## Introduction

The G4C2 hexanucleotide repeat expansion in C9orf72 is the most frequent genetic cause of amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD)1,2. Healthy individuals typically have up to around 20 repeats of G4C2, while patients with C9orf72-mediated ALS/FTD (C9-ALS/FTD) usually have hundreds to thousands repeats1,2,3. The RNA transcripts of this repeat expansion are translated to five types of dipeptide repeat proteins (DPRs): poly-PR, poly-GR, poly-GA, poly-GP, and poly-PA4,5. Toxic gain of function of RNA transcripts6,7 and DPRs4,5,8, and loss of function of the C9orf72 protein1,9 are thought to cause C9-ALS/FTD. Among the DPRs, the positively-charged arginine-containing DPRs (R-DPRs) show the highest levels of toxicity in both cell and animal models8,10,11,12,13,14,15,16.

R-DPRs are hypothesized to cause a wide variety of cellular defects17. Recent evidence suggests a link between R-DPRs and defects in the transport of macromolecular cargoes between nucleus and cytoplasm18,19,20. This nucleocytoplasmic transport (NCT)21,22 is mediated by large multiprotein assemblies called nuclear pore complexes (NPCs). The central channel of the NPC is lined with intrinsically disordered phenylalanine-glycine-rich Nups (FG-Nups) that collectively function as a selective permeability barrier of the NPC. This FG-barrier allows the passive diffusion of small molecules below $$\sim$$ 30–40 kDa, while it increasingly slows down the passage of larger cargoes unless they are bound to nuclear transport receptors (NTRs)23,24,25. The β-karyopherin (Kapβ) family is the largest class of NTRs that includes both import and export receptors26. Importins transport nuclear localization signal (NLS)-containing cargoes into the nucleus, and exportins transport nuclear export signal (NES)-containing cargoes out of the nucleus. NTRs can either bind directly to an NLS/NES-containing cargo (referred to as NLS/NES-cargo), or, in case of importin β1 (Impβ1), bind indirectly through the adaptor proteins importin α (Impα) or snurportin-1 (SPN1)27,28,29. The adaptor proteins bind to Impβ1 through their N-terminal importin β-binding (IBB) domains. Another essential ingredient in NCT is the GTPase Ran which switches between guanosine triphosphate (GTP)- and guanosine diphosphate (GDP)-bound forms30. The directionality of NCT is mediated via a steep RanGTP-RanGDP gradient over the nuclear envelope31. In the import cycle, RanGTP disassembles the importin-NLS-cargo complex in the nucleus by binding to the importin, and the resulting RanGTP-importin complex shuttles back to the cytoplasm. In the export process, RanGTP promotes the formation of a RanGTP-exportin-NES-cargo complex in the nucleus which facilitates the export of the NES-cargo to the cytoplasm. The hydrolysis of RanGTP to RanGDP in the cytoplasm disassembles the RanGTP-importin complex in the import cycle and the RanGTP-exportin-NES-cargo complex in the export cycle30.

Several studies have reported NTRs as potential interactors of R-DPRs13,20,32. Recently, R-DPRs with 25 repeat units have been shown to directly bind to several importins: Impβ1, Imp5, Imp7, Imp9, TNPO1, and TNPO3, but not to exportin CRM1 in in vitro experiments19. R-DPRs (with 10 to 25 repeat units) have also been found to cause defects in Impβ1- and TNPO1-mediated import19,20. Although these studies provide interesting insights into potential pathways for R-DPRs-mediated NCT defects, the molecular basis for the interaction of longer R-DPRs with different Kapβs and the resulting NCT defects has not yet been identified. In this study, we use coarse-grained (CG) molecular dynamics models33,34,35,36,37 to investigate the length-dependent interaction of poly-PR (known to be the most toxic DPR11,12,13) with different members of the Kapβ family of NTRs with the aim to provide mechanistic insight into the way poly-PR interferes with the transport functionality of Kapβs.

## Results and discussion

### Coarse-grained models of poly-PR and Kapβs

We use a CG modeling framework to investigate the interaction between poly-PR and several members of the Kapβ family of NTRs in their free, unbound state. In this study, we consider human Kapβs: importins Impβ1, Imp5, TNPO1, TNPO3, and exportins Exp1 (also known as CRM1), Exp5 (also known as XPO5). Because the number of human Kapβs with known crystal structures of the unbound state is limited, we use the yeast homologs of Imp9 and Imp11 (KAP114, KAP12030,38). In previous studies, poly-PR toxicity and its effect on NCT kinetics have also been investigated in simpler organisms like yeast11,39. Therefore, we also included the yeast importins KAP95 and KAP121 and the exportin KAP124 to our analysis. Thus, adding yeast Kapβs does not only allow us to draw more statistically relevant conclusions, it also helps understanding the mechanistic pathways of poly-PR–toxicity in the model system of yeast.

