Free Energy Balance Predicates Dendrimer Binding Multivalency at

Jul 4, 2007 - Self-assembled monolayers (SAMs) terminating in β-cyclodextrin cavities can be used to bind ink molecules and so provide a molecular ...
0 downloads 0 Views 1MB Size
Download PDF
Langmuir 2007, 23, 8441-8451

8441

Free Energy Balance Predicates Dendrimer Binding Multivalency at Molecular Printboards D. Thompson* Tyndall National Institute, Prospect Row, Lee Maltings, Cork, Ireland ReceiVed March 26, 2007. In Final Form: May 16, 2007 Self-assembled monolayers (SAMs) terminating in β-cyclodextrin (β-CD) 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 to the printboard, yielding more robust patterns. We performed fully atomistic molecular dynamics (MD) simulations in bulk explicit solvent to probe the conformational space available to dendrimer and dendrite ink molecules, in both free and bound environments. We show that accurate treatment of both pH effects and binding conformations gives calculated binding modes in line with known binding multivalencies. We identify and quantify the steric frustration causing small, low-generation dendrimer inks to bind to the printboard using just a subset of the available anchor groups. Furthermore, we show that the enhanced binding energy of multisite attachment offsets the steric strain, the feasibility of a given binding mode thus determined by the relative magnitudes of the unfavorable steric strain and favorable multisite binding free energies. We use our experimentally validated model of dendrimer binding to predict the binding mode of novel fluorophoric dendrites and find divalent binding, consistent with confocal microscopy imaging of pattern formation at molecular printboards.

1. Introduction Molecular recognition is used extensively by nature to build complex structures via specific noncovalent guest/host interactions. In recent years, “molecular printboards”, exploiting the guest complexation properties of cyclodextrin, have been developed and used for nanopatterning applications.1-19 β-Cyclodextrin (β-CD) molecules can be tethered to gold1-6,8,11,13,15-17 * Author to whom all correspondence should be addressed. Phone +35321-490-4327. Fax +353-21-427-0271. E-mail damien.thompson@ tyndall.ie. (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, 49634967. (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.sEur. J. 2000, 6, 1176-1183. (3) de Jong, M. R.; Huskens, J.; Reinhoudt, D. N. Chem.sEur. J. 2001, 7, 4164-4170. (4) Huskens, J.; Deij, M. A.; Reinhoudt, D. N. Angew. Chem., Int. Ed. 2002, 41, 4467-4471. (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, 6988-6994. (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, 369-373. (7) Onclin, S.; Mulder, A.; Huskens, J.; Ravoo, B. J.; Reinhoudt, D. N. Langmuir 2004, 20, 5460-5466. (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, 1577-1584. (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, 6627-6636. (10) Huskens, J.; Mulder, A.; Auletta, T.; Nijhuis, C. A.; Ludden, M. J. W.; Reinhoudt, D. N. J. Am. Chem. Soc. 2004, 126, 6784-6797. (11) Nijhuis, C. A.; Huskens, J.; Reinhoudt, D. N. J. Am. Chem. Soc. 2004, 126, 12266-12267. (12) Bruinink, C. M.; Nijhuis, C. A.; Pe´ter, M.; Dordi, B.; Crespo-Biel, O.; Auletta, T.; Mulder, A.; Scho¨nherr, H.; Vancso, G. J.; Huskens, J.; Reinhoudt, D. N. Chem.sEur. J. 2005, 11, 3988-3996. (13) Crespo-Biel, O.; Pe´ter, M.; Bruinink, C. M.; Ravoo, B. J.; Reinhoudt, D. N.; Huskens, J. Chem.sEur. J. 2005, 11, 2426-2432. (14) Mulder, A.; Onclin, S.; Pe´ter, M.; Hoogenboom, J. P.; Beijleveld, H.; ter Maat, J.; Garcı´a-Parajo´, M. F.; Ravoo, B. J.; Huskens, J.; van Hulst, N. F.; Reinhoudt, D. N. Small 2005, 1, 242-253. (15) Nijhuis, C. A.; Yu, F.; Knoll, W.; Huskens, J.; Reinhoudt, D. N. Langmuir 2005, 21, 7866-7876.

