# Single Cell Center of Mass for the Analysis of BMP Receptor Heterodimers Distributions

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## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. ComRed-Based Analysis Detects Changes in Experimental Data

#### 2.2. Cell Geometry Strongly Influences BMPR Subunit Distribution

## 3. Discussion

## 4. Materials and Methods

#### 4.1. Photo-Micropatterning

#### 4.2. Cell Culture

#### 4.3. Immunofluorescence Staining

#### 4.4. Microscopy

#### 4.5. Seeding Human Umbilical Vein Endothelial Cells on Micropatterns and Induction with Bone Morphogenetic Protein 2 (BMP-2)

#### 4.6. Image Processing and Analysis

#### 4.7. Center of Mass Calculations

^{3}). The virtual mass ${v}_{i}={\overline{I}}_{i,g}\xb7{n}_{i}$ is analogous to the real world mass, which is given by density times volume. Inserted into the original center of mass formula ${I}_{g}$ cancels out, leaving $r={\displaystyle \frac{\sum {I}_{i}\xb7{n}_{i}\xb7{r}_{i}}{\sum {I}_{i}\xb7{n}_{i}}}$. Pictures might differ in size (physical dimensions, and/or pixel volume, and/or pixel number), and cell orientation and position. Therefore object coordinates or center of mass coordinates need to be compared to a frame of reference. $d={r}_{o}-{r}_{r}$ where d is the difference between an object and its reference, ${r}_{r}$ is the reference position and ${r}_{o}$ is the object position. After the positions for all spatial directions were calculated the arithmetic mean might be calculated $\overline{d}=\sqrt{{\left({d}_{x}\right)}^{2}+{\left({d}_{y}\right)}^{2}+{\left({d}_{z}\right)}^{2}}$. In the end, the difference in pixels might can be converted into a length scale of choice (here micrometer). In this study, we used two metrics-a reference metric and a spread metric. In the reference metric, the object (as indicated by ${r}_{o}$ is the center of mass of a receptor distribution, while the reference (${r}_{r}$) is the center of mass of the cells nucleus). In the spread metric, the object is every receptor accumulation detected (so every spot on the picture would be one object), and the reference is the center of mass of all found accumulations of the same receptor type. Then, the mean of the spread values was calculated for every cell. The current version of ComRed is available through https://github.com/hendrikboog/comred (last accessed: 13 October 2021).

#### 4.8. Statistics

#### 4.9. Data Simulation

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BISC | BMP-induced signaling complex |

BMP | Bone morphogenetic protein |

BMPR | Bone morphogenetic protein receptor |

ComRed | Center Of Mass REeptor Distribution |

DAPI | 4${}^{\prime}$,6-Diamidine-2${}^{\prime}$-phenylindole-dihydrochloride |

HUVEC | Human umbilical vein endothelial cell |

PFC | Preformed complex |

## Appendix A

**Figure A1.**Histograms and similarity metrics of x-, y-, and z-coordinates, as well as mean intensity and volume of Control Circle BMPRIb data with n = 0.

**Figure A2.**Comparison of experimental data randomly split into two groups for reference metric. Then, ComRed was used to assess differences in distributions. No significant differences were found. - = not significant.

**Figure A3.**Comparison of experimental data randomly split into two groups for shift metric. Then, ComRed was used to assess differences in distributions. No significant differences were found. - = not significant.

**Figure A4.**Visualization of the BMPRIb of an example control cell grown on a circular micropattern. Three projections of the receptor accumulation coordinates and virtual masses in the x-y, x-z, and y-z planes. Virtual masses are indicated by the size of the dots. Different dot colors were chosen to differ between overlapping dots. These plots can be automatically generated by ComRed for checkup of found accumulations and their respective weight in the final center of mass.

