Figure 5A depiction of the Entropic Penalty Compensation (E/CPC) mechanism. The energy contribution of WT RAD51 polymerisation enables RAD51 to overcome the entropic penalty to binding flexible DNA (here depicted as ssDNA). F86E RAD51 has a lower RAD51 protomer-protomer affinity and a consequent lower protomer-protomer enegy contribution to polymerisation, and thus cannot overcome the entropic penalty for binding to flexible DNA. Both WT and F86E RAD51 can overcome the modest entropic penalty to binding stiff DNA (here depicted as dsDNA). Thick arrows indicate fast capture and fast unbinding, while thin arrows indicate slow capture and slow unbinding. As in Fig. 4B, but F86E RAD51 was injected at the indicated concentration to measure association and dissociation kinetics. The flexibility of respective DNA, the expected relative entropic penalties upon F86E RAD51 binding to each DNA molecule and protomer-protomer binding enegy contribution of F86 RAD51 are indicated in gray, green and blue boxes. H and L shown in each box indicate high and low, respectively. The mean number of F86E RAD51 bound to respective DNA oligonucleotides, as measured by SPR (dotted lines) and corresponding model fits (solid lines) using the model shown in panel D. Using ABC-SMC, individual forward rates (kp) and reverse rates (kpr) were fitted to each experimental curve, while a single KD was fitted to all experimental curves. Kinetic representation of the ordinary differential equation (ODE) model describing F86E RAD51 polymerisation on ssDNA and dsDNA, consisting of three parameters: kp (polymerisation forward rate), kpr (polymerisation reverse rate), KD (protomer-protomer dissociation constant). The KD predicts the concentrations of F86E RAD51 polymers of variable length in solution, while kp and kpr predict the speed of formation of F86E RAD51 polymers on ssDNA and dsDNA. A simplified model compared to the models in Fig. 3 A and B was used for F86E RAD51 because the kinetics of F86E RAD51 to the dN-5, dN-5p, dN-8, dN-8p, dN-11, dN-11p, dN-14 and dN-17 were not systematically assessed due to low F86E purification yield. The predicted KD value for F86E is shown. Mean value of mode particles ± 1 SD derived from the ABC-SMC fits (n=3). Bar plots of fitted kp values for the SPR curves. Mean values of mode particles ± 1 SD derived from the ABC-SMC fits (n=3). Un-paired, one-tailed Mann-Whitney-Wilcoxon tests. * p ≤ 0.05; ns = non-significant. Predicted concentrations of F86E RAD51 polymers in solution at equilibrium as a function of F86E RAD51 monomer concentration (150 nM, 3 µM, 30 µM), prior to RAD51 injection onto DNA-coated SPR CM5 chips. Predicted % F86E RAD51 within each polymer state in solution at equilibrium as a function of F86E RAD51 monomer concentration (150 nM, 3 µM, 30 µM), prior to RAD51 injection onto DNA-coated SPR CM5 chips. In panels F and G, the KD was fixed to the mean value identified in Fig. 5D (i.e. KD = 10.2 µM), and the concentration of F86E RAD51 monomer concentration was varied accordingly. In panel G, the % F86E RAD51 values were calculated by multiplying the polymer concentrations by their respective polymer length, and dividing each value by the total RAD51 monomer concentration (i.e. % F86E RAD51 = [n-mer] * n / [F86E RAD51monomer]). [F86E RAD51monomer] was calculated via coomassie staining image quantification using a BSA standard curve. Bar plots of fitted kpr values for the SPR curves. Mean values of mode particles ± 1 SD derived from the ABC-SMC fits (n=3). Un-paired, one-tailed Mann-Whitney-Wilcoxon tests. * p ≤ 0.05; ns = non-significant.