# Optimization of Mechanosensitive Cross-Talk between Matrix Stiffness and Protein Density: Independent Matrix Properties Regulate Spreading Dynamics of Myocytes

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Glass Preparation

#### 2.2. Hydrogel Preparation

#### 2.3. Mechanical Testing

#### 2.4. Height Determination

#### 2.5. Surface Functionalization

#### 2.6. Cell Culture

#### 2.7. Image and Time-Lapse Acquisition

#### 2.8. Fluorescence Staining

#### 2.9. Lifeact Transfection

#### 2.10. Image Acquisition of Fluorescent Cells

#### 2.11. Actin Quantification Analysis (AQuA)

## 3. Results

#### 3.1. Cell-Morphological Response to Substrate Properties

#### 3.2. Cytoskeletal Actin Response to Substrate Properties

#### 3.3. Quantification of Proliferation Dynamics

## 4. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FN | fibronectin |

RT | room temperature |

ECM | extracellular matrix |

AQuA | actin quantification analysis |

DMEM | Dulbecco’s modified Eagle’s medium |

eLoG | elongated Laplace of Gaussian |

PED | protein equilibrium distance |

## References

- Urbanczyk, M.; Layland, S.L.; Schenke-Layland, K. The Role of Extracellular Matrix in Biomechanics and Its Impact on Bioengineering of Cells and 3D Tissues. Matrix Biol.
**2020**, 85–86, 1–14. [Google Scholar] [CrossRef] [PubMed] - Hörning, M.; Kidoaki, S.; Kawano, T.; Yoshikawa, K. Rigidity Matching between Cells and the Extracellular Matrix Leads to the Stabilization of Cardiac Conduction. Biophys. J.
**2012**, 102, 379–387. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hörning, M.; Nakahata, M.; Linke, P.; Yamamoto, A.; Veschgini, M.; Kaufmann, S.; Takashima, Y.; Harada, A.; Tanaka, M. Dynamic Mechano-Regulation of Myoblast Cells on Supramolecular Hydrogels Cross-Linked by Reversible Host-Guest Interactions. Sci. Rep.
**2017**, 7, 7660. [Google Scholar] [CrossRef] [PubMed] - Yin, L.; Bien, H.; Entcheva, E. Scaffold Topography Alters Intracellular Calcium Dynamics in Cultured Cardiomyocyte Networks. Am. J.-Physiol.-Heart Circ. Physiol.
**2004**, 287, H1276–H1285. [Google Scholar] [CrossRef] - Erben, A.; Hörning, M.; Hartmann, B.; Becke, T.; Eisler, S.A.; Southan, A.; Cranz, S.; Hayden, O.; Kneidinger, N.; Königshoff, M.; et al. Precision 3D-Printed Cell Scaffolds Mimicking Native Tissue Composition and Mechanics. Adv. Healthc. Mater.
**2020**, 9, 2000918. [Google Scholar] [CrossRef] - Harburger, D.S.; Calderwood, D.A. Integrin Signalling at a Glance. J. Cell Sci.
**2009**, 122, 159–163. [Google Scholar] [CrossRef] [Green Version] - Takagi, Y.; Homsher, E.E.; Goldman, Y.E.; Shuman, H. Force Generation in Single Conventional Actomyosin Complexes under High Dynamic Load. Biophys. J.
**2006**, 90, 1295–1307. [Google Scholar] [CrossRef] [Green Version] - Lo, C.W. Role of Gap Junctions in Cardiac Conduction and Development. Circ. Res.
**2000**, 87, 346–348. [Google Scholar] [CrossRef] [Green Version] - Miura, K.; Siegert, F. Light Affects cAMP Signaling and Cell Movement Activity in Dictyostelium Discoideum. Proc. Natl. Acad. Sci. USA
**2000**, 97, 2111–2116. [Google Scholar] [CrossRef] [Green Version] - Ali-Murthy, Z.; Kornberg, T.B. Bicoid Gradient Formation and Function in the Drosophila Pre-Syncytial Blastoderm. eLife
**2016**, 5, e13222. [Google Scholar] [CrossRef] - Zhang, Z.; Zwick, S.; Loew, E.; Grimley, J.S.; Ramanathan, S. Mouse Embryo Geometry Drives Formation of Robust Signaling Gradients through Receptor Localization. Nat. Commun.
