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SUPPLEMENTARY INFORMATIONdoi: 10.1038/nchem.1005

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Supplementary Information

Gradient-driven motion of multivalent ligand molecules along

a surface functionalized with multiple receptors

András Perl,1 Alberto Gomez-Casado,1 Damien Thompson,2 Henk H. Dam,1 Pascal

Jonkheijm,1 David N. Reinhoudt,1 Jurriaan Huskens1,* 1 Molecular Nanofabrication group

MESA+ Institute for Nanotechnology, University of Twente,

P. O. Box 217, 7500 AE Enschede, The Netherlands. *E-mail: [email protected]

2 Tyndall National Institute, University College Cork, Ireland

MATERIALS AND METHODS

Synthesis of the guest molecules. All moisture-sensitive reactions were carried out

under an argon atmosphere. All solvents and reagents were obtained from commercial

sources and used without further purification. Solvents were dried according to standard

procedures and stored over molecular sieves. GI and GII were synthesized according to

literature procedures.1,2 GIII was synthesized according to Scheme S1, with the

intermediate compound 4 synthesized according to literature procedures.2 1H NMR

chemical shift values (300 MHz) are reported as (ppm) using the residual solvent signal

as an internal standard (CDCl3, 7.257 ppm), and coupling constants J in Hz. 13C NMR

chemical shift values (100 MHz) are reported as using the residual solvent signal as an

internal standard (CDCl3, 77.0 ppm).

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SUPPLEMENTARY INFORMATION doi: 10.1038/nchem.1005

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OO O

O O

O O O O O

O O O O O

NH2

O O O O Br

O O O O OH

OO O

O O

O O O O O

O O O O O

NO2O

O OO O

O O O O O

O O O O O

Br

OH O O O OH

OH

OH

OH

SO OO

OO

O OO O

O O O O O

O O O O O

NH

SO

O

N+

N

SO OO

OCl SO

O

N+

N

SiO2, HNO3

CH2Cl2,rt, 5 min, 68%

1

3

6

4+

7

K2CO3,Acetone, reflux,24h, 82%

2

5

8

9

DIPEA,CH2Cl2, rt,8h, 6%

Pd/C 10%, H2 (g)

CH3OH,rt, 4 h, 89%

Scheme S1. Synthesis of GIII (9).

1,2,3-tris[2-(2-{2-[2-(adamantan-1-yloxy)ethoxy]ethoxy}ethoxy)-ethoxy]benzene (6).

A suspension of pyrogallol (3.00 g, 8.64 mmol), 4 (0.363 g, 2.88 mmol) and K2CO3 (1.20

g, 8.64 mmol) was refluxed in 30 ml acetone for 24 h. Thereafter, the volatiles were

removed under vacuum and the crude product was extracted from the residue with 40 ml

of Et2O. The Et2O layer was washed with H2O (3 × 30 ml) and dried with MgSO4.

Evaporation of the volatiles gave 6 as a slightly colored oil (2.5 g, 82%) which used

without further purification in the subsequent reactions. 1H NMR (ppm): = 6.91 (1 H, t,

J 8.4, PhH), 6.58 (2 H, d, J 8.4, PhH), 4.23 (2 H, t, J 4.2, 2-PhOCH2CH2-), 4.19-4.10 (4




S3

H, m, 1,3-PhOCH2CH2-), 3.88 (4 H, t, J 4.2, 1,3-PhOCH2CH2), 3.79 (2 H, t, J 2.4, 2-

PhOCH2CH2), 3.72-3.58 (36 H, m, -OCH2CH2O-), 2.13 (9 H, s, CH2CHCH2[Ad]), 1.74

(18 H, s, CHCH2C[Ad]), 1.65-1.55 (18 H, t, CHCH2CH[Ad]). 13C NMR (ppm): =

152.8, 138.5, 123.5, 107.9, 72.3, 71.2-68.7, 59.2, 41.4, 36.4, 30.4. ESI-MS m/z = 1079.5

[M+Na]+, calcd. 1079.7. MALDI-TOF-MS m/z = 1079.2 [M+Na]+, calcd. 1079.7.

3,4,5-tris[2-(2-{2-[2-(adamantan-1-yloxy)ethoxy]ethoxy}ethoxy)ethoxy]phenylnitrate

(7). A solution of 6 (0.400 g, 0.38 mmol) in 3 ml CH2Cl2 was added to a well stirred

suspension of 0.400 g of SiO2 and HNO3 (0.08 ml, 1.89 mmol) in 1 ml CH2Cl2. After

stirring for 5 min, the solution was quenched with 3 ml saturated K2CO3. The solids were

filtered off and the filtrate was diluted with 10 ml CH2Cl2. The organic layer was washed

with H2O (3 × 10 ml) and dried with MgSO4. Evaporation of the volatiles gave 7 as an oil

which was subjected to column chromatography (eluent CH2Cl2/MeOH, 9/1) yielding 7

(0.284 g, 68%) as a colorless oil. 1H NMR (ppm): = 7.54 (2 H, s, PhH), 4.27 (2 H, t, J

5.1, 4-PhOCH2CH2-), 4.22 (4 H, t, J 4.8, 3,5-PhOCH2CH2), 3.88 (4 H, t, J 4.2, 3,5-

PhOCH2CH2), 3.79 (2 H, t, J 2.4, 4-PhOCH2CH2), 3.72-3.58 (36 H, m, -OCH2CH2O-),

2,13 (9 H, s, CH2CHCH2[Ad]), 1.73 (18 H, s, CHCH2C[Ad]), 1.66-1.55 (18 H, m,

CHCH2CH[Ad]). 13C NMR (ppm): = 152.4, 144.3, 143.2, 103.4, 72.9-69.3, 59.6-59.2,

41.6, 36.6, 30.6. ESP-MS m/z = 1102.5 [M]+, calcd. 1102.4. MALDI-TOF MS m/z =

1124.6 [M+Na]+, calcd. 1125.4.

