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# System-wide organization of actin cytoskeleton determines organelle transport in hypocotyl plant cells

Edited by Natasha V. Raikhel, Center for Plant Cell Biology, Riverside, CA, and approved May 25, 2017 (received for review April 26, 2017)

### This article has a Correction. Please see:

## Significance

In the crowded interior of a cell, diffusion alone is insufficient to master varying transport requirements for cell sustenance and growth. The dynamic actin cytoskeleton is an essential cellular component that provides transport and cytoplasmic streaming in plant cells, but little is known about its system-level organization. Here, we resolve key challenges in understanding system-level actin-based transport. We present an automated image-based, network-driven framework that accurately incorporates both actin cytoskeleton and organelle trafficking. We demonstrate that actin cytoskeleton network properties support efficient transport in both growing and elongated hypocotyl cells. We show that organelle transport can be predicted from the system-wide cellular organization of the actin cytoskeleton. Our framework can be readily applied to investigate cytoskeleton-based transport in other organisms.

## Abstract

The actin cytoskeleton is an essential intracellular filamentous structure that underpins cellular transport and cytoplasmic streaming in plant cells. However, the system-level properties of actin-based cellular trafficking remain tenuous, largely due to the inability to quantify key features of the actin cytoskeleton. Here, we developed an automated image-based, network-driven framework to accurately segment and quantify actin cytoskeletal structures and Golgi transport. We show that the actin cytoskeleton in both growing and elongated hypocotyl cells has structural properties facilitating efficient transport. Our findings suggest that the erratic movement of Golgi is a stable cellular phenomenon that might optimize distribution efficiency of cell material. Moreover, we demonstrate that Golgi transport in hypocotyl cells can be accurately predicted from the actin network topology alone. Thus, our framework provides quantitative evidence for system-wide coordination of cellular transport in plant cells and can be readily applied to investigate cytoskeletal organization and transport in other organisms.

The cell interior is a heterogeneous and crowded space comprising a large range of molecules and organelles (1, 2). Because diffusion through this complex environment is not sufficient to match varying demands for cell maintenance and growth, intricate cellular transport schemes have evolved (3, 4). Transport of cellular components across large distances relies substantially on the cytoskeleton (4⇓⇓–7). Moreover, in plant cells, many organelles move rapidly due to actomyosin-based cytoplasmic streaming (8⇓–10). For instance, Golgi transport relies on the actomyosin system, and an impaired actin cytoskeleton leads to Golgi aggregation and reduced secretion and endocytosis (10⇓–12). Although many molecular features of actin-based transport in plant cells have been elucidated (13, 14), quantitative measures of the structure of the actin cytoskeleton, and how this structure relates to organelle transport, remain elusive. This is largely due to the difficulties in accurately segmenting the actin cytoskeleton and organelle movement, in particular in growing plant cells.

Theoretical models have been used to analyze the interplay between cytoplasmic streaming and actin organization, demonstrating the emergence of self-organized, rotational streaming patterns (3, 15). However, these studies neglected the discrete, filamentous structure of the cytoskeleton. Theoretical investigations that have considered discrete cytoskeletal structures revealed different regimes of transport, depending on the contribution from diffusion or motor-protein–driven transport along random networks of segments (16); the impact of motor-protein movements on cytoplasm in lattice networks (17); and the effect of length, orientation, and polarity of random filament segments on transport rates (18). The studies that do incorporate biological data have suggested that plant cytoskeletal networks, approximated as grids, may support efficient transport processes in hypocotyl cells (19, 20) and that organelle movement depends on local actin structures in root epidermal cells (10). A detailed study of leaf trichome growth demonstrated the importance of organized actin networks for efficient and targeted distribution of new cell wall material (21). However, a global, system-wide view of actin-based organelle transport remains elusive and is complicated by differences between cell types and developmental stages.

Here, we developed a network-based framework that accurately segments the actin cytoskeleton from three developmental stages of hypocotyl plant cells and combined it with an automated tracking of Golgi transport. This approach allowed us to analyze the four aspects of the actin cytoskeletal transport system, including its structure, design principles, dynamics, and control (22). We found that the actin cytoskeleton maintains properties that support efficient transport over time in growing, partially and fully elongated hypocotyl cells, despite rapid reorganization. We also show that Golgi wiggling behavior is reminiscent of optimized search strategies that might indicate efficient uptake and deposition of Golgi-related cell material. In addition, we demonstrated that features of Golgi transport can be predicted from properties of the system-wide organization of the actin cytoskeleton. Altogether, our framework opens up a systems perspective to dissect and understand the transport functionality of the actin cytoskeleton.

## Results

### A Pipeline to Extract and Represent the Actin Cytoskeleton as a Network.

Because the actin cytoskeleton is composed of discrete and interconnected filaments, it can be efficiently represented in a network-based framework (19, 23, 24) with nodes representing crossings or end points of actin filaments (AFs) and weighted edges capturing AF segments. We extracted network representations from partially elongated *Arabidopsis thaliana* (*Arabidopsis*) hypocotyl cells, around *F* for pipeline; *Materials and Methods*). To study actin-based transport at different cell developmental stages, we further analyzed fully elongated as well as growing hypocotyl cells, around *A*), manually cropped to the cellular region of interest, and filtered to enhance tube-like structures of the cytoskeleton with a parameter *B*). AFs were segmented by applying an adaptive median threshold of block size, *C*). The binary images were skeletonized to obtain AF center lines and spurious fragments smaller than *D*). Networks were obtained by identifying the nodes, adding edges between pairs of nodes directly connected via the skeleton, and assigning edge weights reflecting features of AF segments, e.g., average thickness (Fig. 1*E*).

To test whether our network-based framework captured relevant biological features of the actin cytoskeleton, we compared our automated segmentations against synthetic images of known cytoskeleton-like structures (Fig. 1*G*) as well as manually segmented cytoskeleton images as a gold standard (Fig. 1*H*). Because the accuracy of the network representation relies on four parameters (*I* and *J*) and identified those ensuring best agreement between manual and automated segmentations measured by the Haussdorf distance, i.e., the average minimum distance between pixels of the two segmentations (25, 26). Parameter gauging yielded an optimal average of *J* and *K*; mean*SI Materials and Methods*). Thus, whereas errors in the automated segmentation occur, our parameter optimization ensures an optimal compromise between over- and undersegmentation across different recordings.

