1.1 The cytoskeleton

Amongst a multitude of other functions, the cytoskeletal network, prevalent in almost all eukaryotic cells, provides physical shape and structure to cells, aids in cell growth, and plays a key role in trafficking [1]. Formed from polymerisation of discrete protein sub-units, the cytoskeleton connects to various organelles (including the nucleus) and the plasma membrane. This modular nature of the cytoskeleton allows it to be dynamic, adapting as necessary to environmental changes relayed via a host of signalling processes [2]. Many of the cytoskeletal sub-units have been highly conserved during evolution and are found in most eukaryotic cells, with homologues even present in some prokaryotes [3].

The cytoskeleton is typically divided into three distinct components: microtubules, intermediate filaments and actin [4, 5]. Microtubules, the cytoskeletal component with the widest cross-section at about 25nm in diameter, are hollow tubes consisting of repeated α- and β-tubulin sub-units [6]. In animals and fungi, they play a number of roles including aiding in the formation of flagella or cilia [7], providing structures for material transport, and positioning of the mitotic spindle during cell division [8]. In plants, microtubules retain a role in cell division but also guide cell wall development through their relationship with wall-building enzyme complexes in the plasma membrane [9].

Unlike the globular units of microtubules and actin filaments, intermediate filaments are themselves constructed from filamentous sub-units, and confer strength as well as stress resistance to the cell [10]. Although they are present in almost all mammalian cells, their existence in plants is still hotly debated [11].

Finally, actin filaments, also known as microfilaments, are the narrowest components of the cytoskeleton and are constructed from globular actin sub-units (G-actin) that assemble to form a helical structure 5–7nm in diameter [12]. In combination with myosin motors, actin aids in transport by providing the roads and pathways for cellular cargo [13]. Actin microfilaments are present as both individual filaments and bundled into thicker filaments, and play a key role in plant cell growth and internal transport [14]. It is actin that will be our primary concern here, although the approach we develop is likely to be easily adaptable to other cytoskeletal components.

1.2 Actin in plants

Although actin is present across eukaryotes, there are important differences between kingdoms, not least in plants. The versatility of actin enables it to play a key role in many aspects of plant life, including root tip growth [15] and cell division [16]. The ubiquity of the actin cytoskeleton, alongside the fact it can be constantly remodelled in response to external forces and environmental factors, means that active, directional transport is always available throughout plant cells. This transport is particularly fast in plants, with Golgi speeds reaching up to 7μm s^-1 [17]. To enable these speeds the actin cytoskeleton typically runs mainly parallel to the long axis of an expanded cell, sandwiched between the vacuole and the plasma membrane and perpendicular to the orientation of microtubules [18]. The network consists of two distinct populations: the fine F-actin arrays that undergo rapid and stochastic remodelling with polymerisation rates in A. thaliana hypocotyls reaching 1.7μm s^-1 [19], and the thicker bundles responsible for long-range transport.

The actin cytoskeleton in plants is regulated through a large array of genes and proteins that are coordinated by numerous signalling pathways. External influences on the cell, whether from environmental factors (such as light or temperature) or other organisms (such as pathogens like Blumeria graminis that can attack the cell well through enzymes or physical forces), can stimulate these pathways, triggering adaptations in the actin network to counter the stimulus. Actin plays a key role in the response to pathogen attack, rapidly remodelling itself at the site of the plasma membrane where the pathogen makes contact [20, 21]. F-actin aggregation at the attempted penetration site, which enables cytoplasm accumulation [22], can occur within approximately 20 seconds and can be triggered by small applied forces of only 4μN [23]). Depolymerisation of actin using drug treatments causes the catastrophic failure of this focused penetration defence [24]. Conversely, crop breeders have taken advantage of a mutation named mlo that enhances the actin response in barley to offer increased protection against some types of fungi [25]. Pathogens are under selective pressure to adapt their repertoire of secreted effector proteins to suppress plant defences, including the actin cytoskeleton [26]. Climate change is forcing pathogens to migrate globally and is leading to novel encounters between agricultural cultivars of plant and virulent strains of microbes [27], which adds urgency to the need to understand how plant defences can be enhanced. The ability to detect and measure these changes in actin structure and dynamics will be critical in understanding the defensive systems that plants deploy.

1.3 Properties of actin

Monomers of actin (G-actin) can be assembled into filamentous actin polymers (F-actin), initially through the nucleation of G-actin into a trimer, before additional G-actin units are sequentially added (see Fig 1) [28]. One end of the filament (called the barbed or positive end) has an exposed ATP binding site that is missing from the other end (the pointed or negative end), thus giving the structure an overall polarity [29]. While polymerisation occurs at both ends, the barbed end has a significantly increased rate of assembly. G-actin monomers can also leave both ends, resulting in disassembly. G-actin monomers bound to ATP are more likely to be assembled, shortly after which the ATP is converted to ADP-P_i through nucleotide hydrolysis. After a delay, estimated to be around the order of seconds [30], the P_i is then released, leaving just ADP in the binding site [31]. The various ADP-ATP combinations contained within the nucleated monomers gives an indication of the age of that part of the filament, which can be detected by disassembly machinery such as Actin Depolymerising Factors (ADFs; also known as cofilins) [32]. Filament polarity results in frequent growth at the barbed end and disassembly at the pointed end, known as treadmilling, which allows the structure to be adaptive to changes in conditions and external forces. F-actin can also bundle together, forming thicker and straighter filamentous structures that are more stable and have a longer lifetime. These cross-linking and bundling processes are initiated by proteins such as villin and fimbrin [33].