3,4,5-tris[2-(2-{2-[2-(adamantan-1-yloxy)ethoxy]ethoxy}ethoxy)ethoxy]phenylamine

(8). A suspension of 7 (0.220 g, 0.20 mmol) and a catalytical amount of Pd/C (10%) was

stirred under 1 bar H2(g) atmosphere in 3 ml methanol for 4 h. The suspension was

filtered over celite and the volatiles were evaporated giving the product as a colorless oil

(0.19 g, 89%). The product was used in the subsequent reaction without further

purification. 1H NMR (ppm): = 6.32 (2 H, s, PhH), 4.12-4.02 (6 H, m, PhOCH2CH2-),

3.84-3.73 (6 H, PhOCH2CH2), 3.69-3.56 (36 H, m, -OCH2CH2O-), 2,12 (9 H, s,

CH2CHCH2[Ad]), 1.72 (18 H, s, CHCH2C[Ad]), 1.64-1.54 (18 H, m, CHCH2CH[Ad]). 13C NMR (ppm): = 153.2, 136.2, 108.0, 99.6, 72.8-69.1, 59.4, 41.6, 36.6, 30.6.

MALDI-TOF MS m/z = 1072.7 [M+H]+, calcd. 1072.7.

GIII (3,4,5-tris[2-(2-{2-[2-(adamantan-1-yloxy)ethoxy]ethoxy}ethoxy)-ethoxy]phenyl-

lissamide) (9). A solution of 8 (0.120 g, 0.11 mmol), lissamine sulfonyl chloride (0.065




S4

g, 0.11 mmol) and an excess of DIPEA was stirred for 8 h at rt in 3 ml CH2Cl2. Hereafter

the volatiles were evaporated and the crude product was subjected to column

chromatography (eluent gradient CH2Cl2/MeOH, 10/3, 9/1 and 7/1 subsequently)

yielding one isomer of 9 (0.011 g, 6%) as a purple oil. 1H NMR (ppm): = 8.67 (1 H, s,

ArH), 8.07 (1 H, d, J 8.4, ArH), 7.26 (2 H, d, J 9.9, ArH), 7.02 (1 H, d, J 7.8, ArH), 6.70

(2 H, d, J 8.4, ArH), 6.57, 6.56 (4 H, 2 s, 2 ArH), 4.08-3.94 (6 H, m, PhOCH2CH2-),

3.76-3.40 (42 H, m, PhOCH2CH2 + OCH2CH2O), 2.06 (9 H, s, CH2CHCH2[Ad]), 1.66

(18 H, s, CHCH2C[Ad]), 1.59-1.49 (18 H, m, CHCH2CH[Ad]). MALDI-TOF MS m/z =

1614.3 [M+H]+, calcd. 1614.1.

The starting lissamine sulfonyl chloride consists of several isomers. TLC and NMR of the

product after the coupling reaction showed a mixture including the isomeric mixture of

products as well as starting compounds, and MS confirmed the successful coupling.

Column chromatography yielded a fraction of 11 mg of a pure isomer of 9 (similar to

isolation of one of the isomers of the divalent guest GII)2 which was used directly in the

spreading experiments. The coupling between 8 and lissamine was not complete since a

fractions lissamine (30 mg) and a fraction containing the starting amine 8 were collected

after the column. No optimization of this reaction was attempted.

Substrate preparation. Monolayers of β-cyclodextrin (CD) on glass were prepared in

four steps, using a method developed by our group previously:3 after the formation in

solution of a monolayer of 1-cyano-11-trichlorosilylundecane, the cyano-terminated

monolayer was reduced to an amine layer, followed by the transformation to

isothiocyanate-bearing layers which were finally reacted with per-6-amino-β-

cyclodextrin.

Our previous studies4 revealed that: (i) the efficient multivalent binding at surfaces is

governed by a high effective concentration of free receptor sites, (ii) multivalent

molecules bind preferentially with the highest valency that is sterically allowed, (iii)

binding affinities and surface coverages can be predicted quantitatively based on the

molecular structure of the multivalent ligand, also in the presence of competing receptor

in solution, and (iv) increase of the valency causes the system to change from

thermodynamically reversible to kinetically stable.




S5

Assembly of dye guests on CD substrates. Patterning on the CD monolayers on glass

with the fluorescent dyes was achieved by microcontact printing. Stamps were prepared

from commercially available Sylgard-184 poly(dimethyl siloxane) (Dow Corning). The

curing agent and the prepolymer were manually mixed in a 1:10 volume ratio and cured

overnight at 60 oC against the master. The cured stamp was peeled off from the master at

the curing temperature. Silicon masters with 5 μm wide line features separated by 25 μm

spacing were fabricated by photolithography. This high spacing / feature ratio was

necessary to ensure a large enough free spreading space for the guest molecules during

the measurements, and for easy data transformation.

The stamps were mildly oxidized in an oxygen plasma reactor before use. Before

printing, the stamps were inked by soaking them in an aqueous solution of the fluorescent

dye (≈ 10 μM). After drying the surface of the stamps with nitrogen, conformal contact

was achieved manually. The stamps were weakly pressed against the printboard surface

at the initial stage of the printing to induce the formation of conformal contact. The

printing time in all cases was 1 min. The samples with the patterned SAMs of the guest

were rinsed immediately after the printing with a continuous flow of pure water (GI: 10 s;

GII and GIII: 30 s) to remove the physisorbed molecules and dried in a stream of nitrogen.

Backfilling with GdII was achieved by immersion of the samples in a 0.1 mM aqueous

solution of GdII for 10 s. Low coverage (40%) of the mixed divalent SAM was achieved

by rinsing with 20 % ethanol in water for 30 s, and measured from fluorescence

intensities.