Our approach is directly applicable to 3D image data. However, our focus in the main text on 2D networks is justified by the cylindrical shell geometry of the cortical cytoskeleton (19, 27) as well as the size of the transported Golgi, which may bridge gaps between cortical AFs that are not resolved in 2D images (28⇓–30). Moreover, we show that our findings remain valid for 3D image data (Fig. S2 and below). Thus, our approach yields an accurate and mathematically powerful network representation of the cytoskeleton in hypocotyl plant cells from image data.

### The Network Representations Capture Biologically Relevant Features of the Actin Cytoskeleton.

To ensure that our framework captured known changes in the actin cytoskeleton, we determined differences in cytoskeletal organization between partially elongated hypocotyl cells of plants treated with Latrunculin B (LatB; Fig. 2*A*), a drug that inhibits actin polymerization (31), and control cells (Fig. 2*B*; seven cells from seven different seedlings per treatment). To quantify actin network phenotypes, we computed the number of connected components after removal of edges with capacities below the *D* and ref. 32; mathematical definitions and interpretations of all studied network properties are given in Table S1). Fragmentation was lower in networks of control than of LatB-treated cells (Fig. 2*E*; independent two-sample

To further assess the filamentous structure of the actin cytoskeleton, we compared the arc length of filament segments to their Euclidean length and found a strong correlation (Fig. 2*F*; Pearson correlation coefficient *F*, *Inset*). This limited bending of longer filament segments is plausible because actin bundles, typically resulting in longer filament segments, exhibit greater stiffness compared with AFs (33, 34). Furthermore, we found that filament segments were preferentially oriented in parallel to the major cell axis in control cells, but not in LatB-treated cells (Fig. 2*G*). To demonstrate the robustness of our findings, we showed that the differences in network properties between control and treatment were not affected by removal of a random fraction of edges, simulating effects of erroneous network extraction (Fig. S3).

Next, we compared cytoskeletal networks in hypocotyl cells at different developmental stages, i.e., in growing and fully elongated cells, and found notable differences (Fig. S1). In particular, in contrast to both partially and fully elongated hypocotyl cells, the actin cytoskeleton in untreated growing hypocotyl cells showed stronger fragmentation and weaker bundling than in their LatB-treated counterparts. These differences are in agreement with the more even distribution and more strongly branched structure of the actin cytoskeleton in growing hypocotyl cells (35, 36) (Fig. S1), as well as the continuous gradient in cell elongation rates along the hypocotyl in dark-grown *Arabidopsis* seedlings (37). Moreover, our findings from 2D image data were corroborated by analyses of 3D image data and networks (Fig. S2). Therefore, our results show that the extracted network representations of the actin cytoskeleton enable automated phenotyping of cytoskeletal structures.

### The Actin Cytoskeleton Supports Efficient Transport.

A major function of the plant actin cytoskeleton is to mediate transport of a range of organelles and compartments. To assess the transport efficiency of actin networks in partially elongated hypocotyl cells, we computed a number of seminal network properties and compared them against ensembles of two types of randomized null model networks (each network was randomized *C* for first null model that shuffles node positions and edges and Fig. S3 for second null model that shuffles edge properties only). We determined the average path length (32), which reflects the reachability of a network, and compared it against an ensemble of networks from the first null model (Fig. 2*H*). We found that the average path length of the extracted networks was smaller than that of the null model networks (Fig. 2*I*;

To investigate the structural origin of this transport efficiency, we reconsidered the assortativity (32) of the cytoskeleton and found that it was higher in the extracted networks than expected by chance (

To ensure that our results were robust, we used an additional and more restricted null model, which shuffles only edge properties. Whereas the first null model is more flexible, the second one excludes potential artifacts that could arise from an increased number of edge crossings or a more homogeneous distribution of node positions compared with the extracted networks (Fig. S3). Our findings from the first null model were consistently confirmed by the second one. Hence, differences in the studied network properties between extracted and null model networks are not an artifact of the randomization procedures.

Despite organizational differences of the actin cytoskeleton in hypocotyl cells at different developmental stages, the actin network in partially elongated as well as fully elongated and growing hypocotyl cells showed properties of efficient transport (Fig. S1). For example, both reachability and robustness of the actin networks were better than expected by chance. Again, our findings remained valid when studying actin networks extracted from 3D image data (Fig. S2).

A potential issue, shared by all current approaches that extract transport-related networks from image data, is the unknown edge directionality. Individual AFs usually allow unidirectional movement of motor proteins only, and actin bundles in root hairs and other tip growing cells are typically composed of parallel AFs (9, 38, 39). In contrast, our analyses of cytoskeletal transport capacity rely on the assumption of bidirectional transport along edges. Indeed, our data showed that

### Automated Quantification of Golgi Movement.

To quantify actin-based cellular transport, we studied partially elongated hypocotyl cells dually labeled with FABD-GFP and tdTomato-CesA6 (tdT-CesA6), used as a proxy for Golgi movement (42, 43). We analyzed the flow of Golgi through automated tracking (44, 45) in image series from control and LatB-treated cells (Fig. 3 *A* and *B*). Golgi bodies moved with velocity *C*), which is higher than *D*), correlating with the orientation of actin bundles (compare with Fig. 2*G*). Thus, our automated tracking captures known features of Golgi movement and may therefore be suitable for further, more detailed analyses of Golgi behavior.

