix of the Gaussian likelihood function ( Sivia and Skilling, 2006 ). Measurements of the bile canaliculi radius, porosity and branch density from 3D reconstructions of confocal image stacks from WT, control, Fasudil-treated or APAP-treated mice ( Figures 3C , S2F , 5C , and 7B ) represent the mean ± SEM for each zone. The uncertainty of the inferred peristaltic contribution to the local bile velocity ( Figure 5F ) and the prediction of bile velocity in control or APAP-treated mice ( Figures 7D and S5G ) was obtained by propagation of the SEMs of the measured bile canaliculi radius profiles shown in Figures 5C and 7B , respectively. In Figures 7D and S5G , the propagated uncertainty was then extrapolated across the CV-PV axis. The significance for the difference between the model prediction of control from Fasudil vs. the experimental measure in control mice and for the difference between the model prediction of Fasudil from control vs. the experimental measure of Fasudil-treated mice ( Figure 5E ) was estimated using the complementary error function. The significance of the peristaltic contribution to local bile velocity in the CV vs. PV zone was estimated by Student’s t-test ( Figure 5F ). The significance of the differences between the radius of control and Fasudil or APAP-treated mice ( Figures 5C and 7B ) was estimated by Student’s t-test. The average p value for each zone comparing the difference between experimental measurements from APAP mice vs. model prediction of APAP from control ( Figure 7D ) was calculated using the complementary error function.

DATA AND SOFTWARE AVAILABILITY

The software FitModel and Matlab were used to fit and predict parameters for the 3-compartment model of CFDA transport and the model of osmotic fluid secretion and peristalsis, respectively. The scripts are available as supplemental data files ( Datas S1 and S2 ).

EXPERIMENTAL MODEL AND SUBJECT DETAILS Mouse Work

Animal experiments performed at the National

Institutes of Health (Bethesda, MD, USA) were approved by the National Institute of Dental and Craniofacial Research (NIDCR, National Institutes of Health, Bethesda, MD, USA) Animal Care and Use Committee.

Animal experiments performed a the Max Planck

Institute of Molecular Cell Biology and Genetics (MPI-CBG, Dresden, Germany) were conducted in accordance with German animal welfare legislation and in strict pathogen-free conditions in the animal facility of the MPI-CBG, Dresden, Germany. Protocols were approved by the Institutional Animal Welfare Officer (Tierschutzbeauftragter) and all necessary licenses were obtained from the regional Ethical Commission for Animal Experimentation of Dresden, Germany (Tierversuchskommission, Landesdirektion Dresden). Experiments were performed on 6–10 weeks old male C57BL/6JHsd mice (Harlan laboratories) and male or female Lifeact-EGFP mice (obtained from the laboratory of R. Wedlich-Soldner ( Riedl et al., 2010 )). For IVM of CF(DA) transport, animals were starved for 6 h (water ad libitum) prior experiments. For imaging of bile canaliculi contractility in Lifeact-EGFP mice, animals were not starved. Fasudil and APAP were dissolved in 0.9 % saline and administered at 20 mg/kg (Fasudil) or 150 mg/kg (APAP) by i.p. injection at 1.5 h (Fasudil) or 2 h (APAP) prior imaging or organ collection. As controls, mice were administered 0.9 % saline.

METHOD DETAILS Experimental Techniques Protein Extraction and Western Blot

Liver tissue was lysed in ice-cold 20 mM Tris-hydrochloride (Tris-HCl) pH 7.5, 150 mM sodium hydrochloride (NaCl), 1 mM ethylenediaminetetraacetic acid (EDTA), 1 mM ethylene glycol-bis(2-aminoethylether)-tetraacetic acid (EGTA), 1 % (w/v) sodium dodecyl sulfate (SDS), 1 % (w/v) NP-40 using a pestle. Cell debris were removed by centrifugation for 10 min at 12 000 × g at 4 °C and protein was denatured at 95 °C in presence of 100 mM dithiothreitol (DTT). A total of 10 mg protein was separated by sodium dodecyl sulfate polyacrylamide gel electrophoresis, and transferred onto a nitrocellulose membrane. Membranes were blocked and incubated with primary antibodies against glyceraldehyde 3-phosphate dehydrogenase (GAPDH, 1:2000) or phospho-myosin light chain (pMLC, 1:500) and HRP-conjugated secondary antibodies (1:10000) in 5 % dry-milk, 10 mM Tris-HCl pH 8.0, 200 mM NaCl, 0.1 % Tween20. Protein was detected using the enhanced chemiluminescence (ECL) detection kit (GE Healthcare, Buckinghamshire, UK) and chemiluminescence films (GE Healthcare, Buckinghamshire, UK) according to manufacturer’s instructions.

Liver Tissue Fixation and Immunofluorescence Staining

Liver tissue of WT and Fasudil-treated animals was fixed by trans-cardial perfusion (3.7 ml/min) with 4 % paraformaldehyde (PFA), 0.1 % Tween in phosphate buffered saline (PBS) and post fixed in 4 % PFA, 0.1 % Tween, PBS (for immunofluorescence microscopy, IF) or in 2 % glutaraldehyde, PBS (for electron microscopy, EM) at 4 °C overnight. Liver tissue of APAP-treated animals and controls were only immersion fixed in 4 % PFA, 0.1 % Tween20 in PBS for 48 h at 4 °C to avoid artefacts (trans-cardial perfusion caused bile canaliculi network blebbing). For IF stainings, fixed liver tissue was mounted in 4 % low melting agarose in PBS and sectioned into 100 μm thick slices using a vibratome (Leica VT1200S). Floating sections were permeabilized in 0.5 % Triton-X100 in PBS for 1 h, quenched by incubation with 10 mM ammonium chloride (NH 4 Cl) in PBS for 30 min and blocked by incubation with blocking buffer (0.2 % fish gelatin, 300 mM NaCl, 0.3 % Triton-X100 in PBS) 3 times for 5 min. Sections were incubated sequentially with a primary antibody against CD13 (1:500) in blocking buffer for 2 overnights, washed 5 times for 5 min with 0.3 % Triton-X100 in PBS, incubated with secondary antibody labelled with Alexa fluorophore 568 (1:1000), DAPI (1:2000) and Alexa fluorophore 488-conjugated Phalloidin (1:400) in blocking buffer for 2 overnights and washed again with 0.3 % Triton-X100 in PBS 5 times for 5 min. Sections were optically cleared with SeeDB (See Deep Brain) and imaged using 80 % (v/v) 2.2’-thiodiethanol as immersion medium as described previously ( Ke et al., 2013 ). All steps were performed at room temperature.

