GeoV: An Open-Source Software Package for Quantitative Image Analysis of 3D Vesicle Morphologies

Bottom‐up synthetic biology has reconstituted processes like adhesion, cortex formation, or division of giant lipid vesicles (GUVs), which all rely on changes in the vesicle morphology. However, oftentimes, GUV morphologies and shape transitions are described qualitatively, which makes it difficult to quantitatively compare results from different studies and to advance precision engineering. Herein, open‐source software package GeoV for the 3D reconstruction and analysis of GUV shapes from confocal microscopy z‐stacks is presented. The accuracy of the reconstruction by comparing the output for the Hausdorff distance of the surface, the curvature, and the bending energy to ground truth data for simulated shapes of different complexities is quantified. Next, GeoV on a variety of confocal microscopy datasets, including z‐stacks from spherical GUVs and GUVs deformed with DNA origami, adherent GUVs, DNA droplets, and cells, is tested. Additionally, the effect of membrane‐binding DNA origami on the vesicle shape, volume, and bending energy is quantified. It is found that osmotic deflation and attachment of DNA origami can increase the bending energy of GUVs by a factor of 10. All in all, GeoV as an open‐source software package for the quantitative analysis of confocal microscopy data for bottom‐up synthetic biology is provided.


Introduction
The adaptation of three-dimensional (3D) cellular morphology plays an important role for many fundamental biological processes such as cell division or cell migration.[16][17][18][19] This led to the realization of several important function such as GUV adhesion, [20][21][22][23] division, [24,25] or morphogenesis. [26]In particular, for relatively easy systems like these with only few components a quantitative analysis of the resulting shapes can provide important information to guide precision engineering.Comparability of these results requires standardized methods for data analysis.Thus far, GUV shapes have oftentimes been described qualitatively or by analyzing 2D images.
The recently published open-source software "DisGUVery" provides a useful tool for the detection and analysis of GUVs in 2D. [27]However, the synthetic biology community is currently lacking an integrated workflow that enables the routine analysis of GUV morphologies in 3D.Since the most common techniques for GUV visualization are confocal microscopy methods that provide 2D slices of the 3D object such a workflow would need to be able to reconstruct the 3D shape from 2D images.Shelton et al. provided a tool for the 3D reconstruction and analysis of microscopy images of fluorescently labeled oil droplets. [28]This tool works well for the analysis of sphere-like objects, however, has not been optimized and runs into errors for more complex shapes, which can often be observed for GUVs. [5,29]Here we want to provide a tool for the 3D shape reconstruction and quantitative analysis based on fluorescent confocal microscopy z-stacks.Our opensource software package "GeoV" has been developed to vizualize the shape and compute important parameters such as area, volume, curvature, and bending energy of GUVs.It can also be applied to other types of datasets such as confocal microcopy images of cells.

Analysis Workflow with GeoV
In order to obtain 3D meshes that allow for quantitative analysis of confocal microscopy z-stacks, multiple steps have to be implemented.Figure 1 displays the workflow for the surface reconstruction process carried out by our software package GeoV (see Table S1, Supporting Information).First, a confocal z-stack has to be recorded of the object of interest, which is used as an input for GeoV (Step 1). Figure S1, Supporting Information, displays the userinterface of GeoV.GeoV can handle multiple file formats used in confocal microscopy (currently ".czi", ".tiff", and ".lif").GeoV now converts the confocal z-stack into a point cloud (Step 2).Most surface reconstruction algorithms require an oriented point cloud of the surface as an input, i.e., a set of points with their respective surface normals. [30,31]However, confocal microscopy provides only multiple gray scale images as an output.Thus, GeoV converts the confocal z-stack to a point cloud by thresholding the images.Further prepocessing steps have been included as an optional feature in order to reduce noise or remove signal which does not originate from the surface of interest (e.g., lipid dirt in the background).Once the point cloud of the surface of the object is obtained, the corresponding surface normals are calculated (Step 3).For this purpose, we implemented an algorithm for the estimation of the surface normals from the pymeshlab library. [32]Since the sign of the resulting normals is ambiguous, we use one or more reference points to orientate the surface normals accordingly, pointing toward the outside of the object surface.Once the data from the confocal z-stack have been converted into an oriented point cloud, a 3D triangulated mesh of the object is generated (Step 4).This is done by the user's choice of one of several implemented algorithms, namely screened poisson, [31] ball pivoting, [30] and APSS marching cubes [33,34] surface reconstruction.The final step of our workflow is the on-demand calculation of essential physical properties such as volume, total surface area, local curvatures, or, in particular for GUVs, the bending energy of the surface for quantitative analysis of the objects shape (Step 5).In this way, GeoV serves as a simple to use open-source software package that integrates multiple steps in the analysis of confocal stacks and enables quantitative and comparable data analysis for the bottom-up synthetic biology community.

