Appendix 2—table 1. The transition rates between all possible states of a crosslinker ${\displaystyle U\rightleftharpoons (S_A,S_B)\rightleftharpoons D}$.

${\displaystyle \left(S_A,S_B\right)}$ means either head $A$ or $B$ is bound but the other is unbound. All binding rates account for the linear binding density ${\displaystyle ϵ}$ is the length of filament $i$ with center-of-mass position ${\displaystyle {\mathit{x}}_i}$ and orientation ${\displaystyle {\mathit{p}}_i}$ inside the capture sphere with cutoff radius $r_{c,s}$ relative to position of motor/crosslinker ${\displaystyle \mathit{x}}$. The sum is over all possible candidate filaments $i$. The unbound-singly bound transition $U\rightleftharpoons (S_A,S_B)$ is determined by the association constant $K_{\mathrm{a}}$ and the force-independent off rate ${\displaystyle k_{\mathrm{o},s}}$. Similarly, the singly bound-doubly bound transition $(S_A,S_B)\rightleftharpoons D$ is determined by the association constant $K_{\mathrm{e}}$ and force-independent off rate ${\displaystyle k_{\mathrm{o},d}}$ with an additional factor $V_{\mathrm{bind}}$, the effective volume explored by the unattached head while the motor/crosslinker is singly bound. Energy dependence in the $(S_A,S_B)\rightleftharpoons D$ transition rates is imposed by the Boltzmann factor that is a function of $\beta =1/(k_{B}T)$, the tether length of the motor/crosslinker attached to filaments $i$ and $j$ at locations s_i and s_j${\displaystyle \ell (s_i,s_j,{\mathit{x}}_i,{\mathit{p}}_i,{\mathit{x}}_j,{\mathit{p}}_j}$), the characteristic length of the tether not under load ${\mathrm{\ell }}_o$, and the filament diameter $D_{\mathrm{fil}}$. The dimensionless factor λ determines the energy dependence in the unbinding rate while the x_c is the characteristic length that determines the force dependence. The latter is not used in the simulations of the main text but is implemented in the code base.

Process	Rate	Value
$U\to (S_A,S_B)$	${\displaystyle R_{\mathrm{o}\mathrm{n},S}(\mathit{x},t)}$	${\displaystyle {\displaystyle \frac{3ϵK_{\mathrm{a}}{k}_{\mathrm{o},S}}{4\pi r_{c,S}^3}\sum _i{L}_{\mathrm{i}\mathrm{n},i}(\mathit{x},t)}}$
$(S_A,S_B)\to U$	${\displaystyle R_{\mathrm{o}\mathrm{f}\mathrm{f},S}}$	${\displaystyle {\displaystyle k_{\mathrm{o},S}}}$
$(S_A,S_B)\to D$	${\displaystyle R_{\mathrm{o}\mathrm{n},D}(s_i,t)}$	${\displaystyle {\displaystyle \frac{ϵK_{\mathrm{e}}{k}_{\mathrm{o},D}}{V_{\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{d}}}\sum _j{\int }_{L_j}d{s}_j\exp \left[-\beta {\kappa }_{\mathrm{x}\mathrm{l}}\left(\frac{1-\lambda }{2}{\left(\ell -{\ell }_o-D_{\mathrm{f}\mathrm{i}\mathrm{l}}\right)}^2-x_c\left(\ell -{\ell }_o-D_{\mathrm{f}\mathrm{i}\mathrm{l}}\right)\right)\right]}}$
$D\to (S_A,S_B)$	${\displaystyle R_{\mathrm{o}\mathrm{f}\mathrm{f},D}(s_i,s_j,t)}$	${\displaystyle {\displaystyle k_{\mathrm{o},D}\exp \left[\beta {\kappa }_{\mathrm{x}\mathrm{l}}\left(\frac{\lambda }{2}{\left(\ell -{\ell }_o-D_{\mathrm{f}\mathrm{i}\mathrm{l}}\right)}^2+x_c\left(\ell -{\ell }_o-D_{\mathrm{f}\mathrm{i}\mathrm{l}}\right)\right)\right]}}$