# A multiscale theory for spreading and migration of adhesion-reinforced mesenchymal cells

## Cite this dataset

Kaplan, Nadir C.; Shu, Wenya (2023). A multiscale theory for spreading and migration of adhesion-reinforced mesenchymal cells [Dataset]. Dryad. https://doi.org/10.5061/dryad.h9w0vt4qr

## Abstract

We present a chemomechanical whole-cell theory for the spreading and migration dynamics of mesenchymal cells that can actively reinforce their adhesion to an underlying viscoelastic substrate as a function of its stiffness. Our multiscale model couples the adhesion reinforcement effect at the subcellular scale with the nonlinear mechanics of the nucleus-cytoskeletal network complex at the cellular scale to explain the concurrent monotonic area-stiffness and non-monotonic speed-stiffness relationships observed in experiments: We consider that large cell spreading on stiff substrates flattens the nucleus, increasing the viscous drag force on it. The resulting force balance dictates a reduction in the migration speed on stiff substrates. We also reproduce the experimental influence of the substrate viscosity on the cell spreading area and migration speed by elucidating how the viscosity may either maintain adhesion reinforcement or prevent it depending on the substrate stiffness. Additionally, our model captures the experimental directed migration behavior of the adhesion-reinforced cells along a stiffness gradient, known as durotaxis, as well as up or down a viscosity gradient (viscotaxis or anti-viscotaxis), the cell moving towards an optimal viscosity in either case. Overall, our theory explains the intertwined mechanics of the cell spreading, migration speed and direction in the presence of the molecular adhesion reinforcement mechanism.

## README

Title of Dataset: A multiscale theory for spreading and migration of adhesion-reinforced mesenchymal cells.

Author Information

A. Principal Investigator Contact Information

Name: C.Nadir Kaplan

Institution: Virginia Polytechnic Institute and State University

Address: Blacksburg, VA 24061, USA.

Email: nadirkaplan@vt.edu

B. First author Information

Name: Wenya Shu

Institution: Virginia Polytechnic Institute and State University

Address: Blacksburg, VA 24061, USA.

Email: wenya@vt.edu

Simulation code Overview:

- For speed and area calculation, use RacRho_reinforced1.py
- For durotaxis simulation, use RacRho_reinforced2.py
- For (anti-) viscotaxis simulations, use RacRho_reinforced3.py

Data Overview

file List:

A) Fig2A_E.txt

B) Fig2B.txt

C) Fig2C.txt

D) Fig2F_Biphasic.txt

E) Fig2F_Monotonic.txt

F) Fig3A_B_D_F.txt

G) Fig3C.txt

H) FIg3E.txt

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DATA-SPECIFIC INFORMATION FOR: Fig2A_E.txt

Number of variables: 3

Number of cases/rows: 64

Variable List:

* ks: The stiffness of the elastic substrates is given in pN/nm units and is non-dimensionalized by ks/k0, where k0 equals 5 pN/nm. Please refer to the x-axes of Figures 2A and 2E.

* v: The average cell migration speeds on elastic substrates with different stiffness. The speed is measured in μm/s and can be non-dimensionalized by v/v0, where v0 is set at 0.12 μm/s. Each data point in Figure 2E gives the mean and standard deviation of v across multiple simulations.

* A: The average cell spreading areas on elastic substrates with different stiffness. The area is measured in μm^2 and can be non-dimensionalized by A/L^2, where L is defined as 2π × 5 μm. Each data point in Figure 2A gives the mean and standard deviation of A across multiple simulations. Fig.2D can be obtained from Fig.2A using Eqs.10-12.

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DATA-SPECIFIC INFORMATION FOR: Fig2B.txt

Number of variables: 3

Number of cases/rows: 10

Variable List:

* ks: The stiffness of the elastic substrates is given in pN/nm unit and is non-dimensionalized by ks/k0, where k0 equals 5 pN/nm. Please refer to the x-axes of Figures 2B.

* Fsub at vertex 8: average focal adhesion force at the vertex 8 in one simulation, with the unit pN. It can be non-dimensionized by Fsub/F0, where F0 = Nm*fm = 200 pN.

* Fsub at vertex 0: average focal adhesion force at the vertex 0 in one simulation, with the unit pN. It can be non-dimensionized by Fsub/F0, where F0 = Nm*fm = 200 pN.

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DATA-SPECIFIC INFORMATION FOR: Fig2C.txt

Number of variables: 2

Number of cases/rows: 73

Variable List:

* ks: The stiffness of the elastic substrates is given in pN/nm unit and is non-dimensionalized by ks/k0, where k0 equals 5 pN/nm. Please refer to the x-axes of Figures 2C.