### Golgi Bodies Exhibit Wiggling, Which Does Not Change Over Time or with Distance to the Actin Cytoskeleton.

The movement of Golgi bodies is characterized as saltatory or stop and go (11, 30), whereby Golgi switch between periods of directed movement and undirected “wiggling” behavior (Fig. 3*E*). Whereas it has been suggested that Golgi wiggling is not specific to individual Golgi bodies (10), it is yet unclear whether Golgi wiggling changes over time or depends on the distance of the Golgi from the actin cytoskeleton. To quantify these characteristics, we computed the angles between consecutive Golgi track segments (referred to as “relative angles”; Fig. 3*E*) and refer to movement with relative angles above *F*). For LatB-treated cells, the average relative angle *G*) peaked at around

To test whether the prevalence of Golgi wiggling changes over time, we calculated the distribution of average relative angles over time (Fig. 3*H*, *Left*). We found that Golgi motility did not change during the course of the recordings (Fig. 3*H*, *Upper Right*). Moreover, the prevalence of Golgi wiggling showed only very minor fluctuations within and across time series (Fig. 3*H*, *Lower Right*; *I*, *Left*). The frequency of Golgi was dependent on the distance to the AFs (Fig. 3*I*, *Right*), with high Golgi densities up to

### Movement Patterns of Golgi Resemble Search Strategies and Might Optimize Uptake and Delivery.

We note that the Golgi wiggling resembles the searching behavior of foraging animals (46, 47) or microbial motion (48) that has been suggested to optimize search efficiency. This type of motion is characterized by random reorientations (Fig. 3*D*) and step sizes *J*). Indeed, the distributions of step sizes of these straightened tracks followed truncated power laws with exponents *K*; in particular, truncated power laws yielded higher likelihoods than exponential distributions (49)]. These exponents are larger than those typically reported for foraging animals or bacteria,

Despite obvious differences in mechanisms underlying Golgi movement and animal foraging there may be similar goals. Namely, it is plausible that Golgi-derived material may need to be exchanged between parts of the plasma membrane, the endoplasmatic reticulum (ER), and other compartments. Assuming that these sites are not globally coordinated by the cell, the switching of Golgi between directed movement and wiggling behavior may therefore provide an efficient search strategy. This is compatible with proposed models of Golgi movement (30), such as the “vacuum cleaner” model (Golgi move through the cell and pick up products from the ER) or the “recruitment” model (Golgi pause in the vicinity of active ER sites to facilitate trafficking). Our findings might therefore indicate a connection between Golgi wiggling and the optimization of uptake and delivery of Golgi-related material throughout the cell.

The Golgi search behavior is compatible with the movement of Golgi along the actin structures. Whereas, at a given time step, the majority of Golgi stayed at the same AF, some faster Golgi moved to different AFs (Fig. S5). Moreover, it remains unclear whether Golgi bodies are transported through the cell by direct interactions with motor proteins or indirectly via cytoplasmic streaming (54). By investigating the relative movement of different Golgi at a given time step (referred to as “pairwise angles”; Fig. 3*E*), we found substantial antiparallel movement of close-by Golgi (Fig. S5). Taking into account the low Reynolds numbers of the cytoplasm (1), this antiparallel movement contradicts the assumption of indirect, cytoplasmic-streaming–induced movement and instead supports myosin-based transport of a substantial fraction of Golgi bodies. In conclusion, our data suggest that switching of Golgi to adjacent AFs is myosin dependent, whereas switching to nonadjacent AFs is due to cytoplasmic streaming that may carry the Golgi over large distances.

### Local and Global Actin Network Architecture May Be Used to Predict Direction and Velocity of Golgi Movement.

Our previous analyses assumed that the capacity of a given actin network edge, i.e., its average thickness, reflects its potential to transport cellular cargo (Fig. 2). To test this hypothesis, we studied the Golgi flow on two levels: First, we computed pairwise correlations between the properties of Golgi flow and actin structures, as modeled by our extracted networks. Second, we combined different edge properties of the actin networks to predict features of Golgi flow (e.g., direction and velocity), using a multiple–linear-regression approach. To this end, for the extracted actin networks (Fig. 4 *A* and *B*), we determined the local edge capacities and global edge properties that incorporate information about the importance of any given edge in the network context. Namely, we studied edge degree (measuring the total thickness of adjacent edges), the edge page rank (measuring the probability that cargo that randomly traverses the network is found at the given edge), the edge path betweenness (measuring the likelihood that the given edge lies on a shortest path through the network), and the edge flow betweenness [measuring the total maximum flow between any two nodes through the given edge (32); see Table S1 for mathematical definitions and explanations]. In parallel, from the Golgi tracks at each time step, we constructed an auxiliary Golgi flow network by copying the structure of the actin network and assigning new edge weights in the Golgi flow network according to various features of Golgi movement in the vicinity of the respective edge [e.g., the number of Golgi (Fig. 4*E*) or the direction and velocity of close-by Golgi (Fig. 4*F*)].

To investigate the relationship between actin structure and Golgi dynamics in partially elongated hypocotyl cells, we first computed the correlation between the determined edge properties of actin and Golgi flow networks. For instance, we studied the dependence of the Golgi direction and velocity on the actin edge rank. The correlation between the two properties varied over time and across cells (Fig. 4*G*). Across all studied partially elongated cells, this correlation was significant for control cells with *C*) and increased wiggling behavior of Golgi (Fig. 3*F*) in LatB-treated cells. We further evaluated the correlations between all pairs of edge properties, averaged across the studied cells and time points (Fig. 4*H*). Some pairs of properties, such as Golgi direction and velocity and actin edge rank discussed above, were correlated for the control cells (*G*). Only the number of Golgi close to a given edge was correlated with the respective edge capacity and edge degree for both control and LatB-treated cells (Fig. 4*I*). These findings show that although the flow of Golgi is severely altered by the LatB treatment, Golgi still agglomerate in the vicinity of the actin stubs (Fig. 3*I*). However, for most pairs of actin and Golgi flow network edge properties, there was no or only weak correlation (

Because pairwise correlations were of moderate value, we then used multiple linear regression to see whether certain aspects of Golgi flow could be predicted from a combination of actin edge properties. Indeed, the number of Golgi close to an actin edge (Fig. 4*K*; coefficient of determination

Interestingly, these correlations between actin structures and Golgi movement were very similar for growing and fully elongated hypocotyl cells (Fig. S1). Our results were confirmed by analysis of 3D data of actin cytoskeleton and Golgi (Fig. S2). Therefore, the system-wide organization of the actin cytoskeleton in hypocotyl cells shapes, and may be used to predict, the dynamic flow of Golgi.