Our simulations adopt one-bead-per-amino-acid (1BPA) CG models of poly-PR and the selected Kapβs, see Fig. 1a,b. In this approach, initially designed to represent the FG-nups in the NPC33,40, each residue is represented by a single bead located at the position of the α-carbon atom. The CG model of poly-PR, see Fig. 1a (left panel), has already been applied in a previous study on the length-dependent phase separation of poly-PR and negatively-charged peptides35. Kapβs consist of tandem HEAT repeats, arranged into superhelical structures in case of importins and ring-shaped/U-shaped structures in case of exportins41,42,43. Each HEAT repeat contains two antiparallel alpha helices, referred to as A- and B-helices, connected by loops of varying length43. In Fig. 1a (right panel), some α-carbon beads are shown on top of the crystal structure of Impβ1. The crystal structures used to build residue-scale CG models of Kapβs, see Fig. 1b, are summarized in Table S3 in the SI. The overall structure of Kapβs is preserved using a network of stiff harmonic bonds. In addition, the distribution of charged and aromatic residues that are relevant for the interaction of R-DPRs with NTRs are included in the model. Our implicit-solvent CG force field also accounts for the screening effect of ions. More details about the CG modeling and force field are provided in the “Methods” section and section 1 of the SI.

### Poly-PR interaction with Kapβs correlates with the net charge per residue (NCPR) of Kapβs

Among the Kapβs shown in Fig. 1b, TNPO1, TNPO3, Imp5, and Impβ1 have been shown to directly bind to PR25 (poly-PR with 25 PR repeat units), and no binding has been observed for CRM1 in vitro19. In Fig. 1c, we show our simulation results for PR25 interacting with the selected Kapβs. In order to allow for a comparison with experimental findings, simulations in this section are performed at a monovalent salt concentration $${C}_{\mathrm{salt}}=$$ 200 mM. In each simulation, the periodic simulation box contains one copy of PR25 and one copy of a Kapβ. To quantify the interaction between PR25 and Kapβs, we calculate (i) the time-averaged number of contacts $${C}_{t}$$ between PR25 and each Kapβ using a cutoff of 1 nm, and (ii) the binding probability, taken as the probability of having more than 10% of the poly-PR residues within 1 nm proximity of each Kapβ. In Fig. 1c, the values of $${C}_{t}$$ and the binding probability are plotted against the net charge per residue (NCPR) of the Kapβs, with NCPR being the total charge of the protein (in units of elementary charge) divided by its sequence length (see Tables S3 and S5 for the sequence lengths and amino acid compositions of the Kapβ models used). The values of $${C}_{t}$$ are normalized by the sequence length of the importins/exportins ($${N}_{\mathrm{Kap\beta }}$$) and the sequence length of poly-PR ($${N}_{\mathrm{PR}}$$). Our results in Fig. 1c (top panel), show a linear correlation between the normalized number of contacts $${C}_{t}$$ and the negative NCPR of the Kapβs. PR25 makes more contacts with the importins, especially KAP95, TNPO1, Impβ1, Imp5, KAP121, and KAP114, than with the three exportins, XPO5, CRM1, and KAP124, due to the difference in negative NCPR. No such correlation is observed between $${C}_{t}$$ and the aromatic residue content, see Fig. S2 of the SI. The results also reveal high binding probabilities (> 0.85) for importins, and lower values for the exportins. CRM1 shows the lowest binding probability ($$\sim 0.15$$), consistent with the absence of binding in experiments19. We show in Fig. S3 of the SI that varying the binding criterion does not affect the binding probabilities for Kapβs with high binding probabilities ($$\sim 1$$), and only slightly changes the binding probabilities for other Kapβs. Overall, our results show that the poly-PR interaction with Kapβs is mostly driven by electrostatic interactions, in correspondence with in vitro binding assays.

