Supplementary Material: A slide-and-exchange binding mechanism for rapid and selective transport through the nuclear pore complex

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1 Supplementary Material: A slide-and-exchange binding mechanism for rapid and selective transport through the nuclear pore complex Barak Raveh #, Jerome M. Karp #, Samuel Sparks #, Kaushik Dutta, Michael Rout, Andrej Sali*, and David Cowburn* Supplementary Methods System Preparation The simulation boxes used in this study are summarized in Table S1a and S1b. Since we conducted several simulations of similar systems, we constructed an initial model of the disordered FSFG 6 construct (125 residues) in complex with the NTF2 dimer (250 total residues), and used this model as a template for the other systems, as described below. Bound NTF2-FSFG 6 system. Initial coordinates for the receptor structure were taken from PDB entry 1GYB chains A and B (1), a N77Y mutant of the NTF2 dimer in complex with two FSFG motifs at symmetric binding sites (chains E and F). The N- and C-terminal residues of NTF2, which are missing in the crystal structure, were modeled using the software MODELLER (2), and residue 77 was changed from the mutated Tyr to the native Asn. The coordinates of the third FSFG motif (residues 50-53) were set according to chain E in 1GYB. The chain was then extended with the remaining residues of the FSFG 6 construct (residues 1-49 and ) using MODELLER with 180 ψ and φ dihedral angles and ideal bond geometry. Next, the construct was minimized using the AMBER99SB force field (3) in an implicit-solvent box using a modified generalized Born solvation model (4), with heavy (500 kcal mol -1 A -2 ) restraints on NTF2 and the bound FSFG repeat. Following this minimization step, the ab initio protocol in Rosetta FlexPepDock (5), a protocol for modeling interactions between globular proteins and flexible peptides, was extended here to remodel the entire disordered FG Nup as a random coil that interacts with NTF2 at the crystallographic binding site. The protocol allows for substantial backbone movements of the FG Nup in the presence of the receptor, as well as sidechain modeling of all FG Nup and NTF2 residues using the Dunbrack rotamer library (6). In a first iteration, 50,000 models were generated from the initial structure, in order to optimize the binding mode between the NTF2-bound FSFG repeat and NTF2. Half of these models were created using the unbiased version of the FlexPepDock protocol, while the other half was generated with constraints that favor interactions at the crystallographic binding sites. The 100 top-scoring models, based on the reweighted_sc energy score (5), were sorted by RMSD over the FSFG residues in the 1GYB crystal structure, and those with the lowest RMSD were manually inspected. The model selected for the subsequent modeling iteration ranked 63 out of 50,000 models, and was selected from the pool of models generated with no binding site constraints in the scoring function. Next, the coordinates of NTF2 and FG Nup construct residues (the residues which interact with NTF2) were retained, while the dihedral angles of residues 1-46 and were reset in an extended geometry by setting the φ and ψ dihedral angle values to -135 and +135 respectively, with retained bond length and angle values. This model was again subject to the FlexPepDock ab initio protocol using identical settings. The 30 top-scoring models were visually inspected, and the model ranked 9 out of 50,000 models was selected for the following step, because of its native-like conformation of the 1

