The Effective Concentration of Unbound Ink Anchors at the Molecular

Apr 2, 2008 - ns fully atomistic molecular dynamics (MD) simulations to measure the effective local concentration of unbound ink anchor groups at the ...
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J. Phys. Chem. B 2008, 112, 4994-4999

The Effective Concentration of Unbound Ink Anchors at the Molecular Printboard D. Thompson† Tyndall National Institute, Prospect Row, Lee Maltings, Cork, Ireland ReceiVed: January 31, 2008; In Final Form: February 19, 2008

Self-assembled monolayers terminating in β-cyclodextrin cavities can be used to bind ink molecules and so provide a molecular printboard for nanopatterning applications. Multivalent or multisite binding strengthens the attachment of large inks and provides more robust patterns. In the present work we use computer simulations to probe the behavior of functionalized dendrimer inks at the printboard. We performed a series of long 10 ns fully atomistic molecular dynamics (MD) simulations to measure the effective local concentration of unbound ink anchor groups at the printboard for a variety of binding modes and also for the partial unbinding prerequisite for ink diffusion on the printboard. These simulations allow us to describe the conformational space occupied by partially bound inks and estimate the likelihood of an additional binding interaction. Furthermore, by simulating the shift from a divalent to monovalent binding mode we show that the released anchor quickly moves to the periphery of the dendrimer binding hemisphere but then reapproaches the printboard and remains in the vicinity of alternative binding sites. Secondary electrostatic interactions between the protonated dendrimer core and hydroxyl groups at the entrance to the β-cyclodextrin cavities give “flattened” dendrimer binding orientations and may aid dendrimer diffusion on the printboard, allowing the dendrimer to “walk” along the printboard by switching between different partially bound states and minimizing complete unbinding to bulk solution, crucial for the application of the printboard in, for example, medical diagnostics.

Introduction “Molecular printboards” exploit the guest encapsulation properties of β-cyclodextrin (β-CD) and have been used extensively for nanopatterning applications.1-21 β-CD molecules can be tethered to gold or silicon oxide surfaces, forming densely packed self-assembled monolayers (SAMs) on which uncharged “ink” molecules may be “printed” via hydrophobic guest-βCD binding interactions. The use of large functionalized molecules such as dendrimers, polymers and nanoparticles allows simultaneous binding of multiple anchor sites on the ink molecule to the printboard,4,6,7,9-20 where this multivalent binding is driven by the high effective concentration of unbound anchor sites10 and enhances the overall complexation strength, providing a more robust but still reversible patterning.11,15,19,20 Understanding the conformational properties of dendrimers at interfaces is central to the use of such large inhomogeneous molecules in nanopatterning15-20 and also in medical applications such as drug/gene delivery and noninvasive imaging.22 The structure and dynamics of dendrimers in solution have been extensively probed using computational techniques,23 and in the present work we use fully atomistic molecular dynamics (MD) simulations to probe the behavior of functionalized dendrimer inks when partially bound to the molecular printboard. We recently showed that the binding of low-generation dendrimers functionalized with four ferrocene anchor groups, poly(amido amine) G0-PAMAM-(Fc)4, and poly(propylene imine) G1-PPI(Fc)4 involves a payoff between favorable multisite complexation and unfavorable steric strain,23s the resulting “net energy” dictating the observed and nonobserved binding modes.15 We use a series of long 10 ns MD simulations, including an explicit representation of the molecular printboard surface, to † Phone: +353-21-490-4327. Fax: [email protected].

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explore the conformational space available to strongly bound dendrimers:15,23s 10 ns each for monovalent G0-PAMAM-(Fc)4 and G1-PPI-(Fc)4, divalent G0-PAMAM-(Fc)4 in two possible orientations, and divalent G1-PPI-(Fc)4 in one orientation. These simulations allow us to describe the effective concentration of unbound anchors at the printboard and estimate the likelihood of an additional binding interaction. Furthermore, forcing the release of one G0-PAMAM-(Fc)4 anchor from the printboard and simulating the divalent f monovalent partial unbinding prerequisite to the diffusion of divalent dendrimers, we see that the released anchor moves to the periphery of the dendrimer binding hemisphere within 0.5 ns, and then reapproaches the printboard, sampling alternative binding sites within an additional 2 ns. Additional weaker interactions between the protonated dendrimer core and hydroxyl groups at the entrance to the β-CD cavities give “flattened” dendrimer binding orientations and may aid dendrimer diffusion on the printboard, allowing the dendrimer to “walk” along the printboard by switching between different binding modes, e.g., divalent and monovalent, while minimizing complete removal to bulk solution. The quantitative analysis of effective concentration presented in the current work, together with the strain vs binding free energy balance recently described23s for dendrimer attachment to the printboard can, in principle, be applied to predict the extent of multivalent binding available to any polyvalent molecule in a given environment. Hence, novel polyvalent molecules can be designed to “fit” the spacing between binding sites on both a surface and on other polyvalent molecules in, e.g., the “layer-by-layer” printboard [dendrimer/nanoparticle/ dendrimer/nanoparticle...] assemblies used for fabricating structured and functional films on solid substrates.17 As well as applications in nanopatterning and, more generally, nanoelectronics, multivalency may be exploited in the design of novel