Microscopy of Fixed Tissue

Fixed tissue was imaged with a Zeiss laser scanning microscope 780 NLO using a 63× 1.3 numerical aperture (NA) glycerol immersion objective (Zeiss), a Chameleon Ti-Sapphire 2-photon laser (780 nm), 488 and 561 laser lines and Gallium arsenide phosphide (GaAsp) detectors. Intravital Imaging of CFDA Transport Mouse anaesthesia was induced with 3–4 % isoflurane/ 0.3 % oxygen and maintained by i.p. injection of ketamine/xylazine throughout the experiment. Mice received 20 U of heparin dissolved in 0.9 % (w/v) NaCl by i.p. injection to prevent ischemia of the liver during the course of imaging. To visualize hepatocyte nuclei, Hoechst 33258 dissolved in 0.9 % (w/v) NaCl was administered retro-orbitally at a dose of 2 mg/kg and in a total volume of 50 μl. To expose the liver for imaging, the abdominal fur was removed using an electric shaver and a small transversal incision of 1 cm was made at the height of the sternum to expose the left lateral liver lobe using a surgical scissor and cauterizer. The mouse was positioned on the stage of an IX81 inverted confocal microscope equipped with a Fluoview 1000 scanning head (Olympus America) and a heat-adjustable UPLSAPO30X, 30× 1.05 NA silicon oil objective (Olympus). The objective was heated to 37 °C. To avoid compression of the liver lobe and to stabilize the tissue, the stage was designed with a small hole in the center into which the left lateral lobe was carefully placed. The residual volume of the hole was filled with a water-based and transparent 1 % carbomer gel (0.3 M Sorbitol, 1 % (w/v) Carbomer 940, polymerized by addition of triethanolamine and adjusted to pH 7) to immobilize the organ and prevent the organ from drying out. The bottom of the hole was designed with a cover-slide through which the organ was accessible for imaging. The animal body temperature was kept at 37 °C using a red lamp. Prior to imaging start, 18 mg/kg of 70 kDa Rhodamine-dextran or 20 ml of Qtracker 655 vascular label dissolved in 0.9 % (w/v) NaCl was injected retro-orbitally to identify the lobule orientation from the vascular flow pattern. To monitor the flux of CFDA in the liver, CFDA, dissolved in dimethyl sulfoxide (DMSO), was injected retro-orbitally at a dose of 0.2 mg/kg in a total volume of 50 μl. CFDA injection was performed slowly (approx. 30 sec) to avoid hydrodynamic effects and performed at 1 min after image acquisition start. The imaging field covered an entire CV-PV axis in the first cell layers below the liver capsule. Movies were acquired at temporal resolution of 1 min (WT, APAP and APAP control) or 2 min (Fasudil and Fasudil control) over a time course of 1 h. For each time point a 20 mm stack with an image size of 320 × 320 μm, a pixel size of 0.5–1 mm and 1 μm z-steps was acquired. Intravital Imaging of Bile Canaliculi Contractility For intravital imaging of bile canaliculi contractility the mouse preparation was the same as described for imaging of CFDA except of the following steps: Anaesthesia of Lifeact-EGFP mice was maintained using 3–4 % isoflurane/ 0.3 % oxygen throughout the entire experiment and imaging was performed using a Leica-DMI6000 inverted microscope with a heated stage (37 °C). Images were acquired using a 8 kHz resonant galvo-scanner and a Leica HC CS2 PL APO 63× 1.3 NA glycerol objective that was heated to 37 °C. Lifeact-EGFP was excited using a 488 laser and detected using a hybrid detector. Bile canaliculi were imaged within the first 1–2 cell layers below the liver capsule. Elastin fibres of the liver capsule were imaged by SHG microscopy using a tuneable 2-photon laser at 900 nm and a non-descanned photomultiplier tubes (PMT) detector. Movies were acquired with a pixel size of 0.09 mm and 0.020 or 0.025 sec frame rates. Electron Microscopy 1–2 mm 3 pieces of fixed liver tissue were processed for SBF-SEM pre-embedding staining, and flat embedding on glass slides in hard Durcupan resin as described previously ( Deerinck et al., 2010 ). Small pieces of embedded tissues were cut from the slides, remounted on SBF-SEM pins using conductive glue and carbon coated. SBF-SEM was performed on a Magellan 400 SEM (Fei, The Netherlands), equipped with a Gatan 3ViewXP2 (Gatan, Munich) at 1.5 kV, 100 pA beam current, using a 12.4 nm pixel size and 40 nm-thick sections. Mathematical and Computational Models 3D Reconstruction and Spatial Analysis of Bile Canaliculi Network Geometry 3D reconstructions of the bile canaliculi network were performed on high-resolution IF image stacks of fixed liver tissue stained for the apical marker CD13 (voxel size: 0.28 × 0.28 × 0.3 mm, 70–80 μm in depth). A tile of 2 × 1 image stacks was stitched to cover an entire CV-PV axis. Images were processed, analyzed and reconstructed using the software MotionTracking as described in ( Morales-Navarrete et al., 2015 ). In brief, images were segmented using a local thresholding algorithm (maximum entropy), segmented objects were corrected for artefacts using standard morphological operations (opening/closing) and the triangulation mesh of the segmented surfaces was generated by the cube marching algorithm. The active mesh was tuned to align the triangle mesh vertexes to the maximum gradient of fluorescence intensity in the original image. A representation of the skeletonized image was generated using a 3D graph describing the geometrical and topological features of the bile canaliculi network. For the spatial analysis of the bile canaliculi radius, porosity and network branch density, the CV-PV axis was computationally divided into 20 equidistant zones with relative coordinate x based on the two distances of each position from the CV ( d CV ) and PV ( d PV ): x = d C V d C V + d P V Then, the average radius and porosity was determined per zone. For the radius, the minimal distance of each node of the central line of the bile canaliculi network was quantified in the xy-plane. For the bile canaliculi network branch density, the network length per tissue volume was calculated. For the tissue porosity, the bile canaliculi network was computationally divided into cubes of 20 μm 3 that had a 5 μm grid spacing. For each cube, the porosity ε was calculated as the ratio of the void tissue volume of the bile canaliculi network V V to total tissue volume V T : ε = V V V T Then, the average porosity from all cubes within a zone was determined. To determine the shortest bile canaliculi network path between the PV and CV area, bile canaliculi network end-nodes were defined based on their distance to the CV and PV. For each end-node in the CV area the shortest distance through the bile canaliculi network to an end-node in the PV area was calculated using the Dijkstra’s algorithm. From the calculated paths, the shortest one was chosen. To determine the direct CV-PV axis distance, the distance from each point of the CV to the closest one of the PV was calculated. 3D Reconstruction of a Bile Canaliculus from EM Image Stacks SBF-SEM images were de-noised by applying a median filter and aligned using Matlab. The images were segmented by intensity thresholding and size filtering using the Imaris software and the bile canaliculi volume meshes were generated using the snappyHexMesh utility in openFoam ( http://www.openfoam.org ). Correction and Quantification of IVM Movie Shift Frames of CFDA transport movies were aligned by transitional image registration. The dextran or Hoechst channel was used as reference to align the frames of all other channels (target image) to it. The relative shift ([x,y] in 2D and [x,y,z] in 3D) of the target image stack was calculated using the phase correlation approach. The cross-correlation between stacks was computed using the Fast Fourier Transform. To determine the stability of the IVM setup, the same algorithms were applied to calculate the image shift in 2D on movies of elastin fibres.

