Effect of loading conditions on the dissociation behaviour of catch bond clusters

Abstract

Under increasing tensile load, the lifetime of a single catch bond counterintuitively increases up to a maximum and then decreases exponentially like a slip bond. So far, the characteristics of single catch bond dissociation have been extensively studied. However, it remains unclear how a cluster of catch bonds behaves under tensile load. We perform computational analysis on the following models to examine the characteristics of clustered catch bonds: (i) clusters of catch bonds with equal load sharing, (ii) clusters of catch bonds with linear load sharing, and (iii) clusters of catch bonds in micropipette-manipulated cell detachment. We focus on the differences between the slip and catch bond clusters, identifying the critical factors for exhibiting the characteristics of catch bond mechanism for the multiple-bond system. Our computation reveals that for a multiple-bond cluster, the catch bond behaviour could only manifest itself under relatively uniform loading conditions and at certain stages of decohesion, explaining the difficulties in observing the catch bond mechanism under real biological conditions.

Figure 1.

Schematic of conceptual energy landscape of Evans' model [21]. The dissociation pathways x₁ and x₂ are indicated by the two solid lines. These two pathways originate from two bound states, 1 and 2, respectively. At low forces, state 1 is more favourable; as force on the bond increases, state 2 also becomes more favourable. The dissociation via pathway 1 is fast and has a constant rate k_1rup. The dissociation rate along pathway 2 is lower at small forces, but increases significantly with increasing forces by lowering its energy barrier (as denoted by the dashed line), leading to an exponential increase of the dissociation rate k_2rup.

Figure 2.

Schematic of bond clusters under constant force F. (a) F is equally shared by all closed bonds. (b) An inclined angle θ is kept between two rigid plates, so that the force is linearly distributed on each row of bonds. (c) The detachment of a BFP-loaded cell from the substrate surface; the force at the adhesion front is nonlinearly distributed on each bond.

Figure 3.

Single-bond lifetimes versus the loading force for both slip and catch bond models. Dashed line represents the Evans model and solid line represents the Bell model.

Figure 4.

Lifetime analyses for uniformly loaded bond clusters. (a,b) Change of bond number versus time t at different loading forces: (a) slip bond model (solid line with dots, 7.1 pN; solid line, 10 pN; dashed line, 20 pN; dashed dotted line, 30 pN; dotted line, 40 pN; dash double-dotted line, 50 pN); (b) catch bond model (solid line with dots, 3.7 pN; solid line, 10 pN; short dashed line, 20 pN; dashed dotted line, 30 pN; dotted line, 40 pN; long dashed line, 50 pN; dash double-dotted line, 60 pN). The curves with the circle symbols denote the equilibrium status. (c,d) Rupture time versus the loading force at different decohesion stages: (c) slip bond model (lines with squares denote time for one-third bonds broken, lines with diamonds denote time for two-third bonds broken and lines with circles denote lifetime); (d) catch bond model (lines with squares denote time for one-third bonds broken, lines with diamonds denote time for two-third bonds broken and lines with triangles denote lifetime).

Figure 5.

Lifetime analysis for linearly loaded bond clusters. (a,c,e) Bond number versus time t at different loading levels—(a) tan θ = 0.1; (c) tan θ = 0.2 and (e) tan θ = 0.3 (solid lines, 20 pN; short dashed lines, 25 pN; dashed dotted lines, 30 pN; dotted lines, 35 pN; long dashed lines, 40 pN; dash double-dotted lines, 50 pN). (b,d,f) Rupture time versus loading force at different stages of decohesion—(b) tan θ = 0.1; (d) tan θ = 0.2; and (f) tan θ = 0.3 (lines with squares denote time for one-sixth bonds broken, lines with diamonds denote time for one-third bonds broken and lines with triangles denote time for one-half bonds broken; lines with circles denote lifetime).

Figure 6.

Rupture time of BFP-manipulated cell detachment versus loading force at four different decohesion stages: catch bond model is denoted by solid lines, while slip bond model is denoted by dashed lines. Lines with squares denote time for 10% bonds broken, lines with triangles denote time for 30% bonds broken and lines with diamonds denote time for 60% bonds broken; lines with circles denote lifetime.

Figure 7.

The calculated configuration of the BFP-manipulated cell detachment from a substrate surface, and the close-up view of the cell–substrate contact front. This configuration was obtained at the beginning of the detachment with a loading force F = 700 pN.