Finally, we note that our imaging setup captured only the outer periclinal cell side, for both 2D and 3D data. Because 3D imaging of the complete, quickly rearranging plant cytoskeleton is not yet feasible, we modeled the cylindrical geometry of the cortical cytoskeleton by periodically extending the original, 2D extracted network. Whereas cytoskeletal structures on different cell sides generally differ (e.g., refs. 59 and 60 for actin and ref. 61 for microtubules), it is parsimonious and avoids an unbiological plane-like cytoskeletal geometry. Indeed, taking into account this cylindrical geometry moderately but significantly improved the predictive power of our regression-based analyses of Golgi movement (Fig. S4). Taken together, our data show that Golgi transport in hypocotyl cells is not merely determined by the local structure of the cortical cytoskeleton, but also depends on larger architectural contexts, as well as its cylindrical geometry.

## SI Materials and Methods

### Plant Material and Experimental Setup.

We used *Arabidopsis* Columbia-0 35S:FABD-GFP and pCesA6:tdT-CesA6 dual-labeled seedlings (12, 36) to study actin cytoskeleton and Golgi bodies. The seedlings were surface sterilized (ethanol), stratified for

For the comparison of actin-based Golgi transport across different developmental stages, i.e., between growing and elongated hypocotyl cells (Fig. S1), we used a slightly modified imaging setup yielding

### Image Preprocessing of Actin and Golgi Recordings.

We preprocessed the confocal recordings, using the image-processing package Fiji (45) (see Fig. 1*A* for illustration and mathbiol.mpimp-golm.mpg.de/CytoSeg/ for the open-source code and examples): We corrected the potential drift of the seedlings under the microscope by applying the Fiji-StackReg stack registration algorithm to the image series, which allows rigid body transformations, minimizes the mean square intensity difference between subsequent frames, and does not require any parameter selection (65). To enable simultaneous registration of the dual-labeled plant recordings, we merged actin and Golgi recordings from one cell as different color channels and split the channels after registration. We compensated photobleaching by normalizing the mean intensity of each frame. We improved the signal-to-noise ratio by using the Fiji-BackgroundSubtraction rolling ball filter with radius of *G*).

### Extraction of Actin Networks from Image Data.

From the preprocessed 2D and 3D image data, we represented the actin cytoskeleton as a network through a custom procedure that has been developed and implemented using Python (70) (see Fig. 1 *B*–*E* for illustration and mathbiol.mpimp-golm.mpg.de/CytoSeg/ for the open-source code and examples): First, to obtain the filamentous actin skeleton, we applied a 2D tubeness filter to each frame of the preprocessed actin images to enhance the signal of the filamentous structures of width *B*) (for 3D images, the filters were applied to each z slice separately). Next, we obtained binary images by applying an adaptive median threshold with block size *C*). We determined the center lines of the actin structures by skeletonizing the thresholded image (69); i.e., the skeleton and the background are given in a binary representation by *D*). The image processing parameters *J*).

Second, for each skeletonized, binary actin image, we identified the nodes of the network as crossings or endpoints of filaments by checking the *E*).

Third, we constructed a weighted network by starting from an empty multigraph

In general, the extracted network is a multigraph (e.g., two curved filaments may cross twice, leading to two edges between the same pair of nodes; Fig. 1*E*). For simplicity, we projected the multigraph onto a simple graph by summing the multiple-edge capacities *E*). Network extraction procedures similar to ours are reviewed below.

Finally, we derived several higher-level edge properties that not only reflect the local structure of the cytoskeleton but also capture global features (Table S1). As a simple measure of the importance of an edge

### Gauging of Network Extraction Parameters.

To ensure an accurate network representation of the actin cytoskeleton, we performed extensive gauging of the four imaging parameters

First, for the manual segmentations, we randomly chose *Materials and Methods* and manually segmented the center lines of the filaments (Fig. 1*H*).

Second, we created *G*). Whereas noise in digital camera images is typically a combination of Gaussian-distributed sensor noise, gamma-distributed speckle noise, and Poisson-distributed shot noise, we adhered to simple gamma-distributed noise for simplicity here, which was similar to that in the biological cytoskeleton images.

We then varied all four parameters in a wide range with 10 linear steps each, *I* and *J*) for all *I*, *Left*), whereas small values for *I*, *Right*). Therefore, we minimized the Haussdorf distance *J*).

The optimal parameters and their confidence intervals were determined as follows: We randomly selected *K*). Using these optimized parameters guaranteed small average distances between the pixels of manual and automated segmentations and, hence, accurate network representations of the cytoskeleton.

### Review of Network Extraction Methods.

Finally, we review other, existing methods for the extraction of networks from different image sources and systems of interest. The first class of approaches typically relies on 2D image data and uses classical image segmentation for network extraction: From high-contrast dark-field microscopy images of leaves, venation networks were extracted in a supervised procedure (71). However, due to the high signal-to-noise ratio (

Using a fully automated extraction procedure, photographic image series were used to extract networks formed by slime molds (72). Again, the high

Our network extraction procedure was inspired by another, more sophisticated method for the extraction of fungal networks from photographs (75). Whereas there the curvilinear vein structures were enhanced using a contrast-independent phase-congruency filter (76), we used a faster and widely used tubeness filter for simplicity (67). As for the slime mold network above, the vein thickness was determined only based on the average pixel numbers per unit vein length and we extended the thickness computation by taking into account pixel intensities. Moreover, we adopted the gauging of the free image analysis parameters by computing the average smallest distances between the center lines of manually segmented gold standard images and automated segmentations. However, ref. 76 considered only one direction, *I*). Instead, we included the opposite direction and minimized the Haussdorf distance *J*) (25, 26). Thus, although the average smallest distance

Another class of approaches for the detection of networks from image data does not rely on segmentation but encompasses tracing-, tracking-, or open contour-based approaches (26, 77, 78). Instead of (global) image segmentation, these approaches typically identify two or more points on the network and find a connecting path through the network by optimization of an (usually local) energy function. Because many of these approaches have been originally developed for the reconstruction of neural networks, they are directly suitable for the extraction of 3D network structures. However, because most existing approaches in this class require manual user input, we focus our discussion on SOAX, a software for quantification of 3D biopolymer networks (26). SOAX represents a recent and fully automated open contour-based approach whose strengths and limits are largely representative for the related approaches: Especially for large sets of 3D image data, SOAX is faster than segmentation-based approaches. Furthermore, we note that SOAX incorporates resampling of the 3D image data to compensate for the decrease in

Despite the differences in the image segmentation procedures, which have been designed for different image sources and systems of interest, systematic gauging (Fig. 1) provides a means to adjust the free parameters of any of the above segmentation procedures. Whereas automated segmentation methods are steadily improving, a quantitative comparison with manual, expert-driven segmentations remains crucial.

