Lipid droplets are intracellular mechanical stressors that impair hepatocyte function

Significance Deformation of the nucleus as a result of extracellular sources of stress, including increased substrate stiffness, constricted migration, and compression, has been well documented to lead to increased nuclear rupture, changes in gene expression, and accumulation of DNA damage. Lipid droplet accumulation in hepatocytes provides a unique scenario to investigate potential intracellular mechanical stresses and sources of nuclear deformation. Our results show that lipid droplets are significant mechanical elements in the cell: deforming the nucleus in a way that impairs hepatocyte function, disrupting cytoskeletal networks, and preventing stiffness-driven alignment of actin fibers.


Supplemental Methods
Cell Culture -Lipid Loading To solubilize the fatty acids and facilitate uptake by PHHs, sodium oleate was preconjugated to BSA. 20 mM oleic acid solution was prepared in 0.01 M NaOH and incubated for 30 min at 70 o C. Next, the solution was diluted to 4 mM in 5% FFA-free BSA in PBS and incubated at 37 o C for 10 min. The fatty acid-BSA solution was then mixed 1:9 with serum-free DMEM with 1% penicillinstreptomycin to obtain a 400 µM fatty acid, 0.5% BSA solution in DMEM.
Animal Studies All animal work was carried out in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. Animal protocols were approved by the Institutional Animal Care and Use Committee of the University of Pennsylvania (protocol #804031). Ob/ob mice were obtained from the Jackson Laboratories (strain #000632) and were housed in a temperature-controlled environment with appropriate enrichment, ad libitum feeding of standard rodent chow and water, and 12h light/dark cycles. Euthanasia was carried out by CO2 inhalation followed by exsanguination.
Immunofluorescence Staining and Microscopy Images of fixed cells were taken with a Leica TCS SP8 laser scanning confocal microscope with 40X water immersion lens. (numerical aperture: 1.1, XY resolution 177.25nm, Z resolution 377.06nm). Confocal z-stacks for volume measurements and cytoskeletal analysis used a system optimized z-step size of 0.42 µm. An additional 10X digital magnification was used to zoom in on individual nuclei for measurements of irregularity, γH2AX foci, and lamin A/C and HNF4α intensity. To ensure quantitative imaging, samples for all groups in an experiment were stained simultaneously and imaged at the same laser intensity during a single imaging session. Laser intensity was kept similar between each imaging session. Replicates were normalized to a single experimental group (noted in each case in the y-axis label, ex. % BSA Glass) to account for any biological variation and staining variability.
Quantification of Cell and Nuclear Volume Reconstruction of confocal z-stacks is a common method for estimating volume (1, 2) and we confirmed the validity of confocal volume measurements by imaging 15μm FocalCheck Beads (Thermo Fischer Scientific), where we found this measurement had a less than 1% error in both the green and red laser channels (Fig S1F). The cell boundary was segmented by applying smoothing and thresholding the phalloidin stain in each slice. The binary images were processed to fill holes to generate an ROI inclusive of the entire cytoplasmic volume. Individual cells were then segmented using the Simple Segmentation Tool applied to the thresholded stack and cell volumes were calculated using the 3D ROI Manager. Nuclear volumes were calculated similarly with the DAPI channel used to segment the cell nuclei. Specifically for the cell vs nuclear volume and cytoplasmic vs nuclear volume plots, volumes were analyzed using a MATLAB program that would calculate the cell, nuclear, and lipid volume in each cell. This was done first by smoothing and thresholding the phalloidin channel of 3D confocal image stacks, which was used to generate a label matrix to identify individual cells. 3D image properties (regionprops3) were used to calculate cell volume. The cell label matrix was then used to calculate the nuclear and lipid volume (in the DAPI and BODIPY channels respectively) within each cell ROI, applying a mask of each cell and then calculating volume with regionprops3. Cytoplasmic volume was estimated by subtracting nuclear and lipid volume from the cell volume.

Measurements of Nuclear Irregularity
Binary images of the cell nuclei were generated in FIJI as described and read into MATLAB. The MATLAB Imaging toolbox was used to identify the nuclear boundary and the center of each nucleus. The program linearized the membrane boundary by measuring the distance between the center point and each point along the boundary and plotted this against the angle (see Figure 2b for schematic). To account for the difference in cell area, the linearized membrane boundary was normalized to the mean radius of the nucleus. The program then calculated the nuclear irregularity: the area between the membrane boundary and a perfect circle with the same mean radius. The membrane boundary is smoothed with a loess filter and points of inflection are estimated using two finite differences (analogous to taking the second derivative of a continuous function). Segments of the membrane boundary between two inflection points were then fit with a circle using the Pratt method (6). The radii of curvature along the membrane was collected for each cell and pooled within a group and the probability distribution was estimated with a histogram.