Spreading experiments. 280 μL aqueous solutions with 0-12 mM CD were applied on

top of the patterned surface confined by a rubber ring with a diameter of 11.6 mm. The

printboard surface / rubber ring / liquid system was immediately covered with a clean

glass slide to close the volume and to avoid any evaporation. A thin layer of vacuum

grease on the rubber ring was used to stick together the solid components.

Fluorescence micrographs were frequently taken. To avoid the effect of photobleaching,

new areas were selected after each shot. The focusing time before taking the micrographs

was in all cases 20 s. In case of a faster focusing, the analyzed spot was further irradiated,




S6

until the 20 s time period was reached. Imaging was continued as long as the intensity

difference between the dark and bright areas allowed proper focusing and reliable

assessment of I.

Fluorescent images were taken using an Olympus inverted research microscope IX71

equipped with a mercury burner U-RFL-T as a light source and a digital camera Olympus

DP70 (12.5 million-pixel cooled digital colour camera) for image acquisition. Green

excitation light (510 nm ≤ λ ≤ 550 nm) and red emission light (λ > 590 nm) was filtered

using a U-MWG Olympus filter cube. Typical spreading results for GII are shown in Fig.

S1 (partly also shown in Fig. 2B, main text).

Fig. S1. Fluorescence microscopy images (top) and integrated line profiles (bottom) of GII on a printed Hs surface after incubation for given amounts of time in a solution with 0.6 (a, d), 2 (b, e) or 4 (c, f) mM CD (Hl).

At all CD concentrations a decrease of Imax and an increase of w were observed (Fig. S2).

The maximum peak intensity decreased faster when the CD concentration was increased.

The decrease of Imax is caused initially only by spreading on the surface and later ([Hl]tot

> 1 mM) also by complete desorption of GII from the CD monolayer followed by

diffusion into the bulk of the surrounding solution. A linear increase in time of w was




S7

observed in all cases as a result of the spreading of GII on the surface of the molecular

printboard.

For all guests at any given concentration of Hl, the change of w in time t appeared to be

linear initially, often for hours. Therefore, line fits of w vs t were used to obtain the

spreading rate r (= (∂w/∂t)0). Also plots of I vs t appeared linear, but the scatter was

rather large so that only the overall average intensity was used to qualitatively assess

whether or not desorption occurred concurrent with the observed spreading in the time

frame for which r was constant.

The slope of the linear increase of w, defined as the spreading rates, did not increase

continuously with the CD concentration in the solution, as is shown in Fig. S2 (right) and

Fig. 2C (main text). In pure water the spreading rate of GII was low (0.02 nm s-1). When

the CD concentration was increased, a maximum in the spreading rate (~1.3 nm s-1) was

observed at 0.8 mM CD concentration.

Fig. S2. Peak maximum fluorescence intensities (left) and peak widths (right) of integrated line profiles (see Fig. S1, bottom) of GII on a printed Hs surface after incubation for given amounts of time in a solution with varying concentrations of CD (Hl).

To assess the effect of this developing gradient on the spreading rate, patterned substrates

with printed GII were put in a solution of the also divalent but non-fluorescent (“dark”)

GdII (Fig. 1A) for backfilling the nonprinted areas.5 The binding properties of this guest

are identical to those of GII because of the equal valency and molecular structure, and this




S8

guest is therefore assumed to exhibit equal spreading characteristics as well. One set of

backfilled samples was rinsed thereafter with water, another set with a 20:80 (v:v)

ethanol:water mixture promoting desorption resulting in line patterns with a fluorescence

intensity of only 40% of the first set. Spreading experiments were performed as described

above, in aqueous solution with or without CD. Typical results are shown in Fig. S3. A

discussion on the comparison of the spreading rates between printed-only and backfilled

samples is given in the main text.

Fig. S3. Fluorescence microscopy images (a-c) and integrated line profiles (d) of GII on a printed Hs surface, after backfilling with Gd

II and incubation for given amounts of time in a solution with 0.8 mM CD (Hl).




S9

Thermodynamic and mass transport modeling

Binding of mono- or multivalent guests to the β-CD printboard is a reversible interaction

governed by an intrinsic binding constant Ki (Ki = ka/kd). Competition for guest binding

with monovalent hosts in solution infers additional equilibria.

All equilibria of GI with CD monolayers in the presence of competitive CD in solution

are shown in Fig. S4A. The monovalent equilibria contain two solution guest species (GI

and GIHl) and one surface complex (GIHs) and they describe the interaction of GI with

CD in solution (from top to bottom) and with CD at the surface (from left to right).




S10

Fig. S4. Equilibria for monovalent guest GI (A) and trivalent guest GIII (B) binding to surface host Hs and solution host Hl, with indications of stability constants and surface diffusion mechanisms.




S11

The binding constants can be expressed in terms of intrinsic binding constants for binding

to a surface host (Ki,s) and to a solution host (Ki,l). It has been shown previously that the

binding strength of a guest to a CD from solution is equal to the binding strength to a CD

of the surface,6 therefore a common intrinsic binding constant (Ki) will be used here for

all the involved equilibria as shown in Equation 1:

][H][G]H[G

][H][G]H[GKKK

lI

lI

sI

sI

i,li,si

(1)

where [Hs] represents the unbound, surface-confined host concentration and [Hl] the

concentration of unbound CD cavities in the solution. The equilibrium constants are

expressed in terms of volume concentrations (in M), using the fixed volume of the

experimental cell to calculate the concentrations of the surface species.