2 bound FSFG motif and a mixture of inter- and intra-molecular interactions which were anticipated to allow the FG Nup to explore a wide range of interactions with NTF2. Equilibration of bound FSFG 6 :NTF2 system. Missing hydrogen atoms in the NTF2-FSFG 6 complex were added using the reduce tool in AMBER. Crystal water molecules from the 1GYB PDB structure were added, if the oxygen atom was over 1.5 A from any protein atom. Eleven Na + counterions were added to neutralize the protein charge, and the protein was aligned by its principal axes using the alignaxes command in tleap, and solvated in an orthorhombic box with anisometric solvent buffering with 20.0 A, 9.0 A, and 13.0 A of solvent in the x-, y- and z-axes respectively. Solvent was added and parametrized based on the TIP4P-Ew water model, initially. Simulations were performed using the AMBER99SB-ILDN model (7). Periodic boundary conditions were imposed. For equilibration simulations in AMBER, short-range electrostatic interactions and van der Waals interactions were included within a cutoff of 8 A, and long-range electrostatic interactions were treated using the periodic mesh Ewald algorithm (8). Each box was minimized for 250 steepest descent steps, followed by 250 conjugate gradient descent steps, with strong constraints (500 kcal mol -1 A -2 ) on the coordinates of NTF2 and the third FSFG repeat, as well as a constraint of 50 kcal mol -1 A -2 on two water molecules closest to the FSFG-NTF2 interface. This was followed by a second minimization with a 10 kcal mol -1 A -2 constraint on all protein atoms, using steepest descent minimization for 250 steps and conjugate gradient minimization for 750 steps. Each box was then heated to 300 K over 20 ps using Langevin dynamics with a collision frequency of 1 ps -1, followed by equilibration in the NPT ensemble for 200 ps, using a pressure of 1 atm and a relaxation time of 2 ps. After this, the systems were equilibrated for another 10 ns with AMBER before switching to Anton (9, 10). The time step for the AMBER simulations was 2 fs. For simulations using the TIP4P-D water model, the equilibrated simulation box with TIP4P-Ew water was used, and the parameters were tuned to match those of the TIP4P-D model. Since these parameters only slightly differ from the TIP4P-Ew model, there was no need to re-equilibrate the simulation box in order to guarantee the stability of the subsequent Anton simulation. Equilibration of free FSFG 6 system. For the initial model of the free FSFG 6 system, we removed NTF2 from the pre-equilibration model of the NTF2-FSFG 6 complex. The initial model was equilibrated in AMBER as described above, using three Cl - counter ions and either TIP4P-Ew or TIP4P-D water with a 27.0 A x 8.0 A x 18.0 A solvation buffering, following aligning by the principal axes as in the FSFG 6 :NTF2 system. Equilibration of unbound FSFG 2 :NTF2 system. The initial model for this system was again derived from the FSFG 6 :NTF2 pre-equilibration model by extracting NTF2 and the last 54 residues of FSFG 6 in the conformation used for FSFG 6 :NTF2 simulations. The second FSFG motif of FSFG 2 was then aligned to the crystallographic binding site for the FSFG motif, and translated by 10 A along the axis that connects the centers of mass of NTF2 and the FSFG motif, in order to bring FSFG 2 to an unbound starting orientation. The system was equilibrated as above, using three Cl - counter ions, in a 9.0 A x 14.4 A x 12.5 A solvation buffering with TIP4P-Ew water, or with isometric solvent buffering of 11.0 A with TIP4P-D water. The TIP4P-D buffering box is much larger (Table S1) due to the isometric solvation, but was required to prevent periodic boundary interactions, due to the large radius of gyration, consistent with high randomness, that the FSFG 2 construct adapted in simulations with this water model. 2

3 Free FSFG 2 system. The initial model for this system was derived from the NTF2-FSFG 2 preequilibration model by removing NTF2, following equilibration with two Cl - counter ions in a 20.3 A x 8.0 A x 12.9 A solvation buffering of TIP4P-Ew water or TIP4P-D water. Simulation with Anton Long-timescale simulations were run on the Anton supercomputer at the Pittsburgh Supercomputing Center (11). These simulations also used a 2 fs time step. The Gaussian-split Ewald algorithm (12) was used to compute electrostatic interactions. Parameters for the simulation were chosen based on the system-optimized parameters chosen by the Anton software. The van der Waals interactions and the direct part of the electrostatic interaction calculations were calculated for all atoms within a cutoff which was at least 11 A for all boxes. The Multigrator thermostat/barostat (13) was used to keep the simulation temperature at 300 K and the pressure at 1 atm. Anton simulations of Bound NTF2-FSFG 6 system with Temperature-Accelerated Molecular Dynamics (TAMD) In the TAMD enhanced sampling scheme of the bound NTF2-FSFG 6 system, a time-dependent restraint was placed on the distance between the center of mass of the FG Nup residues (in the spacer residues between the second and third FSFG motifs) and the center of mass of residues (between the fourth and fifth FSFG motifs). This distance at time was subjected to a harmonic restraint whose equilibrium value r 0 changes over time, and is given by r 0 (t + dd) = r 0 (t) + k dd r(t) r γ 0 (t) + 2k BT dd η(t) (S1) γ where r(t) is the distance at time t, dd is the time step (ps), k B is the Boltzmann constant, η(t) is a Gaussian white noise with mean zero and variance 1, k is a spring constant equal to 100 kcal mol -1 Å -2, γ is a frictional coefficient equal to 50 ps kcal mol -1 Å -2, and T is an artificial temperature associated with the restraint, set in our simulations to 1000 K. The TAMD restraint allows the simulation to sample the conformational space associated with the normal simulation temperature at a faster rate than would be sampled without the restraint. Random Acceleration Molecular Dynamics (RAMD) In these simulations, steering forces of fixed magnitude k are applied to the center of mass of a single FG motif, but the direction of steering is randomly chosen. The steering continues until the displacement over the last 20 steps has been smaller than A, at which point a new steering direction is chosen. The RAMD simulations were performed on a system containing NTF2 and KPAFSFGAK sequence, namely a single FSFG motif and its flanking residues. We added the ACE and NME peptide caps to the sequence in order to avoid significant electrostatic interaction between the termini of the FSFG motif and NTF2. As in the other simulations, the AMBER99SB-ILDN force field was used. 12 Na + ions were added to neutralize the protein, which was then solvated in a box of TIP4P-D solvent large enough to allow an 8.0 A margin of solvent on all sides of the protein. The box was first set up using AMBER. 250 steps of steepest descent and 250 steps of conjugate gradient minimization were run with the protein fixed using 20 kcal mol -1 A -2 restraints, and then another 250 steps of steepest descent and 750 steps of conjugate gradient minimization without restraints. Heating and NPT equilibration were run in 3

