Continuous observation of the stochastic motion Continuous … · 2015-01-06 · Supplementary...

Supplementary Information

Continuous observation of the stochastic motion of an individual small-molecule

walker

Gökçe Su Pulcu* , Ellina Mikhailova , Lai-Sheung Choi and Hagan Bayley*

Department of Chemistry, University of Oxford, Oxford OX1 3TA, UK.

Continuous observation of the stochastic motion of an individual small-molecule walker

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NNANO.2014.264

NATURE NANOTECHNOLOGY | www.nature.com/naturenanotechnology 1

© 2014 Macmillan Publishers Limited. All rights reserved.

http://dx.doi.org/10.1038/nnano.2014.264

CONTENTS:

Table S1: The heteroheptameric staphylococcal αHL pores used in this work.

Table S2: Nomenclature used in the paper.

Section 1: Preparation of SPAA and its reaction with MEET

A. NMR analysis of the reaction between SPAA and MEET

B. Calculation of Kd of SPAA and MEET reaction by NMR

Section 2: Preparation of αHL heteroheptamers

Section 3: Planar lipid bilayer recordings

Section 4: Analysis of current traces

A. Models used in the kinetic analysis of double-Cys mutants

B. Calculation of the rate constants for the double-Cys mutants

C. Interpretation of the models

Section 5: Comparison of the current levels of PI and PII in (113C/115C)1(WT)6,

(115C/117C)1(WT)6, (117C/119C)1(WT)6, and (119C/121C)1(WT)6.

Section 6: Possible reactions of As(III) with thiol footholds and MEET

Section 7: Simulations of the walk


Table S1: The heteroheptameric staphylococcal HL pores used in this work

Cysteines Mutant pore

Single cysteine

(113C)1(WT)

6

(115C)1(WT)

6

(117C)1(WT)

6

(119C)1(WT)

6

(121C)1(WT)

6

Double cysteine

(113C/115C)1(WT)

6

(115C/117C)1(WT)

6

(117C/119C)1(WT)

6

(119C/121C)1(WT)

6

(115C/137C)1(WT)

6

Triple cysteine

(113C/115C/117C)1(WT)

6

Five cysteine

(113C/115C/117C/119C/121C)1(WT)

6


Table S2: Nomenclature used in the paper.

Symbol Chemical terminology Description

SP

EC

IES

SPAA 4-sulfophenylarsonous acid precursor of walker

MEET 2-(2-methoxyethoxy)ethanethiol thiol ligand

SPAA-MEET2 bis(2-(2-methoxyethoxy)ethyl)-4-

sulfophenylarsonodithioite

walker

LE

VE

LS

Po open pore level empty track

PI mono-adduct level one foot on the track

PII cyclic adduct level both feet on the track

TR

AN

SIT

ION

S

k+n

Po P

I

rate constant for formation of a mono-

adduct at foothold 'n'

entry onto the track

k-n

PI P

o

rate constant for MEET-mediated

release of a mono-adduct from

foothold 'n'

dissociation from the

track

knm

or kmn

PI P

II

rate constant for formation of a cyclic

adduct at footholds 'm' and 'n'

step making

kmn

n or k

mn

m

PII P

I

rate constant for MEET-mediated

formation of a mono-adduct at

foothold 'm' or 'n' from the cyclic

adduct at footholds 'm' and 'n'

lifting one foot from

the track


1. Preparation of SPAA and its reaction with MEET

4-Sulfophenylarsonous acid (SPAA) was prepared as described32

. MEET (2-(2-

methoxyethoxy)ethanethiol) was from Sigma Aldrich (no. 632295). The reaction of

SPAA with MEET to form SPAA-MEET2 (Fig. 1a) was analyzed by ESI-MS and

NMR. For MS, SPAA (7.5 mM) and MEET (150 mM) were mixed (Fig. S1). To

determine the Kd value for the reaction, the titration of SPAA with MEET was

monitored by NMR (Fig. S2 and S3). For comparison to the MS results, single-

channel recordings were performed with 200 nM to 25 M SPAA and 7.5 mM to 30

mM MEET.


Figure S1. Characterization of the SPAA, MEET and SPAA-MEET2 by ESI-MS.

a, Negative-mode ESI-MS of SPAA. 4-(Diiodoarsino)benzenesulfonate was dissolved

in water and the pH was adjusted to 8.5 by adding NaOH causing hydrolysis to

SPAA32

. The peaks at 126.9 and 264.9 m/z are assigned to iodide and SPAA,

respectively. The calculated mass of SPAA is 264.9 Da. b, Positive-mode ESI-MS of

MEET in water. The calculated mass of MEET is 136.21 Da. The peak at 293.1 m/z

may represent the MEET dimer with a Na+ ion. c, Negative-mode ESI-MS spectra of

the mixture of 7.5 mM SPAA and 150 mM MEET. The calculated mass of SPAA-

MEET2 is 501.01 Da.


A. NMR analysis of the reaction between SPAA and MEET

The Kd value for the reaction between SPAA and MEET (Fig. 1a) was determined by

NMR measurements.

Initial measurements were made by 400 MHz 1H NMR by titrating 5 mM SPAA with

1.25 mM, 2.5 mM, 5 mM, 9 mM, 13 mM, 19 mM and 29 mM MEET (Fig. S3a, b).