### Salt concentration and poly-PR length affect the poly-PR–Kapβ binding behavior

It has been found that the toxicity of poly-PR increases with the number of PR repeat units8,11,44,45,46, but this has so far not been linked to the interaction of poly-PR with Kapβs. To provide insight into this, we study the interaction of one copy of poly-PR that has either 7, 20, 35, or 50 repeat units with one copy of each Kapβ. To quantify the interaction, the normalized number of contacts $${C}_{t}/({N}_{\mathrm{Kap\beta }}{N}_{\mathrm{PR}})$$ and binding probability are reported in Fig. 2a. The simulations are performed at two monovalent salt concentrations: $${C}_{\mathrm{salt}}=200$$ mM, as in the previous section and similar to previous in vitro experiments19, and $${C}_{\mathrm{salt}}=100$$ mM, to study the effect of salt concentration on poly-PR binding to kapβs especially the ones with lower negative net charges. Increasing the poly-PR length increases the number of contacts $${C}_{t}$$ (only the normalized $${C}_{t}$$ is shown), and the binding probability (Fig. 2a, bottom panel). The effect of the poly-PR length on the binding probability is much more pronounced at $${C}_{\mathrm{salt}}=200$$ mM. The reason for this is that reduction of the salt concentration to 100 mM reduces screening effects and thus increases the binding probability, thus confirming the important role of electrostatic interactions in poly-PR–Kapβ interactions. This increased binding probability is especially visible for the interaction of shorter poly-PRs with Kapβs that have lower negative NCPR. At $${C}_{\mathrm{salt}}=100$$ mM, poly-PR with more than 20 repeat units also bind to CRM1 and Kap124 with binding probabilities $$\sim 1$$, showing that a reduction of the salt concentration can significantly increase the binding probability for these two exportins. The high binding probability ($$\sim 1$$) for Kapβs with a NCPR $$<-0.052$$ also indicates that, even for short poly-PRs, the binding is almost irreversible in the time-scale of our simulations (at least 2.5 µs). As can be seen in Fig. 2a, when the poly-PR–Kapβ binding probability is high ($$\sim 1$$) for a certain Kapβ (e.g., Impβ1), a shorter poly-PR makes more contacts per unit length ($${C}_{t}/{N}_{\mathrm{PR}}$$) with the Kapβ compared to a longer poly-PR. When a relatively short poly-PR chain (for example PR7 or PR20) binds to a Kapβ, almost all its residues make contact with the Kapβ. However, in the bound states of a relatively long poly-PR (for example PR50), some regions make less or no contact with the Kapβ thus resulting in a lower time-averaged number of contacts per unit length of poly-PR. The snapshots of Fig. 2b and the movies S1 and S2 clearly illustrate this difference in binding of PR7 and PR50 to Impβ1. For Kapβs with a lower NCPR (e.g., CRM1), shorter poly-PRs bind to the Kapβ with a lower probability and therefore on average make less contact compared to a longer poly-PR (that binds to the Kapβ with a higher probability), and thus the time-averaged number of contacts per unit length of a shorter poly-PR is lower for these cases.

To study in more detail how poly-PR targets Kapβs, we first identify the A-helices, B-helices and linkers in the crystal structures of Kapβs (see Fig. 2c), using the STRIDE secondary structure prediction algorithm47 (for details, see section 3 of the SI). The linker regions contain residues that connect A- and B- helices in each HEAT repeat as well as the residues that connect consecutive HEAT repeats. In Fig. 2c, the A- and B-helices for all 19 HEAT repeats of Impβ1 are highlighted. For the other Kapβs, see the snapshots in Table S4 in the SI. In general, the A-helices form the outer convex surface and the B-helices form the inner concave surface of Impβ1. In the bottom panel of Fig. 2c, we report $${N}_{\mathrm{contact}},$$ the number of residues in the A-helices, B-helices, and linkers of Impβ1 that make contact with poly-PR at $${C}_{\mathrm{salt}}$$ of 100 mM. For the calculation of $${N}_{\mathrm{contact}}$$, a Kapβ residue is considered to be a contact site if the contact probability for this residue is larger than 0.10 (for details see Sect. 2 of the SI). Longer poly-PRs are seen to make more contact with Impβ1 residues. The results in Fig. 2c also show that poly-PR interacts more with the B-helices and the linkers than with the A-helices. The larger number of contacts with the B-helices can be explained by the higher negative electrostatic potential of the inner surface of Impβ1, see Fig. 2c bottom right. The same binding behavior can also be seen for other importins: KAP114, KAP121, Imp5, TNPO1, KAP95, and TNPO3, see the left column of Fig. S5 in the SI. The result for TNPO1 is consistent with the binding of poly-PR to a negatively-charged cavity in the inner surface of the TNPO148. Snapshots presented in Table S4 of the SI show that all the importins contain regions with a relatively high negative electrostatic potential at their inner surface. The results in Fig. S5 and S6 show that longer poly-PRs are also able to interact with the outer surface of the importins because increasing poly-PR length increases the number of contact residues in the A-helices. This effect is most pronounced for Imp5, Impβ1, TNPO1, KAP95, and TNPO3. It has been shown that R-DPRs promote aberrant phase separation of their target proteins. It is also probable that, for longer poly-PRs, the importins phase separate together with the poly-PRs (as in19) with poly-PRs possibly binding to the inner surface of several importins. This, however, is outside the scope of the current paper.