**2019**, 10, 4516. [Google Scholar] [CrossRef] [PubMed] - Capron, A.; Chatfield, S.; Provart, N.; Berleth, T. Embryogenesis: Pattern Formation from a Single Cell. Arab. Book/Am. Soc. Plant Biol.
**2009**, 7, e0126. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Engler, A.J.; Sen, S.; Sweeney, H.L.; Discher, D.E. Matrix Elasticity Directs Stem Cell Lineage Specification. Cell
**2006**, 126, 677–689. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Engler, A.J.; Griffin, M.A.; Sen, S.; Bönnemann, C.G.; Sweeney, H.L.; Discher, D.E. Myotubes Differentiate Optimally on Substrates with Tissue-like Stiffness: Pathological Implications for Soft or Stiff Microenvironments. J. Cell Biol.
**2004**, 166, 877–887. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Engler, A.J.; Carag-Krieger, C.; Johnson, C.P.; Raab, M.; Tang, H.Y.; Speicher, D.W.; Sanger, J.W.; Sanger, J.M.; Discher, D.E. Embryonic Cardiomyocytes Beat Best on a Matrix with Heart-like Elasticity: Scar-like Rigidity Inhibits Beating. J. Cell Sci.
**2008**, 121, 3794–3802. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zemel, A.; Rehfeldt, F.; Brown, A.E.X.; Discher, D.E.; Safran, S.A. Optimal Matrix Rigidity for Stress Fiber Polarization in Stem Cells. Nat. Phys.
**2010**, 6, 468–473. [Google Scholar] [CrossRef] - Engler, A.; Bacakova, L.; Newman, C.; Hategan, A.; Griffin, M.; Discher, D. Substrate Compliance versus Ligand Density in Cell on Gel Responses. Biophys. J.
**2004**, 86, 617–628. [Google Scholar] [CrossRef] [Green Version] - Schreiber, C.; Amiri, B.; Heyn, J.C.J.; Rädler, J.O.; Falcke, M. On the Adhesion–Velocity Relation and Length Adaptation of Motile Cells on Stepped Fibronectin Lanes. Proc. Natl. Acad. Sci. USA
**2021**, 118, e2009959118. [Google Scholar] [CrossRef] - Yoshikawa, H.Y.; Rossetti, F.F.; Kaufmann, S.; Kaindl, T.; Madsen, J.; Engel, U.; Lewis, A.L.; Armes, S.P.; Tanaka, M. Quantitative Evaluation of Mechanosensing of Cells on Dynamically Tunable Hydrogels. J. Am. Chem. Soc.
**2011**, 133, 1367–1374. [Google Scholar] [CrossRef] - Li, J.; Zhang, L.; Yu, L.; Minami, I.; Miyagawa, S.; Hörning, M.; Dong, J.; Qiao, J.; Qu, X.; Hua, Y.; et al. Circulating Re-Entrant Waves Promote Maturation of hiPSC-derived Cardiomyocytes in Self-Organized Tissue Ring. Commun. Biol.
**2020**, 3, 1–12. [Google Scholar] [CrossRef] [Green Version] - Trappmann, B.; Gautrot, J.E.; Connelly, J.T.; Strange, D.G.T.; Li, Y.; Oyen, M.L.; Stuart, M.A.C.; Boehm, H.; Li, B.; Vogel, V.; et al. Extracellular-Matrix Tethering Regulates Stem-Cell Fate. Nat. Mater.
**2012**, 11, 642–649. [Google Scholar] [CrossRef] [PubMed] - Kern, W.; Puotinen, D. Cleaning Solutions Based on Hydrogen Peroxide for Use in Silicon Semiconductor Technology. RCA Rev.
**1970**, 31, 187–206. [Google Scholar] - Kidoaki, S.; Matsuda, T. Microelastic Gradient Gelatinous Gels to Induce Cellular Mechanotaxis. J. Biotechnol.
**2008**, 133, 225–230. [Google Scholar] [CrossRef] [PubMed] - Buxboim, A.; Rajagopal, K.; Brown, A.E.X.; Discher, D.E. How Deeply Cells Feel: Methods for Thin Gels. J. Phys. Condens. Matter
**2010**, 22, 194116. [Google Scholar] [CrossRef] [Green Version] - Butt, H.J.; Cappella, B.; Kappl, M. Force Measurements with the Atomic Force Microscope: Technique, Interpretation and Applications. Surf. Sci. Rep.