To follow the substitution of the hydroxyls of SPAA with MEET, we focused on the

aromatic protons, between 7.92 and 7.72 ppm (Fig. S3b). Two new peaks appeared at

around 7.87 ppm after the addition of 1.25 mM MEET (brown, Fig. S3b (1H NMR

(400 MHz, D2O) δ 7.87 (d, J = 8.5 Hz, 2H)). The multiplet between 7.85 and 7.72

ppm consisted of the quadruplet from unreacted SPAA (1H NMR (400 MHz, D2O) δ

7.79 (d, J = 8.0 Hz, 2H), 7.74 (d, J = 8.0 Hz, 2H)), and a new overlapping doublet.

The new doublet of doublets (1H NMR (400 MHz, D2O) δ 7.87 (d, J = 8.0 Hz, 2H),

7.74 (d, J = 8.0 Hz, 2H)) was almost fully developed after the MEET concentration

reached 9 mM (light blue, Fig. S3b), at which point the original SPAA quadruplet had

disappeared.

The identification of the reaction product as SPAA-MEET2 was made by assignment

of the complete 400 MHz 1H NMR spectrum (Fig. S2b).


a

b

Figure S2. Characterization of SPAA and MEET by

1H NMR. a, 400 MHz

1H

NMR spectrum of 5 mM SPAA in D2O at pD 8.2. The pD was adjusted to 8.2 by

titrating the sample with NaOD. Inset: The four aromatic protons of SPAA spanning

the region between 7.81 and 7.72 ppm are shown. 1H NMR (400 MHz, D2O) δ 7.79

(d, J = 8.0 Hz, 2H), 7.74 (d, J = 8.0 Hz, 2H). b, 400 MHz 1H NMR spectrum of 100

mM MEET in D2O pD 7.4. 1H NMR (400 MHz, D2O) δ 3.52 (dt, J = 21.5, 4.2 Hz,

m), 3.24 (s, 3H), 2.59 (t, J = 6.3 Hz, 2H).


B. Calculation of Kd for SPAA-MEET2.

The data for the Kd determination were collected by 700 MHz 1H NMR. The

measurements were carried out in 10 mM Bis-tris propane, 2 M KCl, 100 µM EDTA

at pH 8.0 with 5% D2O. 50 µM SPAA was used and the MEET concentrations were

from 40 µM to 1.4 mM (Fig. S3c).

To determine the Kd value, peaks developing at δ 8.1-8.05 (set one) and the peaks

disappearing at δ 7.98-8.02 (set two) (Fig. S3c) were followed. The integrated areas

of each set of peaks at each MEET concentration were determined. The concentration

of the SPAA-MEET2 formed was calculated by multiplication of the ratio of the peak

integrations (set one/ (set one+ set two)) with the initial SPAA concentration (SPAA-

MEET2

(µM) = (set one/ (set one+ set two)) x (50 µM)). The values were plotted

against the total concentration of MEET (i.e. the MEET added to the tube = free

MEET + bound MEET at equilibrium, Fig. S3d) and fitted to Eqn. 1.

a b

c d

Figure S3. 1H NMR analysis of the MEET titration on SPAA and calculation of

the Kd value of the reaction. a, SPAA titration with MEET followed by 400 MHz 1H


NMR. SPAA (red spectrum, 5 mM) at pD 8.2 in D2O was titrated with MEET: 1.25

mM (brown spectrum), 2.5 mM (light green), 5 mM (dark green), 9 mM (light blue),

13 mM (dark blue), 19 mM (purple), 29 mM (magenta). The SPAA sample was

prepared in D2O and the pD was adjusted by titrating the sample with NaOD. A

separate solution was prepared for each MEET concentration by using neat MEET

(7.4 M, Sigma). b, Expansion of the aromatic region. The spectrum in a was

expanded. SPAA (red spectrum, 5 mM) at pD 8.2 in D2O was titrated with MEET:

1.25 mM (brown spectrum), 2.5 mM (light green), 5 mM (dark green), 9 mM (light

blue), 13 mM (dark blue), 19 mM (purple), 29 mM (magenta). c, SPAA titration with

MEET followed by 700 MHz 1H NMR. SPAA (red spectrum, 50 M) in 10 mM Bis-

tris propane, 2 M KCl, 100 M EDTA, pH 8.0, containing 5% D2O, was titrated with

MEET: 0 M (red), 40 M (brown), 80 M (light green), 120 M (dark green), 180

M (cyan), 260 M (light blue), 400 M (dark blue), 800 M (purple), 1400 M

(magenta). A single NMR sample of 160 µL was used. Each step of the titration used

0.2 µL of titrant. For MEET at M final concentrations, a stock solution of 32 mM

was used. For MEET at mM final concentrations, a stock solution of 320 mM was

used to avoid dilution. SPAA: 1H NMR (700 MHz, H2O+D2O) δ 7.99 (d, J = 8.0 Hz,

2H), 7.96 (d, J = 8.0 Hz, 2H); SPAA-MEET2: 1H NMR (700 MHz, H2O+D2O) δ 8.09

(d, J = 8.0 Hz, 2H), 7.96 (d, J = 8.0 Hz, 2H). d, Plot of SPAA-MEET2

versus total

MEET concentration. 50 µM SPAA was titrated in 10 mM Bis-tris propane, 2 M KCl,

100 µM EDTA pH 8.0, 5% D2O. MEET concentrations ((i.e. the MEET added to the

tube = free MEET + bound MEET at equilibrium) spanned a range between 40 M

and 1.4 mM. SPAA-MEET2

concentrations were calculated by multiplication of the

concentration of the starting material by the peak area ratio (SPAA-MEET2

(µM) =

(set one/ (set one+ set two)) x (50 µM)). The black line is a fit to a 1:2 (SPAA:

MEET) binding model with KD(1) = 500 μM and KD(2) = 20 μM generated by using

Eqn.1.


