# 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.

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**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