Accuracy of the Reconstruction
Next, we set out to quantitatively test the accuracy of GeoV by quantifying the error of the 3D reconstruction.For this purpose, we generated 3D meshes of GUV shapes as a ground truth.In particular, we computer-generated a discocyte-shaped GUV.From this idealized test image, we simulated confocal z-stacks using a previously published MATLAB code for confocal z-stack simulations. [35]Subsequently, the simulated z-stacks were used to reconstruct the 3D meshes with GeoV.We then compared the resulting 3D mesh with the original ground truth mesh as illustrated in Figure 2a.To evaluate the accuracy of GeoV, we compared the spatial position, the local curvatures, and the total bending energy of the reconstructed 3D mesh to the ground truth 3D mesh.For the spatial accuracy, we calculated the minimal distance of each vertex of the ground truth 3D mesh to the reconstructed mesh.Figure 2b displays the average distance of all vertices for different effective sizes of the initial 3D mesh.To compute z-stacks corresponding to different object sizes d 0 , the point spread function (PSF) used for the confocal z-stack simulations was adapted accordingly (see Materials and Methods and Figure S2, Supporting Information).For object sizes of around 23 μm or larger, the average spatial displacement is less than 1% of the object size.For smaller objects, the average spatial deviation increases and lays at around 2.5% for an object size of 11 μm.These small deviations confirm that GeoV faithfully reconstructs 3D objects in the size of typical GUVs and cells.This can also be seen in Figure S3, Supporting Information, which shows a representative comparison of a slice of the reconstructed mesh with the original confocal fluorescence image.
Since the purpose of GeoV goes beyond optical visualization of the recorded z-stack but also allows for quantitative analysis of physical properties, it is important to estimate the accuracy of the latter.Therefore, we furthermore compared the local mean curvatures and the total bending energy of the reconstructed meshes to those of the original mesh.Figure 2c shows the average deviation of the curvature of the reconstructed mesh to the curvature of the original mesh.In order to avoid potential division by zero, the deviation of the curvatures was normalized by the curvature of a sphere with the same surface area instead of the curvature of the original mesh.Similar to the spatial deviation, the deviation of the curvature is quite low (less than 5% deviation compared to Figure 1.Illustration of the GeoV software package and its main steps for the 3D surface reconstruction of GUVs.First, the raw or preprocessed z-stack is binarized to obtain a 3D point cloud.Subsequently, the binarized point cloud is used to calculate the surface normals from which, ultimately, the surface can be reconstructed.The output is a 3D mesh which allows for the calculation of essential physical properties, such as volume, surface area, local curvatures, or bending energy. the curvature of a sphere with radius r 0 ) for object sizes larger than 11 μm, while it increases by a factor of around 5 for small objects.Nevertheless, also for small objects, GeoV gives a good curvature estimate in the correct order of magnitude.From the curvature, GeoV calculates the total bending energies , with C 0 the spontaneous curvature and k the bending rigidity of the reconstructed meshes and compare them to the bending energy E b;orig ¼ 47.5κ of the original mesh (Figure 2d). [5]Here, we assumed the spontaneous curvature to be zero for all cases.For all object sizes, the calculated bending energy matches very well with E b,orig , with a maximal deviation of 2.5%. Figure S4, Supporting Information, furthermore, shows the comparison of the total surface area and volume of the reconstructed meshes with the original mesh, which are in good agreement.Hence, GeoV can extract physical properties such as the area, volume, local curvature, and bending energy of GUVs and similar objects in a reliable and quantitative manner.
In addition to the relatively simple, however, relevant example of a discocyte-shaped GUV, we also tested how GeoV performs for more general shapes.We used the Stanford bunny taken from the Stanford University Computer Graphics Laboratory as a more complex and feature-rich ground truth object (see Figure 2e).As before, we test the spatial accuracy (Figure 2f ), the accuracy of the local curvature (Figure 2g), as well as the total bending energy (Figure 2h) for the Stanford bunny.In general, the reconstruction of the Stanford bunny worked well for different sizes.For an object size of 11 μm, the scale of the features approaches the optical resolution limit of typical confocal z-stacks, which we also assumed for our simulation.In fact, the length scale of the fine features of the bunny is smaller compared to the z-spacing of the simulated z-stacks (which were chosen to be 0.5 μm to resemble realistic experimental settings).In such a regime, a faithful reconstruction cannot be expected.For larger object sizes, the spatial error is comparable to the spatial error of the discocyte-shaped GUV with an average deviation of below 1% of the object size.A clear difference to the results of the discocyte-shaped GUV can be seen, however, in the deviations of the local curvature where the deviation of the Standford bunny is significantly higher compared to the discocyte-shaped GUV.This increase can most likely be explained by the larger number of small-scale features with comparatively higher curvatures.We obtain a bending energy of the reconstructed meshes of E b;rec ¼ 575κ, which agrees well with the bending energy of the original meshe (E b;orig ¼ 585.6κ) for the 230 μm object as well as for other object sizes (see Figure 2h).Only for the bunny with a size of 23 μm, the bending energy of the reconstructed mesh deviates quite strongly with 25% from the bending energy of the original mesh.Most likely the highly curved small-scale features were too small compared to the z-spacing of the z-stack and could therefor not be reconstructed correctly.This in turn leads to an underestimation of the total bending energy.Our simulated test datasets show that GeoV can be used to reliably reconstruct objects from z-stacks with a small spatial error, whereby the reconstruction is limited by the optical resolution of the z-stack.Therefore, small feature-rich objects have to be imaged at highest resolution to ensure faithful reconstruction.Furthermore, relevant physical properties can be determined from the resulting meshes which agree well with the physical properties of the original mesh.

