Curvature regulates subcellular organelle location to control intracellular signal propagation

The shape of cell is intimately connected to its function; however, we do not fully understand the underlying mechanism by which global shape regulates cell functions. Here, using a combination of theory, experiments and simulation, we investigated how global cell curvature can affect numerous subcellular activities and organization to control signal flow needed for phenotypic function. We find that global cell curvature regulates organelle location, inter-organelle distances and differential distribution of receptors in the plasma membrane. A combination of these factors leads to the modulation of signals transduced by the M3 muscarinic receptor/Gq/PLCβ pathway at the plasma membrane, amplifying Ca dynamics in the cytoplasm and the nucleus as determined by increased activity of myosin light chain kinase in the cytoplasm and enhanced nuclear localization of the transcription factor NFAT. Taken together, our observations show a systems level phenomenon whereby global cell curvature affects subcellular organization and signaling to enable expression of phenotype. peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/161950 doi: bioRxiv preprint first posted online Jul. 11, 2017;


INTRODUCTION
Cells utilize receptors on the plasma membrane to transduce a range of extracellular signals to regulate function in the cytoplasm and the nucleus 1 .Reaction kinetics of the biochemical interactions that comprise the signaling networks regulate the temporal dynamics of activation and inactivation of signaling components and effectors 2 .However, information flow within cells is not just temporally regulated, it is also spatially regulated by the shape of the cell [3][4][5] and surface-to-volume ratio at the plasma membrane 6 .An additional layer of complexity is conferred by the spatial transfer of information by signaling reactions that occur within or at intracellular organelles.Recently, studies have shown that signaling at the endosomes plays an important role in prolonging cAMP dynamics through GPCRs 7 and in EGFR dynamics 8 .An important compartmental regulation of organelle-based signaling is Ca 2+ dynamics, since endoplasmic/sarcoplasmic reticulum is a regulatable Ca 2+ store in cells.Ca 2+ is a ubiquitous signaling molecule that controls many cellular functions including fertilization, proliferation, migration and cell death [9][10][11][12] .Ca 2+ is able to participate in controlling this diverse array of functions due to the precise control of Ca 2+ concentration across the cell.In vascular smooth muscle cells (VSMC), Ca 2+ regulates both contractility and gene expression through IP 3mediated Ca 2+ release by IP 3 R receptors located on the membrane of the sarcoplasmic reticulum (SR) and through Ca 2+ influx at the plasma membrane [13][14][15] .Ca 2+ -calmodulin activates myosin light chain kinase (MLCK), which phosphorylates the light chain of myosin, initiating contraction 16 .Ca 2+ also activates protein kinases and phosphatases that regulate transcription regulators that define the phenotypic status of VSMC 17 .Ca 2+ activates calcineurin, which dephosphorylates the transcription factor nuclear factor of activated T-cells (NFAT) in the cytoplasm, resulting in its nuclear accumulation and expression of NFAT-regulated genes 18 .Ca 2+ also activates calmodulin kinase II (CaMKII), that phosphorylates the transcription factor serum response factor (SRF) 19 which, as a complex with myocardin, controls the expression of proteins necessary for the contractile function of VSMC 20 .
VSMC in the medial layer of blood vessels are not terminally differentiated and can undergo phenotypic transitions during injury and disease states [21][22][23] .VSMC shape and function are closely related; increasing elongation or aspect ratio (AR, defined as the ratio of the short axis to long axis) is correlated with differentiation and contractility 24,25 .How cell elongation is mechanistically linked to contractility is poorly understood.Based on the observations that cell shape and Ca 2+ signaling closely regulate the contractile phenotype of differentiated VSMCs, we hypothesized that cell shape regulates organelle location, including the relative distances between plasma membrane, endoplasmic/sarcoplasmic reticulum (ER/SR) and the nucleus, to modulate cellular function.In other words, we sought to answer the question --how does cell shape dependent organelle localization drive spatial control of information transfer?The answer to this question is critical for understanding how mechanochemical relationships control cell shape, signaling, and phenotype.We used micropatterned substrates to culture VSMCs in different shapes and developed theoretical and computational models to represent the spatiotemporal dynamics of Ca 2+ transients mediated by Muscarinic Receptor 3 (M 3 R)/Phospholipase Cβ (PLCβ) pathway.Activation of M 3 R mediates contractility in VSMC by activating PLCβ resulting in phosphoinositide hydrolysis and IP 3 mediated Ca 2+ release from the SR 26,27 .Our studies show an unexpected modulation of organelle location as a function of membrane curvature and that this change in organelle location results in signal amplification in the cytoplasm and nucleus.
peer-reviewed) is the author/funder.All rights reserved.No reuse allowed without permission.

Reaction-Diffusion model predicts that the distance between PM and SR membrane affects signaling dynamics in the cytoplasmic volume.
We tested the hypothesis that a change in membrane curvature and distance between two membranes affects signaling dynamics using a phenomenological reaction-diffusion model (Fig. 1a).A signaling molecule of interest, A, is produced at the PM with an on-rate k on (1/s) and binds to a receptor located at the SR membrane, with a rate k off (1/s) and is free to diffuse in the sandwiched cytoplasmic space and is degraded by a degrading enzyme with a rate k deg (1/s).This model essentially captures the lifecycle of a second messenger such as IP 3 that is produced at the PM through PIP 2 hydrolysis by phospholipases, binds to inositol 3 phosphate receptor (IP 3 R) channel at the SR membrane and is degraded in the cytoplasm by 1,4,5-trisphosphate-5phosphatase 28 .These events can be mathematically represented by the following system of reaction-diffusion equations.The dynamics of A in the cytoplasm are governed by diffusion and degradation and is given by, Eq. ( 1) Here, D is the diffusion coefficient of A (μm 2 /s), and C A is the concentration of A (μM).The boundary condition at the PM is a balance between the rate of production of A at the membrane and the diffusive flux from the membrane to the cellular interior and is given by, Eq. ( 2) Here, n is the normal vector to the surface and ∇ represents the gradient operator.At the SR membrane, similarly, we can write the boundary condition for the consumption of A as the balance of diffusive flux to the SR and consumption rate at the SR.