Quantification of CF Intensities from Intravital Movies

Quantification of the CF intensity in the hepatocyte cytoplasm and bile canaliculi from IVM movies was performed using the image analysis software MotionTracking. Following correction for shift, IVM movies contained 16–21 frames per stack, covering 15–20 μm in z. To avoid liver damage from photo-toxicity, IVM movies were acquired with minimum laser intensities resulting in low signal-to-noise ratio. The resulting difference of intensity between the background and the CF fluorescence in the hepatocyte cytosol was in the range of 5–20 intensity units and varied with depth. Therefore, we used the modified Mean-Shift algorithm to separate the CF fluorescence from the background. The result of the background/foreground discrimination was checked manually ( Figure S1C ). The bile canaliculi were detected in three steps. First, the image was convolved with Laplacian of Gaussian. Second, pixels with an intensity > 2 standard deviations of the local noise were defined as potential bile canaliculi. The local noise was determined from the local intensity minimums in at least one of 4 discrete directions. Third, along the line of the local maximum intensity direction of a bile canaliculus, pixels that co-localized with sharp intensity transitions between the cytoplasm and sinusoids were excluded from the bile canaliculi compartment. For all compartments (cytoplasm, bile canaliculi and background), the mean intensity was calculated. To avoid mixing of compartments from light scattering of bright objects (bile canaliculi to cytoplasm and cytoplasm to background), the area within the radius of 2 pixels from the object border was excluded from the calculation. Following segmentation, the mean intensity of the bile canaliculi and cytoplasm was corrected for the intensity of the background. Due to the low signal-to-noise ratio, the direct subtraction of background intensities from the cytosolic intensities sometimes resulted in negative values and consequently created artefacts. To avoid these artefacts, we developed a Bayesian estimation of the most probable value of the foreground intensity by considering the noise of the background and foreground intensity measurements. In short, we denoted f and b to be the foreground and background intensities which we want to estimate and m and n to be the foreground and background intensities we have measured. Then the probability of f , b given m , n is p ( f , b ∣ m , n ) = 1 Z ( m , n ) p ( m , n ∣ f , b ) p ( f ) p ( b ) where p ( f ) and p ( b ) are prior distributions of the foreground and background. We assumed that m , n are independent and normally distributed. This assumption is reasonable, because the intensities were estimated by the summation of thousands of pixels (see above) and according to the Central Limit Theorem these distributions have to converge to a normal one. Therefore: p ( m , n ∣ f , b ) = 1 2 π σ 1 σ 2 m n e x p ( − 1 2 ∗ ( l n 2 ( f + b m ) σ 1 2 + l n 2 ( b n ) σ 2 2 ) ) Since we were not interested in the background value, we marginalized it: p ( f ∣ m , n ) = p ( f ) Z ( m , n ) ∫ 0 ∞ e x p ( − 1 2 ∗ ( l n 2 ( t + b m ) σ 1 2 + l n 2 ( b n ) σ 2 2 ) ) p ( b ) d b We assumed uniform improper prior for f and b : p ( b ) = c o n s t and p ( f ) = c o n s t that resulted in: p ( f ∣ m , n ) = 1 Z ( m , n ) e x p − 1 2 ( m − n − f ) 2 σ 1 2 + σ 2 2 ) ( 1 + e r f ( m − f ) σ 2 2 + n σ 1 2 2 ( σ 1 2 + σ 2 2 ) S ) ) where S 2 = ( 1 σ 1 2 + 1 σ 2 2 ) − 1 and Z ( m,n ) is normalization constant. The planes in a 3D stack were split on 16 sub-images and the values σ 1 and σ 2 were estimated from the variation of the intensity measurements between the sub-images within z-planes and across z-planes in a 3D image stack. The most probable value of f was found numerically as f = max f ∈ [ 0 , ∞ ] { e x p − 1 2 ( m − n − f ) 2 σ 1 2 + σ 2 2 ) ( 1 + e r f ( m − f ) σ 2 2 + n σ 1 2 2 ( σ 1 2 + σ 2 2 ) S ) ) } Then, the resulting estimations of the compartment intensities were multiplied by their total pixel number to calculate the final integral intensity of the compartment. Within an experimental condition (WT, controls, Fasudil or APAP-treated mice) intensities from each movie were scaled to the mean value of the condition by applying a scaling factor that was calculated as: f i = ∑ j = 1 N y i , j y j ∑ j = 1 N y i , j 2 Where y i , j is an intensity of i -th curve in j -th time point, y j is a mean intensity in j -th time point and f i is a scaling factor for i -th curve. For each experimental condition, the mean intensity curve was calculated from 4–5 IVM movies and later used for further mathematical modelling. IVM movies of Lifeact-EGFP were de-noised by applying a mean filter using the Fiji software. All other IF images and movies were intensity threshold adjusted but not processed otherwise. Mathematical 3-Compartment Model of CF(DA) Transport in the Liver The transport of CF(DA) from the blood into and through the biliary network was described in a mathematical model that considers 3 hepatic compartments: the blood (s), hepatocyte cytoplasm (c) and bile canaliculi (b) (see Figure 2F ). Dye propagation through these three compartments was modelled for three spatially distinct zones within the liver lobule: The CV, MD and PV zone as defined in Figure 2C (see also Figure S2B ). The different zone geometries of the kite-shaped CV-PV axis were accounted for by introducing respective geometry factors ( Figure S2C ). The model considers that only a fraction of the injected CFDA is delivered to the liver, whereas the rest is cleared by other tissues at rate k clear . The injection of CFDA into the blood circulation is described by Pulse ( t ). It is defined by the time point of injection start ( τ 1 ) and the injection duration ( τ 2 ) assuming that CFDA is injected with constant rate in time t > τ 1 and t < τ 1 + τ 2 . Both τ 1 and τ 2 were fitted by the model with