DOI: 10.5061/dryad.h9w0vt4qr
title: A multiscale theory for spreading and migration of adhesion-reinforced mesenchymal cells

description: 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. 
description: 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: B. First author
 Information Name: Wenya Shu Institution: Virginia Polytechnic Institute
 and State University Address: Blacksburg, VA 24061, USA. Email:
 Simulation code Overview: 1. For speed and area
 calculation, use RacRho_reinforced1.py 2. For durotaxis simulation, use
 RacRho_reinforced2.py 3. 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
 \#########################################################################
 DATA-SPECIFIC INFORMATION FOR: Fig2A_E.txt 1. Number of variables: 3 2.
 Number of cases/rows: 64 3. 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.
 \#########################################################################
 DATA-SPECIFIC INFORMATION FOR: Fig2B.txt 1. Number of variables: 3 2.
 Number of cases/rows: 10 3. 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.
 \#########################################################################
 DATA-SPECIFIC INFORMATION FOR: Fig2C.txt 1. Number of variables: 2 2.
 Number of cases/rows: 73 3. 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.
 \#########################################################################
 DATA-SPECIFIC INFORMATION FOR: Fig2F_Biphasic.txt 1. Number of variables:
 2 2. Number of cases/rows: 231 3. 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.
 \#########################################################################
 DATA-SPECIFIC INFORMATION FOR: Fig2F_Monotonic.txt 1. Number of variables:
 2 2. Number of cases/rows: 77 3. 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.
 \#########################################################################
 DATA-SPECIFIC INFORMATION FOR: Fig3A_B_D_F.txt 1. Number of variables: 5
 2. Number of cases/rows: 1690 3. 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.
 \#########################################################################
 DATA-SPECIFIC INFORMATION FOR: Fig3C.txt 1. Number of variables: 3 2.
 Number of cases/rows: ~50 3. 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".
 \#########################################################################
 DATA-SPECIFIC INFORMATION FOR: Fig3E.txt 1. Number of variables: 2 2.
 Number of cases/rows: ~50 3. 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.