For the exportins, on the other hand, we observe different binding behavior with a more dominant role for the linker regions. For poly-PR with length $$\le$$ 20 repeat units interacting with CRM1 and its yeast homolog KAP124, we observe a slightly higher $${N}_{\mathrm{contact}}$$ for the B-helices. However, longer poly-PRs interact equally with both A- and B-helices of these two exportins, see right column of Fig. S5. This can be due to a less significant difference between the electrostatic potential of the inner and outer surfaces of these exportins compared to importins. The interaction of XPO5 is different from the other exportins and importins as in this case the poly-PR mostly interact with the linkers that connect the A and B-helices. XPO5 has a closed U-shaped conformation in its cargo-free state, and in contrast to other Kapβs, the inner surface of XPO5 is positively charged and used for the binding and export of miRNA49. A more detailed analysis of the contact sites will be provided in the following section.

### Poly-PR interacts with NLS-cargo, IBB, RanGTP and FG-Nup binding sites of different Kapβs in a poly-PR length-dependent manner

To provide more molecular insight into the way poly-PR target each Kapβ, we investigate the contact probability of each Kapβ residue in interacting with poly-PR (for more details about contact probability see the Methods section and section 2 of the SI). In Fig. 3a, we show the results for the interaction of PR7 and PR50 with the importin Impβ1 and the exportin Kap124. Results for the other Kapβs can be found in Fig. S7. For comparison, we also highlight the known NLS-cargo, IBB, RanGTP, and FG-Nup binding sites of the importins, as well as the known NES-cargo, RanGTP, and FG-Nup binding sites of the exportins. These binding sites are obtained from the crystal structures of the bound states of Kapβs using the PiSITE webserver51, giving results for the importins KAP121, Impβ1, TNPO1, KAP95, and TNPO3, and the exportins KAP124, CRM1, and XPO5. The crystal structures used to find the binding sites are listed in Table S3 of the SI. The A- and B-helices are also highlighted in Fig. 3a. As expected, for all cases an increasing poly-PR length increases the contact probability for individual residues. Our results in Figs. 3a and S7 show that certain regions of Kapβs have a very high contact probability, indicating that, in the bound states, these regions are always in contact with poly-PR. More interestingly, we observe that, depending on the poly-PR length and the type of Kapβ, poly-PR can make contact with Kapβ residues that are also used for the recognition of cargo, IBB domain, RanGTP, and FG-Nups. In Fig. 3b we show the number of contact residues shared between poly-PR and the native binding partners of the Kapβs, $${N}_{\mathrm{shared}}$$. It is seen that poly-PR makes contacts with importins at several known cargo-NLS, IBB, and RanGTP binding residues. Although for KAP95 no cargo or IBB binding sites are known, the observed binding of poly-PR to the inner surface of KAP95 in Fig. S5 suggests poly-PR binding to cargo/IBB binding sites of KAP95 as well because the inner surface of importins is known to have cargo/IBB binding sites43,52,53. At a poly-PR-importin molar ratio of 1:1, we find no overlap between poly-PR and the known FG-Nup binding sites. For all importins and exportins, the number of shared contact sites between poly-PR and the native binding partners of Kapβs increases by increasing poly-PR length (see Fig. 3b).