10.1021/jp8009386 CCC: $40.75 © 2008 American Chemical Society Published on Web 04/02/2008

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Figure 1. (a) G0-PAMAM-(Fc)4 and (b) G1-PPI-(Fc)4 dendrimer structures are shown along with a schematic (center) for the different interanchor distances. Vertical arrows mark distance between anchors on the same branch; the horizontal and diagonal arrows mark distance between anchors on opposite branches. (c) Plan view of the molecular printboard, with β-CD anchored using disulfide chains. Hydrogens are omitted for clarity. The 20.6 Å lattice constant2 is marked by arrows.

biosensors and therapeutic nanodevices based on, e.g., protein immobilization.24 Methods Molecular models for the four-legged dendrimer molecules shown in Figure 1, G1-PPI-(Fc)4 and G0-PAMAM-(Fc)4, were each built with protonated core amines to simulate the low-pH conditions used experimentally.15,23s β-CD molecules were then added to make dendrimer-printboard complexes. A 70 Å cubic box of water was overlaid, and waters overlapping the complex removed. Periodic boundary conditions were assumed; i.e., the entire 70 Å box was replicated periodically in all directions, completely solvating the complex. Standard CHARMM force field parameters25 were used for β-CD and the dendrimers, with the low-pH core and ferrocene anchors treated as described in references 23s and 26. A slightly modified TIP3P model was used for the water.27 Bonds involving hydrogen were constrained to their experimental lengths with the SHAKE algorithm,28 allowing the use of a 2 fs time step for dynamics. We used the CHARMM program29 version c31b2 for all calculations.

Ten nanoseconds of MD were performed (for each system) at constant room temperature and pressure with a Nose´-Hoover algorithm, following 100 ps of thermalization. Solvated dendrimer-printboard complexes were simulated in six alternative binding mode and dendrimer combinations: (1) monovalent G0PAMAM-(Fc)4, (2) monovalent G1-PPI-(Fc)4, (3) divalent samebranch G0-PAMAM-(Fc)4, (4) divalent opposite-branch G0PAMAM-(Fc)4, (5) divalent opposite-branch G1-PPI-(Fc)4, and (6) divalent opposite-branch f monovalent G0-PAMAM-(Fc)4, with release of one anchor initiated electrochemically. Samebranch and opposite-branch binding modes refer to the relative positions of the bound anchors, as illustrated in Figure 1. Systems 1-5 correspond to stable binding modes15,23s; for system 6, the divalent f monovalent partial unbinding was initiated by charging up one ferrocene anchor, scaling its formal charge from 0 au to +0.5 au and then back to 0 au over 300 ps, sufficient to release the ferrocene from the β-CD cavity and then recover the nonoxidized state.11,15,26 In all, over 50 ns of dynamics were performed and used to explore the dendrimerprintboard conformational space, calculate the effective con-

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Figure 2. Monovalently bound G0-PAMAM-(Fc)4. Schematic shows structurally inequivalent unbound anchors, the unbound anchor on the same branch as the bound anchor (black) and the unbound anchors on the opposite branch (gray). Panel i shows minimum/unbound anchor empty printboard binding site/distances sampled over 10 ns of dynamics for “same-branch” (black line) and “opposite-branch” (gray line) anchors. Panel ii shows probability distribution functions for these distances, with lowest sampled distances marked with diamonds. Panels iii and iv show views from above (iii) and the side (iv), with one representative monovalently bound G0-PAMAM-(Fc)4 structure shown and the positions of empty binding sites marked as black spheres; the gray lines map out the conformational space sampled by unbound anchors over 10 ns. Panel v summarizes the distribution of unbound anchors at the printboard, giving the % time during which each binding site is nearest unbound anchors, and, in parentheses, the % time each binding site is within 5 Å of an unbound anchor. Figures SI1-SI4 in the Supporting Information show (SI1) monovalently bound G1-PPI-(Fc)4, (SI2) divalent opposite-branch G0-PAMAM-(Fc)4, (SI3) divalent same-branch G0-PAMAM-(Fc)4, and (SI4) divalent oppositebranch G1-PPI-(Fc)4. In each case, panels are as for Figure 2.

