Tissue morphogenesis is a complex, multi-scale process that ultimately results in an organ or tissue of a specific size and shape and characteristic 3D cellular architecture. Advances in imaging increasingly allow generation of 3D digital organs with cellular resolution, which are useful tools for unraveling the integration and feedback processes between molecular regulatory circuits and the cellular architecture of developing tissues and organs. Plants are excellent systems for generating 3D digital organs because their cells are immobile and the cellular architecture of plant organs can be easily observed using various types of microscopy.

Over the years, and partly through the application of artificial intelligence, powerful open-source software packages have been developed for 3D cell segmentation of confocal microscopy images (Barbier de Reuille et al., 2015; Eschweiler et al., 2019; Fernandez et al., 2010; Schmidt et al., 2014; Sommer et al., 2011; Stegmaier et al., 2016) . Machine learning based software, including CellPose, PlantSeg and StarDist, represents a recent advance in this area, providing improved 3D segmentation of tissues at cellular resolution (Eschweiler et al., 2019; Stringer et al., 2021; Weigert et al., 2020; Wolny et al., 2020) . The output of such pipelines can then be quantitatively analyzed in image analysis software like MorphoGraphX (Barbier de Reuille et al., 2015; Strauss et al., 2022) . The advances in these computational resources have enabled the generation of a number of digital 3D models of a variety of plant organs, which have allowed single-cell analysis in 3D and have been instrumental in gaining fundamental insights into various processes in plants, including embryo, root, and ovule development (Bassel et al., 2014; Fridman et al., 2021; Graeff et al., 2021; Hernandez-Lagana et al., 2021; Lora et al., 2017; Montenegro-Johnson et al., 2015; 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107

Ouedraogo et al., 2023; Pasternak et al., 2017; Schmidt et al., 2014; Vijayan et al., 2021; Yoshida et al., 2014).

An important feature that is presently missing from these 3D digital models is the integration of the size and shape of the nuclei into the cellular framework. The ability to not only robustly segment nuclei in 3D, even in deeper tissues, but also to link the 3D architectures of nuclei and their surrounding cells in a tissue-specific context enables the study of central biological processes such as nuclear size control (Cantwell and Nurse, 2019c) . Another key process is the control of gene expression. Spatial gene expression patterns as well as expression levels can be assessed with cellular resolution, for example, using ratiometric nuclear reporters driven by genespecific promoters (Federici et al., 2012).

ClearSee-based protocols for cleared whole-mount preparations of plant organs allow staining of cell walls and nuclei with various cytological dyes without the need for transgenic plants carrying the appropriate reporter constructs and maintain compatibility with reporters based on fluorescent proteins (Kurihara et al., 2015; Musielak et al., 2015; Tofanelli et al., 2019; Ursache et al., 2018). The establishment of the 3D digital reference atlas of Arabidopsis ovule development represents a recent example that used this approach (Vijayan et al., 2021). During the preparation of the atlas, ovules were fixed and cleared with ClearSee (Kurihara et al., 2015). Cell outlines were stained with the cell wall stain SCRI Renaissance (SR2200) (Harris et al., 2002; Musielak et al., 2015), while the nuclei were stained with TO-PRO-3 (Bink et al., 2001; Van Hooijdonk et al., 1994). The digital ovule atlas provided detailed insight into the 3D cellular architecture of the ovule but lacked information on the size and shape of the nuclei. TO-PRO-3 stains double-stranded nucleic acids and can therefore be a useful tool for 3D volumetric nuclear extraction. However, the signal 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 intensity of any typical nuclear stain can exhibit variable intensities, scatter, and photobleaching when imaging deeper tissue layers, rendering accurate 3D nuclear segmentation extremely difficult.

Therefore, our overall goal is to accurately segment plant nuclei in 3D images with weakly stained nuclei. Several deep learning-based segmentation algorithms have recently been proposed for this task: PlantSeg (Wolny et al., 2020), Cellpose (Stringer et al., 2021) , and StarDist (Weigert et al., 2020). However, none of them can be used out of the box. PlantSeg and CellPose pre-trained models have not been exposed to weakly stained plant nuclei while 3D StarDist does not provide trained models and requires retraining. The main bottleneck for model training is the lack of publicly available 3D ground truth with correctly delineated nuclei. This step is famously labor-intensive even for high-contrast, high signal-to-noise ratio (SNR) image volumes.