The extension of the monovalent binding scheme to a divalent system requires the

introduction of the parameter Ceff. Fig. 1B (main text) depicts all equilibria for the

sequential divalent binding of GII to CD monolayers and to CD in solution. The equilibria

contain surface species as a consequence of interaction of the divalent guest (GII) with

surface-confined hosts (from left to right) and solution species upon interaction with CD

in solution (from top to bottom). The sequential binding events in the solution and at the

surface are considered equal and independent.

The first, intermolecular binding event of GII to a host is given by Equation 2:

][H][G]H[G

][H][G]H[GK

lII

lII

sII

sII

i

2 (2)

The second, intramolecular, interaction at the printboard surface is the product of Ki and

Ceff. The concentration of accessible, unbound host sites in the probing volume of the

unbound guest moiety, Ceff, is dependent on the coverage of free host sites. It is equal to

the limiting value reached at infinitely low surface coverage (Ceff,max) multiplied by the

fraction of unbound surface host sites (Equation 3).7,8




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tots

seffeff ][H

][HCC max, (3)

Previous studies with a divalent bis-adamantyl calix[4]arene guest with flexible

tetra(ethylene glycol) linkers have found 0.2 M as an approximate value for Ceff,max.7

The equilibria of the trivalent GIII to the printboard contain surface and solution species

(Fig. S4B) and the transition from the fully surface-bound form (top row, right end) to the

form where the trivalent guest GIII binds only to solution hosts (most left column) is

abundantly represented by various surface-bound forms of the trivalent guest.

Fig. 1B and S4 represent all species that can occur, as well as the elementary association

and dissociation steps between them. „Walking‟ is defined as the dissociation of a

surface-bound site of a multivalently bound guest species and its re-association to another

free host site on the surface. It can therefore only occur for multivalent guests, according

to the steps indicated in Fig. 1B and S4B. „Hopping‟ is defined as the dissociation of the

surface-bound site of a monovalently bound guest species and the re-association of any

available site of the molecule to another free host site on the surface. The dissociated

guest molecule with at least one unsaturated site diffuses close to the printboard surface

and travels a mean path length determined by its lifetime. Binding of all free sites of the

dissociated guest molecule to CDs from solution initiates the complete desorption

followed by re-adsorption mechanism, where the fully saturated guest molecule diffuses

into the bulk and after the stochastic re-approach to the printboard surface and

dissociation of a CD moiety from the solution, the association to a free host site on the

surface can occur.

Assuming equilibrium close to the surface in a system similar to the experimental setup,

where a CD printboard homogeneously covered with a guest monolayer is placed in a

solution with or without native CD, the equilibrium concentrations of all species present

in the system can be calculated. Assuming that the free CD concentration in solution

close to the surface is equal to the free CD concentration in the bulk (for which [Hl] =

[Hl]tot), the combination of the equilibrium constant definitions with the mass balances

for the total surface-confined host concentration [Hs]tot and the total guest concentration




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(for mono-, di- and trivalent systems [GI]tot, [GII]tot and [GIII]tot, respectively) gives

numerically solvable sets of equations. Printboard surfaces before immersion in water

with or without CD, for 90 % covered by guest molecules (the printed guest SAMs were

rinsed with water and therefore 10 % loss of the guest from the surface is assumed), were

used to simulate the experimental conditions, and calculate the equilibrium

concentrations of all species for the mono-, di- and trivalent systems.

Numerical calculations of the equilibrium8 concentrations and the diffusion profiles were

performed using Matlab software. Values of 4.6 × 104 M-1 for the intrinsic binding

constant, 0.2 M for the maximum effective concentration, 2 nm for the CD cavity lattice

periodicity on the printboard and 10-10 m2 s-1 for the diffusion constant of the solution

species were used to perform the calculations.

Spreading of the monovalent guest is realized by a sequence of events including

desorption of GIHs from the printboard to form GI which after a certain stay in the

solution readsorbs to the surface. Formation of GIHl increases the residence time in the

solution, and thus the diffusion length, because it is only after the dissociation of GIHl

that re-adsorption of GI to the surface can take place. Fig. S5 (a,b) shows the calculated

concentrations of all species in the monovalent system (Fig. S4A) as a function of the CD

concentration in solution. In pure water, only „hopping‟ of the guest (GIHs → GI → GIHs)

can contribute to spreading (which is here indistinguishable from the regular desorption

and re-adsorption). Because the concentration of both species contributing to hopping

(GIHs and GI) are decreasing upon increase of the CD concentration in the solution, the

increased spreading rate can be assigned to desorption and formation of GIHl, which is

increasing in concentration (Fig. S5b).




S14

Fig. S5. Thermodynamic equilibrium concentrations of surface (A, C) and solution (B, D) species of the monovalent GI (A, B) and the trivalent GIII (C, D), assuming a total guest concentration sufficient for 90% coverage.

Spreading of the divalent guest occurs according to different spreading mechanisms as a

function of [Hl]tot. In pure water, only walking and hopping can occur. „Walking‟ (Fig.

1B) starts with the dissociation of one guest site of GII(Hs)2, while „hopping‟ involves a

similar dissociation step of GIIHs. Because the intrinsic attempt frequency of the

dissociation of GII(Hs)2 is twice as likely and the concentration of GII(Hs)2 is more than

two orders of magnitude larger, „walking‟ is most likely the only spreading mechanism

under these conditions. Upon increase of [Hl]tot, the concentrations of both species

involved in walking (GII(Hs)2 and GIIHs) decrease monotonously (Fig. 3), indicating that

the observed increase in spreading rate is caused by another mechanism.

Fig. S5 (c,d) presents the calculated concentrations of all species involving the trivalent

guest (GIII) (Fig. S4B) as a function of the CD concentration in the solution. Many

species (GIIIHs, GIIIHl and GIII) have insignificantly low equilibrium concentrations and




S15

their contribution to spreading can be ignored. Thus, similarly to the divalent system,

„walking‟ of the molecules causes the spreading in water involving several surface-bound

guest species, as indicated in Fig. S4B. According to the high affinity of the trivalent

guest to the printboard, no desorption of GIII(Hs)3 was observed experimentally within the

studied host concentration range and thus no complete desorption followed by re-

adsorption contributes to the spreading. In the presence of low amounts of CD in the

solution, the concentrations of species involved in „walking‟ decrease monotonously (Fig.