Eqn. 1 is the expression for formation of AB2 according to the reaction scheme A +

2B ↔ AB2 reaction39

.

where Δmax is the maximum concentration of the complex formed during the reaction

(here it is 50 M), y is the concentration of SPAA-MEET2 formed, and x is the total

MEET concentration (i.e. the MEET added to the tube = free MEET + bound MEET

at equilibrium).

The reaction of SPAA with MEET is of the form of A + 2B ↔ AB2 (Fig. 1a). The

equilibrium dissociation constant (Kd) for the formation of SPAA-MEET2 can be

expressed as a combination of two equilibrium constants.

Fig. 1a.

A + B ↔AB K1

AB + B ↔ AB2 K2

A + 2B ↔ AB2 K1 K2 = Kd

However, no resonances were observed for the intermediate state (AB) (Fig. S3a, b,

c), suggesting cooperative association of the two ligands. Consistent with this idea,

the fitting of the data to Eqn. 1 yielded K1 = 500 M and K2 = 20 M, resulting in a

Kd value of 10-8

M2.


2. Preparation of HL heteroheptamers.

Heteroheptameric staphylococcal -hemolysin (HL) pores with a single cysteine,

with two cysteines, with three cysteines and five cysteines (Table S1) were prepared

as described earlier38

(Fig. S4).

Figure S4. SDS polyacrylamide gel used to prepare HL heteroheptamers. Lanes

1 and 2: (113C/115C/117C/119C/121C)1(WT)

6. Lane 1: the sample comprised WT:

113C/115C/117C/119C/121C in a ratio of 6: 1; lane 2: the sample comprised WT:

113C/115C/117C/119C/121C in a ratio of 7: 1; lane 3: Bio-Rad dual-color protein

standards. Cartoons illustrating the different subunit combinations and permutations

are shown to the right48

. The top band (WT)7 is a homoheptamer containing only WT

subunits (green). The second band, which is the desired product (arrow at left), is

(mutant)1(WT)

6 and contains one mutant subunit (red) and six WT subunits (green).

The gel does not display all the subunit combinations due to the high WT: mutant

DNA ratio used in the preparations.


3. Planar bilayer recordings.

Single-channel current recordings were performed as described previously32

. Both

compartments contained 2 M KCl, 10 mM Bis-tris propane, 100 M EDTA, pH 8.0.

The bilayer was formed from 1,2-diphytanoyl-sn-glycero-3-phosphocholine.

Solutions of thiols (Sigma-Aldrich) were prepared fresh daily in degassed ultrapure

water. A stock solution of EDTA was added to the thiol solution to give a final EDTA

concentration of 100 M and a final thiol concentration of 7.5 or 30 mM. These

solutions were kept on ice for the duration of an experiment.

After the insertion of a single HL pore into the bilayer from the grounded cis

compartment, a typical experiment involved the addition of SPAA to the trans

compartment (200 nM to 300 M, the final concentration depended on the

experiment). The thiol solution was added to the cis compartment (final

concentration: 7.5 to 30 mM).

Events corresponding to the reversible reaction with a Cys residue in the pore were

recorded under a -50 mV potential by using an Axopatch 200B patch-clamp amplifier

(Axon Instruments). The signal was filtered with a low-pass Bessel filter (80

dB/decade) with a corner frequency of 2 kHz. The data were sampled at a frequency

of 10 kHz, and digitized with a DigiData 1200 A/D converter (Axon Instruments).

Experiments with the five-Cys HL mutant (113C/115C/117C/119C/121C) were

performed in a glove bag under an N2 atmosphere to prevent oxidation of the

cysteines. The entire set-up including the Faraday cage was placed inside the glove

bag. The bag was purged with N2 or Ar for at least 1 h. The bag was then deflated and

filled with argon before the recording chamber was assembled inside it. The gas flow

was turned off during the measurements to avoid evaporation and mechanical noise.

4. Analysis of the current traces

To analyze the current traces, we used Clampfit (version 10.0, Axon Instruments) and

QuB software34

which are normally used for the analysis of ion channel activity. In

the first step, the traces were filtered at 100 Hz [(113C1)(WT)6, (115C1)(WT)6,

(117C1)(WT)6, (119C1)(WT)6, (121C1)(WT)6 and (113C/115C)1(WT)6] and 300 Hz

[(115C/117C)1(WT)6, (117C/119C)1(WT)6, (119C/121C)1(WT)6] with a low-pass

Bessel filter in the Clampfit software. Filtering was necessary to allow the various

current levels to be distinguished during data idealization (event picking). Care was

taken to avoid an excessive level of filtration and thereby retain events. The filtered

data was then idealized by Clampfit, defining the levels 1 (Po), 2 (PII) and 3 (PI).