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Fig 1. Actin network dynamics.

Actin within the cell consists of both single monomers (G-actin) and branched filaments (F-actin). Filaments have an orientation, with a pointed end (-) and a barbed end (+). Polymerisation and disassembly can occur at both ends, but polymerisation typically occurs at a higher rate at the barbed end, while disassembly is more common at the pointed end. A range of proteins and signalling pathways contribute to the turnover of actin monomers, which drives the structure of the actin cytoskeleton and enables a high level of organisation and adaptation. The Arp2/3 complex is involved in filament nucleation and branching, while capping proteins bind to the barbed end to prevent both polymerisation and depolymerisation. Severing proteins such as ADF/cofilin can sever the filament creating an additional barbed and pointed end.

https://doi.org/10.1371/journal.pcbi.1011407.g001

A range of actin binding proteins (ABPs) work in harmony with the cytoskeleton to enable a higher level of organisation (see Fig 1). For example, the actin related protein (ARP) 2/3 complex is an actin nucleator [34, 35], which works alongside formin proteins and other nucleators to aid in the control of the rate and timing of actin assembly and branching [36, 37]. ADF/cofilin and cyclase associated protein (CAP) bind to G-actin and help to regulate the available pool of actin monomers for assembly [38]. Capping proteins bind to the barbed end of F-actin and prevent both assembly and disassembly, thus controlling length and growth. Conversely, severing proteins such as ADF/cofilin and villin sever filaments [39], usually towards the pointed end where the actin is bound to ADP [40] and so shorten the filament whilst creating a new barbed and pointed end.

Profilins are proteins that work in collaboration with plant formins to regulate several aspects of cytoskeletal development and growth. A. thaliana contains five isoforms of profilin, of which AtPRF3 has an atypical N-terminal extension that enhances the affinity for the polyproline region of formin AtFH1. AtPRF3 binding to formin and subsequent oligermerisation has been shown to inhibit AtFH1-mediated actin nucleation. In response to pathogen associated molecular patterns, the transcription of AtPRF3 and protein degradation are altered in order to modulate actin turnover [41]. Furthermore, formin AtFH4/FORMIN4 has been found to interact with AtPRF2 [42]. During plant immune responses to fungi and oomycetes this contributes to cytoskeletal remodelling and ensures the maintenance of the filamentous actin arrays in proximity to sites of attempted penetration site [43, 44].

The numerous types of protein working in concert to keep the cytoskeletal network organised allows it to be adaptive and efficiently restructured as required. ADF [32], profilin [41], formin [44] and the ARP2/3 complex [43] have all been implicated in the changes in structure and dynamics that place the actin cytoskeleton in a defensive poise against microbes. Each will have a subtle input into the behaviour of the actin array and decoding these contributions provides information about the key control points driving defence.

1.4 Analysing the actin network structure

Being able to observe and measure quantitatively the structure of the cytoskeleton is important for understanding wild-type behaviour, mutant phenotypes, the effect of drug treatments, and the cellular response to external stimuli such as pathogen attack. The fact that the cytoskeleton is highly adaptive and versatile, rapidly responding to changes when required, only makes this task more difficult, not least because some small perturbations (such as HopW1 from Pseudomonas syringe [45]) are able to cripple the entire network and, by extension, the cell itself.

Typically, progress in this area requires significant amounts of data. This has become increasingly viable due to the development of genetically encoded probes (e.g. GFP-Lifeact and GFP-Fimbrin) which can be used across a range of imaging modalities to give significant insight into the actin network structure and its turnover. Analysing such large datasets by hand is undesirable for at least three reasons: subconscious bias can skew results, human error is hard to avoid, and the time required can be prohibitive. What is needed instead is a consistent, automatic, reproducible, objective method that can quickly and quantitatively analyse network changes.

The constant remodelling and treadmilling of the actin cytoskeleton poses a problem for any analysis method. Live-cell imaging can be limited by exposure times that lead to motion-blur of highly dynamic features. Cell fixation methods can alleviate this, but only give a single snapshot in time and are prone to artefacts from the fixation process. Modalities ideal for capturing highly dynamic actin networks such as Total Internal Reflection (TIRF) microscopy can be limited in their ability to capture the complete three-dimensional network. This can be better achieved by forms of confocal microscopy, but here too there can be limitations such as poor Z resolution. No imaging system will be able to capture perfectly every detail of the actin network, which makes maximising the information available from current methods a priority. The algorithm we develop here is a step towards achieving this.

1.5 Previous work in this direction

The importance of the cytoskeleton across many areas of cell biology has resulted in significant interest in automatic methods that enable visualisation and extraction of the network. Here we review those that are most relevant to our work here. For a recent review that summarises many of these tools and the different methods they employ, see Özdemir and Reski [46].