S5c), with the exception of GIII(Hs)2Hl and GIIIHsHl. Dissociation and association of one

guest site of GII(Hs)2Hl can contribute to the spreading of the trivalent molecule. The

rapid increase of the concentrations of GIIIHs(Hl)2 and GIII(Hl)2 can also contribute to the

increase of the spreading rate by a „hopping‟ mechanism. Their equilibrium

concentrations are about one order of magnitude lower than GIIHsHl and GIIHl in the

divalent system. The contribution to spreading of other species possibly involved in a

„hopping‟ mechanism is minimal due to their significantly lower equilibrium

concentrations. Thus, both „walking‟ of GIII(Hs)2Hl and „hopping‟ of GIIIHs(Hl)2 may

induce a spreading rate increase at 0 < [Hl]tot < 1.5 mM. The maximum in spreading rate

occurs at higher [Hl]tot than in the case of the divalent system, indicating the need for a

higher amount of CD in the spreading mechanism. This suggests that „hopping‟ of

GIIIHs(Hl)2 is the main contributor to the spreading, because its formation requires a

higher concentration of Hl compared to the equivalent GIIHsHl in the divalent case.

The difference in behavior between the divalent and trivalent guests at high [Hl]tot

follows in part from the mass transport issues discussed below: Fig S6 (right) shows that

the mass transport of the trivalent guest is, at a given time and background CD

concentration, always more than 3 orders of magnitude less than for the divalent guest.

Even at the highest CD concentrations probed (10 mM), the concentration of GIII(Hl)3

(which is the „flying‟ species of the trivalent guest) near the interface remains (just)

below the concentration of the divalent GII(Hl)2 formed near the interface at [Hl]tot = 1.5

mM. This follows from a comparison of the corresponding equilibrium species

concentrations given in Figs 3B and S5D. We interpret this therefore such that the

concentration of GIII(Hl)3 becomes high enough to suppress the hopping mechanism but




S16

not high enough to note any desorption, similar to the decreasing spreading rate observed

for [Hl]tot = 0.8 - 1.5 mM in the divalent case (Fig. 2C).

Mass transport considerations

In order to elucidate the underlying diffusion mechanisms of the spreading behavior

observed here, it is important to establish whether the observed desorption is rate-limited

by the intrinsic surface dissociation step(s) of a surface-bound species or by the diffusion

of an already fully dissociated species close to the interface into the bulk. Cyclodextrins

are known to exhibit diffusion-controlled association, with association rate constants as

high as 108 - 109 M-1s-1.9,10,11 This means that (i) a free, uncomplexed (uncapped) Ad

group near the interface will bind to a free receptor site within a fraction of a s, while

(ii) spontaneous dissociation occurs on the order of 0.1-1 ms. An estimation of desorption

based on Fick‟s laws of diffusion (see below) shows that, when putting a solution on top

of a sample, a gradient of solution species is established near the interface which

stretches 10s of m out into the bulk within 1 s, and then extends further at a decreasing

pace. For all systems other than pure water, the concentration of free Hl is so large that Hl

consumed by complexation at or near the interface is readily replenished from the bulk,

so that its concentration near the interface can be assumed equal to the bulk. All pieces of

information together support the view that desorption is rate-limited by the diffusion of

an already fully dissociated species into the bulk, and thus that the concentration of this

species near the interface is in (local) equilibrium with surface-adsorbed species and that

the value of this concentration governs the absolute rate of desorption. This also indicates

that thermodynamic equilibrium models may be used to predict trends of concentrations

of different solution and surface species and their relative roles at different stages of the

spreading process.

This conclusion has another consequence as well. The importance of the relative rates of

association/dissociation vs. diffusion is well known and well documented.12 When

association/dissociation rates are slow compared to diffusion, the kinetics of binding and

unbinding can be directly assessed, e.g. from surface plasmon resonance (SPR)

adsorption experiments. However, when association/dissociation rates are fast compared

to diffusion, so-called „rebinding‟ occurs, and the data of such experiments are partially




S17

or completely masked by mass transport limitation.12 In the case of CD host-guest

binding, association is diffusion-controlled as discussed above, which means that mass

transport limitation occurs here as well. In the system studied here, the „rebinding‟ is

directly observable (in the form of spreading) because we start from patterned surfaces

rather than fully covered ones (like in SPR sensograms). This holds not only for the

uncapped („hopping‟) species, but also for capped („flying‟) species. In particular for the

monovalent GIHl and GII(Hl)2, concentrations of these species formed near the interface

are apparently high enough to (partly) lead to observable spreading before they get the

chance to move into the bulk.

As a function of valency, coverage and CD concentration in solution, certain

concentrations of guest species are established near the interface assuming equilibration

is rapid. These concentrations can be calculated as described above. The guest species in

solution, formed near the interface upon desorption, will start diffusing into the bulk

according to Fick‟s laws of diffusion. Similarly, when CD in solution is present, the

desorption near the interface leads to complexation of guest with Hl and therefore,

potentially, to depletion of Hl near the interface. Model calculations based on Fick‟s laws

were performed. The maximum desorption rates for all the guests can be calculated

assuming that the guest-covered printboard functions as an infinite source of the free

guest (concentrations summed for all G(Hl)n, where n = 0 – nmax).