centration of unbound anchor groups at the printboard and propose a mechanism for dendrimer diffusion on the printboard. Results and Discussion Five 10.0 ns simulations were performed on stable23s dendrimer-printboard complexes: monovalently bound G0PAMAM-(Fc)4 and G1-PPI-(Fc)4, G0-PAMAM-(Fc)4 divalently bound using both opposite-branch and same-branch anchors, and finally G1-PPI-(Fc)4 divalently bound using opposite-branch anchors. These simulations provide extensive sampling of the conformational space available at the dendrimer-printboard interface and allow us to measure the effective concentration of unbound anchors poised for an additional binding interaction. An additional 7.0 ns simulation of divalent f monovalent G0PAMAM-(Fc)4 partial unbinding measured the time needed for the released anchor to move to the periphery of the dendrimer binding hemisphere (0.5 ns) and then reapproach the printboard (a further 2.0 ns), supporting the mechanism for dendrimer diffusion involving “walking” along the printboard, switching between monovalent and multivalent states and minimizing complete unbinding to bulk solution. Taken together, these simulations provide a quantitative description of the effective concentration of unbound ink anchors at the molecular printboard, a model system for the multivalent binding ubiquitous in nature19 and potentially a very powerful tool for (bio)nanotechnology.20 The conformational space sampled by unbound anchors in monovalently bound G1-PPI-(Fc)4 is shown in Figure 2 below; panel i shows the anchor-printboard closest contacts sampled

over 10 ns, summarized by the distance distribution function plotted in panel ii, while panels iii, iv, and v show the 3-D space occupied by the unbound anchors, and panel v summarizes where the anchors sit relative to the printboard binding sites. Similar analyses for the other dendrimer binding modes are given in the Supporting Information. Figure 3 shows the “unbinding” path taken by a released ferrocene anchor. Together, these data give a comprehensive overview of the effective concentration of unbound ink anchors at the printboard, and comparison between the different systems is instructive. First of all, comparing Figure 2 monovalent G1-PPI-(Fc)4 and Figure SI1 monovalent G0-PAMAM-(Fc)4, it is clear that G0-PAMAM-(Fc)4 has a higher population of unbound anchors at positions conducive to an additional binding interaction and formation of a divalently bound complex. Furthermore, for both G1-PPI-(Fc)4 and G0-PAMAM-(Fc)4, unbound anchors on the branch opposite the bound anchor are closest to empty printboard binding sites. This behavior is in agreement with dendrimer “stretchabilities” calculated from CPK models15 and earlier short solution MD runs using just an implicit printboard model.23s The more diffuse distribution of unbound anchors for monovalent G0-PAMAM-(Fc)4 (Figure SI1) is due to reduced core-printboard binding relative to monovalent G1-PPI-(Fc)4 (Figure 2). Trajectory analysis showed that monovalent G0PAMAM-(Fc)4 adopts an orientation conducive to coreprintboard H-bonding after approximately 3 ns of dynamics, and these core-printboard interactions are present for ∼70% of the remaining 7 ns, with distances of 1.5-2.0 Å between a dendrimer core proton and secondary hydroxyl oxygens at the

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Figure 3. G0-PAMAM-(Fc)4 opposite-branch divalent f monovalent, with one anchor released electrochemically as described in the text. Panel i shows distances between the released anchor and the printboard over 7 ns of dynamics. Panel ii shows the probability distribution function for the minimum released anchor to printboard distances sampled from 2.0 to 7.0 ns (i.e., sampled after the dendrimer reapproaches the printboard; see text), with the lowest sampled distance marked with a diamond. Panels iii and iv show views from above (iii) and the side (iv), with one representative G0-PAMAM-(Fc)4 structure shown and the positions of empty binding sites marked as black spheres; the light gray lines map out the conformational space sampled by the released anchor over 7 ns. Panel v summarizes the distribution of the released anchor at the printboard, giving the % time during which each binding site is nearest the released anchor, and in parentheses, the % time each binding site is within 5 Å of the released anchor. Panels vi, vii, and viii show the conformational space occupied by all unbound anchors, not just the released anchor.