### Construction of Golgi Flow Networks from Tracking Data.

To automatically track the movement of Golgi through the cell in 2D and 3D, we used Fiji-TrackMate to detect the Golgi as particles of

Next, we constructed networks from the tracking data, referred to as Golgi flow networks, for comparison with their actin cytoskeleton counterparts (Fig. 4). For a given time step, we copied the nodes and edges of the actin network and computed the minimum distance

A crucial step in the computation of several edge properties of the Golgi flow network involves the scalar product between a segment vector of a Golgi track and an actin network edge vector (i.e., the vector connecting the two edges’ nodes). Although the actin filaments may be curved, we showed that the bending of a filament segment is typically very small with *E*), justifying the assumption of straight edge vectors.

### Randomization and Null Models of Actin Networks.

We investigated the structure of the actin networks, using a number of seminal and biologically relevant properties, such as assortativity and average path length (Fig. 2 and Table S1). Whereas some of these properties may be interpreted by themselves (like the sign of the assortativity that provides information about whether thick actin bundles are grouped together or whether they are intermingled with filaments), a suitable reference is needed to interpret others (like the average path length whose value depends, e.g., on the size of the network and the sum of edge weights).

Therefore, for any given actin network, we introduced two types of null models that randomize certain properties of the network while preserving relevant others (see Fig. S3 and mathbiol.mpimp-golm.mpg.de/CytoSeg/ for the open-source code and examples). From both null models we generated an ensemble of

We further used a second, more restricted model that does not increase the number of edges and edge crossings and does not randomize the node positions (Fig. S3). These null model networks were generated by shuffling only the edge properties of the original network (19, 20). The second null model, too, leaves the distribution of edge capacities unchanged.

## Concluding Remarks

Although the molecular details of actin monomers and filaments as well as actin-associated proteins are relatively well studied, quantifying actin-based transport in a larger cellular context remains challenging. To address this gap, we introduced an accurate image-based network representation of the actin cytoskeleton to facilitate automated and unbiased quantification of cytoskeletal phenotypes and functions. We used this framework to establish that system-level properties of the actin cytoskeleton determine key features of Golgi transport in *Arabidopsis* hypocotyl cells.

Our approach of integrating cytoskeletal network structures with tracking data of organelles is directly transferable to various biological systems and functions: In plants, in addition to the analysis of different cell types, transport of mitochondria (4, 10) and photodamage avoidance movement of chloroplasts (62) represent interesting test grounds. In animals, it has been shown that cytoplasmic streaming in fruit fly oocytes (63) and transport of lysosomes in monkey kidney cells depend on microtubules (7). Although these are interesting local correlations of cytoskeletal features and organelle transport, we expect broader, system-level understanding of these processes by the application of interdisciplinary approaches such as ours. Our automated framework paves the way for quantitative assessment of the actin cytoskeleton and trafficking in, for example, large-scale chemical and genetic screens. Moreover, our findings indicate that network-based models could be used to predict potential exchange sites of Golgi-related material. Altogether, the presented combination of experimental imaging techniques and theoretical network-based analyses provides an important step toward a systems understanding and, ultimately, control of cytoskeleton-based transport.

## Materials and Methods

### Plant Material and Experimental Setup.

We used *Arabidopsis* Columbia-0 35S:FABD-GFP and pCesA6:tdT-CesA6 dual-labeled, 3-d-old, and dark-grown seedlings (12, 36) to study actin cytoskeleton and Golgi bodies (*SI Materials and Methods* and Movie S1). For drug and control treatment, seedlings were floated on distilled water with and without

### Extraction and Randomization of Actin Networks.

We corrected the potential drift of the seedlings using Fiji-StackReg rigid body stack registration (45, 65), compensated photobleaching by normalizing mean intensities, and improved the signal-to-noise ratio by using the Fiji-BackgroundSubtraction filter with a radius of *SI Materials and Methods*; see mathbiol.mpimp-golm.mpg.de/CytoSeg/ for open-source code and examples). To represent the actin cytoskeleton as a network in 2D and 3D, we enhanced filamentous structures of width

### Quantification of Golgi Movement.

We automatically tracked the movement of Golgi in 2D and 3D, using Fiji-TrackMate (*SI Materials and Methods*). We detected the Golgi as particles of around

## SI Text

### Differences in Actin Architecture and Golgi Transport Between Growing and Fully Elongated Hypocotyl Cells.

To further assess the accuracy of our network extraction procedure, we analyzed and compared actin networks from hypocotyl cells at different developmental stages. In addition to partially elongated hypocotyl cells studied in the main text (Fig. S1*A*), we analyzed image data from growing and fully elongated hypocotyl cells around *B*). The slightly modified experimental setup captured larger sections of the cortical actin cytoskeleton and is described in detail in *SI Materials and Methods*. The actin structures at the two cell developmental stages showed clear differences, with a more uniform distribution of actin, fewer bundles, and more fine branches in growing hypocotyl cells (35, 36).

To quantify these structural differences, we computed the number of connected components after removal of edges with capacities below the *C* and Fig. 2). In particular, the actin networks in growing, untreated hypocotyl cells showed consistently larger fragmentation than in fully elongated cells. Combining the data of all three studied cells over the full imaging periods (Fig. S1*D*), we confirmed that the actin networks in growing, untreated hypocotyl cells were significantly more fragmented than in their LatB-treated counterparts, opposite to the results for fully elongated hypocotyl cells. Similarly, the average edge capacity (“bundling”) in growing, untreated hypocotyl cells was lower than in their LatB-treated counterparts, whereas the ratio was reversed for fully elongated hypocotyl cells. For the assortativity, no significant differences between growing and elongated hypocotyl cells were observed. These findings are in agreement with the finer and more branched structure of the actin cytoskeleton in growing hypocotyl cells (35, 36) in combination with the actin-disrupting effect of LatB, which especially affects fine AFs and leads to the formation of actin stubs (31). Moreover, these differences are compatible with the continuous gradient in cell elongation rates along the hypocotyl in dark-grown *Arabidopsis* seedlings (37).