boundary intervals 40–80 sec ( τ 1 ) and 20–60 sec ( τ 2 ) . In the liver, the model considers that CFDA is taken up from the blood with a permeability coefficient Perm = 3 sec −1 (according to ( Breeuwer et al., 1995 ), considering a mammalian plasma membrane thickness of 4 nm), converted into CF by cytoplasmic esterases with cleavage rate k cleav and secreted by apical transporters with transporter activity k pump . To account for the spatial heterogeneity of esterase and transporter levels within the CV-PV axis, the amounts of both esterases ( q i ) and apical transporters ( q 1 i ) were determined for each zone ( i = cv, md, pv). The model further considers passive back flux of CF from the bile canaliculi into the hepatocyte cytoplasm at rate k l i . The bile canaliculi compartment of the three zones is connected, occurs unidirectional and sequential from the CV to the MD with transport rate k t c v m d and form the MD to the PV zone with rate k t m d p v and exits the network from the PV zone into the bile duct with transport rate k t p v out . The dynamics of CF(DA) were described by a set of ODEs. In the blood compartment ( C s ), the flux of the tracer was described as: d C s d t = P e r m ∗ P u l s e ( t ) − k c l e a r ∗ C s The flux of the tracer was described separately for the cytoplasmic compartment ( C c i ) as: d C c c v d t = v c v ∗ k c l e a v ∗ q c v ( q c v + C s ) ∗ C s + k l c v ∗ C b c v − k p u m p ∗ q 1 c v ( q 1 c v + C c c v ) ∗ C c c v d C c m d d t = v m d ∗ k c l e a v ∗ q m d ( q m d + C s ) ∗ C s + k l m d ∗ C b m d − k p u m p ∗ q 1 m d ( q 1 m d + C c m d ) ∗ C c m d d C c p v d t = v p v ∗ k c l e a v ∗ q p v ( q p v + C s ) ∗ C s + k l p v ∗ C b p v − k p u m p ∗ q 1 p v ( q 1 p v + C c p v ) ∗ C c p v And for the bile canaliculi compartment ( C b i ) as: d C b c v d t = k p u m p ∗ q 1 c v ( q 1 c v + C c c v ) ∗ C c c v − k l c v ∗ C b c v − k t c v m d ∗ C b c v d C b m d d t = k p u m p ∗ q 1 m d ( q 1 m d + C c m d ) ∗ C c m d − k l m d ∗ C b m d + k t c v m d ∗ C b c v − k t m d p v ∗ C b m d d C b p v d t = k p u m p ∗ q 1 p v ( q 1 p v + C c p v ) ∗ C c p v − k l p v ∗ C b p v + k t m d p v ∗ C b m d − k t p v out ∗ C b p v All parameters were fitted to the experimental data by maximizing the Gaussian likelihood function using the simulation software FitModel ( Zeigerer et al., 2012 ). Since the rate parameters could vary by orders of magnitude the logarithms of the rates were used as fitting parameters. The confidence intervals for parameters were estimated by numerical calculation of the inverse Hessian matrix of the Gaussian likelihood function ( Sivia and Skilling, 2006 ). Apical secretion rates sq i were calculated relative to the MD zone as follows: s q i = q 1 i ∗ v m d q 1 m d ∗ v i Bile flow velocity v i at the interfaces of the lobule zones was estimated from the volume flux rates k t c v m d , k t m d p v and k t p v out considering the size of the zone volumes V i and zone boundaries A i ( i = cv , md , pv ) as well as a CV-PV axis distance L of 229 μm (see Figure S2E ): v c v = k t c v m d ∗ V c v A c v ∗ L v m d = k t m d p v ∗ V m d A m d ∗ L v p v = k t p v o u t ∗ V p v A p v ∗ L Computational Fluid Dynamics Simulation of Bile Flow in a 3D EM-Reconstructed Bile Canaliculus The simulation of bile flow in a 3D reconstructed bile canaliculus from EM was carried out in the laminar regime as an incompressible and Newtonian fluid for physiologically relevant bile pressure conditions (10 −3 –10 5 Pa) and in steady state mode using the open-source software openFoam ( http://www.openfoam.org ) and, specifically, the simpleFoam laminar solver therein. Grid convergence studies were conducted in the standard way in order to ascertain robustness and accuracy of the numerical simulation. To verify that bile flow inside bile canaliculi is laminar, we calculated the Reynolds number (Re) from the orders of magnitude of our measured bile velocity and bile canaliculi diameter as well as bile density and bile viscosity ( Luo et al., 2007 ) and obtained R e ∼ 1 μ m s e c ∗ 10 3 k g m 3 ∗ 1 μ m 1 m P a ∗ sec = 10 − 6 which lies 9 orders of magnitude below the threshold to turbulent flow. Mechanistic Model of Osmotic Fluid Secretion and Bile Flow We developed a mechanistic model of osmotically driven secretion of biliary fluid to predict the spatial water influx profile j ( x ) into the bile canaliculi network and the bile flow velocity v i at the borders of zones i = cv, md, pv along the CV-PV axis (see Figure 2C , S2B , and S2C for the definition of the zones). The model takes into account previously reported fluid mechanic properties of bile ( Luo et al., 2007 ) and the measured geometrical parameters, including the canaliculus radius profile a ( x ) = a a ( x ) * r corr with apparent radius a a ( x ) (e.g. shown in Figure 3C for WT mice) and correction factor r corr = 0.344 for the hydraulic diameter or radius, a mean cumulative bile canaliculi path length L between the CV and PV of 344 μm ( Figure S2D ) and a linear coordinate x along a shortest path of bile canaliculi branches from a tip of the bile canaliculi network near the CV ( x = 0) to a junction with a draining bile duct in the PV area ( x = L ), neglecting potential effects of branch points ( Figure 4B ). The osmotic driving due to osmolites with concentration c in the bile canaliculi lumen is considered spatially uniform (see justification below) and static (independent of the CF pulse) p osm = RTc , causing bile canaliculi water influx j ( x ) to be proportional to the pressure surplus of p osm over the local fluid pressure p ( x ). The local fluid pressure p ( x ) is monotonously decreasing from a self-organising pressure maximum at the closed central tip to zero at the open outlet, hence also j ( x ) is non-uniform in the general case. This feedback mechanism ( Figure 4B ) was modelled by a first order ODE for the fluid velocity profile v ( x ) at