SUPPORTING INFORMATIONS

Well-tempered metadynamics. Metadynamics1 is a technique for enhancing sampling in molecular dynamics simulations. It is able to reconstruct the free-energy surface as a function of few selected degrees of freedom, called collective variables (CVs), S. In metadynamics, an external history-dependent bias potential which is a function of the CVs, is added to the Hamiltonian of the system. The bias potential is built during the simulation as a sum of Gaussian functions centered on the previously visited configurations in the CVs space discouraging the system from revisiting configurations that have already been sampled. The free energy surface, as a function of the CVs, can be reconstructed as the negative of the sum of the added gaussians. At variance with metadynamics, in the welltempered formalism2 the initial deposition rate ω0 of the bias potential decreases with the bias accumulated over time. This is achieved by rescaling the Gaussian height W according to:

W =ω0τGe−VG (S,t )kBΔT

where τG is the Gaussian deposition stride, ΔT a temperature and VG(S,t) is the bias potential accumulated in S over time t. At variance with standard metadynamics, the bias potential does not fully compensate the Free-energy Surface (FES), but it converges to:

VG S, t→∞( ) = − ΔTΔT +T

F(S)

where T is the temperature of the system. In other words, at convergence the CVs are sampled at a (fictitious) higher temperature T+ΔT :

P S, t→∞( )∝ e− F (S )kB T+ΔT( )

Therefore, for ΔT → 0 , ordinary MD is recovered, whereas the ΔT →∞ corresponds to standard metadynamics. In between one can regulate the extent of FES exploration by tuning ΔT. This avoids overfilling and might save computational time when a large number of CVs are used. For a comprehensive description of metadynamics see also.3 System equilibration. The system have been minimized and heated step by step from 0 K to 300 K constraining the heavy atoms with a decreasing force constant (from 12 to 0 kcal/mol). After we equilibrate the system under constant pressure, 1 atm, and temperature, 300 K, (NPT ensemble) for 4 ns using a time step of 2 fs, rigid bonds4 and Particle-Mesh Ewald5,6 for the long-range electrostatics interactions with a non-bonded cutoff of 9 Å. For the temperature control we apply the V-rescale thermostat7, instead we use the Berendsen barostat8 for the pressure.

Backbone restraints. In order to prevent unfolding events at higher temperatures in the PT-WTE simulation we applied an external potential to restrain the protein backbone allowing a significant degree of conformational flexibility. The functional form of this potential is the following:

Vwall = k s − s0( )2 where k is an energy constant and so is the limit value. In order to tune the restraint parameters, all the available information about the local flexibility of the system were exploited. Experimental NMR structures of MLL:KIX and MLL:KIX:pKID complexes were carefully superimposed and analysed. Multiple preliminary MD simulations in the timescale of hundred of nanoseconds were performed starting from these experimental structures. We want to highlight that all the constraints relative to the conformational dynamics are not active at room temperature and the natural behaviour of the system is respected. For the PT-WTE simulation we employed four different restraints in the Distance Mean Square Displacement (DMSD) space using the Cα atoms: 1. From residues Q597 to K667, excluding aminoacids from P613 to D623, for the α-helices stability of the KIX domain. We put the limit value at 3 Å2. 2. From residues Q597 to K667, for the overall KIX dynamics. The limit value was 8 Å2. 3. From residues L2845 to N2856, for the MLL domain α helix stability. The limit value was set at 7 Å2. 4. From residues Q597 to K667, excluding aminoacids from P613 to D623, and from L2845 to N2856, to keep bound the MLL with the KIX domain. 3 Å2 was the limit value. In Table S1 we report the averaged DMSD values of these four restraints. In brackets we indicate the maximum value.

Restraint MLL:KIX

NMR structures

MLL:KIX:pKID NMR

structures

MLL:KIX versus

MLL:KIX:pKID

100ns MD simulation MLL:KIX

100ns MD simulation

MLL:KIX:pKID

Limit Value s0

1 0.8 (1.0) Å2 1.0 (1.5) Å2 0.6 (1.2) Å2 0.8 (1.7) Å2 1.2 (2.0) Å2 3 Å2 2 0.8 (1.0) Å2 1.2 (1.6) Å2 0.7 (1.2) Å2 2.1 (6.8) Å2 1.5 (3.2) Å2 8 Å2 3 1.0 (2.0) Å2 1.6 (2.2) Å2 0.3 (0.9) Å2 0.7 (2.8) Å2 3.0 (4.4) Å2 7 Å2 4 1.3 (1.7) Å2 1.7 (2.2) Å2 0.8 (1.6) Å2 1.1 (2.3) Å2 1.8 (2.5) Å2 3 Å2

As mentioned before these restraints did not influence the natural conformational dynamics of the MLL:KIX system at room temperature. This fact is also well shown by the comparison of the Root Mean Square Fluctuations (RMSF) between the restrained PT-WTE simulation and the MD simulation without restrains.

Fig S1. Cα atoms RMSF for the restrained PT-WTE simulation (in red) and for the

unrestrained 300 ns MD simulation (in black).

Free-energy surfaces of the KIX allosteric residues.

Fig. S2. Reweighted FES as a function of the Ile657 χ1 angle and the Phe612 χ1 angle using isosurfaces of 1 kcal/mol.

Fig. S3. Reweighted FES as a function of the Ile657 χ1 angle and the Tyr650 χ1 angle using isosurfaces of 1 kcal/mol.

Fig. S4. Reweighted FES as a function of the Ile657 χ1 angle and the His651 χ1 angle using isosurfaces of 1 kcal/mol.

Fig. S5. Reweighted FES as a function of the Ile657 χ1 angle and the Tyr658 χ1 angle using isosurfaces of 1 kcal/mol.

Fig. S6. Reweighted FES as a function of the Ile657 χ1 angle and the Lys659 χ1 angle using isosurfaces of 1 kcal/mol.

Excited and ground state MD simulations.

Fig. S7. Ile657 χ1 angle variations during 300 ns of standard MD simulations, in the excited state A) and in the ground state B). Ile611 χ1 angle variations during 300 ns of

standard MD simulations, in the excited state C) and in the ground state D).

PCA eigenvalues/eigenvectors variance.

Fig. S8. The first ten PCA eigenvalues variance of the PT-WTE simulation.

Validation of the free-energy surface with experimental structures.

Fig. S9. Free-energy surface as a function of the RMSD respect to the NMR loop position and the inertia moment. The red square represents the average value of the two CVs for

the MLL:KIX experimental structures, instead the light-violet triangle indicates the average for the KIX:pKID structures (pdb code: 1KDX9).

Residual Dipolar Couplings (RDCs).

Fig. S10. Comparison of experimental RDCs of the KIX domain in the binary complex (in black) with the predicted ones (in red). We use PALES10 to back-calculate the RDC from

our PT-WTE simulation, adopting the SVD method to calculate the alignment tensor.

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