However, no significant differences were observed regarding transport efficiency (Fig. S1*E*) or the correlations of actin edge properties and features of Golgi movement (Fig. S1 *F* and *G*). This indicates that despite differences in actin organization (and especially actin bundling), the cytoskeleton in hypocotyl cells may work as an efficient transportation network.

### Extension of Analysis to 3D Image Data of Actin Cytoskeleton and Golgi.

Whereas the cytoskeleton is an inherently 3D structure, in the main text we focused on 2D image data and networks (Figs. 1–4). As explained in *Results*, this focus is justified by the thin cylindrical shell geometry of the cortical actin cytoskeleton (19, 27) (Fig. S2*A*, the confinement of finer actin meshes to the plasma membrane with only rare thick actin cables pervading the cell interior) and the size of the Golgi, which may bridge gaps between cortical AFs (28⇓–30) (Fig. S6).

However, our approach is directly applicable to 3D image data (*SI Materials and Methods*). To test the validity of our 2D results, we therefore recorded 3D image data from growing and fully elongated hypocotyl cells under control conditions and after LatB treatment, respectively, and repeated our previous analyses. The extracted 3D networks confirmed the localization of the actin to the plasma membrane (Fig. S2*A*). For comparison, we further z projected the 3D image data by taking the average intensity across z slices and extracted 2D networks as before (Fig. S2*B*). For a given cell, the network properties of 3D and 2D networks generally differ (Fig. S2*C*, *Left*; time series of numbers of connected components after removal of edges with capacities below the *C*, *Right*; Pearson correlation coefficients

Moreover, we computed various structural (Fig. S2*D*) and transport-related (Fig. S2*E*) properties of the 3D actin networks from growing and fully elongated hypocotyl cells as before. Our findings support those reported for the 2D analyses (Fig. S1). Similarly, the correlations between various edge properties of 3D actin and Golgi flow networks (Fig. S2*F*) confirmed our findings from 2D analyses (Fig. S1). In conclusion, our results suggest that the actin cytoskeleton at the outer periclinal side of hypocotyl plant cells can be approximated by a 2D network representation (Fig. S4).

### Inference of Network Design Principles Using Two Different Null Models and Negative Controls.

We demonstrated that the actin cytoskeleton displays network properties supportive of efficient transport processes (Fig. 2). In particular, by proposing suitable null models, we showed that this transport efficiency arises from the specific organization of the cytoskeleton in biological cells, hence indicating an evolutionary basis. Here, we discuss and justify our proposed null models in more detail.

The first null model randomly and uniformly distributes the node positions across the cell and assigns the edges to new, randomly chosen pairs of nodes whose distance matches the Euclidean length of the respective edge, while keeping the number of edges crossings low (Fig. 2 *H*–*J* and *Materials and Methods*). This procedure is a modified version of the Erdős–Rényi model with hidden variables that has been used to identify structural features of various real-world networks (79). In our version, the hidden node variables are given by their positions and the probability of adding an edge between two nodes depends on their Euclidean distance and the fraction of edges from the original network of identical (binned) length that have not already been added to the null model network. Moreover, as an extension to the hidden variable model, for each added edge, we tried

This null model preserves the distribution of edge capacities, whose sum reflects the amount of filamentous actin in the cell. The null model further maintains the length distribution of filament segments. The null model as well as the extracted networks may exhibit crossing edges (*Materials and Methods*) whose frequency was measured by the crossing number,*A*; mean *D*), the reconstructed actin network may exhibit crossing edges because the edges are modeled as straight lines between the nodes, so that *B*), where*C*). This *A*). In addition, the extraction procedure does not allow nodes at neighboring pixels, violating the assumption of a uniform distribution of nodes (Fig. 1 and *Materials and Methods*).

To overcome these shortcomings, we introduced a second, more restricted null model in which all node positions of the original extracted network (Fig. S3*D*) were kept and only edge properties were shuffled (Fig. S3*E*). This procedure has been previously used in refs. 19 and 20 with a similar purpose, i.e., to study the biological relevance of properties in a grid approximation of the cytoskeleton. The null model preserves the total amount of filamentous actin and further leaves the connectedness and planarity of the original network unchanged. All investigated properties of the extracted networks showed the same significant differences for the second null model as for the first null model (Fig. S3*F* and Fig. 2*I*; independent two-sample

Moreover, as a negative control, we assessed the biological relevance of transport-related properties of cytoskeletal networks extracted from recordings of LatB-treated cells (Fig. S3 *G* and *H* and Fig. 2). Indeed, none of the studied properties of the cytoskeletal networks of the LatB-treated cells showed significant differences for either of the two null models (all

Finally, we assessed the robustness of our findings against random removal of edges as a model for errors in the network extraction procedure. To this end, for a given network, we created an ensemble of *Materials and Methods*). Whereas such removal of edges may change the network topology and hence various network properties, most of our analyses concerned differential behavior of the network properties between two scenarios (e.g., control vs. treatment; Fig. 2). For instance, the number of connected components for the network times series of control and LatB-treated cells changed only very moderately with the fraction of removed edges (Fig. S3*I*; all *J*; all *E* and *I*).