Clampfit generates a list of levels (1, 2, 3...) with their dwell times in order of

occurrence in the data trace. The table was copied into QuB in order to calculate the

transition rates between the levels with MIL (the Maximum Interval Likelihood

application). The rates were calculated according to user defined kinetic models. The

choice of the kinetic model is explained in section 4A. The MIL application calculates

mean the dwell time in each current level and counts the number of transitions from


one level to another. The rate of the transition between two levels (x to y) is given by:

vxy = (nxy/nx)/x, where nxy is the number of transitions from level x to level y, nx is the

total number of events in level x, and x is the mean dwell time in level x. The rates of

the transitions were then plotted against the concentrations of the reagents (Fig. S6

and Fig. 4).


A. Models used in the kinetic analysis of the double-Cys mutants

Fig. S5 illustrates the current traces of individual double-Cys mutants (a) and the

corresponding models used to analyze the data trace (b). The number of states in the

models was chosen to reflect the number of observed current levels, bearing in mind

that certain levels included more than one state. For example, there are five levels in

the example trace for (113C/115C)1(WT)6 (Fig. S5a). Therefore, the required number

of states would be five, if every current level represented only one state. However, if

there are two states embedded in the same level (i.e. with indistinguishable current

amplitudes), they must be represented by two different states in the model. In

(113C/115C)1(WT)6, within the level PI, there are two states, PI(1) and PI(2), with the

same current amplitude (ΔIPI(1) = ΔIPI(2)), but with different mean dwell times (τPI(1) ≠

τPI(2)). Therefore, the PI level is represented by two states, and therefore the final

model for (113C/115C)1(WT)6 consists of six states (Fig. S5b(i)); one for Po, one for

PII, two for PI, one for Pex1 and one for Pex2 (for the latter, see Fig. S5c(i) and section

4C).

The connectivity of the states in a model reflected the connectivity of the states in the

experimental data, e.g. if Po can be converted to PI and vice-versa, the model had the

same connectivity between Po and PI. We observed two additional levels (Pex1 and

Pex2) with the double-Cys mutant (113C/115C)1(WT)6, both of which occurred from

the level PI (see the interpretation in Section 4C). These two levels were not present in

the current traces of the other double-Cys mutants.

The final model used to fit the data for (113C/115C)1(WT)6 (Fig. S5b(i)) included

level Po (open pore), which was converted only to the mono-adducts at either of the

footholds 1 and 2; PI(1) or PI(2). Both PI levels were converted to a single PII level. This

diamond model (cf. Fig. S5b(iii)) was further connected to the two additional levels,

Pex1 and Pex2, observed only with (113C/115C)1(WT)6. Initially, both Pex1 and Pex2 were

connected to the same PI level, for example to PI(1). However, data fitting was not

successful with this model. Therefore, one Pex level was arbitrarily connected to PI(2)

and the other Pex to PI(1). QuB analysis then linked Pex1 to PI(1), and Pex2 to PI(2). The

resulting fits to the final model (Fig. S5b(i), see the molecular representation in Fig.

S5c(i)) generated the rates of individual transitions. The transition rates were plotted

against the concentrations of SPAA and MEET used (Fig. S6 (i, ii, iii, iv)) to obtain

rate constants. The dwell time histograms from the fits can be found in Fig. S7.

In the case of the double-Cys mutants (115C/117C)1(WT)6, (117C/119C)1(WT)6 and

(119C/121C)1(WT)6 (Fig. 4a, Fig. S5a), we observed only three current levels (Po, PI,

PII; Pex1 and Pex2 were absent). The data for (115C/117C)1(WT)6 and

(117C/119C)1(WT)6 could not be fitted into the diamond model (Fig. S5b(i)) derived

for (113C/115C)1(WT)6. Instead, a linear model consisting of only three states

corresponding to Po, PI and PII was used (Fig. S5b(ii), Fig. S5c (ii)). The similar

current blocks and mean dwell times of the two PI states for (115C/117C)1(WT)6 and

for (117C/119C)1(WT)6 (see Fig. S7b and c, blue fits), did not allow the separation of

PI into two levels for kinetic analysis. Thus, PI in the linear model included both

potential PI levels (i.e. PI(2) and PI(3)).


Data for the final double-Cys mutant (119C/121C)1(WT)6 could be fitted to the four-

state diamond model (Fig. S5b(iii)), although only three levels were apparent in the

current traces (Fig. S5a). Two PI states displayed the same current amplitude, but

differed in mean dwell time (Fig. S7, blue fitted histogram).


c

Figure S5. Kinetic models for the double-Cys HL pores. a, Short sections of

representative current traces. b, Schematics of the models used to fit the current data

represented in 'a'. Molecular representations of the states shown as boxes in this figure

are given in c. Data were collected in 10 mM Bis-tris propane, 2 M KCl, 100 µM


EDTA, pH 8.0, at -50 mV and at 20°C, in the presence of 10 μM SPAA (trans) and 15

mM MEET (cis). c, Kinetic models for the double-Cys αHL mutants. Molecular

representations of the states illustrated in b. (i) Six-state model for

(113C/115C)1(WT)6. (ii) Three-state model for (115C/117C)1(WT)6 and

(117C/119C)1(WT)6. (iii) Four-state model for (119C/121C)1(WT)6. In the six-state

model (i), we have assigned level Pex1 to one of the enantiomers at the As(III) center

of the mono-adduct at 113C. Level Pex2 was assigned to the characteristic spikes

arising from level PI in (113C/115C)1(WT)6 in a. (see section 4Ca).


