Fig 1.
A sketch of the model interactions.
The diagram shows a simplified overview of the interactions in the models presented in this paper, where the blue ellipses represent the signalling molecules and the green rectangles the mechanical signals. The black arrows represent the reactions of the biochemical model in Eq (1) based on [18], i.e. ECM stiffness activates FAK on the cell membrane which activates RhoA. The grey arrows represent the coupling between chemistry and mechanics introduced in this work and described by Eqs (3)-(6), i.e. activated RhoA affects the cytoplasmic elastic stress which activates FAK and the cytoplasmic stiffness is a function of activated FAK.
Table 1.
Parameter values for simulations of the model in Eqs (3)–(6).
Fig 2.
Numerical simulation results showing ,
,
and
for the model in Eqs (3)–(6) for the axisymmetric shape and in the case of 2xD stimulus at a steady state at T = 100 s.
Four different scenarios are considered: (A) C1 = 0 and Ec = 0.6 kPa
; (B) C1 = 0
and
; (C) C1 = 0.1
and Ec = 0.6 kPa
; (D) C1 = 0.1
and
. Within each subfigure, the rows represent
,
,
and
on a cross-section of the plane x1 = 0 of the axisymmetric cell, and the columns represent
. Parameter values as in Table 1.
Fig 3.
Numerical simulation results showing ,
,
and
for the model in Eqs (3)–(6) for the lamellipodium shape and in the case of 2xD stimulus at a steady state at T = 100 s.
Four different scenarios are considered: (A) C1 = 0 and Ec = 0.6 kPa
; (B) C1 = 0
and
; (C) C1 = 0.1
and Ec = 0.6 kPa
; (D) C1 = 0.1
and
. Within each subfigure, the rows represent
,
,
and
on the surface of the cell, and the columns represent
kPa. Parameter values as in Table 1.
Fig 4.
Simulation results showing the mean, , min and max values of
,
,
and
as functions of substrate stiffness E.
We consider different couplings with four different values for C1 and two different shapes at T = 100 s by which time the results are at a steady state. All other parameter values as in Table 1.
Fig 5.
Numerical simulation results showing ,
,
and
for the model in Eqs (3)–(6) for the axisymmetric shape and in the case of the 3D stimulus at a steady state at T = 100 s.
Four different scenarios are considered: (A) C1 = 0 and Ec = 0.6 kPa
; (B) C1 = 0
and
; (C) C1 = 0.1
and Ec = 0.6 kPa
; (D) C1 = 0.1
and
. Within each subfigure, the rows represent
,
,
and
on a cross-section of the plane x1 = 0 of the axisymmetric cell, and the columns represent
. Parameter values as in Table 1.
Fig 6.
Simulation results showing the mean, , min and max values of
,
,
and
as functions of substrate stiffness E.
We consider different couplings with four different values for C1 and two different shapes at T = 100 s by which time the results are at a steady state. All other parameter values as in Table 1.
Fig 7.
Numerical simulation results showing ,
,
and
for the model in Eqs (3), (4), and (6) for the axisymmetric shape and in the case of the 3D stimulus at a steady state at T = 100 s.
Four different scenarios are considered: (A) C1 = 0 and Ec = 0.6 kPa
; (B) C1 = 0
and
; (C) C1 = 0.1
and Ec = 0.6 kPa
; (D) C1 = 0.1
and
. Within each subfigure, the rows represent
,
,
and
on a cross-section of the plane x1 = 0 of the axisymmetric cell, and the columns represent
kPa. Parameter values as in Table 1.
Fig 8.
Simulation results showing the mean, , min and max values of
,
,
and
as functions of substrate stiffness E, in the case of the model in Eqs (3), (4) and (6) and 3D stimulus.
We consider different couplings, four different values for C1, and two different shapes at T = 100 s by which time the results are at a steady state. All other parameter values as in Table 1.
Fig 9.
Numerical simulation results showing ,
,
and
simulation results showing
and
for the model in Eqs (3), (4), and (6) for the axisymmetric shape and in the case of 2xD stimulus at a steady state at T = 100 s.
Four different scenarios are considered: (A) C1 = 0 and Ec = 0.6 kPa
; (B) C1 = 0
and
; (C) C1 = 0.1
and Ec = 0.6 kPa
; (D) C1 = 0.1
and
. Within each subfigure, the rows represent
,
,
and
on a cross-section of the plane x1 = 0 of the axisymmetric cell, and the columns represent
kPa. Parameter values as in Table 1.