Eq. (3)
We solved these equations using finite element methods on three geometries (1) a rectangle (constant distance, zero curvature) (2) a circle, (constant distance, constant curvature) and (3) an elliptical sector, (varying distance, varying curvature) (Fig. 1b).In cases (1-2), the gradient of A is only along the radial direction (Fig. 1c).In triangular and trapezoidal geometries, varying PM-SR gradients result in two-dimensional gradients (Supplementary Fig. 1).However in case (3), the curvature of the membrane and the PM-SR distance will affect both the production and consumption of A at the PM and SR respectively.Hence, A varies both in the radial and angular directions, indicating that curvature and varying distances between the two membranes amplifies signaling gradients.
We next conducted dimensional analysis to identify when the dynamics of A would be diffusiondominated or reaction-dominated.Non-dimensionalization of Eq. 1 results in a dimensionless group D/(k deg L 2 ), the Damkohler number 29 .This dimensionless number is the ratio of diffusion time scale to reaction time scale.We found that the dynamics of A are diffusion dominated for physiological values of k deg (Fig. 1d).Increasing k deg many-fold or reducing the diffusion constant of A can result in the dynamics of A being reaction dominated for different PM-SR distances (Fig. 1d, shaded blue region).Both the increase in k deg and the decrease in D, to obtain reaction-dominated regimes, are out of the range of physiological values, suggesting that the dynamics of A in the sandwiched space between the PM and SR are primarily diffusion dominated.From this simple phenomenological model, we predict that second messenger signaling networks such as IP 3 , where signaling occurs between PM and SR, will be impacted by global curvature and distance between the PM and the SR.This prediction raises the following questions: (1) does cell shape affect PM-SR distance?(2) Does changing PM-SR distance affect intracellular signaling dynamics?And (3) what is the impact of changing distance between organelles on signaling dynamics?We used VSMCs grown on micropatterned substrates to answer these questions.

Cell shape affects cytoskeleton organization and organelle location
We determined if changing cell shape affects organelle distribution and in particular PM-SR distance.In order to control the large scale cell shape, we used micropatterned substrates with the same surface area but increasing aspect ratio (AR, circles 1:1 to ellipses 1:8) (Fig. 2a).We investigated how cell shape affects cytoskeletal organization since the two are tightly interwoven [30][31][32] .Actin stress fibers increasingly oriented themselves along the long axis of the cell as the aspect ratio increased (Fig. 2b), indicating that the cells were responding to the mechanical forces and tension exerted by the substrate 33 .Microtubules became highly aligned and increasingly sparser in the cell tips compared to the cell body as the cell aspect ratio increased (Supplementary Fig. 2).Because cytoskeletal organization plays an important role in organelle distribution 34,35 , we visualized the effect of cell shape on the bulk distribution and location of the mitochondria (Supplementary Fig. 3), endosomes (Supplementary Fig. 4) and Golgi membrane (Supplementary Fig. 5).These organelles increasingly localized to the cell center (perinuclear region) with increasing aspect ratio, similar to the characteristic central distribution of the endomembrane system in well-differentiated VSMC 24 .Because SR stores Ca 2+ , which controls both excitation-transcription coupling and contractility in VSMC 36 , we focused on SR distribution as a function of cell shape, using calnexin (Fig. 2c), protein disulfide isomerase (Fig. 2d), reticulon-4 (Fig. 2e) and bodipy glibenclamide (Supplementary Fig. 6) as SR markers.All four markers show that in circular cells, the SR was spread uniformly throughout the cell; increased aspect ratio induced the SR to localize in the perinuclear region and become significantly sparser, and mainly tubular, in the cell tips (Fig. 2c-e, Supplementary Fig. 6).Upon close inspection of Airy scan images of these SR markers, we qualitatively observe that in circular cells, the SR appeared to be equidistant from the plasma membrane along the periphery, i.e. there were no angular variations of PM-SR distance, while elliptical cells show a large angular variation in the PM-SR distance (Fig. 2d-e bottom panels and Supplementary Fig. 6, inset).We used transmission electron microscopy (TEM) to quantitatively confirm that the PM-SR distance is shape dependent.The cell periphery of circular cells and the cell body of elliptical cells showed long patches of smooth SR that were positioned close to the plasma membrane.PM-SR distance was indeed dependent on the shape of the cell: PM-SR distance in cell body of elliptical cells was significantly smaller compared to circular cells (Fig. 2g).In the tips of elliptical cells, the SR membrane formed fewer contacts with the plasma membrane, and showed significantly higher PM-SR distance (Fig. 2g).These results are consistent with the recent observation in neurons that PM-ER contacts are more extensive in the cell body compared to elongated projections such as dendrites and axons 37 .While other groups have reported that cell shape can affect organelle location 38,39 , to our knowledge, this is the first quantitative characterization of PM-SR distances and the SR abundance along the juxtamembrane region with controlled cell shape variation.We then determined the relationship between global cell shape and distances between the nucleus and various organelles in VSMC.Nuclear aspect ratio increased with cellular aspect ratio (Fig. 2i) while nuclear size (area µm 2 ) decreased with increasing cell aspect ratio (Fig. 2j).The nucleus became increasingly oriented along the major axis of the cell as the whole-cell aspect ratio increased, evidenced by polar graphs showing the orientation histograms of nuclei of cells in increasing cell AR (Fig. 2k).Circular shaped cells showed a random nuclear orientation whereas increasing the cellular aspect ratio progressively oriented the nucleus in the geometric center of the cell.PM-nuclear distance in the major axis of the cell increased with cell aspect ratio (Fig. 2m) while the PM-nuclear distance in the minor axis decreased with cell aspect ratio (Fig. 2n).These results indicate that in VSMC, cell elongation resulted in nuclear elongation, reduced nuclear size, and a decrease in the PM-nuclear distance in the minor axis of the cell (i.e.near the center of the cell).Thus, we show that cell shape affects not only organelle location, but also affects PM-SR distance, nuclear shape and PM-nuclear distances.