## References

- Kang, Q.; Song, W.X.; Luo, Q.; Tang, N.; Luo, J.; Luo, X.; Chen, J.; Bi, Y.; He, B.C.; Park, J.K.; et al. A comprehensive analysis of the dual roles of BMPs in regulating adipogenic and osteogenic differentiation of mesenchymal progenitor cells. Stem Cells Dev.
**2009**, 18, 545–559. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cunningham, N.S.; Paralkar, V.; Reddi, A.H. Osteogenin and recombinant bone morphogenetic protein 2B are chemotactic for human monocytes and stimulate transforming growth factor 81 mRNA expression. Proc. Natl. Acad. Sci. USA
**1992**, 89, 11740–11744. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gamell, C.; Osses, N.; Bartrons, R.; Rückle, T.; Camps, M.; Rosa, J.L.; Ventura, F. BMP2 induction of actin cytoskeleton reorganization and cell migration requires PI3-kinase and Cdc42 activity. J. Cell Sci.
**2008**, 23, 3960–3970. [Google Scholar] [CrossRef] [Green Version] - Nohe, A.; Hassel, S.; Ehrlich, M.; Neubauer, F.; Sebald, W.; Henis, Y.I.; Knaus, P. The mode of bone morphogenetic protein (BMP) receptor oligomerization determines different BMP-2 signaling pathways. J. Biol. Chem.
**2002**, 277, 5330–5338. [Google Scholar] [CrossRef] [Green Version] - Hartung, A.; Bitton-Worms, K.; Rechtman, M.M.; Wenzel, V.; Boergermann, J.H.; Hassel, S.; Henis, Y.I.; Knaus, P. Different routes of bone morphogenic protein (BMP) receptor endocytosis influence BMP signaling. Mol. Cell. Biol.
**2006**, 26, 7791–7805. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Pohl, T.L.M.; Boergermann, J.H.; Schwaerzer, G.K.; Knaus, P.; Cavalcanti-Adam, E.A. Surface immobilization of bone morphogenetic protein 2 via a self-assembled monolayer formation induces cell differentiation. Acta Biomater.
**2012**, 8, 772–780. [Google Scholar] [CrossRef] [PubMed] - Migliorini, E.; Valat, A.; Picart, C.; Cavalcanti-Adam, E.A. Tuning cellular responses to BMP-2 with material surfaces. Cytokine Growth Factor Rev.
**2016**, 27, 43–54. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bragdon, B.; Thinakaran, S.; Bonor, J.; Underhill, T.M.; Petersen, N.O.; Nohe, A. FRET reveals novel protein-receptor interaction of bone morphogenetic proteins receptors and adaptor protein 2 at the cell surface. Biophys. J.
**2009**, 97, 1428–1435. [Google Scholar] [CrossRef] [Green Version] - Sieber, C.; Kopf, J.; Hiepen, C.; Knaus, P. Recent advances in BMP receptor signaling. Cytokine Growth Factor Rev.
**2009**, 20, 343–355. [Google Scholar] [CrossRef] - Paralkar, V.M.; Hammonds, R.G.; Reddi, A.H. Identification and characterization of cellular binding proteins (receptors) for recombinant human bone morphogenetic protein 2B, an initiator of bone differentiation cascade. Proc. Natl. Acad. Sci. USA
**1991**, 88, 3397–3401. [Google Scholar] [CrossRef] [Green Version] - Hardwick, J.C.H.; van den Brink, G.R.; Bleuming, S.A.; Ballester, I.; van den Brande, J.M.H.; Keller, J.J.; Offerhaus, G.J.A.; van Deventer, S.J.H.; Peppelenbosch, M.P. Bone morphogenetic protein 2 is expressed by, and acts upon, mature epithelial cells in the colon. Gastroenterology
**2004**, 126, 111–121. [Google Scholar] [CrossRef] - Benn, A.; Hiepen, C.; Osterland, M.; Schütte, C.; Zwijsen, A.; Knaus, P. Role of bone morphogenetic proteins in sprouting angiogenesis: Differential BMP receptor-dependent signaling pathways balance stalk vs. tip cell competence. FASEB J.
**2017**, 31, 4720–4733. [Google Scholar] [CrossRef] [Green Version] - Zhou, J.; Lee, P.L.; Lee, C.I.; Wei, S.Y.; Lim, S.H.; Lin, T.E.; Chien, S.; Chiu, J.J. BMP receptor-integrin interaction mediates responses of vascular endothelial Smad1/5 and proliferation to disturbed flow. J. Thromb. Haemost. JTH
**2013**, 11, 741–755. [Google Scholar] [CrossRef] [PubMed] - Benn, A.; Bredow, C.; Casanova, I.; Vukičević, S.; Knaus, P. VE-cadherin facilitates BMP-induced endothelial cell permeability and signaling. J. Cell Sci.
**2016**, 129, 206–218. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zuo, W.H.; Zeng, P.; Chen, X.; Lu, Y.J.; Li, A.; Wu, J.B. Promotive effects of bone morphogenetic protein 2 on angiogenesis in hepatocarcinoma via multiple signal pathways. Sci. Rep.
**2016**, 6, 37499. [Google Scholar] [CrossRef] - Finkenzeller, G.; Hager, S.; Stark, G.B. Effects of bone morphogenetic protein 2 on human umbilical vein endothelial cells. Microvasc. Res.