4 AMBER as described for previous boxes. Following this, the remaining simulation was performed in the NVT ensemble using NAMD (14). In these simulations, a 2.0 fs time step was used. The Langevin thermostat was used on non-hydrogen atoms with a temperature of 300 K. Short-range electrostatic and van der Waals interactions were included below a cutoff of 8.0 A, and long-range electrostatics were handled with the Particle-mesh Ewald algorithm. Equilibration was performed in NAMD for 100 ps, with 5 kcal mol -1 A -2 restraints on the protein. Following equilibration, 5,400 RAMD simulations lasting 150-1,500 ps were performed for different steering force magnitude values. The number and/or length of the simulations was increased for simulations with low-magnitude steering forces in order to compensate for the rarity of displacement events in those simulations, as follows: 900x150 ps simulations were performed with steering force magnitude k=12.5 kcal mol -1 A -1 ; 500 x 400 ps simulations with k= 10.0 kcal mol -1 Å -1 ; 1,000 x 400 ps simulation with k=7.5 kcal mol -1 Å -1 ; and 1,500 x 500 ps, 500 x 1,000 ps and 1,000 x 1,500 ps simulations with k=5 kcal mol -1 Å -1. Targeted Molecular Dynamics of FG motif exchange For the targeted MD simulations of exchange, we have prepared three systems based on the RAMD simulation system, and adding a second, initially non-interacting FSFG motif that retains the same conformation as the first motif, but is translated 50 Å away from it, in either the +PCA1, -PCA1 or +PCA2 directions (Table S2). In each of these three systems, we then added counterions and resolvated this protein in a box with a 10 Å solvent buffer on all sides. The box was minimized using conjugate gradient minimization, followed by gradual heating of the box to 300 K over 120 ps, and NPT equilibration for 200 ps (using the same parameters as in the RAMD simulation setup). During the minimization, heating and equilibration periods, 2 kcal mol -1 Å -2 restraints were placed on all Cα atoms in NTF2, as well as on all atoms of both FG repeats. Using the three equilibrated systems (+PCA1, -PCA1 and +PCA2), we ran a total of 1,500 independent targeted MD simulations (500 per systems), using NAMD 2.10 (14) with PLUMED 2.2 (15). In each simulation, the translated peptide was targeted towards the occupied interaction site. During each step of simulation, the root-mean square deviation (RMSD) of the unbound motif was computed relative to the initial position of the interacting motif, after first superimposing the structure on the initial position based on the Cα atoms of NTF2. This RMSD value was coupled by an harmonic restraint of kcal mol -1 Å -2 to a moving equilibrium value, which was gradually ramped towards the interaction site, first from 50 Å at t = 0 ps to 10 Å at t = 100 ps; then from 10 Å at t = 100 ps to 2 Å at t = 500 ps; and finally from 2 Å at t = 500 ps to 0 Å at t = 700 ps. Throughout the targeted MD simulations, 2 kcal mol -1 A -2 restraints were retained on all of the Cα atoms of NTF2. Chemical shifts analysis NMR spectral assignments of [U- 13 C, 15 N] yeast NTF2 were obtained via standard triple resonance backbone experiments (16, 17). Chemical shift mapping experiments were performed with 200 µm [U- 15 N] NTF2 in the absence and presence of equimolar FSFG-K (18) at 600 MHz. Experiments were performed in 20 mm HEPES buffer, 150 mm KCl, 2 mm MgCl 2 as described previously (18). Chemical shift perturbations using both 1 H and 15 N were calculated as 1 2 [δ H δ N 2 ] and values were mapped onto the x-ray structure of NTF2. 4