**2005**, 59, 1–152. [Google Scholar] [CrossRef] [Green Version] - Sneddon, I.N. The Relation between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile. Int. J. Eng. Sci.
**1965**, 3, 47–57. [Google Scholar] [CrossRef] - Domke, J.; Radmacher, M. Measuring the Elastic Properties of Thin Polymer Films with the Atomic Force Microscope. Langmuir
**1998**, 14, 3320–3325. [Google Scholar] [CrossRef] - Lin, D.C.; Dimitriadis, E.K.; Horkay, F. Robust Strategies for Automated AFM Force Curve Analysis—I. Non-adhesive Indentation of Soft, Inhomogeneous Materials. J. Biomech. Eng.
**2006**, 129, 430–440. [Google Scholar] [CrossRef] [Green Version] - Wouters, O.Y.; Ploeger, D.T.; van Putten, S.M.; Bank, R.A. 3,4-Dihydroxy-L-Phenylalanine as a Novel Covalent Linker of Extracellular Matrix Proteins to Polyacrylamide Hydrogels with a Tunable Stiffness. Tissue Eng. Part C Methods
**2016**, 22, 91–101. [Google Scholar] [CrossRef] [Green Version] - García, A.J.; Vega, M.D.; Boettiger, D. Modulation of Cell Proliferation and Differentiation through Substrate-dependent Changes in Fibronectin Conformation. Mol. Biol. Cell
**1999**, 10, 785–798. [Google Scholar] [CrossRef] [Green Version] - Inoue, S.; Frank, V.; Hörning, M.; Kaufmann, S.; Yoshikawa, H.Y.; Madsen, J.P.; Lewis, A.L.; Armes, S.P.; Tanaka, M. Live Cell Tracking of Symmetry Break in Actin Cytoskeleton Triggered by Abrupt Changes in Micromechanical Environments. Biomater. Sci.
**2015**, 3, 1539–1544. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Otsu, N. A Threshold Selection Method from Gray-Level Histograms. IEEE Trans. Syst. Man Cybern.
**1979**, 9, 62–66. [Google Scholar] [CrossRef] [Green Version] - Matson, J.P.; Cook, J.G. Cell Cycle Proliferation Decisions: The Impact of Single Cell Analyses. Febs J.
**2017**, 284, 362–375. [Google Scholar] [CrossRef] [Green Version] - Lira, L.M.; Martins, K.A.; de Torresi, S.I.C. Structural Parameters of Polyacrylamide Hydrogels Obtained by the Equilibrium Swelling Theory. Eur. Polym. J.
**2009**, 45, 1232–1238. [Google Scholar] [CrossRef] - Oyen, M.L. Mechanical Characterisation of Hydrogel Materials. Int. Mater. Rev.
**2014**, 59, 44–59. [Google Scholar] [CrossRef] - Righetti, P.G.; Brost, B.C.W.; Snyder, R.S. On the Limiting Pore Size of Hydrophilic Gels for Electrophoresis and Isoelectric Focussing. J. Biochem. Biophys. Methods
**1981**, 4, 347–363. [Google Scholar] [CrossRef] - Bian, W.; Bursac, N. Engineered Skeletal Muscle Tissue Networks with Controllable Architecture. Biomaterials
**2009**, 30, 1401–1412. [Google Scholar] [CrossRef] [Green Version] - Finney, D.J. On the Distribution of a Variate Whose Logarithm Is Normally Distributed. Suppl. J. R. Stat. Soc.
**1941**, 7, 155–161. [Google Scholar] [CrossRef] - Kanchanawong, P.; Shtengel, G.; Pasapera, A.M.; Ramko, E.B.; Davidson, M.W.; Hess, H.F.; Waterman, C.M. Nanoscale Architecture of Integrin-Based Cell Adhesions. Nature
**2010**, 468, 580–584. [Google Scholar] [CrossRef] [Green Version] - Rajagopalan, P.; Marganski, W.A.; Brown, X.Q.; Wong, J.Y. Direct Comparison of the Spread Area, Contractility, and Migration of Balb/c 3T3 Fibroblasts Adhered to Fibronectin- and RGD-Modified Substrata. Biophys. J.