Breuer et al. have developed an actin network extraction tool called CytoSeg [47, 48], which leverages a Python backend with GUI implementation in ImageJ. The actin network is described by a weighted graph (i.e. a mathematical network of nodes connected by weighted edges) which builds upon the DeFiNe method [49]. This yields powerful and simple analysis for transport networks, including routing and distances travelled, well-suited for analysis of vesicle and organelle transport. However, one limitation of this approach is that filaments are represented by straight lines, a simplification that can miss key properties of actin networks such as filament curvature. Not knowing the full network shape (with realistic non-straight filaments) can make network analysis more difficult and can miss subtle network changes that are often seen in mutants and drug treatments.

One of the most common methods utilised for cytoskeletal extraction is based on open active contour models [50–52]. These examine changes in the intensity gradient of an image in order to find ridges, which form the backbone of actin filaments. These backbones (often called “snakes”) are defined in terms of the energy of their contour, which is minimised in the gradient field in order to generate the filament segmentation. This process can be computationally expensive depending on the number of iterations required to achieve accuracy, but the results tend to be impressive in terms of accuracy (precision and recall) [53]. Several tools are available which use these models, including imageJ plugins like JFilament [54] and standalone programs such as SOAX [55] and TSOAX [53]. Depending on the implementation, one drawback of these methods is that they often require significant human input to aid in the labelling of filaments and discern crossings. This has to be done separately for each image, which diminishes the utility of automatic methods. The more automated methods, such as SOAX, provide the option for batch processing and therefore require reduced input from start to finish. The number and sensitivity of the input parameters, however, make it difficult to achieve consistently accurate results across a variety of images, cell types and scenarios. While the input parameters can be adjusted on a per-image bases, this may interfere with the validity of any comparisons and could introduce bias into the results.

A complementary approach, based on the molecular mechanisms that govern actin network formation and dynamics, was developed by Schaub et al., and involves simulating the network itself and comparing the output to experimental images to determine the network properties [56]. Comparison between simulation results and experiments required knowledge of the imaging system point spread function, the resolution of the charge-coupled device (CCD), any non-uniform responses from pixels, and the magnification and numerical aperture (NA) of the lens. These methods were able give a good estimate of the underlying network, but only under the assumption that the simulation correctly captures the true underlying network dynamics. At present, with current knowledge of actin biophysics, this may not be the case. Further, fitting a many-parameter simulation to experimental data can both be time consuming and experience problems of model identifiability (where significantly different parameter values lead to similar network structures).

Several approaches have been developed for other imaging modalities, as well as software designed to identify other structures linked to the cytoskeleton. CellArchitect [57] is a tool designed to extract automatically plant microtubule data from large quantities of confocal microscopy data using Gaussian filters and local thresholding to segment the network from the background. From here, two-dimensional measures such as length, density and width can be extracted. SIFNE [58] is a tool designed to extract simple quantitative data (such as filament length and density) from the microtubule array imaged with single-molecule-localisation microscopy. ANNA-PALM [59] is another super-resolution-based tool that can reconstruct microtubule arrays, either via PALM or DNA-PAINT microscopy [60]. BundleTrac [61] and Actin Segmentation [62] both extract the network of actin filaments from Cryo-Electron Tomography images. BundleTrac requires manual input of “seed points” to start filament identificiation, while Actin Segmentation is fully automated with analysis of the resulting networks yielding measurements of filament lengths, orientations and densities. Finally, FIESTA [63] and TipTracker [64] use epifluorescence microscopy to locate microtubules, with the former being shown to also work with TIRF microscopy (as does MTrack [65]).

Segmentation and analysis can be extended to additional biopolymers such as the endoplasmic reticulum. The MATLAB software AnalyzER [66] takes fluorescent labelled ER images from a confocal microscope (up to multi-channel 4D time-series data), enhances the tubular structures and then performs segmentation and skeletonisation. The skeleton is converted to a graph representation with nodes at junctions (containing data such as degree and branch angles) connected by edges (which also described length and average width). This approach was able to quantify the effects on the morphology of the ER under different drug treatments and abiotic stresses.

Depending on the assay, biopolymer of interest and imaging requirements, there are a range of techniques tested and available [67–73]. However, most of these solutions are tailored to specific forms of biological network and research questions, consequently they do not integrate a broad categorisation or quantification of individual network properties.

1.6 Plan of this paper

This paper is organised as follows. We first describe how the DRAGoN (Digital Reconstruction of Actin Global Networks) algorithm was developed and explain the seventeen quantitative measures that are then provided, with further detail provided in S1 Text. We also explain the various validation steps we performed to test and measure algorithm performance.

Next, we apply our algorithm to new data that we have collected from A. thaliana. This includes images of actin in wild-type (Col-0) cells, along with our arp2-1 and formin4/7/8 mutants, both in hypocotyls and in leaves. Further, we consider the effect of powdery mildew infection, which produces a localised response within infected cells.

Finally, we discuss the implications of the significant results that we found, both in the context of understanding the cytoskeleton and future research into plant immunity and food security. We conclude by discussing possible extensions to the algorithm as well as additional routes that could be taken for parameter tuning for various cell types and imaging modalities.

2.1 Algorithm development

Using an initial set of 20 images of GFP-Lifeact [74] labelled actin in wild-type A. thaliana (obtained as described in the Methods), we first developed the DRAGoN algorithm (available at https://github.com/JordanHembrow5/DRAGoN) for automatically extracting the actin skeleton from either a single 2D image or a 3D stack of images. In the case of a 3D stack, we do not attempt here to extract the full three-dimensional network, but rather extract the network in a two-dimensional projection whilst using the full stack information to measure 3D quantities such as branch and filament angles. We decided to base this in MATLAB due to the power of the image processing toolbox. MATLAB also has excellent backwards as well as forwards compatibility, ensuring easy adoption both by users with older versions and by future users with as yet unreleased versions.