A common feature among the importins is the interaction of poly-PR with the linker between A and B helices of HEAT 8 (H8 linker), see Figs. 3a and S7. This specific linker region is highly acidic in several importins, including KAP121, Imp5, Impβ1, TNPO1, and KAP95, and has been shown to play a role in binding of RanGTP54,55,56,57, the IBB domain43, and NLS-cargo53. In the case of TNPO1, the long negatively-charged H8 linker has also been shown to play an important role in cargo release upon binding of RanGTP to the importin58. For exportins, poly-PR mostly interacts with RanGTP and FG-Nup binding residues, and less with cargo-NES binding sites (see Fig. 3a,b). For KAP124 and CRM1, poly-PR interacts with a relatively long linker that connects the A and B helices of HEAT 9 (H9 linker) with a high probability. The H9 linker contains negatively-charged residues and interacts with RanGTP, a process which is necessary for cargo-NES loading59. In the absence of RanGTP, the H9 loop and the C-terminal alpha-helix inhibit the binding of cargo-NES to the exportin42.

At higher poly-PR concentrations, more residues of the Kapβs interact with poly-PR, as shown by the increase of $${N}_{\mathrm{contact}}$$ in Figs. S8, S9, and the increase of $${N}_{\mathrm{shared}}$$ in Fig. S11. The degree of increase depends on the type of the Kapβ and is more pronounced for shorter poly-PRs. Similar to the effect of the poly-PR length on the interaction with the importins, increasing poly-PR concentration also increases the number of poly-PR contact sites on the A-helices of the importins, see Fig. S10. The outer surface of the Kapβs, comprising the A-helices, is known to interact with FG-Nups60,61,62,63. Although for importins, poly-PR only interacts with a limited number of known FG-Nup binding residues, see Fig. S11 for KAP95 interacting with poly-PR (number of repeat units $$\ge$$ 35), the interaction of poly-PR with A-helices suggest a likely overlap between poly-PR contact sites and FG-Nup binding sites. See also movie S3 for the interaction between several PR35 molecules and KAP95 (yeast Impβ1).

To explore the effect of poly-PR length (at a fixed mass concentration) on its interaction with Kapβs, Fig. S12 shows the results obtained from simulations performed with the same total number of PR repeat units $${n}_{\mathrm{PR}}$$ (that is, the same PR mass concentration), but with different lengths of poly-PR. For each Kapβ, we compare the number of contact residues $${N}_{\mathrm{contact}}$$ for five different $${n}_{\mathrm{PR}}$$ values. At a certain $${n}_{\mathrm{PR}}$$, we report the results for two different groups; the first group contains several copies ($$\ge 3$$) of PR7, whereas the second group contains fewer copies of a longer poly-PR, i.e. PR20, PR35, PR50, such that $${n}_{\mathrm{PR}}$$ is the same as in the first group. Fig. S12 clearly demonstrates that for all Kapβs the longer poly-PRs cause more contacts for a fixed mass concentration. At lower $${n}_{\mathrm{PR}}$$ values, where there is only one copy of the longer poly-PR, this effect is less pronounced and for a few cases we even observe a higher $${N}_{\mathrm{contact}}$$ for shorter poly-PRs. In these cases, one copy of the longer poly-PR mostly interacts with one of the favorable regions of the Kapβ while several copies of PR7 are able to make contact with other regions as well. At higher $${n}_{\mathrm{PR}}$$ values, with more than one copy of the longer poly-PR, the poly-PRs can roam a larger region and we observe a higher $${N}_{\mathrm{contact}}$$. At a relatively high mass concentration, longer poly-PRs can potentially interfere more with the function of Kapβ compared to shorter chains, possibly contributing to the poly-PR length-dependence of C9orf72 DPR toxicity.

Based on our results, the following mechanistic picture emerges of the interference of poly-PR with the function of Kapβs as regulators of nucleocytoplasmic transport. In the import cycle, illustrated in Fig. 4a, poly-PR could interfere with the cargo loading of several Kapβs by interacting with the sites used for the recognition of different cargo-NLSes and the IBB domain. The increased interaction of longer poly-PRs at higher poly-PR concentrations with the A-helices also suggests a potential interference of FG-Nup binding to the outer surface of the importins. Inside the nucleus, poly-PR interacts with RanGTP binding sites, and therefore could cause defects in RanGTP-mediated cargo release and the transport of RanGTP-importin complex back to the cytoplasm. In the export cycle (see Fig. 4b), poly-PR could interfere with the RanGTP-mediated cargo-NES loading by interacting with RanGTP binding sites. Poly-PR could also interfere with the transport of the exportin from the cytoplasm back to the nucleus through interaction with the FG-Nup binding sites. Based on the poly-PR length-dependent interaction with the known binding sites of Kapβs, see Fig. 3b, we conclude that a longer poly-PR is likely to play a more important role in the proposed nucleocytoplasmic transport defects described in Fig. 4.