**2004**, 87, 2818–2827. [Google Scholar] [CrossRef] [Green Version] - Sunyer, R.; Jin, A.J.; Nossal, R.; Sackett, D.L. Fabrication of Hydrogels with Steep Stiffness Gradients for Studying Cell Mechanical Response. PLoS ONE
**2012**, 7, e46107. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lovett, D.B.; Shekhar, N.; Nickerson, J.A.; Roux, K.J.; Lele, T.P. Modulation of Nuclear Shape by Substrate Rigidity. Cell. Mol. Bioeng.
**2013**, 6, 230–238. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gong, Z.; Szczesny, S.E.; Caliari, S.R.; Charrier, E.E.; Chaudhuri, O.; Cao, X.; Lin, Y.; Mauck, R.L.; Janmey, P.A.; Burdick, J.A.; et al. Matching Material and Cellular Timescales Maximizes Cell Spreading on Viscoelastic Substrates. Proc. Natl. Acad. Sci. USA
**2018**, 115, E2686–E2695. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chaudhuri, O.; Gu, L.; Darnell, M.; Klumpers, D.; Bencherif, S.A.; Weaver, J.C.; Huebsch, N.; Mooney, D.J. Substrate Stress Relaxation Regulates Cell Spreading. Nat. Commun.
**2015**, 6, 6365. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dupont, S.; Morsut, L.; Aragona, M.; Enzo, E.; Giulitti, S.; Cordenonsi, M.; Zanconato, F.; Le Digabel, J.; Forcato, M.; Bicciato, S.; et al. Role of YAP/TAZ in Mechanotransduction. Nature
**2011**, 474, 179–183. [Google Scholar] [CrossRef] [PubMed] - Yamazaki, M.; Kidoaki, S.; Fujie, H.; Miyoshi, H. Designing Elastic Modulus of Cell Culture Substrate to Regulate YAP and RUNX2 Localization for Controlling Differentiation of Human Mesenchymal Stem Cells. Anal. Sci.
**2021**, 37, 447–453. [Google Scholar] [CrossRef] [PubMed] - Panciera, T.; Azzolin, L.; Cordenonsi, M.; Piccolo, S. Mechanobiology of YAP and TAZ in Physiology and Disease. Nat. Rev. Mol. Cell Biol.
**2017**, 18, 758–770. [Google Scholar] [CrossRef] - Morikawa, Y.; Zhang, M.; Heallen, T.; Leach, J.; Tao, G.; Xiao, Y.; Bai, Y.; Li, W.; Willerson, J.T.; Martin, J.F. Actin Cytoskeletal Remodeling with Protrusion Formation Is Essential for Heart Regeneration in Hippo-deficient Mice. Sci. Signal.
**2015**, 8, ra41. [Google Scholar] [CrossRef] [Green Version] - Xin, M.; Kim, Y.; Sutherland, L.B.; Murakami, M.; Qi, X.; McAnally, J.; Porrello, E.R.; Mahmoud, A.I.; Tan, W.; Shelton, J.M.; et al. Hippo Pathway Effector Yap Promotes Cardiac Regeneration. Proc. Natl. Acad. Sci. USA
**2013**, 110, 13839–13844. [Google Scholar] [CrossRef] [Green Version] - Aratyn-Schaus, Y.; Oakes, P.W.; Stricker, J.; Winter, S.P.; Gardel, M.L. Preparation of Complaint Matrices for Quantifying Cellular Contraction. J. Vis. Exp. JoVE
**2010**, 14, 2173. [Google Scholar] [CrossRef] [Green Version] - Tse, J.R.; Engler, A.J. Preparation of Hydrogel Substrates with Tunable Mechanical Properties. Curr. Protoc. Cell Biol.
**2010**, 10. [Google Scholar] [CrossRef] [PubMed] - Hörning, M.; Blanchard, F.; Isomura, A.; Yoshikawa, K. Dynamics of Spatiotemporal Line Defects and Chaos Control in Complex Excitable Systems. Sci. Rep.
**2017**, 7, 7757. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Loppini, A.; Erhardt, J.; Fenton, F.H.; Filippi, S.; Hörning, M.; Gizzi, A. Optical Ultrastructure of Large Mammalian Hearts Recovers Discordant Alternans by In Silico Data Assimilation. Front. Netw. Physiol.
**2022**, 2. [Google Scholar] [CrossRef]