As an example, Fig. S6 (left) depicts the evolution of the concentration profile of the

solution species GII desorbed from GII SAM-covered printboard in pure water. Upon

increase of [Hl]tot, the time dependence of these curves does not change, only the absolute

values. The calculations show that diffusion for > 1 μm takes > 1 ms, while equilibration

occurs on the order of the lifetime of an individual CD-Ad interaction, which is < 0.1 ms.

This confirms that equilibration is rapid compared to diffusion.




S18

Fig. S6. (Left) Diffusion profiles in time as calculated by Fick‟s laws applied to an infinite source of GII at the surface at an interfacial boundary concentration set to a value of [GII] in solution in equilibrium with a 90%-covered surface in the absence of Hl. (Right) Total amounts of guest dissociated from the surface (per unit area) as a function of time obtained from such an infinite source model, applied to GI, GII and GIII. The red line indicates the amount corresponding to full surface coverage, indicating that GII and GIII are not being depleted from the surface over the course of >1 h in pure water.

The integration of the concentration profiles of Fig. S6 (left) gives the amounts of

desorbed guests per surface area, M, after time t. The guest concentration on the surface

at 90 % coverage is in the range of 10-7 mol m-2. In pure water, the trends are as expected:

the monovalent guest is desorbing very quickly (order of seconds), while the divalent (on

the order of 102 h) and trivalent (~ 106 h) are stably anchored (see Fig. S6, right).

However, upon only small concentrations of Hl, the concentration of free guest species in

solution rapidly increases. This suggests that the divalent and even the trivalent guest, at

relatively low [Hl] would completely desorb from the surface within the given timeframe.

However, in real experimental conditions the concentrations of solution species near the

interface are rapidly decreasing when the guest coverage on the surface is decreasing due

to desorption. The concentration of the divalent solution species [GII] decreases by three

orders of magnitude upon the decrease of the coverage from 90 to 10 %. This significant

decrease of available solution species close to the surface will lower the desorption rate

and the concomitant diffusion into the bulk, and thus quickly increase the projected

timescales for desorption.

For evaluating the effect of depletion of Hl, similar calculations were used. From the fact

that the [Hl]tot is always the same as, or (much) higher than, the free guest concentration

formed near the surface, rapid replenishment of CD from the solution is always expected,




S19

thus confirming the assumption made above that [Hl] near the surface is equal to [Hl]tot

of the bulk.

Molecular dynamics simulations

Molecular dynamics (MD) simulations have shown how varying the multivalent

molecule, receptor surface and printing conditions leads to quantitatively different

binding mechanisms because of (i) different strength potentials for guest-CD binding13,14

and (ii) different numbers of sterically accessible multivalent interactions.15,16,17

Molecular models were constructed as shown in Fig. S7 for the multivalent molecule GII

interacting with cavities Hs on the receptor-functionalized surface. A 3.4 x 5.0 x 4.0 nm

box of water was overlaid and overlapping waters removed. Periodic boundary conditions

were assumed; that is, the orthorhombic unit cell was replicated periodically in all

directions, generating the hexagonally-packed surface shown in Fig. S7. The axis normal

to the surface was extended by a further 4.5 nm to allow for net transport of water away

from the hydrophobic molecules linking CD to the substrate.18

Standard CHARMM force field parameters19 were used for the CD, linker molecules and

the substrate, with GII parameterized as described previously.15 A slightly modified

TIP3P model was used for the water.20 Bonds involving hydrogen were constrained to

their experimental lengths with the SHAKE algorithm,21 allowing the use of a 2 fs

timestep for dynamics. We used the CHARMM program22 version c31b2 for all

calculations.

Molecular dynamics was performed at constant, room temperature and pressure with a

Nosé-Hoover algorithm, following one nanosecond (1.0 ns) of thermalization and

equilibration with gradually reduced positional constraints on the solute non-hydrogen

atoms. The GII(Hs)2 complex was then subjected to 2.0 ns of free dynamics before the

instigation of successive Ad unbinding to form GII(Hs)1 and then uncomplexed GII as

described below.




S20

Fig. S7. Representative structure from the molecular dynamics simulations, showing a planar view of the model used to describe the interaction of the GII divalent molecule with the CD-functionalized surface. Water molecules and hydrogen atoms are omitted for clarity. The central orthorhombic unit cell is marked by the black rhombus; expansion with periodic boundary conditions provides the extended hexagonally-packed CD-functionalized surface. The GII molecule is colored blue with Ad anchors shown as spheres and the remaining atoms shown as sticks. The oxygens of the OH groups at the entrance to the CD cavities are shown as red spheres with the remaining atoms shown as brown sticks. The underlying linkers and substrate, arbitrarily set in the simulations to alkanethioether chains and Au(111), are shown as brown sticks and gold spheres. Surface binding sites are labelled in the central unit cell, with Hs1 and Hs2 denoting respectively the CD site binding GII group Ad1 and Ad2. The remaining two uncomplexed surface sites are labelled Hs-free. The snapshot shows the monovalent GII(Hs)1 complex formed after releasing Ad1 from site Hs1.




S21

Fig. S8 summarizes the main results of the molecular dynamics simulations. Note the

timeline starting point refers to the time at which the first Ad is released, which is

following 1 ns of equilibration and 2 ns of free dynamics for the starting GII(Hs)2

complex. GII maintains a close contact with the surface throughout the course of the

simulation. Ad hydrogens and glycol spacer oxygens and hydrogens engage in polar,

hydrogen-bonding type interactions with the OH groups at the entrance to the CD

cavities. These weak secondary ligand:surface interactions are always present to some

extent, keeping GII close to the surface even after the second Ad is released at t=1.6 ns,

and feature rapid exchange on a ps scale between interaction sites on both the ligand and

surface. Water molecules stabilize these interactions, mediating networks of

ligand:surface interactions, with rapid exchange of water molecules on a sub-ps scale.

