Selective transport control on molecular velcromade from intrinsically disordered proteinsKai D. Schleicher1, Simon L. Dettmer2, Larisa E. Kapinos1, Stefano Pagliara2, Ulrich F. Keyser2,

Sylvia Jeney3 and Roderick Y. H. Lim1*

The selectivity and speed of many biological transport pro-cesses1 transpire from a ‘reduction of dimensionality’2 that con-fines diffusion to one or two dimensions instead of three3. Thisbehaviour remains highly sought after on polymeric surfaces4

as a means to expedite diffusional search processes in molecu-lar engineered systems. Here, we have reconstituted the two-dimensional diffusion of colloidal particles on a molecularbrush surface. The surface is composed of phenylalanine-glycine nucleoporins (FG Nups)5—intrinsically disordered pro-teins that facilitate selective transport through nuclear porecomplexes in eukaryotic cells6. Local and ensemble-level exper-iments involving optical trapping using a photonic force micro-scope7 and particle tracking by video microscopy8, respectively,reveal that 1-mm-sized colloidal particles bearing nuclear trans-port receptors9 called karyopherins can exhibit behaviour thatvaries from highly localized to unhindered two-dimensional dif-fusion. Particle diffusivity is controlled by varying the amountof free karyopherins in solution, which modulates the multiva-lency of Kap-binding sites within the molecular brush10. Weconclude that the FG Nups resemble stimuli-responsive11 mol-ecular ‘velcro’, which can impart ‘reduction of dimensionality’as a means of biomimetic transport control in artificialenvironments.

Selective transport in microfluidic lab-on-chip devices oftenrequires externally controlled pressure or electric field-drivenflows, as well as elaborately designed pumps, channels andvalves12. In contrast, within the complex biological milieu, manyintracellular transport processes are highly selective and extremelyefficient1. To harness these benefits, motor proteins have been usedto drive molecular transport on complementary tracks in artificialenvironments, but chemical energy in the form of adenosine tripho-sphate (ATP) is burned in the process13. In comparison, reduction ofdimensionality (ROD) is an alternative transport mode that relies onfacilitated diffusion and uses thermal energy (kBT) without anyadditional energetic demands. For example, ROD has been impli-cated14 in nuclear pore complexes (NPCs), which regulate the selec-tive translocation of molecular cargoes between the nucleus and thecytoplasm in eukaryotic cells6. The key components within each50-nm-diameter NPC are approximately 200 FG Nups, which impedenon-specific cargoes but simultaneously provide exclusive selectiveaccess to karyopherins (Kaps) that rapidly shuttle signal-specific macro-molecules through6. Being intrinsically disordered5 and thus lackingsecondary structure, the highly flexible FG Nups are attractive asstimuli-responsive biomaterials because of their unique functionalproperties and physical resemblance to synthetic polymers15.

Several lines of evidence support the notion that the FG Nupscan impart selective ROD control in vitro. First, recombinantly

engineered FG Nups form molecular brushes that reconstitute thefunctional selectivity of NPCs when surface-tethered to biomimeticnanopores16,17, nanostructures18 and microbeads19. Second, while alack of binding leads to rejection, multivalent interactions20 betweenthe Kaps and the FG Nups greatly enhance Kap selectivity. Forinstance, the classical import receptor Kapb1 has approximatelyten hydrophobic pockets that can bind multiple FG repeats distrib-uted along the FG Nups21. Third, biophysical characterization usingsurface plasmon resonance shows that the FG Nups respondinnately to Kap binding by extending their conformations in anon-monotonic, concentration-dependent manner to accommo-date large numbers of Kap molecules (that is, equivalent to a fewKap layers) within the brush10. Thus, Kaps that penetrate into a pris-tine FG Nup brush show a higher binding affinity (KD ≈ 100 nM)than Kaps that encounter a pre-occupied brush with limited pen-etration and access to FG repeats (KD ≈ 10 mM)10. This is a keypoint, because it indicates that the occupancy of bound Kaps modu-lates Kap–FG Nup kinetic behaviour in a differential manner.Fourth, this stimuli-responsive property of the FG Nups and thestrength of Kap–FG binding depends solely on the equilibrium con-centration of free Kaps in solution10. We therefore sought to testwhether the soluble Kap concentration represents a single controlparameter that adjusts Kap–FG Nup binding to strike a balancebetween colloidal selectivity and two-dimensional mobility in ascaled-up artificial context.