Multiple Viewpoints for Improved Reconstruction
In addition to the resolution of the acquired confocal z-stack, another important criteria for a successful surface reconstruction is the knowledge about the orientation of the surface normals of the point cloud.Since confocal microscopy does not provide this kind of information, surface normals have to be estimated.For this purpose, we implemented the algorithm from the pymeshlab library to calculate the surface normals. [32]This provides a good estimate for the orientation of the normals; however, their sign is ambiguous.Alternating directions of the normals can lead to artefacts in the reconstructed surface.To solve this problem, we implemented the possibility to choose a reference point or view point with respect to which the sign of the normals can be determined.For simple shapes like the discocyte-shaped GUV, a single viewpoint is sufficient to calculate the orientation of all normals correctly.However, for more complex objects like the Stanford bunny, a single viewpoint is not sufficient to determine the orientation of all normals correctly.In order to make GeoV as broadly applicable as possible also for complex shapes, we implemented the possibility to use multiple viewpoints operating onto all data points within a defined volume.Figure 3a displays the work flow and the resulting surface for the reconstruction with and without multiple viewpoints for the Stanford bunny.In particular, more complex structures such as the bunny's ear can lead to false orientations of the normals and thus to artefacts in the reconstructed surface.To quantify the difference of both methods, we analyzed the spatial accuracy (Figure 3b) and the accuracy of physical properties such as the local curvature (Figure 3c) and the total bending energy (Figure 3d) as before.For both the spatial accuracy and the accuracy of the local curvature, the average deviation from the ground truth is smaller by a factor of about 1.5 for the case with multiple viewpoints.Also the total bending energy of the reconstructed mesh with multiple viewpoints is much closer to that of the original mesh compared to the reconstructed mesh with a single viewpoint.This showcases the importance of using multiple viewpoints for the correct estimation of the surface normals as provided by GeoV.