Upon releasing Ad1 and forming the monovalent GII(Hs)1 complex prerequisite for

“walking” on the surface, Ad1 remains associated with its original CD binding site Hs1

for ~0.5 ns before uncoupling completely and obtaining an approximately equal

probability of re-binding at Hs1 or a nearest-neighbour Hs-free. Thus, after an initial sub-ns

phase favoring an unsuccessful event (as defined in Fig. 3 in the main text), “walking”

quickly becomes equally likely in all directions, under the simulation conditions of

constant ligand concentration. Movie walking.mpg shows how exchange between Ad-

spacer:CD interaction sites facilitates “walking” between neighbouring CD sites.

At t = 1.6 ns the second anchor Ad2 is released. Similarly to Ad1, Ad2 remains close to

the original binding site for a few hundred ps before becoming sufficiently uncoupled

from the surface to obtain an equal likelihood of rebinding at a neighbouring CD. In

common with “walking” then, “hopping” also features a sub-ns tendency towards an

unsuccessful event before losing directionality and restoring the intrinsic statistical

favouring of a successful event. Interestingly, in the current simulations Ad2

reapproaches its original surface cavity Hs2 at t = 2.4 ns following a period of complete

uncoupling and maintains a close contact with Hs2 for most of the remainder of the

simulation, re-establishing the relative bias towards an unsuccessful “hop” for GII. More

generally, the polar interactions slow down, on a ns timescale, the complete dissociation

of GII from the surface and keep the uncomplexed molecule near the surface and the




S22

released Ad groups within ~2 nm of the surface binding sites. Movie hopping.mpg

illustrates the close surface contact maintained by the uncomplexed GII molecule.

Fig. S8. Timelines are shown for the interaction of GII with the CD-functionalized surface. Site labelling is as defined in Fig. S7. GII group Ad1 is released at time = 0 ns (following 1 ns of equilibration and 2 ns of free dynamics for the fully-bound complex) to simulate the transition from divalent GII(Hs)2 to monovalently-bound GII(Hs)1. The remaining anchor Ad2 is released at t= 1.6 ns to simulate complete unbinding to GII. The black line shows the minimum distances sampled between GII and the surface, emphasizing the polar interactions that keep the partially and fully uncomplexed GII close to the surface. The other lines monitor minimum distances between each Ad and surface CD binding sites Hs. The red line monitors the minimum distances sampled between released Ad1 and its original binding site Hs1 while the grey line shows the minimum distances sampled between Ad1 and the other uncomplexed surface binding sites Hs-free. The blue line shows the minimum distances sampled between released Ad2 and its original binding site Hs2 while the green line shows the minimum distances sampled between Ad2 and the other uncomplexed surface binding sites. Note Hs-free is dynamically defined, with Hs1 considered free with respect to Ad2 upon its release at t=1.6 ns.




S23

Movie legends

Movie S1(walking).mpg illustrates the exchange in sites of polar interactions between the

surface and the released Ad plus its glycol spacer group that facilitates “walking”

between neighbouring CD sites. The ligand:surface complex is represented and oriented

as shown in Fig. S7, to highlight interactions between released Ad1 and surface cavity

sites Hs1 and neighbouring Hs-free, with the GII Ad1-glycol moiety exchanging weak

interactions between Hs1 and Hs-free during 0.7 ns of dynamics. The movie is composed of

350 20 ps-spaced structures in the interval spanning 0.9 ns to 1.6 ns along the dynamics

timeline shown in Fig. S8. The molecular dynamics trajectories were visualized using the

VMD program.23

Movie S2(hopping).mpg illustrates the contacts that keep the uncomplexed GII molecule

in close proximity to the surface prior to the transition from “hopping” to solution CD-

mediated “flying.” The ligand:surface complex is represented as shown in Fig. S7, with

the model rotated and tilted to highlight GII interactions with the surface. In this movie,

Hs2 is positioned in the foreground, Hs1 is in the background and the Hs-free sites are on

either side. The movie is composed of 350 20 ps-spaced structures in the interval

spanning 2.5 ns to 3.2 ns along the dynamics timeline shown in Fig. S8. The molecular

dynamics trajectories were visualized using the VMD program.23

Monte Carlo simulations

The state of a 3-Hs-wide slice with periodic boundaries is tracked where one of the edges

is initially occupied with divalent guest molecules. The kinetics involved in the reversible

reactions depicted in Fig. 2A (main text) were simulated using a modified Gillespie

algorithm (24, 25), extended to keep track of the location of bound and free guest

molecules, as well as their diffusive movements in the bulk of the solution volume (see

Fig. 4, main text). The simulation runtimes limit greatly the number of guests on the

modeled system, for this reason we limited the size of the printboard to a 3-Hs-wide slice

with periodic boundaries. Diffusion processes account for most part of the calculation

time, this makes simulations of large solution volumes and high Hl concentration

(directly related to the number of GII(Hl)2 complexes) very slow, further limiting the




S24

range of parameters that could be explored. More details of the simulated geometry and

kinetic parameters are presented in Table S1.