steady state according to ( Mathias, 1985 ): d v ( x ) d x = 2 κ a ( p o s m − p ( x ) ) where κ is the water permeability of the apical membrane of hepatocytes, the factor 2/a accounts for the surface to volume ratio and v ( x ) is the cross-section average of the local fluid velocity. We assumed Poiseuille flow with v ( x ) = − a 2 8 μ d p d x where μ is the fluid viscosity of bile and applied mixed boundary conditions with zero inflow v ( x = 0 ) = 0 at the closed central tip (corresponding to the Neumann boundary condition dp / dx = 0 for pressure as a ( x =0) is finite) and the Dirichlet condition p ( x = L ) = 0 at the open outlet. The solution is v ( x ) = v 0 M sinh ( M × / L ) cosh M with two parameters, a velocity amplitude V 0 = a 2 R T c 8 μ L and the dimensionless Münch number M = 16 κ μ L 2 a 3 . To factor out the measured geometrical parameters, we rewrote V 0 ( x ) = a ( x ) 2 p 1 L and M ( x ) = p 2 L 2 a ( x ) 3 with fit parameters p 1 and p 2 . The heterogeneous radius profile a ( x ) = a a ( x ) * r c o r r weakly modulated both terms such that the analytical solution remained a valid approximation of the heterogeneous problem. Matlab was used to fit p 1 and p 2 such that the analytical solution reproduced the measured bile flow velocity values at the border of each of the three zones (CV, MD, PV) and to determine the full spatial profile of the flow velocity v ( x ). The used approximation of a spatially uniform osmolite concentration profile is valid for the contributing small molecules and ions. These typically have diffusion constants of the order of D = 100 μm 2 /sec. Even if continuously secreted only at one location, decay with a half-life of τ = 20 min results in a steady state concentration profile with a decay length of D τ > L . From the continuity equation we further calculated j ( x ) = j 0 ( x ) c o s h ( M ( x ) x / L ) c o s h M ( x ) with j 0 ( x ) = 2 π a ( x ) κ p osm . The resulting water influx profile was monotonously ffiincreasing ( Figure 4C ). Using the equation for v 0 ( x ) from above to replace p osm , we could express j 0 purely as a function of the geometrical parameters of the canaliculus and the parameters v 0 ( x ) and M ( x ) of the velocity solution above and obtained: j 0 ( x ) = π a ( x ) 2 v 0 ( x ) M ( x ) L Given the measured fluid velocities v i , we could predict the complete fluid source density profile j ( x ) independent of the exact parameter values for membrane permeability κ , fluid viscosity μ or osmotic driving p osm . Inference of Osmolite Concentration Changes and Prediction of Parameter Changes We considered the steady state balance of osmolites for the kite-shaped part of the lobule as a whole. Then the sum of sources from apical secretion, J = j C V + j M D + j P V equals the sum of sinks from portal outflow J = c * A d u c t * v ( x = L ) where A duct is a fixed geometrical property related to the cumulative cross section area of all bile canaliculi junctions with bile ducts. We considered the ratio of this equality for two conditions, denoted by subscripts control and treated for all quantities J t J c = c t ∗ v t ( L ) c c ∗ v c ( L ) We approximated the apical secretion fluxes of osmolites by the measured apical secretion fluxes of CF and obtained flux ratios J t J c at t = 500 sec when image segmentation had the highest accuracy due to near-maximum CF intensities in all compartments, J F a s u d i l J c o n t r o l = 0.464 and J A P A P J c o n t r o l = 0.798 . Next, we considered the ratio of the analytical solutions v ( x ) at x = L , that are proportional to p o s m = R T c , for each pair of conditions and calculated their ratio. From the two equations for J t J c and v t ( L ) v c ( L ) we then eliminated the velocity ratio V t V c and obtained the osmolite concentration ratio α = c t c c = J t J c ∗ a c ( L ) 2 M c ( L ) tanh M c ( L ) a t ( L ) 2 M t ( L ) tanh M t ( L ) as a dimensionless number α . Note that osmolite concentration only grows with the square root of the osmolite secretion flux as a result of the negative feedback by induced water secretion and resulting osmolite washout (see Figure 4B ). Therewith the alteration of parameter p 1 due to osmolite secretion changes compared to a control condition could be calculated p 1 t = R T c t 8 μ = p 1 c ∗ α to then predict corresponding alterations in the velocity profile. Parameter p 2t = p 2c remained unchanged as it is independent of geometric properties and the osmolite concentration. To demonstrate the use of directly measured geometric parameters (apparent bile canaliculi radii a a ( x ) for c(ontrol) and t(reated) conditions: a c ( x ) , a t ( x ) ) and apical secretion fluxes J c , J t for determining parameter values and model predictions upon a change of treatment condition, we here explicitly consider the prediction of v t ( x ) upon Fasudil treatment given velocity measurements v i for the control condition ( i = cv, md, pv). First, the parameter values p 1c and p 2c for the control condition were determined by fitting the curve (just inserted the substitutions v 0 and M into the analytical model solution, see above) v c ( x ) = p 1 c p 2 c r c o r r a c ( x ) sinh ( p 2 c r c o r r 3 a c ( x ) 3 x ) cosh p 2 c L 2 r c o r r 3 a c ( x ) 3 to the experimental data points v i in relative units. This yielded p 1 c = 566.9 μ m − 1 and p 2 c = 6.656 * 10 − 6 μ m which were confirmed by solving the initial ODE numerically using the software Morpheus ( Starruss et al., 2014 ). Second, the apical secretion fluxes (in arbitrary intensity units per time) at t = 500 sec from data shown in Figure S4F were summed over the entire CV-PV axis: J c = 0.0041 + 0.0592 + 0.0209 = 0.0842 and J t = 0.0019 + 0.0312 + 0.0059 = 0.0390. Third, using p 2 t = p 2 c = 6.656 * 10 − 6 μ m and the extrapolated bile canaliculi radii at x = L , a c ( L ) = 1.320 μ m and a t ( L ) = 1.422 μ m , we calculated the osmolite concentration ratio (see above, after cancelling common factors) α = J t J c ∗ a c ( L ) tanh p 2 c L 2 r c o r r 3 a c ( L ) 3 a t ( L ) tanh p 2 t L 2 r c o r r 3 a t ( L ) 3 = 0.6697 . Fourth, the final parameter p 1 t = p 1 c * α = 379.7 μ m − 1 was determined. The parameter values for all conditions are given in Table S2 . Inference of Peristaltic Contribution We defined the contribution of peristalsis v p ( x ) to bile flow velocity as the difference between the measured velocity profile v c ( x ) under control conditions (where osmosis and peristalsis coexist) and the velocity profile of osmotic driving alone v o ( x ) under the same condition. We obtained the velocity profile of sole osmotic driving under control conditions from the different condition of Fasudil treatment by first fitting our mechanistic model to the measured velocity profile v f ( x ) upon Fasudil treatment and then calculating the corresponding velocity profile v o ( x ) under control conditions by inserting the measured radius profile a c ( x ) and the predicted osmolite concentration, see also Figure 5E , Table S2 . The resulting function v p ( x ) = v c ( x ) − v o ( x ) is displayed as solid black curve in Figure 5F . Next we computed the ratio β ( X ) = V p ( x ) V c ( x ) to quantify the relative local contribution of peristalsis to total bile flow velocity, shown by the dashed black curve in Figure 5F . For different experimental conditions with measured total bile flow velocity v t ( x ), we could then estimate the contribution of peristalsis as v t p ( x ) = β ( x ) * v t ( x ) and that of sole osmotic driving as v t o ( x ) = ( 1 − β ( x ) ) * v t ( x ) . Fitting the latter with our mechanistic model, we could predict the corresponding water influx density j t o ( x ) . We applied this workflow independently to the control of APAP treatment and the WT velocity profile. From the latter, we used the predicted fluid source profile in the 3D porous medium model. From V A P A P c o n t r o l o ( X ) we predicted V A P A P t r e a t e d o ( X ) using the measured radius profile and then the peristalsis contribution by v A P A P t r e a t e d p ( x ) = β ( x ) ( 1 − β ( x ) ) ∗ v A P A P t r e a t e d o ( x ) such that V A P A P t r e a t e d ( x ) = V A P A P t r e a t e d o ( x ) + V A P A P t r e a t e d p ( x ) = 1 ( 1 − β ( x ) ) ∗ V A P A P t r e a t e d o ( x ) A 3D Anisotropic Porous Medium Model of Biliary Fluid Dynamics The liver lobule was considered as a regular hexagonal prism, with the z-axis along its center. The top and bottom hexagonal planes were characterized by a translational periodic boundary condition. The bile canaliculi network was considered to transport bile from the center radially to the bile ducts located at the six corners of the hexagon. The network is closed at the central tips surrounding the CV (CV diameter = 90 μm), but has open outlets at the portal triad (portal triad diameter = 60 μm). Based on measurements from the 3D geometric model of the bile canaliculi network, the distance from the surface of the CV to the portal triad is 229 μm (see Figure S2E ). The hexagonal edges (representing the interfaces between lobules) and the center of the lobule (surrounding the central vein) were treated as bile-impermeable solid walls. The length of the z-axis was 269 μm. The lobule was considered as porous medium with a location-dependent porosity ε( x ) along the CV-PV axis as determined by our geometric measurements ( Figure 3C , right y-axis). The porosity profile was described by a 10 th order polynomial fit of the experimental measurements. From the porosity profile, the location-dependent tissue permeability k ( x ) was estimated using the Kozeny-Carman model k = ( r * r c o r r ) 2 * ε 3 where r is the mean bile canaliculi network radius of 1.143 μm ( r = a a ( x ) determined from the geometric model (see also Figure 3C ) and r corr is the correction factor to account for the hydraulic diameter of bile canaliculi (see above). The spatial heterogeneity of the bile canaliculi radius does not enter here since the heterogeneous geometry of the network was already accounted for by considering an anisotropic location-dependent porosity. For the simulation, an average bile pressure of 100 Pa was applied at the bile duct (estimated according to measurements reported in ( Wiener et al., 2000 )) and bile was assumed to have a viscosity of 1 mPa*sec ( Luo et al., 2007 ). Bile flow was considered to be driven by the osmotic effects of bile secretion and peristalsis. To simulate the osmotic effect, the local bile mass production rate (in units k g m 3 * s e c ) was determined. Therefore, an empirical fit of the heterogeneous fluid source profile j t o ( x ) ( in units μ m 3 μ m * s e c ) , predicted from the combined model of osmotic fluid secretion and peristalsis, was multiplied by the spatial bile canaliculi branch density profile (in units μ m μ m 3 , see Figure S2F ) and the bile density (928 kg/m 3 ( Mcintosh and Anderson, 2010 )). To simulate fluid dynamics, the laminar Navier-Stokes equations at steady-state were numerically solved using the software ANSYS CFX (Ansys, Canonsburg, PA, USA). The liver lobule geometry was meshed using the ICEM CFD software (Ansys, Canonsburg, PA, USA). A mesh sensitivity study was carried out in order to define a mesh independent numerical solution. For that reason several grid configurations were used, resulting in 4.2 million tetrahedral elements. The total bile mass source in the liver lobule was estimated to be 9.784*10 −11 kg/sec. To account for the additional contribution to bile flow velocity from bile canaliculi network peristalsis, the bile velocity profile predicted by the porous medium model from the osmotic effects was multiplied by the space dependent factor 1 1 − β ( x ) , with β ( x ) representing the inferred relative contribution of peristalsis (see above). Bile velocity and pressure were normalized to the maximum values.

