*4.2. Statistical Kinetic Modelling of Linker Regions*

To assess the statistical kinetic behavior of DLD proteins we chose the Freely Jointed Chain (FJC) model and simulated it with a Gaussian approximation [36,62]. As shown by details of the model (Supplementary Methods and Figure S1), this only causes minor deviations from the analytical solution at extreme linker lengths.

An important parameter in modelling is the stiffness of the chain that characterizes its nature of spatial distribution. In the FJC model, this is described by Kuhn segments (l\_k), whose measure is two times the persistence length. In a freely moving random-coil polypeptide chain this persistence length is 0.44 nm [62], whereas in a stiff polyproline helix it is roughly an order of magnitude longer. To get the number of Kuhn segments, an amino acid chain can be simulated by calculating the contour length of the chain, l\_c, divided by l\_k.

It is to be noted that the approximation of a kinetic phenomenon of binding and/or dissociation is only tenable if reaching the equilibrium in spatial distribution is much faster than the event of binding and unbinding, i.e., binding/unbinding is not rate-limiting. As diffusion rates of small proteins in water are on the order of 10−<sup>6</sup> cm<sup>2</sup> s−<sup>1</sup> [63], which is equivalent to 102 nm2·s−1, the typical <sup>μ</sup>s time of the unbound ("free," for domain definitions, cf. Figure 1D) domain equilibrating within the boundaries of the model is well below the time scale of processivity steps.