### Directionality of Actin Edges, Correlations of Actin Edge Properties, and Periodic Actin Networks.

Our analyses of the transport capacity of the actin cytoskeleton rely on the assumption of undirected edges, i.e., edges that allow bidirectional transport (Fig. 2). To elucidate the biological plausibility of this assumption, we constructed an additional type of Golgi flow networks (Fig. 4) by weighting the edges according to the average angle between the respective edge and the close-by Golgi track segments (Fig. S4*A*). For an edge that allows predominantly unidirectional transport, this average angle is expected to be below *B*, *Left*) and we found no correlation between the unidirectionality of transport of an edge and its capacity, i.e., its thickness (Fig. S4*B*, *Right*). The computation of edge directionalities relies on a maximum cutoff distance of *C*). We found that smaller cutoff distances led to higher fractions of unidirectional edges. This is expected as Golgi farther away from an actin bundle, and potentially closer to another bundle, are more likely to move in different directions (Fig. S5). Averaging of multiple such Golgi may lead to apparent bidirectional movement along a given edge. However, because smaller cutoff distances reduced the number of edges that were associated with any Golgi and led to poorer statistics, we kept a cutoff distance of

When investigating the flow of Golgi along the actin cytoskeleton, we considered several local and global edge properties of the actin network as regressors or predictors of the Golgi flow (Fig. 4 and Table S1). Across the studied networks, there were on average *D*), via*E*). Although these two properties generally measure different aspects of the importance of an edge in the network context, they are identical for tree-like networks of unit edge capacities and lengths. We therefore quantified how tree-like our studied actin networks were by computing the ratio of their number of edges *F*),

Finally, we note that the 2D rendering of images captured only the outer periclinal part of the actin cytoskeleton. This restriction introduces boundaries and, hence, bias in the extracted network as the cortical actin cytoskeleton follows the near-cylindrical shape of the hypocotyl cells. Because imaging 3D time series of the complete actin cytoskeleton is intrinsically challenging, we modeled the cylindrical geometry of the cortical cytoskeleton by periodically extending the original, 2D extracted network (Fig. S4*G* and *SI Materials and Methods*; see Fig. S2 for 3D data and analyses of the outer periclinal side of the actin cytoskeleton). We refer to these networks as periodic and to the original ones without boundary conditions as nonperiodic.

To model the cylindrical geometry of the cortical cytoskeleton we assumed that the cytoskeleton at the back of the cell is identical to its imaged counterpart at the front (see *Results* for a discussion of this assumption). We implemented the boundary conditions for arbitrary cell shapes by augmenting the original network (see mathbiol.mpimp-golm.mpg.de/CytoSeg/ for the open-source code of the implementation of periodic boundary conditions): We started from the cellular region of interest and created an empty graph

Then, we repeated our correlation- and regression-based analyses for the periodic networks (Fig. S4 *H* and *I*). For the control cells, Golgi velocity and direction were more accurately predicted by the global edge rank rather than other local and global edge measures of the actin network. These results are in agreement with those for the nonperiodic networks above. Intriguingly, the prediction of Golgi direction and velocity was further improved for the periodic networks compared with the nonperiodic ones (Fig. S4*J*; independent two-sample

Our periodic boundary conditions conform to parsimony by assuming identical actin structures at the two sides. Although the actin cytoskeleton at the distant periclinal side of the cell may differ from that at the outer periclinal side, e.g., due to different mechanical forces inside the hypocotyl (see *Results* for a discussion), 3D imaging will be necessary to resolve such differences. However, imaging with sufficient spatiotemporal resolution, and without substantial photobleaching, to accurately capture the fast dynamics of actin rearrangement and Golgi movement in distant parts of the cell introduces major limitations. In addition, absorption and scattering of light by plant cell features will result in images of reduced quality and may not resolve fine AFs. Therefore, our implementation of periodic boundary conditions appears reasonable until high-quality data of the complete cortical actin cytoskeleton become available.

### Passive and Active Transport of Golgi and Switching Between Filaments.

Regions of bundled actin may lead to higher average velocities of Golgi movement in root epidermal cells (10). To test whether our network-based framework supports these findings in partially elongated hypocotyl cells, we computed the average Golgi velocity and compared it to the overall actin bundling in the cell (Fig. S5*A*), measured by the average edge capacity (Fig. 2*E*). Indeed, actin bundling showed a high correlation with Golgi velocities for both control and LatB-treated cells (Pearson correlation coefficients

Reasons for this correlation are manifold: Thick bundles are typically surrounded by fewer AFs that might slow down the Golgi (10, 21) (Figs. 1 and 2*I*). The high rigidity of bundles increases the run length of motor proteins (83), which may be further extended through binding of multiple motor proteins (84). Furthermore, the varying orientations in an array of fine AFs have been suggested to counteract cooperative movement of cargo (10). Thus, the average velocity of Golgi in hypocotyl cells is determined by the prevalence of actin bundles. However, studying overall actin bundling and average Golgi velocities does not consider the identity of individual AFs and the potential movement of Golgi along and between filaments.

To further quantify the movement of Golgi along and between filaments we distinguished three classes (Fig. S5*B*): (*i*) Golgi that maintained positions along an edge in the actin network between consecutive time steps (around *ii*) Golgi that moved to a different edge along a path with angles smaller than *iii*) Golgi that moved to an altogether different AF (around *C*).

To obtain this classification of Golgi, we assigned the start and end points of each track segment to their nearest edge in the actin network that we refer to as start and end edges, respectively. From the original actin network (Fig. S6*C*, green), we constructed the line graph (Fig. S6*D*, gray), i.e., a graph that has a node for each edge in the original network and a link between nodes that represent adjacent edges (ref. 32 and Table S1). We computed the shortest paths from the start to the end edges through the line graph of the actin network. For a given shortest path, we calculated the path length and the maximal angle between any two adjacent edges along the path. We then classified different types of Golgi movement (Fig. S6*E*; the classes are referred to as “stay,” “move,” and “jump”), depending on the minimum number of edges traversed by the Golgi and the associated maximal angle between traversed edges of the cytoskeletal network. The frequencies of Golgi in these different classes showed stationary Golgi, Golgi likely moving along a given filament, and Golgi switching between different, nonadjacent filaments (Fig. S5*B*). A closer inspection further showed that

Next, we investigated the relationship between Golgi velocity and redistribution across AFs. Both the maximal angle along the shortest path from the start to the end edge and its path length were moderately correlated with the velocity of the respective Golgi (Fig. S6 *F* and *G*;

Switching of cargo between different, intersecting filaments has been previously shown for organelles tracking along microtubules in animal cells (7). However, these studies focused on movement and switching of cargo at filament intersections and did not investigate switching of cargo to nonadjacent filaments.