In this study, we combine different staining strategies to quickly achieve 3D segmentation ground truth for model training. Together with human-in-the-loop correction, we use this approach to acquire fully annotated volumes of weakly stained nuclei. On this basis, we train highly accurate segmentation networks, which we show to be generalizable to other datasets obtained by various imaging methods and from a variety of plant and animal tissues labeled with different staining methods. In addition, we introduce a combination of processes in MorphoGraphX that associates each nucleus with the cell in which it resides, and that provides the nucleus with the cells' respective tissue labels. It allows the investigation of various cell-nucleus relationships, such as the nucleus-to-cell volume (N/C) ratio. We demonstrate the

general value and broad applicability of these technical advances in proof-of-concept 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 analyses.

training A novel iterative approach to ground truth generation and 3D nuclear model In a first attempt at 3D nuclear segmentation of TO-PRO-3-stained ovule nuclei in 3D image stacks, we found that the available plant nuclei segmentation model in PlantSeg did not yield segmented nuclei of sufficient quality for ground truth generation. Thus, we employed Cellpose (Pachitariu and Stringer, 2022; Stringer et al., 2021) as it had an existing nuclei model used for 3D nuclear segmentation. However, we still observed improper segmentation with errors in detecting and separating nuclear borders (Fig. 1A-D). This is probably due to the TO-PRO-3 nuclear staining being variable and often quite weak and diffuse, particularly in deeper layers. In addition, the signal was absent in the nucleolus, resulting in an uneven nuclear surface and segmentation that looked like a hole extruded from the nuclear surface (Fig. 1C). To address these issues, we developed a novel strategy based on samples that simultaneously show strong and faint signals in the nuclei that can be collected in separate channels. We first generated a transgenic line expressing a translational fusion of the fluorescent protein tdTomato to histone H2B driven by the UBIQUITIN10 (UBQ) promoter (pUBQ::H2B:tdTomato). Ovules of this reporter line were fixed, cleared, and stained with the cell wall stain SR2200 and the nuclear stain TO-PRO-3. Ovules were imaged and the SR2200, TO-PRO-3, and H2B:tdTomato signals were collected in three separate channels (Fig. 1F,G,I). The broadly expressing 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 nuclear pUBQ::H2B:tdTomato reporter provided a strong and uniform nuclear signal that could be segmented into nuclei using the standard Cellpose nuclear model (Fig. 1D,E,G,H). We then used the results of human proofread instance nuclear segmentation of the strong H2B:tdTomato reporter channel as the “initial ground truth” for training three sets of initial 3D models: PlantSeg_3Dnuc_initial, StarDistResNet_3Dnuc_initial, and Cellpose-Finetune-nuclei_3Dnuc_initial. The PlantSeg and StarDist initial models were trained on the weak TO-PRO-3 nuclear stain channel using the neural networks implemented in the respective pipelines. The Cellpose initial models were trained on the TO-PRO-3 channel by fine-tuning the pretrained Cellpose “nuclei'' model. The segmentation results using the initial models turned out to be still imperfect and required several corrections by an expert.

To obtain further model improvements we applied an iterative training strategy (Fig. 1J). We used the StarDist-ResNet_3Dnuc_initial model to segment the original weak TO-PRO-3-based nuclear stain channel as it provided the best qualitative results, resulting in a modified ground truth. This modified ground truth was then human proofread, resulting in the “gold ground truth”. In a next step, the "gold ground truth" and the original weak TO-PRO-3-based nuclei stain were used to train six sets of 3D “gold models'' using one or multiple neural networks implemented in PlantSeg, Cellpose, and StarDist (Table 2), probing for the best parameter settings. We tested how much model performance improved when human-in-the-loop (HITL) was involved, i.e., initial vs gold model. To this end we employed a quantitative comparison of initial and gold PlantSeg, StarDist-ResNet and Cellpose-Finetunenuclei models. We made use of the imperfect initial models to generate modified and better ground truth by involving a HITL proofreading before using them for the 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 training that resulted in the “gold models''. (Fig. 1J). The detailed description of model training including the datasets used for training and testing are provided in the “Model training and score quantification” section of Materials and Methods. Comparison of model performance between initial and gold PlantSeg, Cellpose-Finetune-nuclei and StarDist-ResNet models was performed by 5-fold average precision (AP) score quantification (Table 1). Results indicate that all methods demonstrate increased performance after gold training. PlantSeg and StarDist-ResNet gold models turned out to be superior to the Cellpose-Finetune-nuclei gold models and demonstrated high precision segmentation compared to the respective initial models.

