Fig 1.
A schematic diagram showing hypothetical conformational changes of the cadherin-catenin-actin complex under force.
A) A cartoon of the complex. In the absence of a crystal structure of the entirety, the diagram is drawn from the following PDB structures of various components: 3Q2V (E-cadherin), 3L6X (p120 catenin), 1I7W (β-catenin), 4IGG (αE-catenin), 1M8Q (F-actin). The arrangement of the structures relative to one another is a guess for the purposes of illustration. The theoretical model described in the text is independent of the details of this arrangement. B) The M region of αE-catenin, showing a conformation with small angle α between the M2 and M3 domains, favored at lower forces. The interactions (red dashed lines) between the adjacent F-actin binding domain (FABD) and F-actin depend on the conformational state of αE-catenin. C) Same as B, but in the large angle conformation, favored at larger forces. This results in an enhancement of FABD-actin interactions, leading to catch bond behavior.
Fig 2.
Energy landscape of the Hamiltonian U from Eqs (1) and (2) in terms of r and α = π − θ − ϕ at force F = 0, with the parameters given in Table 1 and described in the text.
Energy contour labels are in units of kBT. The vertical dashed line corresponds to the transition angle αc, the horizontal dashed line to the natural bond length r0, and the top edge to the distance r0 + d beyond which the bond ruptures. The energy barriers to rupture are smaller in the region α ≤ αc on the left, relative to the region α > αc on the right. Since applied force F > 0 tilts the landscape toward larger inter-domain angles α, the mean bond lifetime will initially increase with force.
Table 1.
Parentheses after the values denote the uncertainty in the last digit.
Fig 3.
Experimental mean bond lifetime τ(F) versus force F (symbols) from Ref. [11] compared to the theoretical model with best-fit parameters from Table 1 (curve).
Fig 4.
Bond survival probability ΣF(t) versus time t for four different forces F.
Theory results are shown as curves, and the corresponding experimental data [11] as symbols.
Fig 5.
The salt bridge network in the hinge region between the M1, M2, and M3 domains of αE-catenin (PDB: 4IGG) [41].
Fig 6.
The effects of mutating the angular barrier height H from the original value of 25 kBT down to zero, in increments of 5 kBT, leaving all other model parameters fixed at their Table 1 values: A) the mean bond lifetime τ(F); B) the mean lifetime τL(F) of remaining in the large angle conformational state, α > αc, measured from the initial time of entry into the state; C) the survival probability ΣF(t) at F = 7 pN.