**Figure 1.**Proliferation dynamic of a single myocyte. Shown is an actin-tagged C2C12 muscle cell on glass that undergoes proliferation at about $t=0$ min. The two daughter cells increase their size and eventually migrate independently ($t\ge 30$ min).

**Figure 2.**Property assessment of the poly-acrylamide hydrogels. (

**A**) Average Young’s modulus E as a function of the total monomer concentration ${C}_{m}$ at fixed cross-linker ratio of $2\%$. The change in ${C}_{m}$ shows a linear increase in E, as illustrated by the dashed line. (

**B**) Three exemplary nano-indentation curves measured at ${C}_{m}=0.6$, $1.0$ and $2.0$ mol·kg${}^{-1}$. Shown is force F as a function of indentation depth $\delta $. (

**C**) Average height $\mathsf{\Delta}z$ of the hydrogels as a function of ${C}_{m}$, obtained by auto-fluorescence measurements using confocal laser scanning microscopy. (

**D**) Example of an auto-fluorescence signal of a hydrogel with ${C}_{m}$ = 2.0 mol·kg${}^{-1}$ ($E=35$ kPa). Shown is the normalized intensity as a function of height z. The two peaks mark the transitions from glass to gel and gel to culture medium, respectively. The gel height $\mathsf{\Delta}z$ is calculated as the peak-to-peak distance.

**Figure 3.**Cell area dependence on functionalized rigid hydrogels. (

**A**) Phase contrast image of C2C12 cells on substrate rigidity $E\simeq 12.4$ kPa and fibronectin coating density ${\rho}_{\mathrm{FN}}\simeq 2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$. (

**B**) Probability histograms of projected cell areas A for two substrate rigidities E at constant fibronectin density ${\rho}_{\mathrm{FN}}\simeq 2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$. (

**C**) Probability histograms of A for two different ${\rho}_{\mathrm{FN}}$ at constant $E\simeq 12.4$ kPa. (

**D**) Mean projected cell areas $\langle A\rangle $ as a function of E for two different ${\rho}_{\mathrm{FN}}$. The solid and dashed lines are fits of the Hill equation (Equation (4)). (

**E**) $\langle A\rangle $ as a function of ${\rho}_{\mathrm{FN}}$ at $E\simeq 12.4$ kPa (left pointed triangles) and $E\simeq 35.4$ kPa (right pointed triangles). The solid and dashed lines are visual guidance. (

**D**,

**E**) Another visualization of the distributions is illustrated in Figure S2. The color scheme used in (

**C**–

**E**) relates to cells that are cultured on substrates functionalized with ${\rho}_{\mathrm{FN}}\simeq 0.4$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ (blue) and ${\rho}_{\mathrm{FN}}\simeq 2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ (orange). (

**F**) Two-dimensional histogram of $\langle A\rangle $ as a function of E and ${\rho}_{\mathrm{FN}}$. The error-bars indicate standard error (see Section 2).