Our algorithm follows five sequential steps (see Methods and S1 Text for full details): initial preparation, skeletonisation, image rotation, skeleton labelling and property measuring. We discuss the first four steps here, leaving the last for the next subsection.

For the first image preparation step, the images were filtered to reduce noise and eliminate uneven background illumination. Any filtering process will result in the loss of information, but is necessary to facilitate extraction of the true actin signal. A range of filters and algorithms were tested, each with a range of parameters, in order to determine the most suitable option. Best results were found by using a top-hat filter with a spherical structuring element. A top hat filter subtracts the morphological opening (an erosion followed by a dilation) of the image from the original image. This is similar to the rolling ball background filter in ImageJ, a commonly-used approach to analyse biological images. This aids in noise removal as well as correcting non-uniform illumination. A radius much larger than the width of the thickest filament was found to be suitable (between 2 to 3 times the width), otherwise filament signal may be removed or contrast at the edges may be lost. An additional Gaussian filter was also tested but made little difference, which is not surprising given that the tubular enhancement in the next step involves computing second derivatives using derivatives of Gaussian filters.

The second step was to convert the filtered image to a binary image of the skeletonised network, attempting to keep the filaments without any of the background. Simply applying a threshold to the raw image led to poor results (either struggling with detecting finer filaments or failing to adequately remove noise), so we first enhanced tubular structures using the Frangi vesselness filter, implemented in MATLAB via the fibermetric function (see Fig 2B). This works by calculating the Hessian of the image, determining its eigenvalues and searching for pixels with a small intensity change in one direction and a large change in the other [75]. Pixels satisfying this signify a tubular structure and so have their signal boosted. The default behaviour of this function is to test various filament thicknesses between four and fourteen pixels, in two pixel increments, the benefit of which is removing the need for any additional parameter tuning. Although this function also allows sensitivity of the vessel edge to be tuned, our testing found that this parameter (even an order of magnitude away from its default value) yielded only small changes with little overall improvement.

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Fig 2. Skeletonisation algorithm.

Two parallel pathways are taken from the initial image (A) after background removal and filtering. The image had vessels enhanced (B) before thresholding into a binary image (C) before being skeletonised and rotated (D). Alongside this, the initial image was separately rotated before vessel enhancement (B_rt) and thresholding (C_rt) followed by skeletonisation (D). The skeleton results were combined to ensure no loss of information occurred in the rotation steps. From the combined skeleton, the labelling and relabelling processes were applied (E) to identify each filament and branch for further analysis.

https://doi.org/10.1371/journal.pcbi.1011407.g002

With the desired structures enhanced, we then created a binary image by using a threshold, shown in Fig 2C. We tested both an adaptive and fixed threshold. For the adaptive threshold we used both the MATLAB default neighbourhood of around eighth of the image size as well as smaller sizes. However, this failed to perform any better than a fixed threshold, while being significantly more computationally expensive and requiring an additional parameter. It is possible that by fine tuning the neighbourhood size and the sensitivity, an adaptive threshold will produce an improved binary for some data sets, but this would require specific tuning for each image, something that would compromise comparisons between images. We therefore decided to use a fixed threshold, with the threshold value determined as a specific percentile of the image intensity distribution. We believe this approach reduces the sensitivity of the threshold parameter, enabling it to work better across multiple images and data sets, although it is worth noting that it is still the most sensitive parameter of our algorithm. A threshold intensity of between the 87^th and 92^nd percentile of the resultant image worked well in various scenarios, so we settled on 90% for the parameter value from this point forward. Future work could re-examine this issue and investigate if other approaches, such as Otsu’s method, could lead to improved final results.

Despite filtering and parameter tuning there was still some remaining noise in the binary image. It was possible to remove some of this, before skeletonisation, by deleting objects with an area below some critical value. This critical value strongly depends on the imaging conditions and modality, and so would likely need to be determined independently for each given dataset.

The final part of the second step was the skeletonisation itself. To do this, pixels were removed from the perimeter of all binary objects until removing more would have altered the topology or Euler number (the number of objects in an image minus the number of holes). This yielded a single-pixel-thick line that represents the backbone of the actin network.

The third step involved image rotation. To simplify downstream analysis, images were rotated such that the long axis of the cell (or ROI) was parallel to the horizontal axis of the image. The rotation angle was determined by fitting an ellipse around the image mask and calculating the orientation of its major axis. When rotating discrete pixels, some positional accuracy is inevitably lost. If the rotation is performed before the binary stage, then this can be remedied by using a smoothing algorithm. However, if performed after skeletonisation then, as with a Gaussian filter, this would smooth the edges we have tried to preserve. The best solution we found to this was to implement the rotation step both before and after skeletonisation, and then combine the two outputs via a pixel-wise OR, as shown by the parallel workflows of Fig 2. If after this step any filaments were thicker than one pixel, they were skeletonised again.