Our minimal NPC-inspired system (Fig. 1a) consists of a surface-tethered FG Nup brush layer of Nup153 (aa 874–1475; 28 FGrepeats; modified with three N-terminal cysteines; henceforthcNup15317) that is approached towards a weak optically trapped1-mm-diameter Kapb1-functionalized colloidal probe (Kap-probe)by a piezo-actuator (Z) built within a photonic force microscope7

(PFM) (for details see Methods and Supplementary Sections 1and 2). Specifically, the PFM allows for the Brownian motion ofthe Kap-probe to be recorded in three dimensions with nanometreand microsecond spatiotemporal resolution between successive100 nm steps. The PFM experiments were conducted in 0.5, 2, 5,10 and 30 mM Kapb1 solutions that span from low to physiologi-cal22 concentrations to assess the impact of soluble Kapb1 as acontrol parameter of Kap-probe mobility, and in bacterial celllysate (with 0.5 mM Kapb1) to test for corresponding effects in amore complex physiological environment. Furthermore, becausepenta-His antibodies (pHis) were used to link Kapb1 to the Kap-probe (Methods), we thereafter used pHis-functionalized probes(without Kapb1; henceforth denoted pHis-probes) as a non-FGNup binding control.

Figure 1b shows the positional fluctuations obtained before andafter each respective probe encounters the underlying cNup153

1Biozentrum and the Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 50/70 CH – 4056, Basel, Switzerland, 2Cavendish Laboratory,University of Cambridge, Cambridge CB3 0HE, UK, 3Biozentrum, University of Basel and the Laboratory of Physics of Complex Matter, Ecole PolytechniqueFederale de Lausanne, Lausanne, Switzerland. *e-mail: roderick.lim@unibas.ch

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layer. No discernable changes are observed with the pHis-probe,except for a slight increase in the Z-axial position that coincideswith a 100 nm step that drives the two surfaces into contact. Thisverifies that pHis does not exert any measurable interaction withcNup153. In contrast, for 0.5–5 mM Kapb1, the Kap-probe exhibitsa ‘jump-into-contact’ (similar to an atomic force microscope tip;Supplementary Section 3) due to attractive biochemical forces inthe immediate vicinity of the cNup153 layer. The substantial ampli-tude reduction that follows in the X and Z directions (Y was foundto be similar to X) is further indicative of Kap-probe binding.Subsequent Z analysis reveals that both the attractive interactionforce and the adhesion or ‘rupture’ force required to separate theKap-probe from the cNup153 layer decreases with increasingKapb1 concentration (Supplementary Section 3). This weakening

provides initial evidence that the number of available FG repeatsdecreases as the Kapb1 occupancy increases within the cNup153layer10. At 30 mM Kapb1, the positional fluctuations of theKap-probe are barely distinguishable from the inert pHis-probeinteraction. To obtain a quantitative measure of these effects, weapplied Boltzmann statistics to compute the influence of Kapb1concentration on the in-plane free energy landscape of each probeusing the positional probability of its lateral fluctuations (Fig. 1cand Supplementary Section 4). Here, the quasi-symmetric flatteningof the energy landscape highlights the gradual transition fromstrong to weak in-plane interactions (that is, from 0.5 mM to30 mM), which approaches non-specific pHis-probe behaviour.Surprisingly, the energy landscape obtained in cell lysate indicatesthat the presence of non-specific interactions (Supplementary

FG-bound Kapβ1 cNup153

ΔZ = 100 nmX

YZ

Non-FG-bound Kapβ1

‘Jump into contact’