Quantification of Chromatin Condensation
Chromatin condensation analysis was performed according to a previously published method (3,4). In brief, the raw images were down-sampled and the intensity redistributed before a Sobel edge detection filter was applied. This was followed by automatic thresholding and morphological thinning as well as removal of the nuclear outline. Finally, the chromatin condensation parameter is the number of remaining edge pixels divided by the nuclear area. Detailed methods, including the exact MATLAB program used, representative images of intermediate steps, and validation can be found in SI references 3 and 4.

Quantification of Cytoskeletal Fiber Analysis
Actin and microtubule fiber length and branching density were determined using the RidgeDetection plugin for FIJI. The maximum z-projection of confocal z-stacks was taken and individual cells segmented. The individual cells were then analyzed for mean fiber length, total fiber length, and total number of junctions with the RidgeDetection plugin, using automated fiber detection and analysis (please see FIJI documentation for additional details). The junction density was calculated by dividing the total number of junctions in the cell by the total fiber length. Actin fiber alignment was further analyzed in MATLAB using a previously published method: the FINE alignment analysis (5). The orientation distribution for each cell was determined with Fourier-based image analysis and then the cumulative orientation distribution was fit with a sum of sigmoid functions. Each sigmoid function represents a "fiber family" of pixels aligned in a specific direction. Cells were then classified based on the number of fiber families detected. This method does not rely on detecting fibers, but instead determines orientation on a pixel-by-pixel basis, avoiding the issues associated with automated fiber segmentation. Additional details of this method, including schematics and validation experiments, can be found in SI reference 5 . Distribution of actin and microtubule density as a function of height was determined by measuring the integrated density of staining in each slice of the stack and dividing by the total integrated density to determine the normalized distribution from bottom to top of the cell. The normalized distribution was resampled in MATLAB to normalize to the cell height and averaged across all cells, then fit with a smoothing spline to visualize distribution.

Traction Force Microscopy
To measure cell traction forces, PHH were seeded on stiff PAA gels embedded with 1 µl/mL red fluorescent beads (Fluorospheres, Invitrogen). Cells were cultured and treated with lipid as described. Brightfield images of cells on the gels and fluorescent images of the beads were taken and the locations marked on a Zeiss Axio Observer 7. Cells were dissociated with the addition of 1% Triton-X 100 for 10 min. Fluorescent images were taken again to determine the bead location without the cells attached. Bead images from before and after cell detachment were aligned using the Linear Stack Alignment with SIFT option of the Registration plugin in FIJI. Displacement fields of the beads were generated using the PIV plugin and then further analyzed with the FFTC plugin to calculate forces. Cell outlines were traced from the brightfield images and used to define larger regions of interest (ROIs). Automatic thresholding was used to isolate the areas where traction forces were being generated in proximity to the cell boundary. These thresholded ROIs were used to measure mean and maximum traction forces.

Theoretical Modeling of Chromatin Condensation
To investigate the effect of epigenetic regulation and mechano-osmotic loading on the nucleus, we developed a mathematical model for chromatin phase-separation in the nucleus. The composition of the nucleus at any point and time was defined in terms of volume fractions heterochromatin ℎ ( , ), euchromatin ( , ) and nucleoplasm ( , ) such that + ℎ + = 1. Equivalently, the physical state of the nucleus at any point can be completely determined via two independent variables -, the volume fraction of nucleoplasm, and = ℎ − , the difference between the volume fractions of heterochromatin and euchromatin. We constructed a free energy density function written as, (1) The first two terms in Eq.
(1) denote the energetic contributions arising from the competition between entropy and enthalpy of mixing of the two distinct phases -euchromatin phase with ℎ = 0 and heterochromatin phase with ℎ = � ℎ . The second term denotes the interfacial energies penalizing the formation of interfaces between the two phases, while the last term for < 0 captures the effect of proteins such as LAP2 , and LBR which mediate the interactions between chromatin and the nuclear lamina. Note that the chromatin-lamina interactions decrease with distance from the lamina, over a length scale 0 .
The steady state chromatin organization in the nucleus was obtained as local minima of the total free energy defined using Eq. (1), giving rise to the governing equations of the steady state using variational principles as, where and are the chemical potentials of nucleoplasm and chromatin, respectively. Spatial gradients of the chemical potential of reactively inert nucleoplasm drive its spatio-temporal evolution via the diffusion kinetics as, where is the mobility of nucleoplasm in the nucleus. The kinetics of chromatin evolution is driven by both the diffusion as well as epigenetic regulated reaction kinetics of acetylation and methylation as, where is the mobility of chromatin in the nucleus and Γ and Γ are the effective rates of methylation and acetylation of chromatin, respectively. Eq. (2), (3), and (4) together govern the organization of chromatin in the nucleus.
In addition, the nuclear envelope may enforce an interchange of water with the cytoplasm via water exchanging channels enforcing a chemical potential ̅ at the nuclear periphery acting as the first boundary condition. Allowing water transport via chemical potential perturbation circumvents the need to know the location of individual nuclear pores and water channels in the nuclear lamina. Lastly, we assumed a no flux boundary condition along the nuclear periphery for chromatin kinetics. We introduced small perturbations to and around their initial values to initiate the separation of chromatin into the two phases, and let the simulation proceed until a steady state was reached.