Computational models predict that IP 3 spatio-temporal dynamics depend on nanometer scale changes in PM-SR distances.
We next asked if changing PM-SR distance will impact the dynamics of IP 3 in VSMCs.It is currently not possible to manipulate PM-SR distances with precise control in cells.Therefore, we developed a computational model for investigating how changing PM-SR distance would affect IP 3 dynamics.This model is composed of a system of multi-compartmental partial differential equations, representing the reaction-diffusion of cytoplasmic species in the volume, coupled with boundary fluxes at the membranes.The reactions capture the biochemical interactions from the ligand binding and activation of M 3 R to IP 3 production by PLC-mediated hydrolysis of PIP 2 release from the SR (Fig. 3a, Supplementary Table 1).As before, we tested three different geometries -rectangles, circles, and ellipses.Each geometry consists of compartments representing the plasma membrane, the cytoplasm, the SR (modeled as thin rectangles) and the SR membrane (Fig. 3b).To test the effect of changing PM-SR distance on signaling dynamics independent of curvature, we computed the spatio-temporal profiles of IP 3 in rectangular geometries.We found that varying the PM-SR distance played a critical role in determining the dynamics of IP 3 (Fig. 3b, Supplementary Fig. 8).When the PM-SR distance is 50 nm, IP 3 is concentrated between the PM and the SR, but as the PM-SR distance increases, the IP 3 microdomain dissipates and no local increase in concentration is observed.Even in this highly idealized scenario, we find that there is a clear dependence of IP 3 spatio-temporal dynamics on PM-SR distance.Furthermore, the SR acts as a diffusion barrier for IP 3 , preventing diffusion of IP 3 away from the PM-SR region.The dynamics of IP 3 in locations with and without SR (Fig. 3c) were also different, indicating that the diffusion distance set up by the PM-SR coupling plays an important role in governing the dynamics of second messengers such as IP 3 and potentially Ca 2+ .
Next, we investigated the role of curvature coupling to PM-SR distances on IP 3 and dynamics.We designed geometries that represented circular cells or elliptical cells with distance parameters based on experimental measurements from TEM analyses (Fig. 2g).We investigated the role of PM-SR distance in circular geometries.Again, we modeled the SR as thin rectangles and this time placed the SR at 98 nm away from the PM based on the experimental measurements.We found that the region between the PM and the SR acts as an IP 3 microdomain since the SR not only consumes IP 3 but also acts as a diffusion trap (Fig. 3e).However, we did not observe any angular variation along the periphery of the domain where the SR was present.We found that the angular variation for IP 3 and Ca 2+ dynamics was a result of the presence or absence of SR (Fig. 3c).There is a small radial variation at early times because the SR act as diffusion barrier but over longer times, these cytoplasmic gradients disappear (See different time points in Fig. 3c).
We also conducted simulations for elliptical geometries with the SR at the variable distance from the PM as per experimental measurements such that the shortest PM-SR distance is 67 nm and the farthest PM-SR distance is more than 150 nm.This allowed us investigate how varying curvature and varying PM-SR distance affects IP 3 dynamics.We found that the curvature of the plasma membrane, coupled with variable PM-SR distance gave rise to variable IP 3 dynamics that was a function of PM-SR distance along the periphery (Fig. 3f).We found that the total amount of IP 3 produced over 5 min was higher in elliptical cells than in circular cells (Fig. 3g).Thus, our simulations indicate that PM-SR distance affects the IP 3 dynamics and curvature coupling serves to amplify this effect.

Cell shape affects receptor activation on the membrane and intracellular calcium dynamics
We tested the model predictions that distance between PM and SR can affect the dynamics of Ca 2+ mediated by the M 3 R/IP 3 /Ca 2+ pathway 13,40 .We stained for M 3 R in circular and elliptical cells under three different conditions -unstimulated, stimulated with carbachol, and stimulated with carbachol in the presence of hypertonic sucrose, which inhibits receptor endocytosis [41][42][43] .In both the basal state and stimulated states, M 3 R was uniformly distributed on the plasma membrane of both circular and elliptical cells (Supplementary Fig. 9).Interestingly, in elliptical cells, when M 3 R was stimulated and endocytosis was inhibited, M 3 R accumulated in the cell body compared to the cell tips while there was no observable spatial asymmetry in the distribution of M 3 R in circular cells (Fig. 4a and Supplementary Fig. 9).We then investigated the effect of shape on cytoplasmic and nuclear Ca 2+ dynamics upon stimulation of M 3 R in patterned VSMC (Fig. 4b-c).In the cytoplasmic region, circular and elliptical showed similar peak Ca 2+ amplitudes.However, elliptical cells showed a slower rate of decrease in Ca 2+ compared to circular cells, resulting in a slightly higher temporally integrated Ca 2+ compared to circular cells, although the differences were not statistically significant (p=0.057,two-tailed t-test).Since small changes in second messenger signals can have large functional effects by being amplified by signaling networks 44 , we measured downstream myosin light chain kinase (MLCK) activity using a CaM-sensor FRET probe 45,46 (Fig. 4e-g).Elliptical cells showed a higher degree of MLCK FRET probe localization on actin filaments (Fig. 4e) and higher maximal activation compared to circular cells (Fig. 4f-g), indicating that the shape-induced increase in cytoplasmic Ca 2+ signal propagates and is amplified downstream through MLCK activation, consistent with the previous finding that higher aspect ratio VSMC are more contractile 47,48 .To our knowledge, this is the first demonstration of a direct relationship between cell shape, Ca 2+ signaling and contractility.The differences in nuclear Ca 2+ between circle and elliptical cells were distinct from cytoplasmic Ca 2+ (Fig. 4h).In the nuclear region, the peak Ca 2+ amplitudes of circle and elliptical cells were similar.However, there is a notable delay in the rate of nuclear Ca 2+ increase to maximum in elliptical cells compared to circular cells, but the decay times in elliptical cells were slower as well, resulting in a significantly higher temporally integrated Ca 2+ in elliptical cells compared to circular cells (Fig. 4i).These results indicate that cell shape affects nuclear Ca 2+ transients mediated by M 3 R/PLCβ and elliptical cells is more prolonged, resulting in higher integrated Ca 2+ compared to circular cells.Increase in nuclear Ca 2+ in elliptical cells is likely to impact the nucleo-cytoplasmic transport of NFAT, which exhibits a Ca 2+ /calcineurin dependent translocation to the nucleus 18,49 .We measured NFAT-GFP localization dynamics in live VSMCs in elliptical and circular micropatterns in response to Gα q activation through M 3 R stimulation (Fig. 4j-m).Elliptical cells exhibited greater NFAT-GFP nuclear localization compared to circular cells (Fig. 4k) and on average displayed higher maximal NFAT nuc/cyto (Fig. 4l).We further validated the differences in NFAT translocation by immunofluorescence of NFAT1 (Fig. 4m, Supplementary Fig. 10a).At basal levels, NFAT nuc/cyto were similar between circular and elliptical cells.However, elliptical cells displayed higher nuclear NFAT compared to circular cells at 30 minutes and 1 hour after stimulation, consistent with live-cell NFAT-GFP translocation results.We asked the question whether other Ca 2+ dependent transcription factors are also impacted by shape.Ca 2+ also triggers the nuclear localization of SRF through nuclear Ca 2+ /CaMKIV 19 and Rho/ROCK/actin dynamics 50,51 .Elliptical VSMC show increased nuclear SRF compared to circular cells at both basal and stimulated levels (Supplementary Fig. 10b).In contrast there was no difference in myocardin intensity or translocation dynamics between circle and elliptical cells (Supplementary Fig. 10c) suggesting that myocardin is constitutively active 20,52 .Taken together, these results indicate that shape-induced modulation of Ca 2+ signaling alters the activities of Ca 2+ dependent transcription factors.