entrance to the β-CD cavity, “localizing” the dendrimer at the printboard. The more compact G1-PPI-(Fc)423s maintains a core-β-CD interaction for ∼80% of its 10 ns trajectory, and so unbound G1-PPI-(Fc)4 anchors remain exclusively at one side of the printboard, as shown in panels iii-v of Figure 2. Second, from Figures SI2, SI3, and SI4, divalent G0PAMAM-(Fc)4 has unbound anchors in positions conducive to trivalent binding, while unbound anchors on divalent G1-PPI(Fc)4 remain at least 5 Å away from empty printboard binding sites, in agreement with the observed15 and calculated23s stability of trivalent G0-PAMAM-(Fc)4 but not trivalent G1-PPI-(Fc)4. Third, G0-PAMAM-(Fc)4 divalently bound using samebranch anchors (Figure SI3) has unbound anchors nearer the printboard than G0-PAMAM-(Fc)4 divalently bound using opposite-branch anchors (Figure SI4). Together with the known enhanced stretchability of opposite-branch versus same-branch pairs of anchors,15,23s the current simulations also show the role of core-β-CD interactions in keeping dendrimers in relatively

flat orientations on the printboard. As shown in Figure SM2 and Figure 4a, the orientation of the G0-PAMAM-(Fc)4 dendrimer core in the divalent opposite-branch binding mode is at approximately 90° relative to the direction of the β-CD cups, and so no core-printboard interactions occur. The dendrimer is kept arched above the plane of the printboard with unbound anchors sampling extensively the available conformational space and occasionally coming within 5 Å of an empty binding site, as shown in panel v of Figure SI2. Divalent same-branch G0PAMAM-(Fc)4 shown in Figure SM3, however, finds a core proton to β-CD interaction after approximately 2.5 ns, which is maintained for ∼90% of the remaining 7.5 ns. Figure 4b illustrates the much flatter orientation of the bound dendrimer legs in this binding mode, which places the core close to β-CD secondary hydroxyls, as shown also in the z-coordinate timeline and “before” and “after” z-coordinate distribution functions in Figure 4c. As shown in Figure SI3, this additional coreprintboard interaction gives a more localized distribution of

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Figure 4. Representative MD snapshots illustrating how both dendrimer type and binding mode dictate the extent of additional core-printboard stabilization. In panels a, b, and d, dendrimer core protons are shown as small white spheres, and all other hydrogens are omitted for clarity. Anchor ferrocene iron atoms and β-CD secondary hydroxyl oxygens are shown as large and medium-sized spheres, respectively. Panel c shows the reduced dendrimer-printboard separation following the formation of the additional core-β-CD interaction. In both the z-coordinate timeline and inset z-coordinate distribution function plot, pre-interaction and post-interaction data are colored black and gray, respectively.

unbound ink anchors and also gives orientations corresponding to trivalent binding modes, with minimum unbound anchor-toprintboard distances of less than 3 Å often found. The divalent opposite-branch G1-PPI-(Fc)4 in Figure SI4 and Figure 4d gives the most extreme example of core-printboard interaction found in the present study. Its binding orientation is extremely flat on the printboard, with both core protons H-bonding strongly to β-CD hydroxyls over the full 10 ns of dynamics. These coreβ-CD interactions may serve to stabilize dendrimer-printboard complexes, especially multivalent complexes necessitating tightstretching between bound anchors and thus “flat” dendrimer binding geometries; the additional core binding to the printboard may offset some of the conformational penalty23s incurred for binding small compact dendrimers using multiple anchors, though competition with water means these core-printboard interactions are very much secondary to the much longer-lived and stronger anchor-β-CD cavity interactions. The primary effect of the core-printboard interaction is its influence on binding geometry and thus its propensity for finding additional

anchor-printboard interactions, rather than the direct (small) stabilization proffered by the core-β-CD H-bonding. Conclusions In the present work, computer simulations were used to probe the behavior of multivalent ink molecules at the molecular printboard. Long multi-nanosecond MD simulations map out the conformational space available to ink molecules bound to the printboard and can be used to estimate the propensity for switching between completely unbound, monovalent, and multivalent states. Furthermore, these fully atomistic simulations, using the CHARMM force field25 expanded where necessary with new parameters derived from high-level quantum mechanical calculations,23s,26 allow us to describe the fine details of ink-printboard binding, information not attainable from experiments alone. MD simulations are becoming increasingly attractive with advances in hardware and software capability, and in the present study help explain observed multivalent binding behavior15 via