Theoretical Modelling of Cytoskeletal/Lipid Droplet Interactions
To study the effect of lipid droplets on the chemo-mechanical behavior of cells, we used our theoretical cell model previously developed in reference (7). The three-dimensional cell model includes the following components: the cytoskeleton, the focal adhesions, and the nucleus (see reference (44) for details).
The cell cytoskeleton was treated as a continuum of representative volume elements (RVEs), each of which was comprised of (i) the myosin motors, (ii) the microtubules, and (iii) the actin filaments. Myosin molecular motors are the first element of the cytoskeleton in our model and generate internal contractility of the cell as experimentally reported (8). We treated the average density of phosphorylated myosin motors as a symmetric tensor ρ , whose components represent cell contractility in different directions (9). The cell contractility ρ generates compressive stress C (MT) ε (MT) and tensile stress σ in the cytoskeletal components that are in compression (e.g., microtubules) and tension (e.g., actin elements), respectively, where C (MT) and ε (MT) are the stiffness and strain tensors of the cytoskeletal components that are in compression. Actin filaments are the second component of the cytoskeleton which are connected to the myosin element in series and subsequently experience tension and transmit myosingenerated tensile forces to the extracellular matrix through focal adhesions as experimentally observed (10)(11)(12). Microtubules are the third component of the cytoskeleton which are connected to the contractile myosin element in parallel and therefore experience compression consistent with experimental observations.
Focal adhesions in our coarse-grained model were modeled as a set of initially soft nonlinear mechanical elements that stiffen with tension to capture the tension-dependent formation of the focal adhesions. When the tensile stress exerted by the contractile cell to the adhesion layer exceeds a certain threshold, mature focal adhesions are formed, and the cell is connected to the substrate, while below this threshold, the stiffness of the adhesion layer remains low and the substrate experiences negligible forces. The nucleus was treated as an elastic thin layer (representing the nuclear envelope) filled with a solid elastic material representing chromatin and other subnuclear components. To perform traction force microscopy simulations, the cell model was coupled to the matrix model which treats the matrix substrate as a thick linear elastic material with an elastic modulus of 10 kPa as used in our traction force microscopy experiments. We treated the lipid droplets as growing mechanical inclusions within the cytoplasm. To this end, we modeled each droplet as a thin spherical membrane with internal pressure representing the enclosed fluid. We simulated the internal pressure by applying uniform and outward force spatially perpendicular to the internal surface of the membrane (outward arrows in Figure 5E). As a result of the internal pressure and droplet growth, the memebrane undergoes tensile stresses tangential to the membrane surface representing the surface tension in lipid droplets. In our model, lipid droplets can only have mechanical interactions with other cellular components and the model does not include any chemical effects of lipid droplets on cell behavior. We used a frictionless contact mode in our model for the contact between droplets and the nucleus as well as between droplets and the matrix substrate.

Statistics and Data Analysis
To avoid over confidence, statistics were performed on the biological replicates using a two-way analysis of variance (ANOVA) that fit a full-effect model followed by multiple comparisons with Tukey correction. In the case of the drug-treated cells in Figure 6 (where the n number for the drugtreated cells and controls were different), a two-way ANOVA that fit only a main-effects model was used, followed by a Fisher's test for multiple comparisons. Correlations were analyzed with linear regression followed by an F-test to determine whether the slope was significant. Analysis of covariance was run to compare the slope and intercept of the fit between groups. When slopes and intercepts were not significantly different, a pooled slope and intercept was calculated. The distribution of indent radii was compared between control and oleate treated cells using multiple Kolmogorov-Smirnov (K-S) tests, one for each stiffness. The symmetry of indent distributions was determined by comparing the positive dent distribution with the absolute value of the negative dent distribution with a K-S test for each group. The frequency of γH2AX-positive nuclei was compared using multiple Chi-Squared tests comparing control to oleate-treated cells within a stiffness. Comparison of nuclear area and irregularity of fully γH2AX-positive nuclei was compared with an unpaired t-test. The prevalence of different numbers of actin fiber families was compared using multiple Chi-Squared tests comparing control to oleate-treated cells. Traction force measurements were compared using a two-way ANOVA with a full effect model on the biological replicates and the shown p-value is the column factor. Analysis of nuclear shape and HNF4α intensity in mouse liver tissue was done using a two-way ANOVA with a main effects model and the shown p-value is the column factor. For all graphs, significance values less than p = 0.05 are labeled. Color-coded significance bars indicate stiffness-dependent differences within a treatment group, either blue for BSA or green for oleate.        Movie S1 (separate file). Z-stack of microtubule organization in control primary human hepatocyte on glass. Nuclei stained with DAPI (Blue), microtubules with α-tubulin (Red) and lipid with BODIPY (Green). Scale bar is 15μm.