An integrated model of shape and organelle location provides insight into curvature coupling of Ca 2+ dynamics in VSMCs.
Our previous models were focused on localized PM-SR interactions in highly idealized geometries (Fig. 3).However, ultrastructural analyses have shown that the ER is a highly dynamic, tubular network that occupies roughly 10% of the cytosolic volume and extends from the nucleus to the cell periphery 53 .We developed an integrated whole cell, multi-compartmental partial differential equation model in Virtual Cell to derive relationships between experimental observations and models at the whole cell level (Fig. 5a-l).Upon stimulation of M 3 R, the concentration gradients of IP 3 and cytoplasmic Ca 2+ were highest in regions where PM-SR distance was lowest (cell body), and lowest in regions where PM-SR were farthest from each other (cell tips) (Fig. 5a and Fig. 5c), establishing an IP 3 and Ca 2+ gradient from the cell body to the tips which progressively became steeper with aspect ratio.More importantly, increasing the AR increased global IP 3 and Ca 2+ levels in both cytoplasmic and nuclear compartments (Fig. 5b, Fig. 5d-h).Hence, elliptical cells are predicted to exhibit increased global cytoplasmic and nuclear Ca 2+ compared to circular cells upon stimulation of M 3 R due to decreased PM-SR and PM-nuclear distance in the short axis of the cell.This model failed to capture the delay in the rate of nuclear Ca 2+ increase to maximum in elliptical cells (Fig. 4h).This suggest that the model specification was incomplete and additional details may be needed to make the model more realistic 54 .Since cell shape determines nuclear shape, we hypothesized that as the cell elongates, invaginations in the nuclear membrane may decrease.As nuclear invaginations have been shown to be related to nuclear calcium dynamics [55][56][57] , we introduced a calcium permeability term in the model, by introducing a second order reaction dependent on the nuclear permeability, NPC, using the same circle and elliptical geometries (Supplementary Fig. 12).NPC represents the net nuclear permeability which may be due to an increase in nuclear membrane surface area and/or increase in nuclear pores; if NPC=0, the nuclear membrane is completely impermeable to cytoplasmic Ca 2+ ; if NPC=1, the nuclear membrane is completely permeable to the cytoplasmic peer-reviewed) is the author/funder.All rights reserved.No reuse allowed without permission.
The copyright holder for this preprint (which was not .http://dx.doi.org/10.1101/161950doi: bioRxiv preprint first posted online Jul.11, 2017; Ca 2+ and mirrors the cytoplasmic Ca 2+ transient.When nuclear permeability in circular cells was three times higher compared to elliptical cells, there was closer agreement between the model and experimental temporal behavior in both cytoplasmic and nuclear Ca 2+ (Fig. 5i-l), suggesting that nuclear membrane of elliptical cells are less permeable to cytoplasmic Ca 2+ , compared to circular cells.The net effect of decreased nuclear permeability led to higher integrated nuclear Ca 2+ signals in cells, which increases its availability for slower downstream processes in the nucleus that are driven by Ca 2+ 25, 26 .Thus the whole-cell model, coupled with organelle location based on curvature, captures key findings of Ca 2+ dynamics in VSMC of different shapes.