Figure S6. The dependence of transition rates on reagent concentrations for

(113C/115C)1(WT)6. The data were analyzed according to a six-state model (Fig.

S5b. (i)). Transitions were examined as a function of SPAA concentration (panels (i)

and (iii)) and MEET concentration (panels (ii) and (iv)): PoPI(1), ; PoPI(2), ;

PI(1)PII, ; PI(2)PII, ; (PI(2)PEx(1), ), (PI(1)PEx(2), ) ((iii) and (iv): (PI(1)Po, ),

(PI(2)Po, ), (PIIPI(1), ) (PIIPI(2), ) , (PEx1PI(2), ), (PEx(2)PI(1), )

concentrations. PI(1) and PI(2) represent the current levels for mono-adducts at each of

the two cysteines (113C and 115C). We assigned level Pex1 to one of the enantiomers

at the As(III) center of the mono-adduct at 113C. Level Pex2 was assigned to the

characteristic spikes arising from level PI. Data were collected in 10 mM Bis-tris

propane, 2 M KCl, 100 M EDTA, pH 8.0, at -50 mV and 20°C, in the presence of 12

to 24 M SPAA (trans) and 7.5 to 22.5 mM MEET (cis).


Figure S7. Dwell time histograms for the double-Cys mutants. Representative

histograms for a, (113C/115C)1(WT)6; b, (115C/117C)1(WT)6; c,

(117C/119C)1(WT)6; d, (119C/121C)1(WT)6. Parts of the current traces used are in

Fig. S5a. The assigned states are indicated at the top of each column. Models used:

(113C/115C)1(WT)6, six-state model (Fig. S5b (i)); (115C/117C)1(WT)6, three-state

model (Fig. S5b (ii)); (117C/119C)1(WT)6, three-state model (Fig. S5b (ii));

(119C/121C)1(WT)6, four-state model (Fig. S5b (iii)). Each state is indicated by a

star. The fitting of the level Pex2 in a is poor due to the missing counts that arise from

the ignore duration (5 ms) used to remove noise in the data idealization step for

(113C/115C)1(WT)6.


B. Calculation of the rate constants for the double-Cys mutants

The dependence of the transition rates of the double mutants (113C/115C)1(WT)6 and

(119C/121C)1(WT)6 on the reagent concentrations were determined (Fig. S6, Fig 4)

and used to calculate the rate constants for each transition. The rates for

(115C/117C)1(WT)6 and (117C/119C)1(WT)6 at fixed concentrations of SPAA and

MEET were used, because no titrations were carried out for these mutants

((115C/117C)1(WT)6, 10 M SPAA, 15 mM MEET; (117C/119C)1(WT)6, 5 M to

10 M SPAA, 15 mM MEET). The measurements were carried out in 10 mM Bis-tris

propane, 2 M KCl, 100 M EDTA, pH 8.0, at -50 mV and 21°C. SPAA was added to

the trans compartment and MEET to the cis compartment.

C. Interpretation of the models

a. (113C/115C)1(WT)6: Current traces from (113C/115C)1(WT)6 in the presence

of SPAA-MEET2 (Fig. S5a(i) showed 5 levels, i.e. two levels in addition to Po, PI

and PII, which were designated Pex1 and Pex2. Both Pex1 and Pex2 were immediately

preceded in the traces by PI. Therefore, we modelled the transitions for

(113C/115C)1(WT)6 with a six-state model: Po (black), PI(1) (blue), PI(2) (blue), PII

(red), Pex1 (purple) and Pex2 (purple) (Fig. S5b(i)). Observed transitions were PoPI(1),

PoPI(2), PI(1) PII, PI(2) PII, Pex1PI and Pex2PI. We examined the rates of these

transitions with respect to the reagent concentrations (Fig. S6). The transitions from

the open pore to the mono-adduct level (PoPI(1), PoPI(2)) were both dependent on

the SPAA concentration, which reflects the effective concentration of SPAA-MEET2.

The transitions from the cyclic-adduct to the mono-adduct (PIIPI(1), PIIPI(2)), and

from the mono-adduct to the open pore (PI(1)Po, PI(2)Po) had a linear dependence

on MEET concentration. The transitions Pex1PI and Pex2PI, and from the mono-

adducts to the cyclic-adduct (PI(1)PII, PI(2)PII) were independent of the reagent

concentrations.

We have assigned the level Pex1 to one of the enantiomers at the As(III) center of the

mono-adduct at 113C. The two isomers can also be seen in (113C)1(WT)6 (Fig. 2a(i)).

By contrast, level Pex2 was only observed with (113C/115C)1(WT)6 and not with

(113C)1(WT)6 or (115C)1(WT)6. Therefore, we assigned Pex2 as characteristic spikes

arising from level PI in (113C/115C)1(WT)6.