0 μMpHis-probe

0.5 μMKap-probe

2 μMKap-probe

5 μMKap-probe

10 μMKap-probe

30 μMKap-probe

LysateKap-probe

200

nm

2 sX

Y

200 nm

a

b cXZ

kB T

–5–6–7–8–9

–4–3–2–1

–10+

Figure 1 | Influence of Kapb1 concentration on Kap-probe binding and mobility. a, A cNup153 layer is driven in 100-nm steps towards a Kap-probe (grey).

b, Raw photonic force microscope position fluctuations obtained in the Z and X directions illustrate probe behaviour in the step before and after contact

(dashed line) with the cNup153 layer. In the Z direction, attractive ‘jump-into-contact’ forces are observed for Kap-probes in 0.5mM Kapb1, which gradually

weaken with rising Kapb1 concentration, with binding in 30 mM Kapb1 barely distinguishable from the non-binding pHis-probe. This is most apparent in the

lack of amplitude reduction in the Z and X position fluctuations after probe–cNup153 contact. c, The two-dimensional free energy (X–Y) landscapes allow

quantitative comparisons between the interactions of each probe with the cNup153 layer. The colour scale represents the energy levels of each probe with

respect to its lateral equilibrium position (energy minimum, red).

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Section 5) interferes only marginally with Kap-probe binding(compare with 10 mM Kapb1).

Individual Kap-probe behaviour can be further ascertained bycomputing the mean square displacement (MSD) from their pos-ition fluctuations to derive the respective diffusion coefficient (D)in each dimension. For free diffusion, the MSD is linear with timefor X and Z under the aforementioned conditions (Fig. 2a,b andSupplementary Section 6). Linear MSD fits provide DX and DZ,which we normalize with D0 (�0.46 mm2 s21), the in-bulk diffusioncoefficient measured for each probe. Here, D0 compares favourablywith the Stokes–Einstein equation (D¼ kBT/6phR, where kBis Boltzmann’s constant, T is temperature, h is viscosity and Ris the probe radius). This gives 0.45 mm2 s21 for a particlewith R ≈ 500 nm, when T¼ 295.15 K and h¼ 1.018 cP(Supplementary Section 7). As shown in Fig. 2c and d, the non-binding pHis-probe is the most diffusive, and the Kap-probe isthe least diffusive in 0.5 mM Kapb1. Increasing the Kapb1 concen-tration evokes qualitative increases to DX/D0,X and DZ/D0,Z ,although DZ/D0,Z is quantitatively less because of the presence ofan underlying surface boundary (Brenner’s Law23). Again, Kap-probe diffusion approaches pHis-probe behaviour at 30 mMKapb1. We interpret this to stem from diminishing multivalentinteractions between the Kap-probe and the cNup153 layer. Thisis consistent with surface plasmon resonance measurements,

which show that a reduction of free FG-repeat binding sitesfollows from a concentration-dependent increase in the occupancyof soluble Kapb1 molecules within the cNup153 layer10

(Supplementary Section 8). Similarly, Kap-probe diffusion in celllysate is remarkably close to that in 5–10 mM Kapb1, which indi-cates that Kap-probe binding to cNup153 prevails in spite of inter-ference from non-specific proteins (Supplementary Section 5).

Next, we wanted to verify that the resulting diffusivity couldinfluence the balance between Kap-probe selectivity and mobility,thereby leading to a two-dimensional random walk. Accordingly,we switched off the optical trap and recorded videos of Kap-probes moving in relation to the cNup153 layer over a period of

a c

b d

DX/D

0,X

DZ/D

0,Z

Time (μs)

MSD

Z (n

m2 )

MSD

X (n

m2 )

Kapβ1 (μM)

pHis0.5 2 105 30

Lysa

te

250

200

150

100

50

200 250 300100 150

Time (μs)200 250 300100 150

Bulk (D0)-- In contact --

pHis30 μM10 μM5 μMLysate2 μM0.5 μM

Bulk (D0)-- In contact --

pHis30 μM10 μM5 μMLysate2 μM0.5 μM

250

200

150

100

50

0.5

0.4

0.3

0.2

0.1

0.5

0.4

0.3

0.2

0.1

Kapβ1 (μM)

pHis0.5 2 105 30

Lysa

te

Figure 2 | Changes to local Kap-probe diffusivity with increasing Kapb1

concentration. a,b, Plots of mean square displacement (MSD) versus time in

X (a) and Z (b) indicate that the probes exhibit free diffusion on cNup153.