Unbound Ink Anchors at Molecular Printboards quantification of the effective concentration of partially bound ink molecules. The analysis described can in principle be applied to rationalize/predict binding strengths attainable in any assembly based on multivalent binding, e.g., protein immobilization on the printboard,24 the design of novel cell-adhesion molecules for nanomedicine.30 The simulations also support an efficient mechanism for dendrimer diffusion based on “walking” along the surface of the printboard whereby the multivalent ink minimizes complete unbinding to bulk solution. “Walking” is facilitated by the flat ink-printboard binding geometries obtained via core-β-CD interactions and the fast switching from weakly bound monovalent to more strongly bound multivalent binding modes due to the high effective concentration of unbound ink anchor groups in the plane of the printboard. The controlled surface diffusion of material under, e.g., a concentration gradient, offers the possibility of using the molecular printboard in sensing and diagnostics applications. Acknowledgment. This work was partially funded by the EC NaPa project (Contract No. NMP4-CT-2003-500120). D.T. wishes to thank Jurriaan Huskens, Andreas Larsson, and Andras Perl for stimulating discussions and acknowledges both an SFI grant for the provision of computational resources at Tyndall and the SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of additional computing facilities. Supporting Information Available: Figures SI1-SI4 show the effective concentration of unbound ink anchors for (SI1) monovalently bound G1-PPI-(Fc)4, (SI2) divalent oppositebranch G0-PAMAM-(Fc)4, (SI3) divalent same-branch G0PAMAM-(Fc)4, and (SI4) divalent opposite-branch G1-PPI(Fc)4. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Schonherr, H.; Beulen, M. W. J.; Bugler, J.; Huskens, J.; van Veggel, F. C. J. M.; Reinhoudt, D. N.; Vancso, G. J. J. Am. Chem. Soc. 2000, 122, 4963. (2) Beulen, M. W. J.; Bu¨gler, J.; de Jong, M. R.; Lammerink, B.; Huskens, J.; Scho¨nherr, H.; Vancso, G. J.; Boukamp, B. A.; Wieder, H.; Offenha¨user, A.; Knoll, W.; van Veggel, F. C. J. M.; Reinhoudt, D. N. Chem. Eur. J. 2000, 6, 1176. (3) de Jong, M. R.; Huskens, J.; Reinhoudt, D. N. Chem. Eur. J. 2001, 7, 4164. (4) Huskens, J.; Deij, M. A.; Reinhoudt, D. N. Angew. Chem., Int. Ed. 2002, 41, 4467. (5) Zapotoczny, S.; Auletta, T.; de Jong, M. R.; Schonherr, H.; Huskens, J.; van Veggel, F. C. J. M.; Reinhoudt, D. N.; Vansco, G. J. Langmuir 2002, 18, 6988. (6) Auletta, T.; Dordi, B.; Mulder, A.; Sartori, A.; Onclin, S.; Bruinink, C. M.; Nijhuis, C. A.; Beijleveld, H.; Pe´ter, M.; Scho¨nherr, H.; Vancso, G. J.; Casnati, A.; Ungaro, R.; Ravoo, B. J.; Huskens, J.; Reinhoudt, D. N. Angew. Chem., Int. Ed. 2004, 43, 369. (7) Onclin, S.; Mulder, A.; Huskens, J.; Ravoo, B. J.; Reinhoudt, D. N. Langmuir 2004, 20, 5460. (8) Auletta, T.; de Jong, M. R.; Mulder, A., van Veggel, F. C. J. M.; Huskens, J.; Reinhoudt, D. N.; Zou, S.; Zapotoczny, S.; Scho¨nherr, H.; Vancso, G. J.; Kuipers, L. J. Am. Chem. Soc. 2004, 126, 1577. (9) Mulder, A.; Auletta, T.; Sartori, A.; Del Ciotto, S.; Casnati, A.; Ungaro, R.; Huskens, J.; Reinhoudt, D. N. J. Am. Chem. Soc. 2004, 126, 6627.

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