System geometry

L Length of stripe 1 µm (500 cavities)

W Width of stripe 6 nm (3 cavities)

H Solution volume height[a] 0.4 / 0.8 / 1.6 µm

Solution sub-volume dimensions[b] 2 x 2 x 6 nm3 (1 x 1 x 3 cavities)

Reaction constants

Keq Intrinsic host-guest equilibrium constant [c]

5·104 M-1

ka Association rate constant [c] 108 M-1 s-1

kd Dissociation rate constant [c] 2·103 s-1

Other parameters

Ceff Effective concentration [d] 0.2 M

D Diffusion constant in solution [e] 10-10 m2 s-1

[Hl] Free host concentration 0 – 1.5 mM

Table S1. Constants and parameters used for the MC simulations. [a] The value 0.8 µm was chosen for most part of the study; [b] ensures many more diffusion reactions than (un)binding reactions, necessary for the well-mixed approximation;25 [c] determined by calorimetry7 and from earlier considerations;8 [d] as reported;7 [e] same order of magnitude as the value (3·10-10 m2 s-1) for β-cyclodextrin.26

The averaged output of ten simulations for each condition set was analyzed by fitting the

bound guest populations to a one-dimensional Fick‟s diffusion model, where the fitting

parameter was the apparent diffusion coefficient Dapp of the bound guest on the surface,




S25

much smaller than the diffusion in bulk solution D. The results are shown in Fig. S9. Dapp

is higher for increasing concentrations of Hl, initially following a second order growth

(black line) that closely resembles the increase of spreading rate in the 0-0.8 mM Hl

range of the experimental data obtained using fluorescence microscopy (Fig. 2C, main

text). This growth levels off for [Hl] > 0.5 mM.

Further simulations were performed to examine the influence of the solution height (and

thus the solution volume) on top of the printboard slice (circles and triangles in Fig. S9).

Unfortunately, simulation of larger volumes is beyond our current computing power. The

spreading appears independent of the volume for [Hl] < 0.5 mM, and its downward trend

at [Hl] > 0.5 mM is more pronounced at bigger volumes. These observations agree with

the explanation proposed in the main text: a transition from “hopping” (a near-to-surface

spreading mechanism, unaffected by the solution height) to “flying” (an in-bulk

spreading mechanism, dependent on the solution height) is happening at this

concentration of free host. It is reasonable to expect that increasing even further the

solution height (to approach the much higher volume used in the fluorescence

experiments) would lead to a drop of Dapp similar to the observed drop in spreading rate.




S26

Fig. S9. Apparent diffusion of the bound guest plotted as a function of free host concentration for different solution volumes (labeled in the plot as cell “heights”). Below a free host concentration ([Hl]tot) of 0.5 mM the spreading appears to be independent of the volume, while above this value a larger volume gives a lower value for the apparent diffusion. The lines are given to guide the eye.




S27

References and Notes

1. V. B. Sadhu, A. Perl, X. Duan, D. N. Reinhoudt, J. Huskens, Soft Matter 5, 1198 (2009). 2. A. Mulder, S. Onclin, M. Péter, J. P. Hoogenboom, H. Beijleveld, J. ter Maat, M. F. García-Parajó, B. J. Ravoo, J. Huskens, N. F. van Hulst, D. N. Reinhoudt, Small 1, 242 (2005). 3. S. Onclin, A. Mulder, J. Huskens, B. J. Ravoo, D. N. Reinhoudt, Langmuir 20, 5460 (2004). 4. M. J. W. Ludden, D. N. Reinhoudt, J. Huskens, Chem. Soc. Rev. 35, 1122 (2006). 5. Fluorescence recovery after photo-bleaching (FRAP) experiments were attempted by assembly of a uniform SAM of GII on a CD surface followed by local irradiation of the surface, however, these were unsuccessful due to the poor edge resolution of the photo-bleached areas. 6. M. R. de Jong, J. Huskens, D. N. Reinhoudt, Chem. Eur. J. 7, 4164 (2001). 7. A. Mulder, T. Auletta, A. Sartori, S. Del Ciotto, A. Casnati, R. Ungaro, J. Huskens, D. N. Reinhoudt, J. Am. Chem. Soc. 126, 6627 (2004). 8. J. Huskens, A. Mulder, T. Auletta, C. A. Nijhuis, M. J. W. Ludden, D. N. Reinhoudt, J. Am. Chem. Soc. 126, 6784 (2004). 9. T. Auletta, M. R. de Jong, A. Mulder, F. C. J. M. van Veggel, J. Huskens, D. N. Reinhoudt, S. Zou, S. Zapotoczny, H. Schönherr, G. J. Vancso, L. Kuipers, J. Am. Chem. Soc. 126, 1577 (2004). 10. Chem. Rev. 98, 1741-2076 (1998). 11. J. Szejtli, Ed. Comprehensive Supramolecular Chemistry (Pergamon Press, Oxford, 1996), Vol. 3. 12. R. B. M. Schasfoort, A. J. Tudos, Eds. Handbook of Surface Plasmon Resonance (RSC, London, 2008). 13. D. Thompson, J. A. Larsson, J. Phys. Chem. B 110, 16640 (2006). 14. D. Thompson, ChemPhysChem 8, 1684 (2007). 15. D. Thompson, Langmuir 23, 8441 (2007). 16. D. Thompson, J. Phys. Chem. B 112, 4994 (2008). 17. M. Cieplak, D. Thompson, J. Chem. Phys. 128, 234906 (2008). 18. G. Gannon, J. A. Larsson, D. Thompson. J. Phys. Chem. C 113, 7298 (2009). 19. A. D. MacKerrell, D. Bashford, M. Bellott, D. L. Dunbrack, J. D. Evanseck, M. J. Field, J. Phys. Chem. B 102, 3586 (1998). 20. W. Jörgensen, J. Chandrasekar, J. Madura, R. Impey, M. Klein, J. Chem. Phys. 79, 926 (1983). 21. J. P. Ryckaert, G. Ciccotti, H. J. C. Berendsen, J. Comput. Phys. 23, 327 (1977). 22. B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaninathan, M. Karplus, J. Comp. Chem. 4, 187 (1983). 23. W. Humphrey, A. Dalke, K. Schulten, J. Mol. Graph. 14, 33 (1996). 24. D. T. Gillespie, J. Phys Chem. 81, 2340 (1977). 25. D. Bernstein, Phys. Rev. E 71, 041103 (2005). 26. S. Fernandes, L. Cabeça, A. Marsaioli, E. de Paula, J. Incl. Phenom. Macrocycl. Chem. 57, 395 (2007).


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