DISCUSSION
One of the key features of signal transduction is the spatial organization of information propagation.Here, we bring together several seemingly independent effects due to change in global cell shape to provide an integrated view of how curvature, affects organelle location as well as distribution of receptors in the plane of the membrane to modulate signal transduction and thus affect cellular function (Fig. 6).Shape and biochemical signaling are coupled together in a feedback loop to maintain phenotype: cell shape integrates external mechanical and chemical signals on the plasma membrane 3,4 while intracellular signaling cascades containing chemical information in the form of reaction kinetics, in turn regulate cell shape 58,59 .We propose that shape-dependent endomembrane and nuclear organization serves as the critical link that connect these two components in the feedback loop.This intricate, non-linear coupling of geometric and chemical information can potentially lead to signal amplification to control phenotype.
We used VSMC as a model system to unravel the complex relationship between global cell curvature, signaling, and endomembrane organization.During atherogenesis, disruption of local microenvironment in the medial layer of blood vessels causes VSMC to lose its native spindle shape, and subsequently lose contractile function 24,60 .It was not clear how loss of shape can to a decrease in contractile function.This study provides a mechanistic explanation for the functional role of shape in VSMC contractile function.Cell shape governs membrane curvature, which enables the emergence of systems level properties; cell elongation simultaneously concentrates plasma membrane receptors in the flatter regions of the membrane and reduces the distance between the PM-SR and SR-nucleus in the same region, hence effectively forming a diffusionrestricted domain where receptors, SR and the nucleus become closer to each other, establishing high effective IP 3 and Ca 2+ concentration in the cell center.Given the slow diffusion coefficient of IP 3 (< 10 µm 2 /s) which limits the range of action over which it can exert its signal 61 and the dimensions of typical spindle-shaped VSMC (long axis >150 µm and short axis length of < 10 µm), control of endomembrane organization by cell shape is a physical, non-genomic mechanism by which IP 3 /Ca 2+ signals can be locally amplified in order to achieve high concentration of Ca 2+ globally.These can further regulate contractility and Ca 2+ -dependent gene expression in the nucleus.Although the effect of cell shape on individual readouts of signaling may appear small, the collective and progressive amplification of signal transduction through coupled reaction kinetics and spatial organelle organization is sufficient to result in different regimes of phenotypic function.
While we have extensively explored the role of cell shape in signaling here and previously 3,4 , features that we have not considered here, such as the forces exerted by the extracellular peer-reviewed) is the author/funder.All rights reserved.No reuse allowed without permission.
The copyright holder for this preprint (which was not .http://dx.doi.org/10.1101/161950doi: bioRxiv preprint first posted online Jul.11, 2017; microenvironment on the cell, and vice versa, also play a critical role in transmitting geometric information 62,63 , trafficking 64 , and signal transduction 65 .Furthermore, the interaction between signaling and cytoskeletal remodeling can lead to changes in cell shape and local curvature 66,67 .Our observations of increasing anisotropy and robustness in expression of actin myofibrils, along with increased nuclear SRF localization with aspect ratio indicate that cytoskeletal signaling also contributes towards the contractile phenotype of VSMC.Cytoskeletal and Ca 2+ signaling may act in concert in maintaining the differentiated phenotype of spindle-shaped VSMC.We were able to uncover unique aspects of signal flow in cells based on geometry and chemical reaction cascades alone and coupling the role of cytoskeletal interactions is a focus of future studies.We conclude that being at the right place at the right time is critical for information to flow from one compartment to another and for short term signals like Ca 2+ to have long lasting effects such as contractility and transcription factor activity.Like real estate, it seems that cells have the same motto -location, location, location!METHODS Cell culture.A10 cells, which are VSMC from thoracic/medial layer of rat aortas, were obtained from American Type Culture Collection (CRL-1476).A10 cells were maintained in Dulbecco's modified eagle's medium (DMEM, Gibco), supplemented with 10% Fetal Bovine Serum, 1% penicillin/streptomycin, at 37 °C and 5% CO 2 .Cells were transfected using Neon Transfection System (Life Technologies) according to manufacturer's instructions.Briefly, 5 x 10 5 cells were electroporated with 1 µg DNA in suspension buffer, with the following electroporation settings: 1400 V, 2 pulses, 20 ms pulses each.Cells were then suspended in DMEM supplemented with 10% FBS and then allowed to adhere on micropatterned surfaces.Forty-eight hours posttransfection, cells were imaged using Hanks Balanced Salt Solution (HBSS) supplemented with CaCl 2, MgCl 2 and 10 mM HEPES.
Micropatterning.Patterned surfaces were fabricated by conventional photolithography using SU8 photoresist 68 .Briefly, cover glass slides were cleaned by sonication in isopropanol and deionized water for 15 minutes and baked at 110 °C overnight and photolithography was subsequently performed using standard vacuum hard-contact mode.Before plating of cells onto micropatterns, microfabricated surfaces were washed with 50 µg/mL gentamicin and then incubated with 0.5% Pluronic for at least 3 hours.Micropatterns were then washed with PBS and were seeded with cells.

Immunofluorescence of cells in micropatterns.
Cells were seeded onto the micropatterned coverslips and were allowed to adhere and comply with the patterns for at least 24 hours.After assay treatments, cells were fixed with 4% paraformaldehyde (Electron Microscopy) for 15 minutes at room temperature, washed with PBS, permeabilized with 0.2% saponin for 30 minutes and blocked with 4% normal goat serum doped with 0.05% saponin for 1 hour.Cells were then incubated overnight with primary antibodies (sources and catalog numbers shown in table below) that had been diluted in blocking solution at 4 °C.Cells were washed with PBS and samples were incubated with secondary antibodies (Alexa 488, Alexa 568 and/or Alexa 647) for 1 hour at room temperature.For organelle staining, cells were counter-stained with Actin Green and DAPI counterstains in addition to the secondary antibodies.Cells were then imaged on a Zeiss LSM 880 microscope equipped with 60x objective.Same acquisition settings were applied across different conditions that were compared (laser power, gain settings, magnification, zoom, pixel size and slice thickness).For quantitative immunofluorescence of M 3 R, a Z-stack of 30-40 slices using a slice thickness of 0.5 µm were obtained for each cell.Z-stack datasets were then pared down to 21-22 slices encompassing the entire height of the cell (mean cell height ~ 10 µm).Alignment, registration and cropping were performed to ensure each image had the same xy dimensions (circular cells = 253 x 246 pixels, elliptical cells (AR 1:10) = 106 x 512 pixels).Per condition, images of cells obtained from the same z-plane (3.0 µm from the confocal slice corresponding to the bottom region of the plasma membrane), were averaged to obtain the averaged distribution of M 3 R in different regions of the cell.For immunofluorescence of transcription factors, multi-channel images consisting of DAPI, Actin Green (Invitrogen), and primary antibodies for NFAT, SRF or myocardin were aligned and stitched using the ZEN 2014 software.Image analysis and quantification was performed using ImageJ scripts.Briefly, nuclei were segmented in the DAPI channel.Corresponding cytosol and whole cell objects were outlined utilizing the contrast enhanced phalloidin channel to define cell boundaries.Nuclear-tocytoplasmic transcription factor ratio was defined as the ratio of the mean transcription factor intensity colocalizing with the nuclear object divided by the mean intensity of the corresponding cytosol object.All measurements were exported directly to csv files and were subsequently analyzed using MATLAB to generate plots.

