## 3 Results
### Allosteric Communication across the Ras-Raf-RBD_CRD Dimer Complex  
We recently demonstrated that the Raf-RBD promotes Ras dimerization and used dynamical network analysis and optimal/suboptimal path calculations based on MD trajectories to identify allosteric connections linking both Ras dimerization and Raf-RBD interfaces in the HRas-CRaf-RBD dimer [8]. We use the same type of analysis here to identify pathways of allosteric connections in the HRas-CRaf-RBD_CRD dimer and compare them with those we found in the absence of the CRD. Briefly, a network is constructed of edges drawn between residues that stay within 4.5 A of each other for at least 75% of the simulation time and edges are weighted as a function of pairwise correlations [46]. The resulting connectivity network allows for the calculation of allosteric paths through residues that link distant regions of the protein or protein complex, with the optimal path representing the shortest sum of edge weights between two residues and suboptimal paths deviating from the optimal path within a user-specified threshold. In our previous work, we studied the paths linking the two Raf-RBD residues D113 in the dimer of the HRas-CRaf-RBD complex due to its positioning, along with Raf-RBD D117, in the Raf-RBD pocket for the scaffold protein Galectin-1, critical for the activation of the MAPK pathway [13]. We observed strong allosteric linkages between the D113 residues extending 85 A across the Ras-Raf-RBD dimer complex, and identified residues D47, located in loop 3 of one Rasprotomer, and E143, in \(\lx@sectionsign\)6 of the other, as a critical point of information transfer across the Ras dimerization interface [8]. It is intriguing that the Raf-CRD is located at the base of the Ras-Raf dimer to interact with both loop 3 of one Ras molecule and residue E143 of the other, therefore in contact with residues identified as critical for extending allosteric communication across the Ras dimerization interface [8]. Dynamical network analysis was performed for each simulation replicate to identify residues with correlated motions within the dimer of the HRas-CRaf-RBD_CRD complex and involved in intermolecular information transfer across the complex [56; 57]. The edge weights, determined as a function of pairwise correlations and used for optimal and suboptimal path calculations, for residues that cross the Ras-Raf-CRD', Ras-Raf-RBD_CRD and Ras-Ras' interfaces in the three MD simulation replicates, demonstrate the variability across both Ras-Raf-CRD interfaces in the global analysis (Tables S2-S4), consistent with the high RMSF associated with the Raf-CRD (Figure S3b). Due to longer simulation run times and the dynamic nature of the Ras-Raf-CRD interactions across the dimer interface (Figures S4a-d, S5a-d and S6a-d), dynamical network analysis was also performed by dividing each simulation into seven segments of 50 ns each in order to capture the diversity in communication extending across the complex (Figure 3a). Analysis of optimal and suboptimal path calculations between the two D113 residues of each Raf-RBD in the networks constructed over 350 ns of simulation time, are consistent with our HRas-CRaf-RBD dimer simulations [8], demonstrating the conservation of intermolecular information transfer involving the interswitch region of one Ras protomer and \(\lx@sectionsign\)6 of the other across the Ras dimerization interface (Figure 3a,b, orange path). Additionally, by constructing networks for smaller simulation segments, we capture four distinct modes of intermolecular information transfer that are consistent across the three replicates (Figure 3a and Figure S8) (Tables S5-S7). The first mode of information transfer involves the interswitch region and \(\lx@sectionsign\)6 as described above (Figure 3b, orange path). The second mode involves \(\alpha\)5 and \(\lx@sectionsign\)6 as described for KRas-CRaf-RBD dimer simulations modelled on the membrane [8] (Figure 3b, red path).