The fourth step was to label the skeleton so that individual filaments were identified by distinct positive integers and is shown in Fig 2E. This required significant testing and development in order to eliminate edge cases. The details of each step taken to achieve this are described in detail in S1 Text. In brief, to leverage the flood-fill labelling algorithms in MATLAB, the filaments first had to be broken apart at every branch point so that branching filaments were given a different label ID to the main filament. It was found to be easier to also fragment the main filament in the process, and then rebuild and relabel afterwards. This was achieved by determining the labels around all (now removed) branch points, looking at the angles relative to each other, and rejoining the two that formed the straightest line.

2.2 Quantitative measures

Once the actin skeleton had been extracted and correctly labelled, the fifth and final step involved extracting quantitative measures that described key properties of the network. It is these measures that can be used to characterise the actin cytoskeleton, providing a way of (i) understanding the underlying nature of the network and (ii) comparing different image sets (e.g. across cell types, mutants or drug treatments) in order to determine if there are significant differences. Seventeen types of measure are defined for 3D data and these are summarised in Table 1 and Fig 3, as well as being described in detail in S1 Text. These measures are split into five different categories: whole cell properties, overall network properties, individual filament properties, curvature properties and branching properties, each of which is described below. Additional measures can easily be added if required at a later date.

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Fig 3. Network quantification.

A visualisation of several of the measurements we define to quantify the actin network. The ROI size is measured as the area encompassed by the black line of the outer bounding box and is used in the calculation of densities such as the skeleton and branch point density. The cell orientation is measured as the angle of the bounding box relative to the horizontal axis. The curvature, both the signed filament curvature and the unsigned filament curvature, are averaged over the whole length of each filament and measured via a series of three points separated by a characteristic length scale, λ. The deviation measures the average distance between a filament and a straight line connecting the end points. The filament width is defined for each filament as an average over the filament length. The filament angle, θ_f, is measured relative to the major cell axis and is calculated both as a 2D and 3D (estimated) version. The branch angle, θ_b, is measured at every branch point and measures the deviation of the branch from the main filament; again, there is a 2D and 3D (estimated) version. Finally, the branch ratio is the number of branch points divided by the number of labelled filaments.

https://doi.org/10.1371/journal.pcbi.1011407.g003

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Table 1. Quantitative network measures.

The seventeen quantitative measures that we calculate for each extracted network along with a description of each. Full details are given in S1 Text. N = single number, L = list of numbers.

https://doi.org/10.1371/journal.pcbi.1011407.t001

2.3 Algorithm testing and validation

Although during development testing the output of our algorithm against manual network segmentation gave some confidence that the algorithm can correctly extract the underlying actin network, this testing approach suffers from the problem that the human extraction may itself be faulty or biased. Rectifying this requires knowing the ground truth for a given network. To address this, we generated over 1,300 200x200px artificial images where the locations and shapes of all filaments were known perfectly in advance. Individual filaments were generated by drawing a smoothing spline between two randomly generated points and their midpoint, which was shifted from the middle by a random amount to ensure a curve was formed. In order to accurately represent various filament thicknesses, each image dimension was scaled by a factor of 19, reducing pixel size from 95nm² (the pixel size in our microscopy assay) to 5nm² such that F-actin can be represented by a pixel-thick line. A Gaussian blur was then applied to match the diffraction limit of our of microscopy assay, before the image was downscaled back to 200x200 pixels by taking the mean of each 19x19 block of pixels. To adjust the signal-to-noise ratio (SNR), the filament brightness was scaled to a desired value, then salt and pepper noise added and randomly (via a uniform distribution) scaled up to a maximum parameter value depending on the SNR level that was targeted. Finally, a Gaussian blur matching the diffraction limit was applied to the noise before the image of the filaments and noise were combined, yielding a simulated microscopy image. Several parameters throughout these steps were varied in order to mimic differences in image quality. This allowed us to test the robustness of the network extraction process. For more detail of this process, see S1 Text.

In order to quantify algorithm performance, two metrics were used: sensitivity and precision. These are calculated using the frequencies of true positives (TP), false positives (FP) and false negatives (FN). Sensitivity, also known as the true positive rate (TPR), describes the proportion of the network that is correctly detected and is given by TPR = TP/(TP + FN). Precision, also known as the positive predictive value (PPV), measures the positional accuracy of the identified network and is given by PPV = TP/(TP + FP). These metrics were applied with a tolerance of a single pixel, as our pixel size is approximately half that of the resolution of our microscope. As expected, there is a trade off between sensitivity and precision, which can be adjusted by altering various parameters, particularly the threshold parameter. To put the results of our artificially generated data into context, we manually segmented the real data shown in Fig 2 and compared this to our automated segmentation method, finding a precision of 96% and a sensitivity of 72% (although these values are only indicative due to the difficulties and subjective nature of human segmentation).

First, by adjusting the maximum noise and filament brightness values, the signal-to-noise ratio (SNR) was varied. Because there is randomness associated with the image generation process, a range of SNR values correspond to a parameter set, and scaling between the parameters and the SNR is non-linear. Three different noise levels were generated (each with 100 images), each containing 10 filaments (see Fig 4A). Precision remained at or above 97% across the three SNR levels, while the sensitivity drops from 89% at an SNR average of 7.3 to 86% at an average SNR of 4.3. For the low SNR group the sensitivity drops significantly to 57% for an average SNR of 3.4, highlighting the point of limitation for the algorithm and the data. Although our algorithm was designed to attempt to try to keep both precision and sensitivity as high as possible, it is possible to optimise for one of these by adjusting the binary threshold and/or the minimum filament size as explained below.