5 NMR relaxation 15 N relaxation experiments were conducted at 600 MHz by preparing a sample containing 200 µm [U- 15 N] FSFG and 2000 µm NTF2. Both the R 1 and R 2 measurement was performed using 8 delay points, 0.01, 0.05, 0.11, 0.25, 0.49, 0.73, 0.99, 1.29 seconds and 0, 0.068, 0.102, 0.136, 0.17, 0.204, 0.271, seconds for R 1 and R 2, respectively. Simulated R 2 /R 1 ratio Theoretical R 1 and R 2 values for backbone N-H bond and standard-error of the mean were calculated by bootstrap resampling. The 1,750 ns TIP4P-D simulation of FSFG 6 :NTF2 was divided into 9 overlapping and equally spaced time segments of 350 ns. R 1 and R 2 values were computed in 50 independent repeats, using random choices of 5 out of the 9 time segments and the mean and the standard-error of the R 2 / R 1 were estimated from the R 1 and R 2 values in each of the 50 repeats. The R 1 and R 2 values were computed as follows in each repeat: (1) The autocorrelation function of each N-H bond C(Δt) = P 2 μ(t), μ(t + Δt) was evaluated for Δt values in the range ns. μ(t) is the orientation of the interatomic vector at time t and P 2 is the second-rank Legendre polynomial. For computational efficiency, the intervals between consecutive Δt values were increased gradually using the recursive relation Δt i+1 = 0.06 ceil 1.03 Δt i ns. This is justified since the autocorrelation function empirically 0.06 changes slowly for large Δt values. (2) Using the software gnuplot ( C(Δt) was fitted to a parametric sum of three exponents and a constant, following the analysis in (19). The fitted parametric function is of the form 2 C (ΔT) = S MM + 1 S 2 u e t τu + 1 S 2 f S 2 u e t τ f + 1 S 2 s S 2 u S 2 f e t τs (S2) such that the order parameters S i 2 and time constants τ i for the ultra-fast (u), fast (f) and slow (s) relaxation processes satisfy: based on equation 4 (19). 2 S MM = S 2 u S 2 t S 2 s, 0 < τ u < τ f < τ s and 0 < S 2 i < 1 for all i, (3) The spectral density J(ω) of C (ΔT) was computed numerically in MATLAB using J = [1 + I(ω 0)] real dfft C ΔT=0.500 nn, (S3) where I(ω 0) equals 1 for positive frequencies to account for the opposite negative frequencies, and real(dfft) is the real part of the discrete Fourier transform; and using numerically the Lorentzian function, the Fourier transform of a two-sided exponential decay. The analytic and numerical computations results in identical spectral densities. 5