**2012**, 84, 81–85. [Google Scholar] [CrossRef] - Fernandez, S.M.; Berlin, R.D. Cell surface distribution of lectin receptors determined by resonance energy transfer. Nature
**1976**, 264, 411–415. [Google Scholar] [CrossRef] [PubMed] - Algar, W.R.; Hildebrandt, N.; Vogel, S.S.; Medintz, I.L. FRET as a biomolecular research tool-understanding its potential while avoiding pitfalls. Nat. Methods
**2019**, 16, 815–829. [Google Scholar] [CrossRef] [PubMed] - Li, Q.; Lau, A.; Morris, T.J.; Guo, L.; Fordyce, C.B.; Stanley, E.F. A syntaxin 1, Galpha(o), and N-type calcium channel complex at a presynaptic nerve terminal: Analysis by quantitative immunocolocalization. J. Neurosci. Off. J. Soc. Neurosci.
**2004**, 24, 4070–4081. [Google Scholar] [CrossRef] [Green Version] - Bolte, S.; Cordelières, F.P. A guided tour into subcellular colocalization analysis in light microscopy. J. Microsc.
**2006**, 224, 213–232. [Google Scholar] [CrossRef] - Medda, R.; Giske, A.; Cavalcanti-Adam, E.A. Challenges in imaging cell surface receptor clusters. Opt. Lasers Eng.
**2016**, 76, 3–8. [Google Scholar] [CrossRef] - Bacia, K.; Kim, S.A.; Schwille, P. Fluorescence cross-correlation spectroscopy in living cells. Nat. Methods
**2006**, 3, 83–89. [Google Scholar] [CrossRef] - Lippincott-Schwartz, J.; Snapp, E.L.; Phair, R.D. The Development and Enhancement of FRAP as a Key Tool for Investigating Protein Dynamics. Biophys. J.
**2018**, 115, 1146–1155. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Nohe, A.; Keating, E.; Underhill, T.M.; Knaus, P.; Petersen, N.O. Effect of the distribution and clustering of the type I A BMP receptor (ALK3) with the type II BMP receptor on the activation of signalling pathways. J. Cell Sci.
**2003**, 116, 3277–3284. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Théry, M. Micropatterning as a tool to decipher cell morphogenesis and functions. J. Cell Sci.
**2010**, 123, 4201–4213. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sommer, C.; Straehle, C.; Köthe, U.; Hamprecht, F.A. ilastik: Interactive Learning and Segmentation Toolkit. In Proceedings of the Eighth IEEE International Symposium on Biomedical Imaging (ISBI), Chicago, IL, USA, 30 March–2 April 2011; pp. 230–233. [Google Scholar]
- Berg, S.; Kutra, D.; Kroeger, T.; Straehle, C.N.; Kausler, B.X.; Haubold, C.; Schiegg, M.; Ales, J.; Beier, T.; Rudy, M.; et al. ilastik: Interactive machine learning for (bio)image analysis. Nat. Methods
**2019**, 16, 1226–1232. [Google Scholar] [CrossRef] [PubMed] - Théry, M.; Racine, V.; Piel, M.; Pépin, A.; Dimitrov, A.; Chen, Y.; Sibarita, J.B.; Bornens, M. Anisotropy of cell adhesive microenvironment governs cell internal organization and orientation of polarity. Proc. Natl. Acad. Sci. USA
**2006**, 103, 19771–19776. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jortikka, L.; Laitinen, M.; Lindholm, T.; Marttinen, A. Internalization and Intracellular Processing of Bone Morphogenetic Protein (BMP) in Rat Skeletal Muscle Myoblasts (L6). Cell. Signal.
**1997**, 9, 47–51. [Google Scholar] [CrossRef] - O’Sullivan, M.J.; Lindsay, A.J. The Endosomal Recycling Pathway-At the Crossroads of the Cell. Int. J. Mol. Sci.
**2020**, 21, 6074. [Google Scholar] [CrossRef] - Mitchell, H.; Choudhury, A.; Pagano, R.E.; Leof, E.B. Ligand-dependent and -independent transforming growth factor-beta receptor recycling regulated by clathrin-mediated endocytosis and Rab11. Mol. Biol. Cell
**2004**, 15, 4166–4178. [Google Scholar] [CrossRef] - Lin, H.Y.; Wang, X.F.; Ng-Eaton, E.; Weinberg, R.A.; Lodish, H.F. Expression and cloning of the TGF-β Type II Receptor, a Functional Transmembrane Serine/Threonine Kinase. Cell
**1992**, 68, 775–785. [Google Scholar] [CrossRef] - Franzén, P.; ten Dijke, P.; Ichijo, H.; Yamashita, H.; Schulz, P.; Heldin, C.H.; Miyazono, K. Cloning of a TGFβ Type I Receptor That Forms a Heteromeric Complex with the TGFβ Type II Receptor. Cell
**1993**, 75, 681–692. [Google Scholar] [CrossRef] - Di Guglielmo, G.M.; Le Roy, C.; Goodfellow, A.F.; Wrana, J.L. Distinct endocytic pathways regulate TGF-beta receptor signalling and turnover. Nat. Cell Biol.
**2003**, 5, 410–421. [Google Scholar] [CrossRef] [PubMed] - Gleason, R.J.; Akintobi, A.M.; Grant, B.D.; Padgett, R.W. BMP signaling requires retromer-dependent recycling of the type I receptor. Proc. Natl. Acad. Sci. USA
**2014**, 111, 2578–2583. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Schindelin, J.; Arganda-Carreras, I.; Frise, E.; Kaynig, V.; Longair, M.; Pietzsch, T.; Preibisch, S.; Rueden, C.; Saalfeld, S.; Schmid, B.; et al. Fiji: An open-source platform for biological-image analysis. Nat. Methods
**2012**, 9, 676–682. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Outline of experiments and mode of operation of ComRed. (