Experimental Techniques Protein Extraction and Western Blot

Liver tissue was lysed in ice-cold 20 mM Tris-hydrochloride (Tris-HCl) pH 7.5, 150 mM sodium hydrochloride (NaCl), 1 mM ethylenediaminetetraacetic acid (EDTA), 1 mM ethylene glycol-bis(2-aminoethylether)-tetraacetic acid (EGTA), 1 % (w/v) sodium dodecyl sulfate (SDS), 1 % (w/v) NP-40 using a pestle. Cell debris were removed by centrifugation for 10 min at 12 000 × g at 4 °C and protein was denatured at 95 °C in presence of 100 mM dithiothreitol (DTT). A total of 10 mg protein was separated by sodium dodecyl sulfate polyacrylamide gel electrophoresis, and transferred onto a nitrocellulose membrane. Membranes were blocked and incubated with primary antibodies against glyceraldehyde 3-phosphate dehydrogenase (GAPDH, 1:2000) or phospho-myosin light chain (pMLC, 1:500) and HRP-conjugated secondary antibodies (1:10000) in 5 % dry-milk, 10 mM Tris-HCl pH 8.0, 200 mM NaCl, 0.1 % Tween20. Protein was detected using the enhanced chemiluminescence (ECL) detection kit (GE Healthcare, Buckinghamshire, UK) and chemiluminescence films (GE Healthcare, Buckinghamshire, UK) according to manufacturer’s instructions.