6 (4) R 1 and R 2 were computed from the spectral densities at the appropriate frequencies using standard equations, specifically from equations 1 and 2 in (20), using the same constants used in the NMR relaxation measurements, namely Larmor frequencies ω Η = MHz, ω Ν = MHz; µ 0 = m kg s -2 A -2 ; h = m 2 kg s -1 ; µ Ν = MHz T -1 ; γ Η = MHz T -1`, r NH =1.01 Ǻ; σ -σ = 160 ppm. Scripts for these calculations are at Flory exponent quantification. The mean radius of gyration R g was calculated for chain segments of increasing length n by averaging over all chain segments of n residues in either the FSFG 2 or FSFG 6 chains over all trajectory frames for each simulation. Due to the high level of flexibility in the TIP4P-D FSFG 6 :NTF2 simulation, the polymer extends in some frames such that some artificial contacts formed between the tail of FSFG 6 and the periodic image of NTF2 in part of the simulation. Consistent with the FSFG 2 simulations, the Flory exponent was 0.51 before the formation of any periodic contacts, and 0.58 for the entire simulation. The same applies to the computations of persistence length in the following section. Entropic spring model for unrestrained ends. Consider either a freely-jointed chain (FJC) of N joined links of length l (with end-to-end root mean squared distance (RMSD) Nl 2 (21) ), or a worm-like chain (WLC) in the limit of short persistence length l p L for a polymer with contour length L (with end-to-end RMSD 2Ll p 2 (21) ). The equations for the entropy-driven free energy F(d) that are cited in the literature for end-to-end distance (d) in either model were derived mostly in the context of experimental methods for measuring the response of polymers to tension, such as optical tweezers (21). In such methods, the polymer ends are constrained to be aligned roughly with the pulling direction. For instance, in the FJC model, F(d) = F 0 + kk 3 2Nl 2 d2 (eq in (21)). The force that resists perturbation to d is the derivative of the free-energy, f (d) = kk 3 Nl2 d, obeying Hooke s law, and implies a resting distance of d = 0. Similarly, the WLC model behaves as an entropic spring except for extreme perturbations (eq in (21)). However, in our simulations, the polymer ends are not externally constrained, and hence the configurational entropy should be adjusted to account for the increasing sphere surface that one end could cover relative to the other at a fixed distance. Formally, omitting normalizing factors, the probability of each macrostate P(d) should be scaled by the sphere surface π d 2 ; the entropy S increases by 2k ln(d) using S(d) = k ln[p(d)]; and the adjusted free energy F (d) decreases by 2k T ln(d), using F(d) = U TT. For the FJC model, and the force F (d) = F(d) 2kkln(d) = F 0 + kk 3d2 2Nl2 2ln(d), (S4) f (d) = kk 3 d 2 2 = kk Nl 2 2 d 2, d d 0 d (S5) 6

7 where d 0 = 2Nl2 is the resting distance for the case where the polymer ends are not 3 constrained along a line (scaling with Nl 2 as expected of the end-to-end RMD). We show that Hooke s law is approximately obeyed for most values of d. In the case that d is close to d 0 (roughly 2 d 3 0 < d < 3 d 2 0), the 2 term in Eq. S5 can be approximated using the first-order Taylor d expansion of 1 1 x = 1 1 a + x a (1 a) 2 and substituting x = 1 d, and a = 1 d 0, we get d (S6) d d 0 d 0 By substituting the second term in Eq. S5 with Eq. S6, we get a close approximation to Hooke s law f (d) kk 2 d 0 2 d 4 d d 0 2 d = kk 4 d 0 2 (d d 0 ) (S7) When d d 0, the contribution of the 2 d term diminishes and f (d) is still approximately linear in d, although with asymptotically lower slope: f (d) kk 2 d 0 2 d kk 2 d 0 2 (d d 0 ) (S7) From Eq. S6 and Eq. S7, we conclude that the force that resists perturbation to the length of an ideal chain with unrestrained ends is approximately Hookean for any value of d>~ 2 d 3 0, and nonlinear only for small values of d, for which it resists over-compression of the polymer. A similar analysis readily follows for the WLC model. Adjust eq in (21) in exactly the same manner, using the approximation in Eq. S6, and neglect the first term for perturbations that are less than 20-25% of the total contour length of the polymer. This last is applicable in our case, where the contour length is 205 Å for FSFG 2 and 475 Å for FSFG 6, based on 3.8 Å per amino acid. f (d) = kk 1 1 d L p 4 L d 2 kk 1 1 d 4 L d L p 4 L d d 4 L d 0 d 0 (S8) 7

8 Supplemental Table S1 A. In absence of NTF2 FG Nup Simulation time system size in atoms FSFG 6 (125 residues) 0.8 μs (TIP4P-Ew) 0.2 μs (TIP4P-D) 123,216 FSFG 2 (54 residues) 6.0 μs (TIP4P-Ew) 0.3 μs (TIP4P-D) 62,642 B. In presence of NTF2 FG Nup Initial state Simulation time system size in atoms TAMD accelerated FSFG 6 Ntf2 anchored μs (TIP4P-Ew) 1.8 μs (TIP4P-D) 137,718 no FSFG 6 Ntf2 anchored 1 8 x μs; 1 x μs; 1 x μs 137,718 yes FSFG 2 Ntf2 unbound 32.0 μs (TIP4P-Ew) 1.5 μs (TIP4P-D) 95,058 (TIP4P-Ew) 197,194 (TIP4P-D) no 8

9 Supplemental Table S2 PCA vectors of the FSFG residues gravity centers in the 10 TIP4P-Ew TAMD trajectories. All coordinates are specified in the reference frame of NTF2 chains A and B in pdb-id 1GYB. The center of all data points lies at [ ] Å. Principal component # Eigenvalue % variance explained principal component vector (in Å) weighted by its eigenvalue PCA % [ ] PCA % [ ] PCA % [ ] 9