We present a collection of computational tools and datasets that extend the capabilities for quantitative analysis of 3D digital organs. We have developed a deeplearning based computational toolkit for 3D nuclear segmentation that enables accurate 3D segmentation of nuclei in a variety of 3D digital organs labeled with a range of nuclear markers or stains, even in faintly stained and noisy images. Importantly, we not only provide a valuable plant nuclear dataset for training 3D nuclear segmentation algorithms but also two accurate platinum models for 3D nuclear segmentation with broad applicability. In addition, we outline novel and processes that we have added to MorphoGraphX to enable the analysis of various cellnucleus geometric parameters in 3D, including the N/C ratio. Finally, we have created a proofreading script that significantly improves the fidelity of 3D cell segmentation. All tools are open source and readily available to the community via public software repositories.

A particular value of the 3D nuclear segmentation toolkit lies in its broad applicability. The method can be successfully used with various nuclear staining 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 methods, ranging from different nuclear stains with variable staining intensities, such as TO-PRO-3 or DAPI, to nuclear reporters based on fluorescent reporters. In addition, nuclei can be segmented in data sets obtained from cleared or live tissue, not only from a range of different plant tissues, but also from animal tissues such as mouse embryos. An optimized workflow from imaging to 3D segmentation of nuclei dataset can be found in the Materials and Methods section.

We used PlantSeg (Wolny et al., 2020), Cellpose (Stringer et al., 2021) and StarDist (Schmidt et al., 2018; Weigert et al., 2020) as three strong baselines for 3D nuclear segmentation and performed a comparative analysis of the performance of the models obtained from each platform. Cellpose was the only tool that provided a pre-trained model which could perform the initial segmentation. However, in the presence of ground truth, it was demonstrated to be less stable, with more variability in the results depending on the training/test split of the data. Re-trained PlantSeg and StarDist both demonstrated excellent, stable performance. The advantage of PlantSeg is its ability to also perform cell segmentation from membrane staining and the general absence of explicit star-convexity prior which can be harmful for segmentation of irregular nuclei. However, in very noisy conditions StarDist is preferred as the shape prior helps it overcome the low SNR. It also needs to be noted that our ground truth annotations are produced through iterative improvement using a StarDist model, so the resulting shapes might be biased towards being more regular and star-convex. An important feature of MorphoGraphX is the projection of secondary signals onto the cell surfaces, which enables the quantification of nuclei, cell wall or cytoplasmic signal intensities based on the cellular segmentation (Barbier de Reuille et al., 2015; Montenegro-Johnson et al., 2015). What up to now was missing, however, was the integration of the size and shape of the nuclei into the cellular framework. We present 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 process identifies the cells in which nuclei are located. It is run on the active 3D cell mesh in MorphoGraphX mesh 1, while the 3D nuclei mesh is loaded in the MorphoGraphX Mesh 2. The process assigns cell IDs as “parents” annotation to the nuclei labels, thereby linking cells IDs to nuclei IDs. On the 3D nuclei mesh (active), the “Mesh/Lineage tracking/Save parents” process was used to save the nuclei IDs and their corresponding parent cell IDs in a csv file, followed by the “Mesh/Lineage tracking/Copy parents to labels” process to rewrite the nuclei labels IDs to that of cells. These processes in combination with “Mesh/Heat map” and “Mesh/Heat map/Operators/Export heat to Attr Map” processes were used to generate csv files containing cell IDs, their corresponding nuclei IDs, parent (tissue) labels, and cell and nuclei geometric attributes.