Based on this scheme, we were able to separate the two mono-adducts (PI(1) and PI(2))

kinetically and found that there is an order of magnitude difference in their mean

dwell times (τPI(1) = 750 ± 66 ms and τPI(2) = 87 ± 5 ms at 15 mM MEET, n = 3, where

n is the number of pores examined).

b. (115C/117C)1(WT)6: The three state model used for this double-Cys mutant

includes the three levels Po, PI and PII. Unlike the cases of (113C/115C)1(WT)6 (Fig.

S5b(i)) and (119C/121C)1(WT)6 (Fig. S5b(iii)), we could not separate the two PI

levels kinetically or by amplitude, i.e. the rates of the transitions from PI to Po from

the two footholds were similar, as were the rates from PI to PII (Fig. S7). As a result, a


single dwell time was used for level PI (τPI(23) = 28 ± 1 ms at 15 mM MEET, n =3,

where n is the number of pores examined).

(117C/119C)1(WT)6: The three state model used for this double-Cys mutant includes

the three levels PO, PI and PII. Unlike the cases of (113C/115C)1(WT)6 (Fig. S5b(i))

and (119C/121C)1(WT)6 (Fig. S5b(iii)), we could not separate the two PI levels

kinetically. As a result, a single dwell time was used for level PI (τPI(34) = 60 ± 7 ms at

15 mM MEET, n = 3, where n is the number of pores examined).

c. (119C/121C)1(WT)6: The four-state model used for the double-Cys mutant

(119C/121C)1(WT)6 with the cysteines located near the trans entrance of the pore

includes Po, PI(4), PI(5) and PII. Here, the dwell-times of the two mono-adducts were

found to differ by ~20-fold (τPI(4) = 166 ± 6 ms and τPI(5) = 10 ± 1 ms at 15 mM

MEET, n = 3, where n is the number of pores examined). Although the rates of

formation and cleavage of the mono-adducts obtained with the corresponding single-

Cys mutants were not drastically different ((119C)1(WT)6, k+4 = (15 ± 2) x 104 M

-1s

-1;

(121C)1(WT)6, k+5 = (5 ± 1) x 104 M

-1s

-1, ((119C)1(WT)6, k-4 = (4 ± 1) x 10

2 M

-1s

-1;

(121C)1(WT)6, k-5 = (3.4 ± 1.7) x 102 M

-1s

-1, Table 1), the rates of formation of the

cyclic-adduct from the two mono-adducts of the double-Cys mutant differed by ~20-

fold (k45 = (7 ± 2) s-1

, k54 = (120 ± 20) s-1

, Table 2). The significant differences in

cyclization rates may arise from the flexibility of the barrel near the trans

entrance40

.


5. Comparison of the current levels of PI and PII in (113C/115C)1(WT)6,

(115C/117C)1(WT)6, (117C/119C)1(WT)6, and (119C/121C)1(WT)6.

The values of the amplitudes of levels PI and PII (Table 2) expressed as

differences (I) from Po gradually decrease as the walker approaches the trans

entrance of the pore.

Figure S8. Events versus amplitude histograms for HL double-Cys mutant

pores. The values of I for PI (blue dashed line) and PII (red dashed line) for the four

double-Cys mutants (Table 2) are illustrated in amplitude histograms generated from

the current traces presented in part in Fig. S5a. The number of counts (y-axis)

represents the number of events. The values of the amplitudes of levels PI and PII

(Table 2) expressed as differences (I) from Po gradually decrease as the site of

walker attachment approaches the trans entrance of the pore.


6. Possible reactions of As(III) with thiol footholds and MEET

In the presence of 7.5 mM MEET, the SPAA walker is fully thiolated forming SPAA-

MEET2 (Kd =10-8

M2, Fig 1a). Mono-adducts with the HL pore are formed by

nucleophilic attack of a cysteine thiol at the As(III) of SPAA-MEET2 with the

concerted release of a MEET molecule. Mono-adducts have several possible fates, as

discussed below. We have focussed on (i) periods when the walker stays on the track;

(ii) monitoring movement though the observation of cyclic-adducts (PII, Fig. 1c).

Scheme S1. Reaction series exemplifying possible substitution reactions at As(III). (i) Formation

of the mono-adduct and release through nucleophilic attack of MEET. (ii) Formation of a cyclic-adduct

by nucleophilic attack of a neighboring cysteine-thiol and (iii) reopening by MEET. (iv) Ligand

exchange reaction by MEET on a mono-adduct, resulting in inversion at As(III). (v) Hopping of a

mono-adduct as the result of cleavage of the cysteine-thiol by nucleophilic attack of a neighboring

cysteine (a rare occurence). (vi) Long distance jumps, as a result of series of hopping reactions.

1. Formation of a cyclic-adduct: A substitution reaction by a neighboring

cysteine thiol on a mono-adduct releases MEET and generates a cyclic-adduct

(PII, Scheme S1(ii)). This reaction is required for the progress of the walk.

2. Cleavage of the mono-adduct (release of the walker from the track):

Attack by MEET and dissociation of the cysteine thiol releases the walker

from the track. The walk is terminated (Scheme S1 (reverse reaction in (i))).