10 Supplemental Table S3 Fitted order parameters for the FG repeat residues based on the TIP4P-D simulation of FSFG 6 :NTF2, as described in Methods. Motif residues are highlighted in grey. There are no values for Pro residues. residue T u [ns] 2 S u T f [ns] S 2 2 u *S f T s [ns] S 2 MD =S 2 u *S 2 2 f *S s

11

12

13 Supplemental Figures Figure S1. Secondary structures assigned by STRIDE (22) during simulations of FSFG 6 repeats in the presence or absence of NTF2, with either TIP4P-Ew or TIP4P-D water. Also see Figure 2A. 13

14 Figure S2. Comparison of radius of gyration (R g ) computed during the simulation trajectories for FSFG 6 with NTF2 (left) and FSFG 6 alone (right), with water models indicated. Based on R g = R h, with R h calculated according to (23). 14

15 Figure S3 Pairwise RMSD heatmap of the FSFG 6 construct in different simulation time frames. RMSD is computed on FSFG backbone atoms following alignment by either FSFG (left) or NTF2 (right) atoms. 15

16 Figure S4 Fraction of hydrophobic contacts of FSFG 6 residues during the TIP4P-Ew (blue) and TIP4P-D (red) simulations of the FSFG 6 :NTF2 complex. The fraction of hydrophobic contacts is defined as the fraction of all pairs of hydrophobic residues in which any pair of sidechain atoms come into close contact (<5 A ). The fraction of hydrophobic contacts in a single globular NTF2 chain (7.86%; dashed gray line) is indicated for reference. To restrict the analysis to tertiary interactions, only pairs of residues that are at least 4 residues apart on the primary sequence of FSFG 6 are considered. Note: FSFG has fewer hydrophobic residues than NTF2, and hence the absolute number of hydrophobic contacts in both water models is significantly lower. 16

17 Figure S5 Maps of contacts between the FG Nup and NTF2. The position of the FSFG peptide in the crystal structure (PDB: 1GYB) is shown. (A) Percentage of frames in which each residue of NTF2 is in contact (< 7 Å) with any residue of FSFG 6, in the simulation using the TIP4P-D water model. (B) Observed NMR chemical shift perturbations (ppm) corresponding to 15 N NTF2 upon addition of FSFG 6. 17

18 Figure S6 Percentage of contacts formed by FSFG 6 in the presence of NTF2 over the simulation and their associated relaxation rates. (A) Contacts for FG repeat residues as a fraction of time in the TIP4P-D simulation of FSFG 6 :NTF2. (B) R 2 /R 1 relaxation values for the FG repeat residues measured experimentally by NMR of FSFG 6 in the presence of NTF2 (blue) and in the TIP4P-D simulation of FSFG 6 :NTF2 (grey). (C) 2 Fitted order parameters S MD for the FG repeat residues based on the TIP4P-D simulation of FSFG 6 :NTF2, 2 as described in Methods. High S MD values indicate high auto-correlation and low tumbling of the N-H vectors within the time scale of the simulations. 18

19 Figure S7 Projection of principal components of the center of mass of the third FG motif of FSFG 6 relative to the crystallographic binding site for 10 independent TIP4P-Ew TAMD simulations and an unbiased TIP4P-D simulation. 19

20 Figure S8 Initial (black line) and subsequent (red line) contacts during randomly accelerated molecular dynamics (RAMD) simulations of FSFG motif unbinding from its primary crystallographic binding site. Initial contacts are all contacts present in the first frame of the simulation, and subsequent contacts are their complement. A contact is defined as a pair of residues having a pair of atoms at distance < 5 A. The first 450 out of 900 simulations at k=12.5 kcal mol -1 A -1 are shown, sorted by the number of time frames where: (1) initial contacts < 10% of initial contacts in frame 0; (2) subsequent contacts > 2 x (# initial contacts); (3) subsequent contacts > 5% of initial contacts in frame 0. See Movie S6. 20

21 21

22 22

23 Legends and snapshots of movies Movie S1. The FG repeats are rapidly moving entropic springs. The distance between the serine Cα atoms of consecutive FG motifs of the FSFG 2 construct are shown through 1500 ns of TIP4P-D simulation of FSFG 2 :NTF2. NTF2 is omitted for visual clarity, but its presence or absence do not affect the elasticity of the FG repeats (Results: FG Nups Are Fast-Moving Entropic Springs. ). 23