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Fig 4. Testing network extraction performance.

Artificially-generated data was analysed with the DRAGoN algorithm and the results compared with the known ground truth. (A) To measure the effect of different signal-to-noise ratios, images were generated with three different levels of signal and noise intensities (100 each), showing that a critical SNR value of at least 4 is required to extract the most from the data in this assay. (B) To measure the effect of network density, images were generated with 5, 10 and 15 filaments (100 images for each), showing increased network density reduces sensitivity. (C) To explore the effect of the threshold parameter, four different threshold values were tested (100 images for each), highlighting the trade off between sensitivity and precision and that the optimal range is 87–92. (D) Finally, to investigate the effect of the numerical aperture (NA) of the lens, images were generated with a range of point-spread functions (100 for each), showing that even with high quality data, a minimum NA of 0.7–0.9 is required to achieve the resolution required.

https://doi.org/10.1371/journal.pcbi.1011407.g004

Second, to test the effect of network density, a range of filament numbers (in a fixed size image) were considered. The noise value was chosen to be around the point where the algorithm performance changes rapidly, so that differences could be seen more easily. As shown in Fig 4B, increased network density leads to a drop in sensitivity while precision remains relatively unchanged. This is because of the high default threshold value, chosen to ensure minimal noise is measured for high quality data. While a reduction in the total number of filaments reduces the chances of filament crossover and close-proximity, it does not remove these possibilities, as can be seen for the precision outliers with only five filaments. A lower network density leads to a reduced network size and therefore any errors will constitute a larger percentage error.

Third, to measure the impact of the algorithm threshold parameter (the most sensitive parameter), this parameter value was varied from its default value of the 90^th percentile of the intensity distribution of the image. The results, shown in Fig 4C, highlight the trade off between sensitivity and precision. A higher threshold ensures greater precision, but at the cost of sensitivity. Conversely, dropping the threshold increases sensitivity, but beyond a point the precision falls and noise begins to adversely effect the output. Depending on the structures of interest, the resolution available and the experimental assay used, this value will need to be adjusted by the user to achieve the desired results.

Finally, to test the effect of the microscopy assay and resolution, the point spread function was varied to mimic various numerical apertures (NA) relevant to confocal microscopy. The results, shown in Fig 4D, were tested using a high signal-to-noise ratio as all other tests were done on the point spread function mimicking the high NA lens setup, allowing the changes purely due to resolution to be clearly seen. For high quality data, we found a critical NA of 0.7–0.9, where the resolution becomes too poor and the sensitivity of the algorithm suddenly decreases. When designing and testing a microscopy assay, it is important to know where this limitation lies in order to ensure the extraction algorithm performs well. This may be particularly important for light-sheet microscopy where NA is limited by the physical configuration of the modality.

For high quality data, the sensitivity only drops when multiple filaments cross or are in close enough proximity that they begin to blur together and the tube-enhancing filter cannot distinguish them. The filaments here are drawn as 5nm thick and then blurred to match the resolution of our microscopy assay. Any filaments that fall within about 200nm of each other are likely to be nearly indistinguishable in accordance with the Rayleigh criterion. This also means that any crossings, even those that are completely perpendicular, are likely to be seen as globular instead of filamentous and may therefore drop below the threshold. In the cases where they do not, the lack of resolution and the skeletonisation process will represent the crossing poorly, typically appearing more as an ‘h’ or ‘x-wing’ shape (see SI for details).

In order to assess algorithm suitability to intermediate filaments and microtubules, we also tested the effect of filament thickness. We used supersampling to create filaments of width 5nm (F-actin), 15nm (intermediate filaments) and 25nm (microtubules) and downscaled to fit a 95nm² pixel size (which matches our microscope assay). No differences were found in the success metrics of our algorithm, as expected for objects significantly smaller than the available resolution. This demonstrates that our algorithm is likely to be easily adaptable to deal with other elements of the cytoskeleton. It is worth noting that one caveat to this analysis is that all tested thicknesses were considered to be single filaments and therefore of identical brightness. Bundles of actin filaments will be brighter than single filaments and this will likely impact measurements of filament thickness. However, we chose to call this parameter ‘thickness’ to remain consistent with previous work that also uses a combination of neighbourhood intensity and filament length [47].

As a final test of our algorithm, we compared untreated Arabidopsis hypocotyl cells with those treated with 150 nM of the actin-disrupting drug Latrunculin B. We used data from https://github.com/jnowak90/CytoSeg2.0/. We were able to identify a number of differences between the treated and untreated cases, with the treated cells having considerably shorter filament lengths, smaller structure sizes, lower skeleton density, smaller branch ratio and lower branch point density. Latrunculin B typically has a dramatic effect on actin organisation, but it is reassuring that DRAGoN is easily able to identify this.