3. Ligand exchange on the mono-adduct: Attack by MEET can replace the

MEET ligand on a mono-adduct (Scheme S1 (iii)). This reaction occurs with

inversion and, because the reactant and the product are similar, it is most

likely (but not always "silent").

4. Hopping reactions: A neighboring cysteine thiol can attack a mono-adduct

with release of the first cysteine thiol generating a mono-adduct at the

neighboring cysteine (Scheme S1 (v)). Cyclization is favored over hopping.

Further, this type of motion may not be detected due to the similar current

levels associated with the reactant and the product.


5. Long distance jumps: As a result of hopping reactions, which may be a result

of dynamic protein movements (especially at the trans entry of the pore), we

have very occasionally observed long distance jumps (Scheme S1 (vi), Fig.

S9).

a

b

Figure S9. Electrical traces of rare events. a, Recording of an HL pore containing

a five-cysteine track (113C/115C/117C/119C/121C) in the presence of

SPAA(MEET)2. The trace shows an unexpected transition from foothold 4 to foothold

2 at 585 s (red circle). The experiment was performed in 10 mM Bis-tris propane, 2 M

KCl, 100 M EDTA, pH 8.0, at -50 mV and at 20°C with 200 nM SPAA (trans) and

7.5 mM MEET (cis). b, Representative missing transition. Electrical recording of

(115C/117C)1(WT)6 in the presence of 10 mM Bis-tris propane, 2 M KCl, 100 μM

EDTA, 10 μM SPAA, 15 mM MEET at pH 8.0. Sampling rate 10 kHz, with 2 kHz

filter. The red arrow points to the missing mono-adduct level. 0.5% of the transitions

PIIPo occurred without observation of the intermediate level PI.


7. Simulations of the walk

The simulations were carried out with QuB software34

by using a 10-state model (Fig.

S10a). QuB was developed for the kinetic analysis of currents produced by stochastic

single channel activity. The 10-states consisted of five mono-adducts, four cyclic

adducts and an open pore state. Transitions were allowed between cyclic-adducts and

neighboring mono-adduct states. In addition, transitions were allowed between the

mono-adduct levels and the open pore state. Further, only one walker was allowed on

the track at a time, which was achieved in practice by using [SPAA] = 200 nM.

By using the rates obtained from the single-Cys mutants (Po PI, and PI Po ,

Table 1) and from double-Cys mutants (PI PII and PII PI, Table 2), we simulated

walks along the five-cysteine track with 200 nM SPAA and 7.5 mM MEET for

comparison with the electrical recordings.

To determine the net directional bias of the walker, we removed the transitions from

the open pore to the mono-adduct states at foothold 1 (113C), foothold 2 (115C),

foothold 4 (119C) and foothold 5 (121C) and only allowed a transition to the middle

of the track at foothold 3 (117C) (Po → ) (Fig. S10c). We then counted the walks

that ended at foothold 1 (113C) and the walks that ended at foothold 5 (121C). In 37

out of 46 events (85% occasions), the walker arrived at foothold 5. In 7 out of 46

events (15% occasions), it arrived at foothold 1.


Figure S10. Simulations of walks along the five-cysteine track. a, The 10-state

model representing the open pore (Po), the five mono-adducts at the 5 different Cys

footholds (113, 115, 117, 119, 121, levels PI), and the four cyclic-adducts (12, 23, 34,

45, levels PII). The following transitions were allowed in the model: Po to all PI

states; all PI states to Po; PIPII and PIIPI for "adjacent" states. The transition rates

are calculated based on 200 nM SPAA and 7.5 mM MEET, by using the experimental

rate constants for double-Cys mutants (Table 2). b, Simulated data traces. Traces (i),

(ii) and (iii) can be compared with the traces in Fig. 6B, D, E, respectively. c, The

reduced 10-state model used to test directional bias. Walks were initiated at 117C.

The arrows show the directions of an "up walk" and a "down walk".


8. Determination of mean first passage time to foothold 5 and the fraction of

walks that reach foothold 5

Simulations were carried out with QuB software34

by using 6-, 5-, 4-, 3-, and 2-state

models (Table S3) representing the individual footholds and the state when the

walker is in solution. The same color coding is used as in section 6 (Simulations of

the walk).

Simulations were first performed for model situations in which the forward and

backward rates for movement between adjacent footholds were the same (kintraforward =

kintrabackwards = 1000 s-1

) and 1000 times higher than the association rates for entry onto

the track (kon = kn = 1 s-1

). The walker was allowed to enter at each foothold with the

same rate (kon = kn = 1 s-1

).

In Model 1, the off rates are essentially zero and the walker does not leave the track

(koff = k-n = 1 x 10-10

s-1

). In Models 2 and 3, the off rates are 1 s-1

and 1000 s-1

,

respectively.

A representative simulation from Model 1 is shown in Fig. S11. Twenty such traces

were used to obtain the mean first passage time (FP5 = 1/kFP5) from solution to

foothold 5.

The kFP5 value for each model increases as the number of footholds is increased

(Table S4). For all three models, a five-foothold track enhances the rate ~5-fold, a

four foothold track ~4-fold, and so on, by comparison with direct association at

foothold 5. In Model 3, the dissociation rate was fast, and a substantial fraction of

walks were incomplete (foothold 5 was not reached) in the cases with 5, 4, and 3

footholds. Nonetheless, in the successful walks, the kFP5 values were similarly

enhanced.