24 Movie S2. The FG repeats remain highly dynamic in the bound state, and form weak, transient contacts contributed by spacer residues, in addition to more stable contacts of FG motifs. The first 1500 ns of the TIP4P-D simulation of FSFG 6 :NTF2 are shown here, with the NTF2 dimer in yellow/orange space fill representation; the FG repeats backbone in gray cartoon, and a subset of its side chains in space fill representation (red - phenylalanines of the six FG motifs; white - proline spacer residues; cyan/red/blue, small vdw balls - other spacer residues while in contact with NTF2). 24

25 Movie S3. Sliding and recontacting of an FG motif on its binding groove on NTF2. The third FG motif of FSFG 6 is shown in stick representation for the first 1500 ns of the TIP4PD simulation of FSFG 6 :NTF2, starting at the crystallographically determined interaction site (pdb-id 1gyb). The NTF2 dimer in yellow/orange space fill representation; the FG repeats backbone in gray cartoon; the two phenylalanine sidechains of the FG motif are in pink space fill representation; the large blue ball is the center of mass of the FG motif. 25

26 Movie S4. Sliding of FG motif along the first principal component (PCA1) within the crystallographically identified interaction site on mutated NTF2 (pdb-id 1gyb), shown for the first 600 ns of the TIP4P-D simulation of FSFG 6 :NTF2 simulation. The NTF2 is shown in surface representation; the third FG motif of FSFG 6 in stick representation; the large pink ball is the center of mass of the FG motif. The principal components of the centers of mass of the FG repeats during all simulations (computed as described in the text) are shown for reference, with the first principal component going from right to left along the interaction pocket. See Figure 4; Figure S7. 26

27 Movie S5. TFs slide on FG motifs. Shown are the first 800 ns of the same trajectory as as in Movie S3 and Movie S4, but in the reference frame of the FG motif (stick representation), with NTF2 (cartoon) seen sliding on the motif. The crystallographically suggested interaction site on NTF2 (pdbid 1gyb) is shown in red surface representation. 27

28 Movie S6. Sliding along PCA1 in a representative trajectory from the thousands of enhanced sampling RAMD simulations of a single FG motif (orange) at the crystallographically suggested interaction site (pdb-id 1gyb; light grey surface representation) on the two monomers of NTF2 (purple and dark grey cartoon representation). As time passes, the FG motif form new contacts with NTF2 (red surface representation), sliding mostly along the first principal component of the centers of mass of FG repeats, computed as described in the text. The principal components are shown as magenta arrows, scaled according to their contribution to the total variance (Table S2). See Figure 4C for tendency to slide along PCA1 in all the RAMD trajectories. 28

29 Movie S7. Displacement of one FG repeat of FSFG 2 by another at an NTF2 interaction site. A strongly-interacting repeat slides out (pink to red) to a weakly-interacting state as a competing repeat (cyan to blue) slides in. The existence of a weakly interacting state enables one FG repeat to slide off a strong interaction site and then to be displaced entirely when another repeat interacts at the site, in contrast to a system with only strong interaction, in which the interacting ligand would be required to unbind completely to enable binding of a new ligand. 29

30 Movie S8. Two different FG motifs are accommodated simultaneously at the crystallographically determined interaction site (pdb-id 1gyb) on NTF2 (surface representation), during the TIP4P-D simulation of FSFG 6 :NTF2. The binding groove is aligned with the first principal component (PCA1) over which the FG motifs tend to slide (Figure 4). Since they are accommodated simultaneously at the interaction pocket, and due to their tendency to slide at the binding pocket, the FG motifs could potentially displace each other from their interaction sites, thereby promoting fast exchange of TFs among FG motifs. 30

31 Movie S9. A representative trajectory of targeted exchange simulations of two FG motifs at the NTF2 crystallographic interaction site. The first FG motif (cyan cartoon/sticks representation) is targeted towards the binding site from the +PCA1 direction (from the left side of the screen) via a moving restraint on its RMSD from the interaction site. As the first FG motif approaches the interaction site, the second FG motif (pink cartoon/sticks representation) is ejected by sliding further along PCA1. The three principal components are indicated by red arrows, scaled proportionally to their eigenvalues. 31

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