**Figure 4.**Cross-talk between hydrogel rigidity and fibronectin density. (

**A**,

**B**) Example of area distributions fitted by the mixture of two normal probability density functions (MN-pdf, see Supplemental Material). Red lines are MN-pdf, and blue lines are the two individual normal distributions. (

**C**) Lower and higher means $\langle A\rangle $ of the obtained MN-pdfs as a function of ${\rho}_{\mathrm{FN}}$ at $E\simeq 12.4$ kPa (left pointed triangles) and $E\simeq 35.4$ kPa (right pointed triangles). Solid and dashed lines are fits of the Lorentz equation (Equation (5)) for the two Young’s moduli. The data correspond to the data shown in Figure 3E. (

**D**) Lower and higher means $\langle A\rangle $ of the obtained MN-pdfs as a function of E for ${\rho}_{\mathrm{FN}}\simeq 0.4$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ (blue circles) and ${\rho}_{\mathrm{FN}}\simeq 2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ (orange diamonds). Solid and dashed lines are fits of the Hill equation (Equation (4)). The error bars in (

**C**,

**D**) indicate the respective standard errors (see Supplemental Material). (

**E**) Two-dimensional relationship of $\langle A\rangle $ as a function of E and ${\rho}_{\mathrm{FN}}$ corresponding to the data in (

**C**,

**D**). The fit was calculated by Equation (6).

**Figure 5.**Actin cytoskeleton formation dependence on fibronectin density. (

**A**) Actin- and cell-nuclei-labeled confocal images of C2C12 cells on $E\simeq 12.4$ kPa hydrogels coated with ${\rho}_{\mathrm{FN}}\simeq 0.4$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ (

**left**panel) and ${\rho}_{\mathrm{FN}}\simeq 2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ (

**right**panel). Two exemplary sections of prior-processed images by AQuA (

**middle**panel) are illustrated from these two ${\rho}_{\mathrm{FN}}$ (dashed selection,

**left**and

**right**panel). (

**B**–

**D**) Statistical analysis of mean projected cell areas $\langle A\rangle $, mean amount of actin $\langle M\rangle $, and fraction of actin amount to cell area $\langle R\rangle $ of the $5\times 5$ tiled images. The respective number of images N and sum of the containing cells, i.e., nuclei, n is written on top of (

**B**). Each brightly colored round data point is calculated from one $5\times 5$ tiled image, and the mean and standard error of those are shown by the darker-colored data points. Substrates functionalized with ${\rho}_{\mathrm{FN}}\simeq 0.4$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ and ${\rho}_{\mathrm{FN}}\simeq 2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ are highlighted in blue and orange. Asterisks depict outliers (see Section 2). (

**E**) Probability density of actin fiber length L. Percentiles of 2%, 10%, 90% and 98% are marked by dashed and dotted white lines. $\langle L\rangle $ is marked as a solid white line.

**Figure 6.**Proliferation dynamic of a single myocyte on a rigid hydrogel. (

**A**) Snapshots of a C2C12 muscle cell that undergoes proliferation at about $t=0$ min on a $E\simeq 12.4$ kPa hydrogel coated with ${\rho}_{\mathrm{FN}}\simeq 2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$. The images were processed by AQuA. (

**B**) Temporal tracking of the projected cell area A, the circularity C, aspect ratio r and fraction of actin amount to cell area R during 15 h of cell migration and proliferation. The mother and two daughter cells are distinguished by gray circles, green upward- and red downward-pointing triangles, respectively.

**Figure 7.**Proliferation dynamics depend on the ECM. (

**A**) Example of a C2C12 muscle cell on a $E\simeq 12.4$ kPa hydrogel coated with ${\rho}_{\mathrm{FN}}\simeq 2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$, and the corresponding projected cell area A as a function of time. (

**B**) The time evolution of the A of cells cultured on $E\simeq 12.4$ kPa hydrogels coated with either $0.4$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ (

**left**panel) or $2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ (

**right**panel). (

**C**) The time evolution of the A of cells cultured on $E\simeq 35.4$ kPa hydrogels coated with either $0.4$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ (

**left**panel) or $2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ (

**right**panel). (

**D**–

**H**) Statistical analysis of the cell trajectories (

**B**,

**C**). Shown are the following extracted parameters: area plateau of the mother cells ${A}_{\mathrm{P}1}$, area plateau of the daughter cells ${A}_{\mathrm{P}2}$, area ratio of mother to daughter cells ${A}_{\mathrm{P}2}/{A}_{\mathrm{P}2}$, initial spreading rate m after cell division, and duration of spreading $\mathsf{\Delta}{t}_{m}$ as a function of E and ${\rho}_{\mathrm{FN}}$. The exemplary parameters are highlighted in solid red lines in (

**A**). (

**I**) Cell cycle duration T, i.e., duration between two successive cell divisions. Means and medians are illustrated by solid and dotted lines, respectively. Number of data points is written on top of the plots as N, excluding outliers that are highlighted by asterisks. Substrates functionalized with ${\rho}_{\mathrm{FN}}\simeq 0.4$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ and ${\rho}_{\mathrm{FN}}\simeq 2.6$ $\mathsf{\mu}{\mathrm{g}/\mathrm{cm}}^{2}$ are highlighted in blue and orange, respectively.