**a**): Scheme of circle and crossbow pattern. White background is passivated with PLL-PEG, while black regions are micropatterned using a photomask in a UV-ozone cleaner and coated with fibronectin (Section 4.1). Circle diameter is 50 µm. (

**b**): examples of confocal microscopy images of HUVECs seeded on a circle (left) and crossbow micropattern (right). Green: BMPRIb, Red: BMPRII, Blue: actin, White: nucleus. Scale bars in all confocal images are 20 µm. (

**c**,

**d**): steps for the calculation of reference and spread metrics. For both metrics, first the center of mass of a receptor distribution is calculated. (

**c**): For the reference metric, a reference point is taken, e.g., the center of mass of the nucleus. Afterwards, the distance between the two center of mass points is calculated. (

**d**): For the spread metric, after determination of the center of mass of the receptor distribution, the distance to each single accumulation is calculated and the mean of these distances is taken.

**Figure 2.**Overlaid histograms of experimental data (black) and simulated data (orange) transformed with factor n. Experimental data were used to generate simulated data, as explained in Section 4.9. Different magnitudes of changes (as indicated with their n-value) were tested. Cosine distance and Hellinger distance, as well as histogram overlap were calculated. Here, data can be effectively simulated by inverse transform sampling. Distributions can be effectively shifted or spread by using functions ${x}_{new}={x}_{exp}+n\xb7\overline{x}$ (for shifting of distributions) or ${x}_{new}={x}_{exp}+{\displaystyle \frac{n\xb7\overline{x}\xb7({x}_{rnd}-\overline{x})}{b}}$ (for spreading of distributions) before inverse transform sampling.