Liver Tissue Fixation and Immunofluorescence Staining

Liver tissue of WT and Fasudil-treated animals was fixed by trans-cardial perfusion (3.7 ml/min) with 4 % paraformaldehyde (PFA), 0.1 % Tween in phosphate buffered saline (PBS) and post fixed in 4 % PFA, 0.1 % Tween, PBS (for immunofluorescence microscopy, IF) or in 2 % glutaraldehyde, PBS (for electron microscopy, EM) at 4 °C overnight. Liver tissue of APAP-treated animals and controls were only immersion fixed in 4 % PFA, 0.1 % Tween20 in PBS for 48 h at 4 °C to avoid artefacts (trans-cardial perfusion caused bile canaliculi network blebbing). For IF stainings, fixed liver tissue was mounted in 4 % low melting agarose in PBS and sectioned into 100 μm thick slices using a vibratome (Leica VT1200S). Floating sections were permeabilized in 0.5 % Triton-X100 in PBS for 1 h, quenched by incubation with 10 mM ammonium chloride (NH 4 Cl) in PBS for 30 min and blocked by incubation with blocking buffer (0.2 % fish gelatin, 300 mM NaCl, 0.3 % Triton-X100 in PBS) 3 times for 5 min. Sections were incubated sequentially with a primary antibody against CD13 (1:500) in blocking buffer for 2 overnights, washed 5 times for 5 min with 0.3 % Triton-X100 in PBS, incubated with secondary antibody labelled with Alexa fluorophore 568 (1:1000), DAPI (1:2000) and Alexa fluorophore 488-conjugated Phalloidin (1:400) in blocking buffer for 2 overnights and washed again with 0.3 % Triton-X100 in PBS 5 times for 5 min. Sections were optically cleared with SeeDB (See Deep Brain) and imaged using 80 % (v/v) 2.2’-thiodiethanol as immersion medium as described previously ( Ke et al., 2013 ). All steps were performed at room temperature.

Microscopy of Fixed Tissue

Fixed tissue was imaged with a Zeiss laser scanning microscope 780 NLO using a 63× 1.3 numerical aperture (NA) glycerol immersion objective (Zeiss), a Chameleon Ti-Sapphire 2-photon laser (780 nm), 488 and 561 laser lines and Gallium arsenide phosphide (GaAsp) detectors. Intravital Imaging of CFDA Transport Mouse anaesthesia was induced with 3–4 % isoflurane/ 0.3 % oxygen and maintained by i.p. injection of ketamine/xylazine throughout the experiment. Mice received 20 U of heparin dissolved in 0.9 % (w/v) NaCl by i.p. injection to prevent ischemia of the liver during the course of imaging. To visualize hepatocyte nuclei, Hoechst 33258 dissolved in 0.9 % (w/v) NaCl was administered retro-orbitally at a dose of 2 mg/kg and in a total volume of 50 μl. To expose the liver for imaging, the abdominal fur was removed using an electric shaver and a small transversal incision of 1 cm was made at the height of the sternum to expose the left lateral liver lobe using a surgical scissor and cauterizer. The mouse was positioned on the stage of an IX81 inverted confocal microscope equipped with a Fluoview 1000 scanning head (Olympus America) and a heat-adjustable UPLSAPO30X, 30× 1.05 NA silicon oil objective (Olympus). The objective was heated to 37 °C. To avoid compression of the liver lobe and to stabilize the tissue, the stage was designed with a small hole in the center into which the left lateral lobe was carefully placed. The residual volume of the hole was filled with a water-based and transparent 1 % carbomer gel (0.3 M Sorbitol, 1 % (w/v) Carbomer 940, polymerized by addition of triethanolamine and adjusted to pH 7) to immobilize the organ and prevent the organ from drying out. The bottom of the hole was designed with a cover-slide through which the organ was accessible for imaging. The animal body temperature was kept at 37 °C using a red lamp. Prior to imaging start, 18 mg/kg of 70 kDa Rhodamine-dextran or 20 ml of Qtracker 655 vascular label dissolved in 0.9 % (w/v) NaCl was injected retro-orbitally to identify the lobule orientation from the vascular flow pattern. To monitor the flux of CFDA in the liver, CFDA, dissolved in dimethyl sulfoxide (DMSO), was injected retro-orbitally at a dose of 0.2 mg/kg in a total volume of 50 μl. CFDA injection was performed slowly (approx. 30 sec) to avoid hydrodynamic effects and performed at 1 min after image acquisition start. The imaging field covered an entire CV-PV axis in the first cell layers below the liver capsule. Movies were acquired at temporal resolution of 1 min (WT, APAP and APAP control) or 2 min (Fasudil and Fasudil control) over a time course of 1 h. For each time point a 20 mm stack with an image size of 320 × 320 μm, a pixel size of 0.5–1 mm and 1 μm z-steps was acquired. Intravital Imaging of Bile Canaliculi Contractility For intravital imaging of bile canaliculi contractility the mouse preparation was the same as described for imaging of CFDA except of the following steps: Anaesthesia of Lifeact-EGFP mice was maintained using 3–4 % isoflurane/ 0.3 % oxygen throughout the entire experiment and imaging was performed using a Leica-DMI6000 inverted microscope with a heated stage (37 °C). Images were acquired using a 8 kHz resonant galvo-scanner and a Leica HC CS2 PL APO 63× 1.3 NA glycerol objective that was heated to 37 °C. Lifeact-EGFP was excited using a 488 laser and detected using a hybrid detector. Bile canaliculi were imaged within the first 1–2 cell layers below the liver capsule. Elastin fibres of the liver capsule were imaged by SHG microscopy using a tuneable 2-photon laser at 900 nm and a non-descanned photomultiplier tubes (PMT) detector. Movies were acquired with a pixel size of 0.09 mm and 0.020 or 0.025 sec frame rates. Electron Microscopy 1–2 mm 3 pieces of fixed liver tissue were processed for SBF-SEM pre-embedding staining, and flat embedding on glass slides in hard Durcupan resin as described previously ( Deerinck et al., 2010 ). Small pieces of embedded tissues were cut from the slides, remounted on SBF-SEM pins using conductive glue and carbon coated. SBF-SEM was performed on a Magellan 400 SEM (Fei, The Netherlands), equipped with a Gatan 3ViewXP2 (Gatan, Munich) at 1.5 kV, 100 pA beam current, using a 12.4 nm pixel size and 40 nm-thick sections.

Supplementary Material Supplemental figures tables S1-4 movie legend Supplemental S2 movie Supplemental S3 movie Supplemental S1cmovie Supplemental S4 movie Supplemental Data S2 Supplemental Data S1