Further, we created a process (“Mesh/Nucleus/Select Duplicated Nuclei”) to detect and automatically select nuclei in cells where multiple nuclei were detected. This process was used to detect segmentation errors. Another process (”Mesh/Nucleus/Distance Nuclei”) was implemented to quantify the Euclidean distance between cell centroids and nuclei centroids. We also included a process (“Mesh/Nucleus/Label Nuclei Surface”) to associate 3D segmented nuclei IDs with the cells of curved surface meshes. All these processes are documented within MorphoGraphX (Help/Process Docs). Specific application and minimal guide on the process can be viewed by hovering the mouse over the process.

We acknowledge support by EMBL IT Services and the Center for Advanced Light Microscopy (CALM) of the TUM School of Life Sciences.

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Figures and figure legends

Fig. 1. 3D dataset for model training. (A) 2D section view of TO-PRO-3-stained nuclei in Arabidopsis ovules. (B) 3D nuclear segmentation of weak nuclei stain performed using Cellpose nuclei model. (C) A zoomed-in view displaying the erroneous segmentation. Typical segmentation errors in the nuclei stains segmentation resulting in improper size, shape and number of nuclei. (D) Fluorescent nuclei reporter H2B: tdTomato raw image. (E) 3D Cellpose nuclei model segmentation of the bright tdTomato nuclei fluorescence. (F-I) 2D section view from one of the five training dataset. (F) Weak nuclei channel (TO-PRO-3-stained) used for training. (G) Strong nuclei channel (nuclei reporter H2B: tdTomato) used for generating ground truths. (H) Initial ground truth used for training initial model. 3D nuclear segmentation of the strong nuclei channel performed using the Cellpose nuclei model. (I) Raw cell wall stain, PlantSeg cell boundary predictions and cell segmentation available with the training dataset (from left to right) (J) Illustration of model training strategy. Scale bars: 5µm (A-E); 20 µm (F-I). models. Qualitative comparison displaying the Arabidopsis ovule testing dataset 1135 (N5 dataset) with trained model (Model-5) using four other training datasets. (A) 3D view of ground truth nuclear segmentation. (B) Zoomed 2D section view of raw weak

TO-PRO-3 iodide nuclei stain. (C) Ground truth nuclear segmentation corresponding to the zoomed view in (B). (D-E) PlantSeg predictions and segmentation using the proposed PlantSeg model. (D) 3D PlantSeg GASP segmentation performed using the proposed PlantSeg model. (E) View corresponding to (B) showing PlantSeg nuclei predictions. Top panel: PlantSeg nuclei center predictions. Bottom panel: PlantSeg nuclei envelope prediction from raw data. (F) PlantSeg GASP segmentation of the corresponding section in (B). (G-I) StarDist ResNet nuclei predictions and segmentation using the proposed ResNet model. (G) StarDist ResNet 3D nuclear segmentation performed using the proposed StarDist model. (H) View corresponding to (B) showing StarDist ResNet nuclei predictions. (I) StarDist ResNet nuclear segmentation of the corresponding section in (B). (J-L) StarDist UNet nuclei predictions and segmentation using the proposed UNet model. (J) StarDist UNet 3D nuclear segmentation performed using the proposed StarDist model. (K) View corresponding to (B) showing StarDist UNet nuclei predictions. (I) StarDist UNet nuclear segmentation of the corresponding section in (B). Scale bars: 10μm.

Fig. 3. Wide applicability of trained nuclei segmentation models in segmenting stained or nuclear reporter-expressing different plant organ nuclei imaged under different conditions. (A-C) Antirrhinum majus ovule nuclei stained with TO-PRO-3 iodide, (D-F) Arabidopsis thaliana ovule nuclei stained with DAPI, (G-I) Arabidopsis sepal nuclei expressing the pATML1::mCitrine-ATML1 reporter, (J-L) Cardamine hirsuta leaf nuclei expressing the pChCUC2g::Venus reporter, (M-O) Mouse embryo nuclei expressing the H2B-miRFP720 reporter. (A,D,G,J,M) 3D confocal images of raw nuclei stained with a nuclear stain or expressing nuclear reporter. Raw images have been adjusted for brightness and contrast for depiction. (B,E,H,K,N) 3D nuclear segmented stacks, segmented using the StarDist-ResNet model generated from this study. Nuclei IDs are represented in different colors. (C,F,I,L,O) Overlay of 3D segmented stack with the corresponding MorphoGraphX-generated 3D nuclear mesh. (A-O) Insets with white outline show the zoomed-in view of 3D nuclei. Scale Bars: 10 μm (organs) and 5 μm (insets).