2.4 Application 1: Arabidopsis hypocotyl cells

Wild-type (Col-0) Arabidopsis hypocotyl epidermal cells with GFP-Lifeact were imaged and the actin network extracted as described above (see example images in Fig 5). These were compared to cells with loss-of-function mutations either in Arp2 [76] or in three formin genes (Formins 4, 7 and 8 [44]). These were chosen as they are both mutants of actin filament nucleation regulators with stress-response phenotypes. First, a MANOVA (multivariate analysis of variance) test was used to determine if significant differences existed based on eleven dependent variables (skeleton density, branch point density, 2D filament angle, structure size and number density, filament width, deviation, signed and unsigned curvature, branch ratio and average 3D filament length). Only these eleven measures were used, rather than the full set of seventeen, because the unused measures were either unimportant (cell orientation), used in other measures (ROI size, filament angle from imaging plane), redundant (2D equivalents of the 3D measurements) or unsuitable for this dataset (branching angles are not defined if no branches are detected). The MANOVA test uses a linear combination of the dependent variables to create a single combination variable that is then tested against the genotypes. This showed significant differences between the three genotypes (p < 0.001), although it cannot reveal exactly where these differences lie. Next, to determine the variables most responsible for this significant difference, the Tukey honest squares difference (HSD) post hoc test was used, which identified a number of key differences between the wild-type, arp2–1 and formin4/7/8 plants.

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Fig 5. Arabidopsis hypocotyl cells labelled with GFP-Lifeact.

Three genotypes were tested with the DRAGoN algorithm: the wildtype (Col-0) and the loss-of-function mutants arp2 and formin4/7/8. Scale bar is 5μm.

https://doi.org/10.1371/journal.pcbi.1011407.g005

First, a statistically significant difference was found in the density of cytoskeletal structures (see Fig 6A). While the arp2–1 knockout showed no significant difference to either the wild-type or the formin mutant, the formin4/7/8 mutant displayed a statistically-significantly increased structure density compared to the wild type (p = 0.046), with an average increase in density of 31%. Given that no differences were found in the average size of these structures, this suggests that the formin mutant cells may have more filamentous actin, leading to a higher network density.

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Fig 6. Comparison of the actin network in hypocotyls of the wild type, formin mutant and Arp2 mutant.

Four measures (structure density, skeleton density, average signed curvature and mean actin width) showed significant changes between the wild type and formin4/7/8 triple mutant. One of these (average signed curvature) also showed a significant difference between the wild type and arp2–1 mutant and another (skeleton density) displayed a significant difference between the arp2–1 and formin4/7/8 mutants. Pairwise testing was performed with Tukey HSD after a MANOVA test. Single/double/triple asterisks represents p < 0.05, 0.01, 0.001 respectively.

https://doi.org/10.1371/journal.pcbi.1011407.g006

Second, the skeleton density was also significantly greater in the formin4/7/8 mutant compared to both the wild type (p < 0.001) and the arp2–1 mutant (p = 0.012), while the arp2–1 mutant was similar to the wild type (see Fig 6B). This again suggests a more tightly packed network in formin4/7/8 deficient cells, perhaps due either to increased filamentous actin content or increased cytoplasmic volume per unit cell surface area. A reduction in coupling of the network to the cell membrane is unlikely to significantly reduce the cell surface tension, however, due to its relatively small contribution compared to the internal turgor pressure.

Third, compared to the wild type, the average signed curvature of filaments was increased in both the arp2–1 (p = 0.029) and formin4/7/8 (p = 0.020) knockouts (see Fig 6C). As the Arp2/3 complex and formins are involved in coupling the cytoskeletal network to the membrane, a reduction in coupling could result in a drop in filament tension. It is plausible that this tension creates more linear filaments, so that a reduction in tension would lead to more curved bundles in the mutants.

Finally, the mean width of actin bundles was higher in the formin4/7/8 knockout compared to the wild type (p = 0.0075) whereas no statistical significance was found with the arp2–1 mutant (see Fig 6D). While the difference in thickness is smaller than our pixel size (32nm versus 95nm), this is an average over filaments, which are then averaged over their length, meaning that small differences can be detected. This may not seem surprising given the greater network density measured in formin4/7/8 knockout cells, but some formins have been shown to have a function related to bundling and thicker bundles tend to be present in hyper-elongated cells, whereas the formin4/7/8 mutant phenotype in hypocotyls showed slower elongation and smaller cells. This suggests that these cells may already be adapting in order to try to reduce these deficiencies.

2.5 Application 2: Comparing hypocotyl and leaf cells

We next examined the actin cytoskeleton in epidermal cells across two tissues: hypocotyl and leaves. To do this, all hypocotyl experiments described above were repeated on 4–6-week-old Arabidopsis leaves, their actin networks were extracted and then compared. The MANOVA test was used again, this time with an additional independent variable (cell type). Inclusion of leaf cells rendered the combined tissue genotype less statistically significant (p = 0.056), whereas the cell type itself showed significant differences (p < 0.001). Hypocotyls and leaves have epidermal cells with distinct morphologies and different rates of cell expansion, which may be the dominant reason for differing cytoskeletal characteristics. For example, hypocotyl cells exhibit accelerated directional growth (these cells must rapidly expand and elongate to reach the soil surface in order to have access to light). This rapid growth needs to be supported by the cytoskeleton [18] and therefore a lack of important actin binding proteins may impact this growth rate and result in more exaggerated differences between the genotypes than in the hypocotyl cells.