Additionally, we have made similar simulations with our experimentally determined

rate constants ((Po PI, and PI Po , Table 1 and PI PII and PII PI, Table 2)

setting free SPAA at 200 nM. The rate of arrival at foothold 5 (kFP5 = 0.048 s-1

) is

enhanced 5-fold with a 5-foothold track compared with direct association at foothold

5 as derived from the single-cysteine mutant 121C in Table 1 (k5 = 0.01 s-1

). Rate

comparisons are listed in Table S4.

Finally, the experimental value of the rate constant kFP5 was determined. It is the

reciprocal of the mean time required to reach to foothold 5. Each dwell time was

measured by adding the value of the dwell time of the walker in solution plus the

dwell time spent on the track until the walker finds foothold 5. This rate (kFP5 = 0.091

s-1

) was compared to the rate of binding directly to foothold 5 obtained from the rate

constant determined with the single-cysteine mutant 121C (Table 1, k5 = 0.010 s-1

) by

setting free SPAA at 200 nM. In this case the rate enhancement is approximately 9-

fold (Table S4).


Figure S11. A representative simulated trace generated by Model 1 with 5-

footholds. For Model 1 see Table S3. The first passage time (tFP5) to reach foothold 5

is indicated. The current levels for each foothold relative to the open pore are arbitrary

and serve to aid foothold identification: , foothold 5, ΔI5 = 3 pA; , foothold 4, ΔI4

= 7 pA; , foothold 3, ΔI3 = 8 pA; , foothold 2, ΔI2 = 9 pA; , foothold 1, ΔI1 = 10

pA.


Table S3. Kinetic models used to determine the mean first passage time (tFP5) to

foothold 5 on 5-, 4-, 3-, 2- and 1-foothold tracks. Models 1a, 2a and 3a have six

states representing each of five occupied footholds and one unoccupied pore state.

Similarly, Models 1b, 2b and 3b have five states representing four occupied footholds

and one unoccupied pore state. The remaining models (c-e) have four, three and two

states. The walker enters stochastically at any foothold and moves stochastically

between each foothold. In these model systems, the walker moves between all

footholds at 1000 s-1

in either direction. The entry rate (1 s-1

in all models) was set to

mimic the high dilution of the walker in bulk solution. The dissociation rate of the

walker from the footholds (release from the track) was varied between Models 1, 2

and 3 (k-n = 0, 1 and 1000 s-1

, respectively) to mimic the situation when the walker is

always on the track (k-n = 0, Model 1), strongly processive motion with occasional

dissociation (k-n = 1, Model 2) and low processivity (k-n = 1000, Model 3). The same

color coding is used to identify the footholds in all the Models: , foothold 1; ,

foothold 2; , foothold 3; , foothold 4; , foothold 5.


31


32

Table S4. Rates and success of finding foothold 5 and percentage of complete walks. Details of Models 1, 2 and 3 are in Table S3. The

simulations were extended to the 5-foothold nanoreactor by using the measured rate constants from the single Cys-mutants (Po PI, and PI

Po , Table 1) and from double-Cys mutants (PI PII and PII PI, Table 2). The SPAA concentration was set at 200 nM. Finally, the mean value

of tFP5 was obtained from the experimental data traces of 32 individual walks collected at 200 nM SPAA. The reciprocal of the value is reported

as kFP5. In Model 1 (k-n = 0), the walker finds foothold 5 with 100% success rate, as expected. In Model 2, the motion is highly processive

motion and the walker also finds foothold 5 with 100% success rate. In Model 3, where the walker is weakly bound, the success rate of finding

foothold 5 dropped to <50% for the five- and four-foothold tracks. The simulated 5-foothold nanoreactor showed 3 complete walks out of 28

(10.7) %. In the experimental 5-foothold nanoreactor, 3 out of the 32 walks were complete (9.3%). A complete walk is a walk in which all 5

footholds were visited, regardless of the starting foothold.


33

number of footholds

5 4 3 2 1

kFP5 (s-1

) kFP5 (s-1

) kFP5 (s-1

) kFP5 (s-1

) kFP5 (s-1

)

Model 1 5.7 4.3 3.1 2.2 1.07

Model 2 5.8 4.4 3.1 2.2 1.02

Model 3 5.1 4.3 3.2 2.3 0.85

5-Foothold nanoreactor rates from simulations with experimentally determined rate constants (simulated data with 200 nM SPAA)

0.048 - - - 0.010

5-Foothold nanoreactor directly measured rate (200 nM SPAA)

0.091 - - - -

% finding 5th

foothold

Model 1 100 100 100 100 100

Model 2 100 100 100 100 100

Model 3 44.8 48.9 60 99 100

% complete walks

5-Foothold nanoreactor rates from simulations with experimentally determined rate constants (simulated data with 200 nM SPAA)

10.7 - - - -

5-Foothold nanoreactor directly measured rate (200 nM SPAA)

9.3 - - - -

References:

39. Thordarson, P. Determining association constants from titration experiments in supramolecular chemistry. Chem. Soc. Rev. 40, 1305

(2011).

40. Song, L. et al. Structure of staphylococcal alpha-hemolysin, a heptameric transmembrane pore. Science 274, 1859 (1996).


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