c,d, Bulk-normalized one-dimensional diffusion coefficients in X (c) and Z

(d) as obtained from linear fits to the MSD. With the non-binding pHis-

probe being the most diffusive, Kap-probe diffusivity is rectified with

increasing Kapb1 concentration and prevails even in the presence of non-

specific proteins from cell lysate (Supplementary Section 5). Error bars

represent standard error of the mean.

1 μM Kapβ130 μM Kapβ1

1 μM Kapβ1

30 μM Kapβ1 pHis

a

b

0.4

0.3

0.2

0.1

0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

MSD

XY, s

urfa

ce (μ

m2 )

Time (s)

Z (μm)

Popu

latio

n (%

)0.5

0.0 0.2 0.4 0.6 0.8 1.0 1.20

5

10

15

20

25

30

60

70

80

Figure 3 | Effect of Kapb1 concentration on ensemble Kap-probe

probability distribution and lateral diffusivity. a, Kap-probe probability

distribution as a function of Z height. The pHis-probe is unmistakably non-

selective, while the Kap-probe is most strongly selective in 1 mM Kapb1.

Selectivity is preserved but reduced in 30 mM Kapb1. b, The slope in the

ensemble-level mean square displacement (MSD) corresponds to DXY¼

0.217+0.009 mm2 s21 in 30mM Kapb1. Diffusion is negligible in 1 mM

Kapb1, because the Kap-probes adhere to the surface over the experimental

duration. Note that the analysis is not applicable to pHis-probes given their

extremely low occupancy and transient behaviour on the cNup153 surface.

Error bars represent standard error of the mean.

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several minutes (see Methods). Ensemble-level Kap-probe behav-iour was then analysed using a custom tracking algorithm8

(Supplementary Section 9) to extract the steady-state probe height(Z) probability distribution and its lateral diffusion coefficients.Figure 3a shows that �100% of the Kap-probes are located in theimmediate vicinity of the cNup153 layer (Z , 0.2 mm) in 1 mMKapb1, with 70% being in direct contact. In 30 mM Kapb1, thepopulation of Kap-probes that contact the layer is reduced to25%. The lateral diffusion coefficients (DXY; Z¼ 0.1 mm) as calcu-lated from the linear MSDXY plots in Fig. 3b are 0.004+0.001and 0.217+0.009 mm2 s21 for the Kap-probes in 1 mMand 30 mM Kapb1, respectively. It is noteworthy that the latterensemble-averaged DXY agrees with the PFM local-probe value(DX ¼ 0.212+0.013 mm2 s21; Fig. 2c and SupplementaryTable 3). This proves that Kap-probe behaviour is diffusive andscales linearly over six orders of magnitude from microsecond tosecond timescales. In comparison, the pHis-probe interaction isunmistakably non-selective based on its negligible population(,1%) at the surface, which is far too infrequent to provide anymeasurable MSD.

Representative probe trajectories (Fig. 4a) (recorded over 8 s;Supplementary Section 10 and Supplementary Movies) providedirect visual proof of the above effects. As expected, pHis-probesthat lack FG binding transiently impinge on the surface anddiffuse away. At the other extreme, the Kap-probes become‘stuck’, with minimal movement, in 1 mM Kapb1, indicatingmaximal binding with cNup153. Quite remarkably, we observethat ROD is achieved at 30 mM Kapb1 where the Kap-probesexhibit a distinctive two-dimensional random walk on thecNup153 layer. In terms of their average (Z) interaction times(Supplementary Section 9), Kap-probes remain permanentlyimmobilized on the surface in 1 mM Kapb1 within the observation

time. However, this reduces to 0.5 s in 30 mM Kapb1, whichsuggests that their long-lived trajectories involve various colloidaldiffusion mechanisms24 such as hopping, sliding and rolling inthe immediate vicinity of the surface.