Given this MANOVA result, the Tukey HSD post-hoc tests were then performed on only the wild-type data in order to minimise any confounding variables. All genotypes are shown in Fig 7 for completeness, which highlights the subtlety of the phenotype in the mutants compared to the significant differences between cell type.

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Fig 7. Effect of cell tissue on actin cytoskeleton.

Four measures showed significant differences between wild-type hypocotyl and leaf cells. Significant differences are only shown between wild-type cells, although similar significance values were found between most genotype pairs. Pairwise testing performed with a Tukey HSD test after a MANOVA test. A double asterisk represents p < 0.01 and a triple asterisk denotes p < 0.001. Error bars show one standard deviation from the mean.

https://doi.org/10.1371/journal.pcbi.1011407.g007

The branch ratio and branch point density, shown in Fig 7A and 7C respectively, were both significantly higher in wild-type leaf cells than hypocotyls (p = 0.0043 and p < 0.001 respectively). The increased branching in leaves may be partly due to the less restrictive nature of the cell shape, allowing the network to form crossover junctions closer to perpendicular angles. This is likely to also be influenced by the large levels of cytoplasmic streaming that are observed in the long, thin hypocotyl cells. This streaming is generated through myosin motors on the actin filaments and bundles. Because the direction of motor assisted transport is defined by the structure of the cytoskeleton, these filaments are mostly aligned in the direction of the cytoplasmic flow [77].

The skeleton density of wild-type leaf cells was lower in leaf cells compared to hypocotyl cells (p = 0.0020), shown in Fig 7B. While the formin4/7/8 knockout was significantly different to the wild type in hypocotyls, the leaf cells appear much more consistent across genotypes. This difference in tissues is again likely down to the different cell shape and size constraints: perhaps more space afforded by wider cells and a smaller vacuole, as well as less reliance on cytoplasmic streaming, reduces the need for such an organised, polarised network in leaves.

Finally, the average deviation of filaments and bundles from linear is significantly different (p < 0.001) between cell types, with greater deviation in leaf cells compared to hypocotyls (see Fig 7D). As with the other differences, this is possibly due to a different set of requirements for the cytoskeletal network due to differences in cell shape and developmental stage. For optimal cytoplasmic streaming in the long and narrow hypocotyls, the actin network needs to be highly parallel to the major cell axis and straight. This is in contrast to the highly irregular shapes of leaf cells, which have a width much closer to their length. The curved cell membrane and cell wall impart significant deviations in the linearity of actin filaments near the cell edges.

2.6 Application 3: Blumeria infections

Wild type, arp2–1 and formin4/7/8 knockout leaves were all infected with Blumeria graminis (Bgh) and imaged at 48 hours post infection. MANOVA testing showed no significant changes due to genotype (p = 0.25), pathogen (p = 0.079), or a combination of the two (p = 0.086). Despite this, it is possible that some combination of measures could still show a significant difference. To test this, a principal component analysis (PCA) was performed, which scales, shifts and combines all variables into an alternative, yet equivalent, set of principal components. The aim of this is to encapsulate as much of the variation in the data as possible using only a subset of the principal components. The variance as a function of the principal component number is shown in Fig 8, with the dotted line showing the mean percentage of variance over all principal components. The first four principal components contribute more than this mean, containing between them 77% of the total variation. By selecting only these four components and performing another MANOVA test, genotype (p = 0.037), pathogen (p = 0.0020) and their combination (p = 0.033) were all significant. Projecting these four principal components back onto our original measures provided very little insight into the contribution of individual measures as five of the eleven measures were weighted almost equally, with the next three contributing only slightly less weight.

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Fig 8. Principal component analysis (PCA) of Blumeria graminis-infected and uninfected leaves.

Shown is the percentage of the variance that is explained by each of the principal components. The dotted line shows the mean percentage of variance over all principal components. The first four components contribute more than or equal to this mean and are therefore kept for future analysis.

https://doi.org/10.1371/journal.pcbi.1011407.g008

Bgh was chosen as a pathogen due to its reported ability to perturb the actin network and direct trafficking during non-host immune responses [22]. Cell wall reinforcement and successful defence have been shown to be dependent upon actin dynamics [78]. These effects are however highly localised and their impact upon the overall properties of the cytoskeleton across the cell is likely to be subtle. However, it is promising that, despite this, our algorithm is still able to identify significant differences between infected and non-infected cells (albeit without allocating these to specific descriptors). With a larger sample size or higher resolution images, a better understanding of the filamentous actin around the infection site would likely be achievable by using our algorithm at the sub-cellular level to compare local network properties.

4.1 Image analysis algorithm

We break our network extraction algorithm into a number of sequential stages—initial steps, skeletonisation, image rotation, skeleton labelling and measuring properties—which we discuss in turn. Prior to these steps, a region of interest (ROI) needs to be drawn manually, creating a mask that is then used for several of the downstream analysis methods. For full details of our method, see S1 Text.

4.2 Plant and pathogen growth

4.3 Imaging methods

Images were taken with a spinning disc confocal microscope, equipped with a 60x lens and NA of 1.35. A laser power of 7mW at a wavelength 488nm was used for imaging GFP-Lifeact. Images were taken with 200ms exposure and z-stacks had a separation of 0.55μm. Entire hypocotyls were mounted while 5x5mm squares of leaf were cut, away from the central vascular tissue, in order to keep everything as flat as possible.