Total Monomer Concentration, ${\mathit{C}}_{\mathit{m}}$ | H${}_{2}$O | AAm | bAAm |
---|---|---|---|

(mol·kg${}^{-1}$) | ($\mathsf{\mu}$L) | ($\mathsf{\mu}$L) | ($\mathsf{\mu}$L) |

0.60 | 780.2 | 104.5 | 92.5 |

0.80 | 714.5 | 139.3 | 123.3 |

1.00 | 648.9 | 174.2 | 154.2 |

1.25 | 566.8 | 217.7 | 192.7 |

1.50 | 484.7 | 261.2 | 231.3 |

1.75 | 402.6 | 304.8 | 269.8 |

2.00 | 320.6 | 348.3 | 308.3 |

FN Coating Density, ${\mathit{\rho}}_{\mathbf{FN}}$ | Volume on Gel | FN Concentration | FN Coating Density | Protein Equilibrium Distance |
---|---|---|---|---|

($\mathsf{\mu}$g/cm${}^{2}$) | ($\mathsf{\mu}$L) | ($\mathsf{\mu}$g/mL) | ($\mathbf{molecules}/\mathsf{\mu}{\mathbf{m}}^{2}$) | (nm) |

0.4 | 300 | 5.00 | 1456 | 17.2 |

1.1 | 250 | 16.72 | 4005 | 10.4 |

1.8 | 250 | 27.36 | 6554 | 8.1 |

2.6 | 250 | 40.00 | 9467 | 6.8 |

3.3 | 250 | 50.16 | 12,016 | 6.0 |

4.0 | 250 | 60.80 | 14,565 | 5.5 |

**Table 3.**Young’s modulus of hydrogels measured via AFM and linear fit (see Figure 2A).

Total Monomer Concentration, ${\mathit{C}}_{\mathit{m}}$ | Young’s Modulus, E (Measured via AFM) | Young’s Modulus, E (Linear Fit) |
---|---|---|

(mol·kg${}^{-1}$) | (kPa) | (kPa) |

0.60 | 3.3 ± 0.2 | 3.2 |

0.80 | 7.2 ± 0.2 | 7.8 |

1.00 | 12.3 ± 1.1 | 12.4 |

1.25 | 19.9 ± 1.8 | 18.2 |

1.50 | 23.4 ± 1.5 | 23.9 |

1.75 | 30.3 ± 2.5 | 29.7 |

2.00 | 34.8 ± 3.7 | 35.4 |

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**MDPI and ACS Style**

Brock, J.; Erhardt, J.; Eisler, S.A.; Hörning, M.
Optimization of Mechanosensitive Cross-Talk between Matrix Stiffness and Protein Density: Independent Matrix Properties Regulate Spreading Dynamics of Myocytes. *Cells* **2022**, *11*, 2122.
https://doi.org/10.3390/cells11132122

**AMA Style**

Brock J, Erhardt J, Eisler SA, Hörning M.
Optimization of Mechanosensitive Cross-Talk between Matrix Stiffness and Protein Density: Independent Matrix Properties Regulate Spreading Dynamics of Myocytes. *Cells*. 2022; 11(13):2122.
https://doi.org/10.3390/cells11132122

**Chicago/Turabian Style**

Brock, Judith, Julia Erhardt, Stephan A. Eisler, and Marcel Hörning.
2022. "Optimization of Mechanosensitive Cross-Talk between Matrix Stiffness and Protein Density: Independent Matrix Properties Regulate Spreading Dynamics of Myocytes" *Cells* 11, no. 13: 2122.
https://doi.org/10.3390/cells11132122