As postulated by Adam and Delbruck2, our work demonstrateshow multivalent interactions can be modulated to exert sufficientstrength to maintain selectivity but are weak enough to permit delo-calized two-dimensional diffusion. In Fig. 4b we consider the Kap-probe and cNup153 layer as opposing surfaces of molecular ‘velcro’,respectively. When the concentration of soluble Kapb1 is suffi-ciently low, the Kap-probes are immobile on the cNup153 layerbecause of maximal binding avidity with largely unoccupied FGrepeats. An interesting observation is that this leads to the near100% population of Kap-probes on the surface, thereby suggestingpossible superselectivity25. In contrast, 25% of Kap-probes exhibittwo-dimensional diffusion in 30 mM Kapb1 solution due to thelimited access to FG repeats on a cNup153 layer pre-occupiedwith soluble Kapb1. Overall, the weakened binding is reminiscentof a ‘dirty velcro effect’, where, in physical terms, Kap-probeadhesion and protein friction26 with the FG Nup layer are signifi-cantly reduced. A further ramification is that the Kap-probes willexhibit non-binding pHis-probe-like behaviour under conditionsthat saturate the cNup153 layer with soluble Kapb1 or othernon-specific binders.

Taken together, these differences in probability distribution anddiffusivity define the inverse correlation between selectivity and themicroscopic mobility of each Kap-probe as controlled by the solubleKapb1 concentration (Supplementary Section 9). Interestingly, thisrecapitulates the observation that increasing Kapb1 concentrationregulates NPC functionality by increasing import efficiency whilereducing the interaction time27. Originally, Peters14 proposed aROD-based scenario where Kaps can diffuse in two dimensions

0 μM Kapβ1 30 μM Kapβ11 μM Kapβ1

Free Kapβ1 Weakly bound Kapβ1 Strongly bound Kapβ1 pHis antibody

a

b1 μm

cNup153

Figure 4 | Reduction of dimensionality by the ‘dirty velcro effect’. a, Trajectories were obtained for pHis-probe (left) and Kap-probe in 1 mM (middle) and

30 mM (right) Kapb1. A superimposition of the on-surface probe trajectories shows a distinct two-dimensional random walk in 30mM Kapb1

(Supplementary Movies). b, Model of various probe interactions with respect to the cNup153 molecular environment (not drawn to scale). Left: A pHis-probe

lacks FG repeat binding and diffuses away from the surface. Middle: Kap-probes are immobilized due to binding to an excess of FG repeats in the cNup153

layer at 1 mM Kapb1. Right: At 30 mM Kapb1, the Kap-probe is held to the surface by a reduced number of Kap–FG repeat interactions due to pre-occupation

of the cNup153 layer by large numbers of soluble Kapb1 molecules. In this state, dirty velcro-like Kap-probe interactions are strong enough to maintain

binding with the cNup153 layer but sufficiently weak to permit diffusion along the interface.

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along a layer of FG Nups lining the central pore. Although this hasnot been validated in vivo, the physical display of two-dimensionaldiffusion indicates that ROD can play a functional role in expeditingselective transport through biological NPCs, particularly withrespect to cargoes that bind multiple Kaps28.

To conclude, our nuclear pore complex-inspired system attests tothe relevance of ROD in controlling selective two-dimensionaltransport in an artificial context. Unlike the lateral diffusion oflipid bilayer-bound membrane proteins29, the transition from bulkto surface diffusion demonstrated here can provide a general strat-egy to regulate the controlled capture, targeting and release ofselective cargoes. This complements efforts to move nano-objects4