Applications of GeoV
Next, we set out to test the versatility of GeoV in the context of applications in synthetic biology.Figure 4a shows sketches of the different types of objects on which we tested our reconstruction algorithm.The simplest example is a plain spherical giant unilamellar vesicle (GUV) 1).In bottom-up synthetic biology, different strategies have been developed to control the morphology of a GUV, including the attachment of DNA origami to the GUV surface [15,19] 2), or the adhesion of GUVs on patterned surfaces [23] 3).GeoV reconstructs both cases well.Beyond GUVs, we test the reconstruction of membrane-less DNA hydrogel beads consisting of DNA y-motifs [17,36,37] 4).As a last example, we chose an adherent HeLa cell.In particular, in this case, the use of multiple viewpoints to calculate the surface normals was essential.Exemplary confocal images from the zstacks used for reconstruction are displayed in Figure 4b.The resulting 3D meshes are displayed in Figure 4c.It is apparent that the reconstruction of the 3D surface helps to get a better understanding for the actual structure of the object, which may not be obvious from a single confocal plane.Beyond the visual representation of confocal z-stacks, GeoV allows for the quantitative analysis of physical properties of the reconstructed surfaces.One example is the local curvature of the objects, which can be easily obtained from the 3D-reconstructed surfaces.Figure 4d shows the reconstructed surfaces with color-coded visualization of the local curvature.Figure 4e shows the corresponding color-coded histograms of the curvatures for the respective objects.For the spherical GUV, the histogram has a narrow distribution.As expected, it is centered around the inverse radius of the GUV À1=R ¼ À0.1 μm À1 with a mean and standard deviation of κ sphere ¼ ðÀ0.1 AE 0.03Þ μm À1 .The curvature distribution of the deflated and DNA origami-coated GUV is much wider, reaching up to positive curvature values due to the indentations visible in the 3D reconstruction.This leads to a shift of the mean value and a higher standard deviation (κ sphere ¼ ð0.0 AE 0.4Þ μm À1 ).Similar to the spherical GUV, the adherent GUV also has a rather narrow distribution, which, however, extends a little further toward higher negative curvatures due to the edges of the adherent area (κ adherent ¼ ðÀ0.1 AE 0.1Þ μm À1 ).The DNA bead has a similar structure as the adherent GUV; however, due to its larger size, the mean value of the curvature distribution is shifted toward lower absolute values κ DNAbead ¼ ðÀ0.07 AE 0.11Þ μm À1 .It is very interesting to observe the rough surface of the DNA bead as compared the GUVs, which is hardly visible in a 2D confocal plane, but becomes apparent in the 3D reconstruction (see Figure S5, Supporting Information).With GeoV, the surface roughness can also be analyzed quantitatively by the wider distribution of the curvatures.For the adherent HeLa cell, one can identify two peaks in the curvature histogram, corresponding to the top and bottom of the cell with lower curvatures (μ Cell;1 ¼ À0.063 μm À1 AE σ Cell;1 ¼ 0.002 μm À1 ) and the adhesion sites with high curvature (μ Cell;2 ¼ À 0.24 μm À1 AE σ Cell;2 ¼ 0.02 μm À1 ).Thus, GeoV is suitable to extract quantitative 3D shape parameters for a variety of micronscale objects relevant in the context of synthetic biology.area, reduced volume, and bending energy of bare GUVs and GUVs coated with DNA origami.We chose a DNA origami plate consisting of a single layer of DNA.The original design [38] has been modified with single-stranded overhangs in four positions that hybridize with complementary cholesterol-tagged DNA strands (for sequences see Note S1, Supporting Information).Figure 5a shows exemplary reconstructions of GUVs before and after addition of cholesterol-tagged DNA origami plates and osmotic deflation.As expected, an analysis of the surface area showed no significant difference for GUVs with and without DNA origami (see Figure 5b).However, when looking at the reduced volume v ¼ V=V 0 ¼ V=ð 4 3 πr 3 0 Þ with V the volume, r 0 ¼ ffiffiffiffiffiffiffiffiffiffiffi A=4π p , and A the area, the effect of the deflation is clearly visible.While the spherical GUVs have a reduced volume of v ¼ 0.996 AE 0.006 which matches the expectations for a perfect sphere, the DNA-coated vesicles show a reduced volume of v ¼ 0.76 AE 0.08, which shows their deflation and matches the expectations for the applied osmolarity increase (see Figure 5c and Materials and Methods).
Lastly, we utilized the curvatures determined from the reconstructed meshes to calculate the bending energy of the lipid membrane of both systems as before.For perfectly spherical vesicles with v ¼ 1, the bending energy is constant given by E B ¼ 8πκ which we could also show for the bending energy calculated from the reconstructed meshes for the spherical GUVs E b;sphere ¼ ð8.9 AE 0.4Þπκ (see Figure 5d).For the DNA origamicoated GUVs, the bending energy of the lipid membrane is much higher E b;defl ¼ ð50 AE 28Þπκ since the deflation forces the membrane into shapes with higher curvatures.All of these properties would be hard or impossible to calculate directly from the original z-stacks of the objects.This, therefore, shows the usefulness of a 3D reconstruction of z-stacks for both visual representation and quantitative analysis.