## Conclusion

We used coarse-grained molecular dynamics models to study the interaction of poly-PR with the unbound state of Kapβs with the aim to gain mechanistic insight in the interference of poly-PR with the functioning of Kapβs in nuclear transport. We showed that poly-PR–Kapβ binding depends on the net charge per residue (NCPR) of the Kapβ, the salt concentration of the solvent, and the poly-PR length. For poly-PR chains with more than 20 repeat units, we observed a linear correlation between the number of poly-PR–Kapβ contacts and the negative NCPR of Kapβs.

We showed that poly-PR tends to make contact with the inner surfaces of most importins (KAP114, KAP121, Imp5, Impβ1, TNPO1, KAP95, and TNPO3) especially at regions with a pronounced negative electrostatic potential. This binding behavior results in the interaction of poly-PR with a large number of cargo-NLS, IBB, and RanGTP binding sites. Our findings also revealed that longer poly-PRs at higher concentrations are able to make contact with the outer surfaces of importins that contain several binding sites for FG-Nups. We also showed that poly-PR binds to exportins, especially at lower salt concentrations, making contacts with several RanGTP and FG-Nup binding sites.

Overall, our results suggest that poly-PR might cause defects in cargo loading, cargo release, and NPC transport of various Kapβs. Furthermore, poly-PR interaction with RanGTP binding sites could also cause defects in the transport of RanGTPs to the cytoplasm, thus interfering with the steep Ran gradient across the nuclear envelop that is necessary to sustain transport. We also observed a pronounced poly-PR length-dependence: increasing poly-PR length increases (i) the poly-PR–Kapβ binding probability, (ii) the contact probability for individual residues of Kapβs, and (iii) the number of contact residues shared between poly-PR and the native binding partners of Kapβs. These findings might provide a molecular basis for the more toxic nature of longer poly-PRs in cell and animal models8,11,45.

In general, the electrostatic-driven binding between poly-PR and Kapβs observed in this study emphasizes that positively-charged poly-PR could interfere with complementary charge-based interactions between Kapβs and their native binding partners. Just how poly-PR and the native binding partners of Kapβs, i.e. cargoes, IBB domains, RanGTP, and FG-Nups compete to bind to the same binding sites on Kapβs would be a very interesting subject for further research.

## Methods

### Coarse-grained model

We use a modified version of the implicit solvent, one-bead-per-amino acid (1BPA) model for disordered proteins developed and applied earlier25,33,34,35,37,40,64,65,66. The bonded potentials in this force field are residue specific and sequence specific, and depend on the patterning of three groups of amino acids, i.e. G, P, and other residues. For non-bonded poly-PR-poly-PR interactions, we take into account hydrophobic/hydrophilic and electrostatic interactions. The interactions between poly-PR and Kapβs can be classified in three categories: electrostatic interactions, cation-pi interactions, and excluded volume interactions. The poly-PR model used in this study has been applied earlier to study the phase separation of DPRs35. For Kapβs, a network of stiff harmonic bonds is used to maintain the secondary and tertiary structure of the protein. The missing regions in the crystal structures of the Kapβs have more than 50% of their residues in the coil conformation, as shown in Fig. S1 based on the results from the PSIPRED predictor67, and are included in the CG model as disordered regions. A more in-depth discussion on the force field is provided in Sect. 1 of the SI.

### Simulation and contact analysis

Langevin dynamics simulations are performed at 300 K at monovalent salt concentrations of 100 mM and 200 mM in NVT ensembles with a time-step of 0.02 ps and a Langevin friction coefficient of 0.02 ps−1 using GROMACS version 2018. Simulations are performed for at least 2.5 µs in cubic periodic boxes, and the last 2 µs are used for the analyzing the interaction between poly-PR and the Kapβs. To calculate the number of contacts, binding probability, and contact probability for individual residues, a cut-off of 1 nm is used. The length of A- and B-helices are estimated using the STRIDE algorithm in VMD47, and depicted using the Bendix plugin in VMD68,69. The binding sites are obtained from the crystal structures of the bound states of Kapβs in the Protein Data Bank using PiSITE51. The electrostatic potentials are calculated using PDB2PQR50, and are shown using Surf representation in VMD on a red-white-blue map. Positive and negative surface potentials are drawn in blue and red. Additional details are provided in sections 2–4 of the SI.