on synthetic polymer brushes by switching between differentenvironmental conditions such as temperature, pH and solvents.However, the use of Kapb1 concentration as a single adjustablecontrol parameter retains physiological aqueous conditions, whichis advantageous when implementing ROD-based trafficking of bio-logical cargoes. Unlike other multivalent systems24,30, our workexploits the unique functional advantages of intrinsically disorderedproteins. These include one-to-many and many-to-one binding,which follow from a decoupling of specificity from binding strengththat is achieved by the binding avidity of several low-affinity inter-actions31. In contrast to monoclonal antibody systems32, a singleFG Nup can bind several copies of the same Kap (one-to-many),while several FG Nups can bind to the same Kap simultaneously(many-to-one). Moreover, their characteristic binding promiscuityenables the FG Nups to serve as transport hubs for approximately20 different human karyopherins, which shuttle key regulatory pro-teins such as transcription factors into the nucleus9. Accordingly,ROD-based translocation may be implemented along surface-patterned diffusional guides consisting of different FG Nups, forinstance to examine Kap-cargo movement and related transportphenomena in vitro. In other respects, this underscores the emer-gence of intrinsically disordered proteins as important biomater-ials33 with innate functional properties that may be beneficial forbiosensing and other biotechnological applications.

MethodsKap-probe functionalization. Polystyrene (PS)–NH2 beads (PA03N, BangsLaboratories, nominal diameter 900 nm) were suspended in 1 ml filtered PBS(pH 7.2, Gibco) to 0.1% solids in low protein binding tubes (Sarstedt), and washedthree times with 1 ml PBS pH 7.2 by 4 min centrifugation at 13,500 r.p.m. in atabletop centrifuge (Eppendorf). Resulting pellets were resuspended by pipettingand briefly vortexed, followed by ultrasonication for 2 min (Bandelin SonorexRK100). Washed pellets were resuspended in PBS containing 10% glutaraldehyde(GA, Sigma-Aldrich, G5882) at pH 7.5, briefly vortexed, and ultrasonicated for5 min before being incubated for 6 h in a Hulamixer (Invitrogen) at roomtemperature. Beads were subsequently washed three times in filtered PBS pH 7.2, asdescribed above. A volume of 100 ml GA-activated beads at 0.1% solids was added to900 ml PBS containing 40 ml 0.2 mg ml21 BSA-free IgG pentaHIS (Qiagen), gentlymixed by pipetting, and incubated over night at 4 8C in a Hulamixer. The next day,BSA (Sigma-Aldrich) was added to 1% (wt/vol) and incubated for 1 h at 4 8C in aHulamixer. The beads were then washed twice with 1% BSA in PBS pH 7.2 bycentrifugation, gently resuspended by pipetting, and stored at 4 8C. Beforeexperimentation, the beads were incubated in 500 ml PBS pH 7.2 containing 1% BSAand 25 mg Kapb1 for 2 h at room temperature on a rotating shaker. UnboundKapb1 was removed by centrifugation and beads were gently resuspended in PBSpH 7.2 containing 1% BSA and the desired concentration of Kapb1. Further testsshowed that each bead exhibited an estimated surface density of approximately oneKapb1 molecule per 58 nm2, with full biochemical functionality preserved beforeand after experimentation (Supplementary Section 11).

cNup153 surface functionalization and chamber preparation. Coverslips #1(20 × 20 mm; Menzel-Glaser) were cleaned for 15 min in 200 mM HCl at roomtemperature, rinsed with H2O, incubated with 2% Helmanex III (Hellma) for 1 h at37 8C, rinsed thoroughly with H2O, dried with N2, subjected to UV-ozone (JelightCompany, model no. 42A-220) for 30 min, immediately immersed in 1% (vol/vol)APTES in anhydrous toluene (both Sigma-Aldrich) and incubated for 2 h at roomtemperature inside a desiccator under an argon atmosphere, then rinsed with largevolumes of (1) H2O, (2) ethanol and (3) H2O again, before drying with N2. A volumeof 500 ml per slide of 2 mg/1.5 ml sulfo-SMCC (Lubio Science) in PBS pH 7.2 wasadded and incubated for 1 h at room temperature in a humidified chamber17. Slides