Despite recent studies, it remains unclear whether Golgi bodies are transported through the cell by direct interactions with motor proteins or indirectly via cytoplasmic streaming (54). The two scenarios are reflected in the behavior of neighboring Golgi tracks. Movement of close-by Golgi tracks in the same direction is indicative of indirect bulk flow. In contrast, movement in opposite directions suggests direct actomyosin-based transport of Golgi. To distinguish these two cases, we measured the angles between any two segments of different Golgi tracks within the same time step (referred to as pairwise angles) in dependence of their spatial separation. For the LatB-treated cells, the frequency of a given pairwise angle of Golgi movement correlated with neither the angle nor the spatial separation of the two Golgi track segments (Fig. S5*H*, *Lower Right*). In contrast, the Golgi movement displayed mainly parallel or antiparallel trajectories in control cells (Fig. S5*H*, *Upper Right*), consistent with Golgi movement occurring preferentially along the major cell axis (Fig. 3*D*). Even for small distances below *H*, *Upper and Lower Left*;

In conclusion, our data suggest that switching of Golgi to adjacent AFs is myosin dependent, whereas switching to nonadjacent AFs is due to cytoplasmic streaming that may carry the Golgi over large distances.

### Golgi Wiggling in Dependence of Actin Cytoskeleton and Consistency Across Cells.

In our quantitative analysis of cellular transport dynamics, we combined automated tracking data of Golgi with automated extraction of actin cytoskeletal networks (Fig. 3). Here, we discuss two of these analyses in more detail: the investigation of Golgi wiggling in dependence of actin structures and the movement of Golgi along and between filaments. Moreover, we present results on the cell-to-cell variability of Golgi movement across different developmental stages.

We confirmed that the Golgi wiggling behavior is not Golgi specific (10) and showed further that the prevalence of Golgi wiggling behavior is stationary over the course of the recording period and does not depend on the distance from the actin cytoskeleton (Fig. 3 *F*–*I*). However, the actin cytoskeleton is composed of filaments and bundles of varying thickness and it has been suggested that arrays of fine actin filaments promote wiggling (10). To test this hypothesis in detail, we used our extracted, weighted network representation of the actin cytoskeleton. We constructed a Golgi flow network in which the edges of the actin network were assigned a measure of Golgi wiggling (Fig. S6*A* and Table S1). To this end, for each edge, we considered all Golgi in a vicinity of *B*). In particular, the average relative angles approached *I*; linear regression yielded a slope of *B*, dotted black lines). These findings suggest that the thickness of close-by actin bundles does not influence the Golgi wiggling behavior. However, this is still compatible with the observation that arrays of fine actin filaments increase Golgi wiggling (10) because the thickness of individual filaments studied here does not capture the surrounding actin environment.

In addition to the relative angles of Golgi tracks, we studied the streaming coefficient as another measure of Golgi wiggling (10, 11). For a given track and time step **S24**), the streaming coefficient combines information about Golgi velocity and directionality. Nevertheless, across Golgi tracks of all studied cells, relative angle and streaming coefficient showed a moderate but highly significant negative correlation (Fig. S6*C*; *C* and *F*), leading to large streaming coefficients. This correlation suggests that using the streaming coefficient as a measure of Golgi wiggling leaves our findings on the persistence of Golgi wiggling largely unchanged.

We note that Golgi size is strongly correlated with the average Golgi intensity (Fig. S6*D*; Pearson correlation coefficients

Furthermore, we analyzed Golgi movement in hypocotyl cells at different developmental stages, i.e., in growing and fully elongated cells both in untreated control plants and after LatB treatment (Fig. S6*E*). A detailed description of the additional recordings is given in *SI Materials and Methods* and Fig. S1. Indeed, the studied features of Golgi movement were nearly identical for growing and fully elongated hypocotyl cells and affected only by the drug treatment (Fig. S6 *F–K*; compare control cells in green and blue and LatB-treated cells in orange and yellow). Moreover, although Golgi movement is generally highly variable over time and across cells, the low-level features of Golgi movement studied here were very consistent and uniform across cells (Fig. S6 *F–K*; compare solid lines and error bars indicating mean

### List of Studied (Edge) Properties of Actin and Golgi Flow Networks.

After extracting the actin cytoskeletal networks from image data, we computed various seminal properties to quantify cytoskeletal phenotypes and evaluate transport efficiency (Fig. 2). The actin cytoskeleton at a given time is represented by a weighted, undirected network *Materials and Methods*). In addition, we derived the filament bending as the ratio of filament and Euclidean length,

The organization of the extracted networks was quantified by various seminal network properties (Table S1): To study the fragmentation of a given network, we removed all edges with capacities below the

Moreover, the average shortest path length was computed as a standard measure of transport efficiency,

The robustness of the transportation network against disruptions was evaluated by the algebraic connectivity,

To correlate the flow of organelles with the structure of the actin network, we derived two networks with identical structure and different edge weightings that we refer to as actin and Golgi flow networks, respectively (Fig. 4 and Table S1). As a (local) edge property of the actin network we studied the capacity

The studied edge properties of the introduced Golgi flow network considered the movement of Golgi close to an edge (Table S1). At a given time, the center points of Golgi track segments are given by

## Acknowledgments

D.B. was funded by an International Max Planck Research School scholarship. S.P. was funded by the Max Planck Society, an Australian Research Council Future Fellowship grant (FT160100218), an R@MAP Professorship at University of Melbourne, and a Dyason travel grant. S.P. and Z.N. acknowledge an International Research and Research Training Fund (Research Network and Consortia) grant.

## Footnotes

- ↵
^{1}To whom correspondence should be addressed. Email: breuer{at}mpimp-golm.mpg.de. ↵

^{2}S.P. and Z.N. contributed equally to this work.

Author contributions: D.B., S.P., and Z.N. designed research; D.B. and J.N. performed research; D.B., J.N., and M.S. contributed new reagents/analytic tools; D.B. and J.N. analyzed data; D.B., J.N., A.I., S.P., and Z.N. wrote the paper; and A.I. and M.S. recorded data.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1706711114/-/DCSupplemental.

Freely available online through the PNAS open access option.

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