**Figure 3.**Comparison of simulated and experimental data for reference metric. (

**a**): Simulations of a shift in distributions (${x}_{new}={x}_{real}+n\xb7\overline{x}$). All tested values for n > 0 showed significant differences. (

**b**): Simulations of a spread in distributions (${x}_{new}={x}_{real}+{\displaystyle \frac{n\xb7\overline{x}\xb7({x}_{rnd}-\overline{x})}{b}}$). Here, for all values of n no significant differences were found. Reference metric is sensitive to shifts in COM position, but not to differences in spread of distributions. *** = p < 0.001, **** = p < 0.0001, - = not significant.

**Figure 4.**Comparison of simulated and experimental data for spread metric. (

**a**): Simulations of a shift in distributions (${x}_{new}={x}_{real}+n\xb7\overline{x}$). (

**b**): Simulations of a spread in distributions (${x}_{new}={x}_{real}+{\displaystyle \frac{n\xb7\overline{x}\xb7({x}_{rnd}-\overline{x})}{b}}$). Here, for all values of n > 0 significant differences were found. Spread metric is sensitive to the spreading of distributions. * = p < 0.05, ** = p < 0.01, **** = p < 0.0001, - = not significant.

**Figure 5.**Comparison of receptor distributions of BMPR subunits in HUVECs. (

**a**,

**c**,

**e**): reference metric data, (

**b**,

**d**,

**f**): spread metric data. Confocal images of cells adhering to micropatterns: Green: BMPRIb, red: BMPRII. (

**a**,

**b**): distributions of BMPRIb compared to distributions of BMPRII. Differences in shift could be observed in crossbow cells under control conditions ($p\approx 0.026$). Also, differences could be observed between BMPRIb and BMPRII ($p\approx {10}^{-3}$) in circular cells without BMP, indicating a preference for BISC. (

**c**,

**d**): Comparison of circle and crossbow cells. No significant differences in shift could be found. BMPRIb is more spread out in circle than in crossbow cells, both under control and BMP conditions ($p\approx {10}^{-6}$ and $p\approx 5\xb7{10}^{-5}$ respectively). (

**e**,

**f**): control cells compared with cells that were induced with BMP-2. Control and BMP-2 treated cells do not show a significant difference in receptor distribution; this suggests, that majority of BMPRs were not internalizing simultaneously after addition of BMP. * = p < 0.05, ** = p < 0.01, **** = p < 0.0001, - = not significant.

**Figure 6.**Boxplots of colocalization values of BMPRIb and BMPRII in HUVECs. (

**a**,

**b**): colocalization values of circle and crossbow cells +/− BMP-2, using Pearson’s score (

**a**) and Li’s ICQ (

**b**). c and d: colocalization values of control and BMP-2 induced cells in circle and crossbow cells, using Pearson’s score (

**c**) and Li’s ICQ (

**d**). Confocal images of HUVECs on circle- and crossbow-patterns were analyzed with the JaCoP imageJ extension [20]. Changes in colocalization between induced an noninduced cells indicated that the BMP-induced signaling complex is preferably used. No change in colocalization suggested that preformed complex is predominantly used. * = p < 0.05, ** = p < 0.01, - = not significant.

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**MDPI and ACS Style**

Boog, H.; Medda, R.; Cavalcanti-Adam, E.A.
Single Cell Center of Mass for the Analysis of BMP Receptor Heterodimers Distributions. *J. Imaging* **2021**, *7*, 219.
https://doi.org/10.3390/jimaging7110219

**AMA Style**

Boog H, Medda R, Cavalcanti-Adam EA.
Single Cell Center of Mass for the Analysis of BMP Receptor Heterodimers Distributions. *Journal of Imaging*. 2021; 7(11):219.
https://doi.org/10.3390/jimaging7110219

**Chicago/Turabian Style**

Boog, Hendrik, Rebecca Medda, and Elisabetta Ada Cavalcanti-Adam.
2021. "Single Cell Center of Mass for the Analysis of BMP Receptor Heterodimers Distributions" *Journal of Imaging* 7, no. 11: 219.
https://doi.org/10.3390/jimaging7110219