Antibody Dilution Source
Calnexin HEPES and 1 mM Trolox, for 5 minutes at room temperature.Images were acquired using Zeiss LSM 880 using Airy-scan imaging equipped with 63x 1.4 Plan-Apochromat Oil objective lens at 30 ºC.Z-stacks using with an interval of 0.15 µm were collected for the entire cell height which approximated 10-12 µm.Z-stack analyses and other post-acquisition processing were performed on ZEN software (Carl Zeiss).
Calcium Measurements.VSMC were seeded on micropattern coverslips.Calcium measurements in micropatterns were performed as previously described with modifications 69 .Briefly, cells in micropatterns were serum-starved for 12 hours and loaded with 5 µM of calcium green (dissolved in DMSO) for 30 minutes at room temperature, with Hanks Balanced Salt solution, (HBSS) supplemented with CaCl 2, MgCl 2 and 10 mM HEPES.Calcium Green was imaged using Zeiss 510 equipped with 40x Apochromat objective at acquisition frame rate of 4 fps (250 ms acquisition time), and Calcium Green was excited using Argon ion laser 488 at low transmittivity (1%) to prevent photobleaching.Image stacks acquired were then imported into Fiji/ImageJ.Background subtraction were performed on the time stacks by using a rolling ball radius of 50 pixels.Cytoplasm and nuclear regions of interest (ROI) were chosen by performing a maximum intensity projection of the time-stack and specifying a 5 µm radius circle within the the nuclear and cytoplasmic regions.To convert intensity values to Ca 2+ concentration, modified Grynkiewicz equation was used, defined as: Where F min is the average fluorescence intensity of the ROI after addition of 100 µM BAPTA AM, F max is the average fluorescence intensity of the ROI after addition of 0.100 µM A23187.Integrated Ca 2+ were obtained using the trapz() function in MATLAB.
FRET imaging.MLCK-FRET plasmid is a kind gift from Dr. James T. Stull (University of Texas Southwestern Medical Center).The MLCK-FRET plasmid is a calmodulin-binding based sensor where calmodulin binding sequence is flanked with eCFP and eYFP and exhibits decreased FRET upon binding with calmodulin 46,18 .Cells expressing MLCK-FRET were imaged using Zeiss LSM 880 (Carl Zeiss, Jena, Germany), at 37 ºC incubator, fitted with Plan-Apochromat 20x, equipped with 458 nm and 514 nm Argon ion laser lines for excitation of eCFP and eYFP respectively.Incident excitation light was split using an MBS 458 nm/514 nm beam splitter and collected on a 32-spectral array GaAsp detector.The fluorescence emission was collected from 463-520 nm (ECFP), 544-620 nm (FRET channel and eYFP channel).Intensity based ratiometric FRET were obtained using custom-written scripts in ImageJ and MATLAB.Since MLCK-FRET is a single-chain construct, decrease in FRET, and increase in MLCK binding to calmodulin, was expressed as the ratio of emission intensity at 520 nm/emission intensity at 510 nm normalized at the basal levels.
NFAT imaging.HA-NFAT1(4-460)-GFP was a gift from Anjana Rao (Addgene plasmid # 11107).Patterned cells expressing NFAT-GFP was imaged using Zeiss 880, using Argon ion laser 488 nm, as described above and 1.4 NA objective, with an acquisition rate of 1 frame every 10 seconds.Time series image stacks were analyzed using ImageJ.Regions of interest of identical size were drawn in the cytoplasmic and nuclear regions of interest and the ratios of these intensities were computed over time.
Electron Microscopy.Micropatterned coverslips containing fixed A10 cells were embedded in Embed 812 resin (Electron Microscopy Sciences (EMS), Hatfield, PA) using the following protocol.Cells were rinsed in 200mM phosphate buffer (PB), osmicated with 1% osmium tetroxide/PB, washed with distilled water (dH20), and en bloc stained with aqueous 2% uranyl acetate, washed with dH2O and dehydrated via increasing ethanol (ETOH) series /distilled water (25%, 60%, 75%, 95% and 100% ETOH).Cells were further dehydrated using propylene oxide (PO), and embedded using ascending PO:EPON resin concentrations (2:1, 1:1, 1:2, pure).Prior to solidification, the coverslips were placed on 1"X 3" microscope slides, and multiple open ended embedding capsule with a 1 × 1 cm face (EMS) were placed on the coverslips covering the areas of interest.The resin was then polymerized in a vacuum oven at of 65 °C for 8-12 hours.After the first layer was solidified, the capsule was topped off with more resin and put back in the oven for another 8-12 hours.Capsules containing micropatterned cells were removed from coverslips using previously described methods 70 .Briefly, to separate the block from the coverslip, a hot plate was heated to 60°C and the microscope slide was placed directly on a preheated hot plate for exactly 3 minutes and 30 seconds.The slide was removed from the hot plate and the capsules carefully dislodged free from the coverslips.Once separated, the block face retains the cells within the micropatterns.The block was coarsely trimmed with a double-edged razorblade, and a Diatome cryotrim 45° mesa-trimming knife (EMS) was used to finely trim the block.Using as large a block face as possible, 70 nm ultrathin sections were cut from the block surface using an ultra-thin diamond knife (EMS), and a Leica EM UC7 ultramicrotome (Buffalo Grove, IL).All sections coming off the block face were collected.Sections were collected using a Perfect Loop (EMS) and transferred to a 2 × 1 mm formvar-carbon coated reinforced slot grid (EMS).The sample was dried on the grid and transferred to Hiraoka Staining Mats (EMS) for heavy metal staining.Grids were stained with 3% uranyl acetate in water for 40 minutes, washed and stained with Reynold's lead citrate for 3 minutes, washed and allowed to dry.Electron microscopy images were taken using a Hitachi 7000 Electron Microscope (Hitachi High Technologies America, Inc.) equipped with an AMT Advantage CCD camera.Cells were viewed at low-magnification to identify areas of interest (cell tip versus cell body) before high magnification imaging.Images were transferred to Adobe Photoshop CS3 (version 10), and adjusted for brightness and contrast.Measurement of plasma membrane to ER distances from electron microscopy images were performed blindly.Briefly, sample information from images were removed and images were saved with a randomized filename.Image contrast was further enhanced using ImageJ using contrast-limited adaptive histogram equalization (CLAHE).Only images with discernible smooth ER closely apposed to the plasma membrane were analyzed and distances were measured at optimal xy orientations at 50 nm intervals using ImageJ.Data was graphed using Excel and MATLAB.
Statistics. Results are presented as mean + standard error of the mean from at least three independent experiments.Normality was determined using Shapiro-Wilk test using a p-value > 0.05.If distribution is normal, a two-tailed Student's t-test was performed.For datasets with nonnormal distribution, two-tailed Mann-Whitney test was used.P < 0.05 was considered statistically significant.