Fig. 4. MorphoGraphX as a platform for mapping 3D nuclei to whole organ cell atlas at single cell and tissue resolution. (A-H) Stage 3-II 3D cell and nuclei meshes for the same ovule sample generated from corresponding segmented stacks. (A) Midsagittal section of 3D mesh showing cell IDs in different colors. (B) Mid-sagittal section of 3D mesh showing cell parent (tissue) labels. (C) Cell-type labeled 3D mesh overlaid with nuclei mesh showing nuclei IDs in different colors. (D) Cell-type labeled 3D mesh overlaid with nuclei mesh showing nuclei lacking parent labels. (E) Cropped section of 3D mesh showing that initially cell IDs are initially independent of nuclei IDs (cells and their corresponding nuclei in different colors). (F) Cropped section and (G) mid-sagittal section of 3D mesh showing cell IDs mapped onto their corresponding nuclei using MorphoGraphX processes, resulting in the same color for cells and their corresponding nuclei. (H) In the final step parent tissue labels of cells are mapped onto the corresponding nuclei in MorphoGraphX. (I) Plot showing N/C ratio of the radial layers, L1, L2, and L3 of stage 2-I ovule primordia. (J-L) Plots showing correlation between nuclear and cell volumes in different layers of stage 2-I primordia along with the respective Pearson correlation coefficients, r. (J) L1, (K) L2, (L) L3. (M) Plot showing nuclear to cell volume ratio (N/C) of different tissues and tissue layers of stage 3-II ovules. (N) Plot showing N/C ratio of the outer layer of the inner integument (ii2) for different stages of ovule development from 2-IV up to 3-V. Asterisks represent statistical significance (ns, p≥0.5; *, p<0.05; **, p<0.01, ***, p<0.001; ****, p<0.0001; Student’s t-test). Scale bars: 10 μm.

Fig. 5. PlantSeg proofreading tools to correct 3D cell segmentation errors. (A-D) Mid-sagittal section Arabidopsis thaliana ovule primordium (dataset 598A, (Vijayan et al., 2021)). (E-H) Cropped section of an Arabidopsis thaliana 3-II ovule (dataset 527, (Vijayan et al., 2021)). (I-L) Mid-sagittal section of a Cardamine parviflora ovule primordium (dataset 1598B, Mody et al., 2023). (A,E,I) 3D cell boundary predictions along with insets showing raw SR2200 (white) and TO-PRO-3 channel (magenta) signals after adjusting for brightness and contrast to show the weak cell wall staining in specific regions (outlined in orange boxes) and resulting in missing or incomplete walls in the cell boundary predictions. (B,F,J) Plant-seg cell segmentations overlaid with cell boundary prediction. Black arrows point to undersegmented cells. (C,G,K) StarDist-segmented nuclei overlaid with cell boundary prediction, showing multiple nuclei in the undersegmented cells in the MMC region (B,J) and in cells of funiculus and chalaza (F). (D,H,L) 3D cell segmentations corrected with PlantSeg proofreading tools (black arrows) and overlaid with the cell boundary prediction. Cardamine parviflora ovule primordia are crassinucellate (K,L); the ability to visualize this is lost after cell segmentation (I,J). PlantSeg proofreading tools enable re-distinguishing the primary parietal cell from the MMC. Scale Bars: 10 μm. 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 human in the loop to train a gold model.

Segmentation of the test dataset was performed using each of the listed initial and gold models and the mean average precision is scored for different methods compared to gold ground truth.

Trained from scratch 51.26% ± 13.75% Segmentation of the test dataset was performed using each of the listed methods and the mean average precision is scored for different methods compared to a human proofread ground truth. The configuration files used for training can be found along 1063 1064 1065 pFD:3xHAmCHERRY-FD pChCUC2g::Ven us