were again rinsed with large volumes of H2O, ethanol and H2O before drying withN2. The PFM sample chamber was then assembled as follows. Standard microscopeslides (76 × 26 mm, Thermo Scientific) were rinsed with ethanol and dried underN2. Double-sided scotch tape was glued on the long sides to �8 mm left and right,leaving a 10 mm gap between. The activated coverslips were then inversely mountedonto the scotch tape with the maleimide residues facing inwards, resulting in achamber with a height of �100 mm. cNup153 was dialysed to PBS pH 7.2 for 3 h atroom temperature (Spectrapore, 3.5 kDa molecular weight cut-off ). A volume of30 ml cNup153 per slide was flushed into the sample chamber and incubated upsidedown over night at 4 8C in a humidified chamber to allow covalent binding. The nextday, the cNup153 solution was replaced by flushing three times with 100 ml PBSpH 7.2 containing 1% BSA using a pipette and filter paper (Whatman), and blockedfor 1 h at 4 8C in PBS pH 7.2 containing 1% BSA upside down in ahumidified chamber.

PFM experiment. The contents of the sample chamber were replaced with 30 ml ofthe functionalized bead solution (at 0.001% solids). The chamber was closed withnail polish (which was briefly dried) before being mounted upside down in the PFM.Approach measurements were performed with custom-made software using thefollowing protocol. Beads were first trapped �12 mm away from the surface and theirposition fluctuation recorded for 20 s. The surface was then subsequentlyapproached in ten steps of 1 mm in 1 s intervals, followed by one step of 0.5 mm.After 10 s of data acquisition, the surface was further approached in 0.1 mm stepsuntil contact. Between each such 0.1 mm step, the bead’s position fluctuations wererecorded for 10 s. Data acquisition was performed at a 0.5 MHz sampling rate (thatis, 2 ms per frame) with average trap stiffnesses of kX¼ 4.3 × 1026, kY¼ 3.5 × 1026

and kZ¼ 1.1 × 1026 N m–1. We chose the trap to be as weak as possible while stillenabling comfortable handling of the bead. Measurements started routinely≥10 min after addition of the bead solution to the sample chamber and wereperformed with more than 10 different beads at T¼ 22 8C per condition. One-dimensional diffusion coefficients of individual probes in contact with the cNup153layer were calculated as described in Supplementary Section 6 and normalized totheir corresponding bulk diffusion coefficients.

Ensemble probe tracking. Measurements were performed at T¼ 22 8C with probesat �0.007% solids using the visible light path (Supplementary Section 2). Probes andsample chambers were prepared as described above for the PFM experiments.Movies were taken between 2 and 5 h after beads were injected into the samplechamber. See Supplementary Section 9 and Supplementary Movies for details.

Received 19 December 2013; accepted 30 April 2014;published online 15 June 2014

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AcknowledgementsThe authors thank R.L. Schoch, M. Grimm and F.M. Mor for assistance and discussions.R.Y.H.L., K.D.S. and L.E.K. acknowledge support from the National Centre of Competencein Research ‘Molecular Systems Engineering’, the Swiss National Science Foundation, theBiozentrum and the Swiss Nanoscience Institute. S.J. acknowledges support from the SwissNational Science Foundation (SNF grant nos R’Equip 206021_121396 and200021_143703). S.L.D. acknowledges the German Academic Exchange Service and theGerman National Academic Foundation. S.P. and U.F.K. acknowledge support from anERC starting grant. S.P. also acknowledges support from the Leverhulme and Newton Trustthrough an Early Career Fellowship.

Author contributionsK.D.S. conceived and carried out the experiments, wrote the manuscript, and analysed andinterpreted the data. S.L.D. developed the tracking software and analysed the data.S.P. developed the tracking software and analysed the data. L.E.K. contributed proteinsand interpreted data. U.F.K. analysed and interpreted data. S.J. designed and built theexperimental set-up, conceived the experiment and the PFM data analysis protocol.R.Y.H.L. conceived the experiment, interpreted data and wrote the manuscript. All authorscontributed to, discussed and commented on the manuscript.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints. Correspondence andrequests for materials should be addressed to R.Y.H.L.

Competing financial interestsThe authors declare no competing financial interests.

LETTERS NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2014.103

NATURE NANOTECHNOLOGY | VOL 9 | JULY 2014 | www.nature.com/naturenanotechnology530

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