Model Development.
We formulated a phenomenological model to study the role of PM-SR distances.The complete derivation and mathematical solution is given in the supplementary material.Complete details of the simulations using finite-element methods in COMSOL and using finite-volume methods in Virtual Cell are given in the Supplementary Material.Biomimetic, microfabricated surfaces with graded aspect ratios fine-tune the shape of VSMC and its enclosed organelles.(b) Actin organization is dependent on cell shape (scalebar, 10 µm).(c-e) SR distribution in VSMC seeded in AR 1:1 to 1:8 staining for SR membrane markers (panels below show 5x magnified Airy scan images of tip and body of images shown) (c) calnexin (d) protein disulfide isomerase (PDI) and (e) reticulon-4 (f) Representative TEM micrographs sampled from corresponding regions in micropatterned cells (cartoon).Singleheaded arrows indicate the plasma membrane and double-arrrows indicate smooth, peripheral SR, apposed to the plasma membrane (scalebar, 500 nm).(g) Distribution plots of PM-SR distances obtained from TEM images, mean and median are shown as crosses and squares respectively (N ellipse tip =329, N cell body = 254, N circle tip = 115, ****P < 0.0001, two-tailed Mann-Whitney test).(h) Cell shape affects nuclear shape size and distance to PM. Representative images of VSMC compliant in patterns with increasing AR stained for DAPI.Scatterplots of whole aspect ratio versus (i) nuclear aspect ratio (j) size (area, µm 2 ) (k) orientation with respect to the major axis of the cell.(l) Distances between nuclear and plasma membrane boundaries were measured along the long and short axes of the nucleus.(m) Increasing the cellular aspect ratio increases the distance between the nucleus and the plasma membrane in the major axis of the cell while (n) decreasing the PM-nuclear distance in the minor axis of the cell (N AR1:1 =82, N AR1:2 =60, N AR1:4 =45, N AR1:6 =65, N AR1:8 =54, **P < 0.05, ***P < 0.0001, two-tailed t-test).temporal dynamics in increasing cell aspect ratio (c).The relationship between IP 3 and cell aspect ratio is preserved downstream, on cytoplasmic Ca 2+ gradients (d) and temporal Ca 2+ dynamics in varying aspect ratios (e) Integrated Ca 2+ (AUC) (f-h) Nuclear Ca 2+ spatio-temporal models predict that higher cell aspect ratio increase integrated Ca 2+ in both cytoplasmic and nuclear compartments.Nuclear compartment of the whole cell model was modified to account for nuclear permeability due to nuclear shape.(i-l) Modified model demonstrates delayed rise to maximal in elliptical cells due to decreased nuclear permeability (circle, P = 0.37, elliptical = 0.1).Bar plot panels next to time course show agreement of spatio-temporal model with experiment.
Figure 6.Systems Approaches to controlling signaling through subcellular organization hierarchy.Physical determinants such as shape and geometrical information within the cell interact with organelle location and chemical information transfer to impact cellular function and gene expression, which in turn, feedback into cell shape.While each of these effects -shape, organelle location and chemical information -may separately lead to small changes in signaling, collectively, these effects can lead to altered cellular function including transcription factor activation and contractility.

NUMERICAL SOLUTIONS FOR REACTION DIFFUSION EQUATIONS WITH ROBIN BOUNDARY CONDITIONS.
We investigate the dynamics of a molecule A, which is formed at the PM and freely diffuses in the cytoplasm and is consumed at the SR membrane.This phenomenon can be represented by the following reaction-diffusion equation with the accompanying boundary conditions.
One of the features of this system of equations is that the boundary conditions at both ends are timedependent and belong to a class of boundary conditions known as Robin boundary conditions 29 .Furthermore, the boundary conditions depend on the local shape, since the surface normal will change as a function of curvature 72 .If the boundary conditions at both membranes were constant values of the concentration of A, the solution to the partial differential equation (Eq. 1) is a linear distribution from one boundary to the other 29 .However, in the current case, where both boundary conditions have Robin boundary conditions, the solution to these equations depends both on the diffusion distance and the reaction rates.The Robin boundary conditions that accompany the reaction-diffusion equation are of the mixed-type and are time dependent.Therefore, writing analytical solutions for them is challenging.Therefore, we use numerical methods to solve this equation.We use finite-element methods to solve the equations in the commercially available software COMSOL Multiphysics®.
Briefly, we used the General Form PDE interface to model the partial differential equation and the flux boundary conditions implemented using the Flux node with the source term set to the reaction rate.We used three different geometries to test the role of curvature and PM-SR distance.The mesh size was set to 'Extremely Fine' and the tolerance was set to relative tolerance was set to 0.01.In addition to the geometries shown in Fig. 1A, simulations were also conducted for a triangle and a trapezium to analyze the effect of varying PM-SR distance without changing curvature (Supplementary Fig. 1).
For a rectangle and a circle, solving the PDE with the boundary conditions shown above amounts to solving a 1-dimensional problem (either in the z-direction or in the radial direction).As a result, a gradient is observed only in one direction.For an elliptical cross section (Fig. 1A), a triangle (Supplementary Fig. 1A) and a trapezium (Supplementary Fig. 1B), the geometric variation is in twodimensions.Therefore, the spatio-temporal dynamics of A is different in these patterns.Furthermore, in an ellipse, the curvature is varying along the membrane, and therefore, the diffusive flux also varies.This is because the diffusive flux is dependent on the local normal and curvature captures the rate of change of the normal along the curve 72 .