* |Fsub|: The average net traction force from all focal adhesion points on elastic substrates with different stiffness. The force is measured in pN and can be non-dimensionized by |Fsub|/F0, where F0 = Nm*fm = 200 pN. Figure 2C depicts the mean and standard deviation of |Fsub| across multiple simulations, plotted against the dimensionless stiffness.

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DATA-SPECIFIC INFORMATION FOR: Fig2F_Biphasic.txt

Number of variables: 2

Number of cases/rows: 231

Variable List:

* ks: The stiffness of the elastic substrates is given in pN/nm units and is non-dimensionalized by ks/k0, where k0 equals 5 pN/nm.

* v: The average cell migration speed on elastic substrates with different stiffness. It is measured in μm/s and can be non-dimensionalized by v/v0, where v0 is set at 0.12 μm/s. The solid line in Figure 2F gives the mean and standard deviation of v across multiple simulations, plotted against the dimensionless stiffness.

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DATA-SPECIFIC INFORMATION FOR: Fig2F_Monotonic.txt

Number of variables: 2

Number of cases/rows: 77

Variable List:

* ks: The stiffness of the elastic substrates is given in pN/nm units and is non-dimensionalized by ks/k0, where k0 equals 5 pN/nm.

* v: The average cell migration speed on elastic substrates with different stiffness. It is measured in μm/s and can be non-dimensionalized by v/v0, where v0 is set at 0.12 μm/s. The dashed line in Figure 2F gives the mean and standard deviation of v across multiple simulations, plotted against the dimensionless stiffness.

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DATA-SPECIFIC INFORMATION FOR: Fig3A_B_D_F.txt

Number of variables: 5

Number of cases/rows: 1690

Variable List:

* Ka: The additional stiffness of the viscoelastic substrates is given in pN/nm units. Please refer to the x-axes of Figures 3A. Only Ka within the range of 0.1-20 pN/nm has been utilized in Fig. 3A.

* Ke: The long-term stiffness of the viscoelastic substrates is set to a fixed value of 0.1 pN/nm in the simulation.

* Gama: The viscosity of the viscoelastic substrates has the range of 0.01-100 pN*s/nm in simulations. Please refer to the y-axes of Figures 3A.

* v: The average cell migration speed on viscoelastic substrates with varying Ka and Gama. It is measured in μm/s and can be non-dimensionalized by v/v0, where v0 is set at 0.12 μm/s. One can calculate the mean and standard deviation of migration speed on a substrate with identical viscoelastic properties from the values of v corresponding to the same Ka and Gama. Each mean value corresponds to one data point in Fig. 3A. For a constant Ka, plotting the mean and standard deviation of the migration speed against Gama produces Fig. 3F.

* A: The average cell spreading area on viscoelastic substrates with varying Ka and Gama. It is measured in μm^2 and can be non-dimensionalized by A/L^2, where L is defined as 2π × 5 μm. One can calculate the mean and standard deviation of the spreading area on a substrate with identical viscoelastic properties from the values of A corresponding to the same Ka and Gama. Each mean value corresponds to one data point in Fig. 3A. For a constant Ka, plotting the mean and standard deviation of the area against Gama (or tau) produces Fig. 3D (3B). Note that tau = Gama/Ka.

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DATA-SPECIFIC INFORMATION FOR: Fig3C.txt

Number of variables: 3

Number of cases/rows: ~50

Variable List:

* fast dmls area: The dimensionless cell spreading on fast relaxing substrates. The mean and standard deivation are reported in Fig. 3C.

* Mdium dmls area: The dimensionless cell spreading on intermediate relaxing substrates. The statistic significance can be analyzed by comparing it to the dataset "fast dmls area".

* slow dmls area: The dimensionless cell spreading on slow relaxing substrates. The statistic significance can be analyzed by comparing it to the dataset "fast dmls area".

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DATA-SPECIFIC INFORMATION FOR: Fig3E.txt

Number of variables: 2

Number of cases/rows: ~50

Variable List:

* fast speed: The average cell migration speeds on a fast-relaxing substrate. The speed is measured in μm/s and can be non-dimensionalized by v/v0, where v0 is set at 0.12 μm/s. The mean and standard deivation are reported in Fig. 3E.

* slow speed: The average cell migration speeds on a slow-relaxing substrate. The speed is measured in μm/s and can be non-dimensionalized by v/v0, where v0 is set at 0.12 μm/s. The statistic significance can be analyzed by comparing it to the dataset "fast speed" in Fig. 3E.