Conclusion
With the recent progress in bottom-up synthetic biology to mimic cells and their behavior, a variety of methods emerged to shape GUVs as synthetic cell compartments.Oftentimes, synthetic cell morphology was analyzed by comparing 2D confocal slices also if the deformations were anisotropic.This is due to the lack of a convenient analysis suite, which is tailored to synthetic cells and vesicles.Additionally, comparability of these results also with theoretical work requires standardized workflows for the quantitative analysis of 3D shapes.Since the most common techniques to observe GUVs rely on microscopy methods which provide 2D slices of the object the main problem the workflow has to solve is the reconstruction of 3D shapes from 2D images.
Here we presented the software package "GeoV" for the quantitative analysis of 3D vesicle morphologies from confocal z-stacks.GeoV takes confocal z-stacks as an input and returns the 3D-reconstructed mesh as well as physical properties such as volume, area, or local curvatures.We confirmed the sufficient accuracy of our software package by simulating confocal z-stacks from 3D meshes functioning as the ground truth and reconstructed the z-stacks with GeoV.In particular, we compared the resulting mesh with the ground truth by analyzing the spatial deviation and the deviation of the local curvature and found good agreement also for complex feature-rich shapes like the Stanford bunny.
We demonstrated the versatility of GeoV by using it for the reconstruction and quantitative analysis of the curvatures of a plain GUV, a DNA origami-coated GUV, an adherent GUV, a DNA bead, and a HeLa cell.Furthermore, we used GeoV to extract surface area, reduced volume, and bending energy of GUVs to quantify the effect of deflation and DNA origami coating on the GUVs physical properties.These properties would be hard or impossible to calculate directly from the original z-stacks of the objects.
In summary, we provide GeoV as an open-source software package for the synthetic biology community.We hope the community will benefit from the straight-forward output of quantitative data from confocal imaging experiments and aspire that GeoV contributes to the comparability of results from labs all over the world.
Generation of Vesicle-Like Ground Truth Meshes: Vesicle-like ground truth meshes (GTM) were produced using the sketch and revolve functions of Onshape version 1.152.

Figure 2 .
Figure 2. Accuracy and error analysis of the 3D surface reconstruction with GeoV.a,e) Illustration of the error analysis procedure.Confocal z-stacks with a z-spacing of 0.5 μm were simulated from 3D meshes (ground truth) and used as an input for GeoV.The resulting 3D mesh was then compared to the ground truth.b,f ) Minimal distance of each vertex of the ground truth mesh from the reconstructed mesh normalized by the object size d 0 .c,g) Deviation of the local curvature of each vertex of the reconstructed mesh compared to the ground truth mesh normalized by the curvature of a sphere with radius r 0 ¼ ffiffiffiffiffiffiffiffiffiffi ffi A=4π p .All plots show the mean and standard deviation of the mean for n = 36 588 vertices.d,h) Bending energy calculated from the original mesh and the reconstructed meshes.

Figure 3 .
Figure 3. GeoV's multiple viewpoint feature as a strategy to avoid artefacts and reduce the error of the reconstruction.a) Reconstruction of the Stanford bunny with multiple viewpoints and with a single viewpoint.b) Minimal distance of each vertex of the ground truth mesh from the reconstructed mesh normalized by the object size d 0 for the reconstruction with multiple viewpoints and with a single viewpoint.c) Deviation of the local curvature of each vertex of the reconstructed mesh compared to the ground truth mesh normalized by the curvature of a sphere with radius r 0 ¼ ffiffiffiffiffiffiffiffiffiffi ffi A=4π p for the reconstruction with multiple viewpoints and with a single viewpoint.All plots show the mean and standard deviation of the mean for n = 36 588 vertices.d) Comparison of the bending energy of the original mesh and the reconstructed meshes with multiple viewpoints and with a single viewpoint.

2. 5 .
Quantitative Comparison of Spherical GUVs with Deflated and DNA Origami-Coated GUVs Finally, we use GeoV to quantitatively analyze the effect of DNA origami adsorption on GUV membranes by comparing surface

Figure 4 .
Figure 4. Versatile reconstruction and analysis with GeoV.a) Sketches of the different systems used for surface reconstruction including a spherical GUV (i), a deflated GUV covered with DNA origami plates (ii), a GUV adhering on onto a cross-shaped pattern (iii), a DNA hydrogel droplet (iv) and a HeLa cell (v).b) Confocal images of the respective systems used for the 3D surface reconstruction.Scale bars: 10 μm.c) Resulting reconstructed 3D meshes.d) Reconstructed 3D meshes displaying the color-coded local curvatures.e) Histograms of the respective local curvatures.

Figure 5 .
Figure 5.Effect of DNA origami adsorption on GUV membranes analyzed with GeoV.a) Illustration and 3D reconstruction of GUVs before and after addition of DNA origami and osmotic deflation to a reduced volume of v ¼ 0.75.b) Surface area of GUVs without DNA origami (spherical GUVs) and with DNA origami (deformed GUVs).c) Reduced volume of spherical GUVs and deformed GUVs in comparison with the theoretical value for for a sphere.d) Bending energy assuming a spontaneous curvature of C 0 = 0 for spherical GUVs and deformed GUVs in comparison with the theoretical value for a sphere.All plots show the mean and the standard deviation for n = 5 GUVs.