Dimensional analysis
Using the PM-SR distance 'L' as a characteristic length scale and k deg as the characteristic time scale, we non-dimensionalized the partial differential equation for A to obtain a dimensionless number D/(k deg L 2 ) which is the Damkohler number 29 .When the Damkohler number is much greater than 1, then the system is diffusion-dominated and when the Damkohler number is much less than 1, it is reaction-dominated.

IP 3 model implementation in COMSOL
The dynamics of IP 3 were modeled using the reaction network model presented in Cooling et al. 73 and implemented in COMSOL using the protocol presented in Vollmer et al. 74 .We modeled multiple compartments -the extracellular space, PM, SR, SR membrane, the nucleus and the nuclear membrane.The Robin boundary conditions were implemented using the Flux boundary condition node for the volume and the general boundary form PDE node for the membranes.The mesh size was set to 'Extremely fine' such that the minimum element size is 0.1 nm and relative tolerance was set to 0.01.These values of mesh size and tolerance were chosen such that smaller values of tolerance or mesh refinement didn't alter the numerical results.

INTEGRATIVE WHOLE-CELL REACTION-DIFFUSION MODEL
To understand how global cell shape can modulate the dynamics of IP 3 and calcium signaling, we developed mathematical models which analyze the relationships between the binding of extracellular ligand to GPCR, G-protein activation and cycling, PLCβ activation, IP 3 activation of IP 3 R in the SR and intracellular calcium dynamics.Reactions were initially implemented as a system of ordinary differential equation in the Virtual Cell environment (http://www.nrcam.uchc.edu/) 75, and then modeled as a system of partial differential equations (PDEs) in two-dimensions.The complete list of model equations, parameters, units and references of the kinetic parameters are listed in Table 1 and the complete list of initial conditions and diffusion coefficients are listed in Table 2.

GPCR Signaling-PLCβ cycling
We adapted the GPCR signaling modules described by Cooling et al. 73 with modifications.Reactions R1-R6 represent GPCR-Ligand-G protein interactions on the plasma membrane.The reactions are modeled as kinetic fluxes following the Law of Mass Action and Michaelis-Menten Kinetics (see Bhalla 2 ).The binding of extracellular ligand to cell-surface receptors are represented by reactions R1 and R4.Binding of the ligand to muscarinic acetylcholine receptors causes a conformational change on the Gα q subunit of the heterotrimeric G-protein, causing replacement of GDP with GTP (R7) and dissociation of the Gα subunit from the heterotrimeric G-protein.The binding of activated Gα q to the enzyme PLCβ are represented by R8 and R10.Gα q -GTP is hydrolyzed to Gα q -GDP by autocatalysis represented by R7.Reactions R13-R16 represent IP3 dynamics, including its production at the plasma membrane, membrane diffusion and degradation at the cytosol.R13 and R14 shows the hydrolysis of PIP2 to IP3 by PLCβ-Ca 2+ and PLCβ-Ca 2+ -Gα q (GTP) respectively.The degradation of IP3, which involves the dephosphorylation and phosphorylation of IP3 to form inositol biphosphate and inositol tetraphosphate are represented by R16.The metabolic recycling of IP3 from these products is not considered.PLCβ inactivation is represented by R5.

IP 3 /Calcium Dynamics
In vascular smooth muscle cells, agonist-induced calcium release from the SR/ER is the main source of intracellular Ca 2+ transient.The opening of the inositol triphosphate receptor channels (IP 3 R) from the ER membrane, leads to an increase in cytoplasmic calcium.We used the simplified version of channel kinetics 76,77 by De Young and Keizer 78 which is represented by R17.Calcium leak from the ER to the cytosol is represented by R18.Calcium is pumped back to the ER by the sarcoplasmic reticulum calcium ATPase (SERCA) pump, represented by R19.Calcium leaks to the extracellular space through an Na + /Ca 2+ exchanger (NCX), (R22), and plasma membrane calcium ATPase (PMCA) pump R23.IP3 dependent influx of calcium through the plasma membrane is represented by J PM,leak which is dependent on IP3.Rapid buffering kinetics of Calcium 79 by exogenous and endogenous calcium buffers, is assumed.

Geometries
The spatial geometries of the cell and organelles were depicted as idealized geometries represented as a series of concentric ellipsoids that represent whole cell, SR and the nucleus.We assumed that cells complying with shapes of increasing AR conserve the cell volume and increase the plasma membrane surface area with increasing AR.Hence, whole cell, cytoplasmic and SR areas were kept constant with increasing aspect ratios.The cellular geometries were approximated from experimentally observed VSMC confined from AR 1:1 to AR 1:8 (Figure 2), whereby the SR is closer to the PM in the perinuclear region compared to the cell tips.Furthermore, as the aspect ratio increased, both PM-SR and PM-nuclear distances decreased in the minor axis and increased in the major axis of the ellipse.Nuclear shapes were based on experimentally observed geometries (Fig. 2h-n).Figure S11 show the geometric details of each compartment (Supplementary Fig. 11A) and the resulting geometries (Supplementary Fig. 11B).To solve the PDEs, geometries were discretized into 0.5 µm x 0.5 µm spatial steps, resulting in a total area of 3,500 µm 2 (10,500 elements).The systems of equations were solved within the Virtual Cell framework using fully-implicit, finite volume, with variable time step solver, with a maximum time step of 0.1 s and an output interval of 1.0 second.