or silicon oxide,7,12,14,18 forming densely packed self-assembled monolayers (SAMs) with β-CD cavities exposed at the surface. The hydrophobic interior of β-CD allows it to bind uncharged guest molecules in its cavity,20 and this combination of host structural order and specific guest ink binding provides a molecular printboard. The use of large ink molecules such as functionalized dendrimers, polymers, and nanoparticles allows simultaneous binding of multiple anchor sites on the ink molecule to the printboard.4,6,7,9-19 This multivalent binding enhances the overall complexation strength, providing a more robust but still reversible interaction. For example, high-generation ferroceneterminated dendrimers cannot be unbound from the printboard using conventional aqueous washing but can be removed by electrochemical desorption.11,15,19 Understanding the conformational properties of dendrimers under nonequilibrium conditions, for example, when partially bound to a monolayer15,19 or passing through a liquid-liquid interface,21 is central to the use of such large inhomogeneous molecules in nanopatterning15-19 and also in medical applications22 such as drug/gene delivery and noninvasive imaging. 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 both in bulk solution and when partially bound to the molecular printboard. We find that the binding of low-generation (16) Crespo-Biel, O.; Ravoo, B. J.; Huskens, J.; Reinhoudt, D. N. Dalton Trans. 2006, 2737-2741. (17) Crespo-Biel, O.; Dordi, B.; Maury, P.; Pe´ter, M.; Reinhoudt, D. N.; Huskens, J. Chem. Mater. 2006, 18, 2545-2551. (18) Nijhuis, C. A.; Sinha, J. K.; Wittstock, G.; Huskens, J.; Ravoo, B. J.; Reinhoudt, D. N. Langmuir 2006, 22, 9770-9775. (19) (a) Huskens, J. Curr. Opin. Chem. Biol. 2006, 10, 537-543. (b) Ludden, M. J. W.; Reinhoudt, D. N.; Huskens, J. Chem. Soc. ReV. 2006, 35, 1122-1134. (20) Lipkowitz, K. B. Chem. ReV. 1998, 98, 1829-1874. (21) Berduque, A. Liquid-Liquid Electrochemistry for Ion Analysis. Ph.D. Thesis, Tyndall National Institute, Ireland, 2006. (22) (a) Kukowska-Latallo, J. F.; Bielinska, A. U.; Johnson, J.; Spindler, R.; Tomalia, D. A.; Baker, J. R. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 4897-4902. (b) Eichman, J. D.; Bielinska, A. U.; Kukowska-Latallo, J. F.; Baker, R. J. Pharm. Sci. Technol. Today 2000, 3, 232-245. (c) Gillies, E. R.; Frechet, J. M. Drug DiscoVery Today 2005, 10, 35-43. (d) Lee, C. C.; MacKay, J. A.; Fre´chet, JM. J.; Szoka, F. C. Nat. Biotechnol. 2005, 23, 1517-1526.

10.1021/la700878y CCC: $37.00 © 2007 American Chemical Society Published on Web 07/04/2007

8442 Langmuir, Vol. 23, No. 16, 2007

dendrimers functionalized with four ferrocene anchor groups, poly(amido amine) G0-PAMAM-(Fc)4 and poly(propylene imine) G1-PPI-(Fc)4,15 using more than three (PAMAM) or two (PPI) of the ferrocene anchors, is strongly penalized due to conformational strain. Combining our calculated conformational penalties with experimental ferrocene/cyclodextrin binding energies,3 we find clear clustering of observed and nonobserved15 multivalent binding modes. For fluorescent dendritic wedges, two well-separated adamantane anchors on opposite branches can bind simultaneously to the printboard without incurring a significant conformational penalty, but anchors on the same branch are unable to stretch apart the required distance for simultaneous binding, yielding the same divalent binding behavior for both the two- and four-legged wedges, in agreement with confocal microscopy images.14 2. Methods 2.1. Model Building. The four-legged dendrimer molecules shown in Figure 1(I), G0-PAMAM-(Fc)4 and G1-PPI-(Fc)4, were each built with protonated core amines to simulate the low-pH conditions used experimentally.15 A 70 Å cubic box of water was overlaid, and waters overlapping the molecule removed. Periodic boundary conditions were assumed; i.e., the entire 70 Å box was replicated periodically in all directions, solvating the dendrimer. Low-pH dendrimer atomic charges were derived by mapping computed ab initio charges to the CHARMM22 force field24 as described in section SM1 of Supporting Information. Goddard and co-workers used a similar scheme to account for pH effects.23q Standard CHARMM22 force field parameters were used for β-CD (Figure 1(III)) and the dendrimer legs,23o,23n with ferrocene anchors treated as described in ref 25. The adamantane-terminated dendritic wedges7,14 were treated as described in section SM5 of Supporting Informationsthe two-legged wedge has long, flexible tetraethylene glycol spacers to ensure a divalent interaction with the β-CDs at the printboard surface, and the four-legged wedge is based on a secondgeneration PPI dendritic wedge with four adamantyl groups at its periphery, similar to an adamantyl-functionalized G1-PPI dendrimer. A standard TIP3P model was used for the water.26 Bonds involving hydrogen were constrained to their experimental lengths with the SHAKE algorithm,27 allowing the use of a 2 fs time step for dynamics. We used the CHARMM program28 version c31b2 for all calculations. (23) (a) Naylor, A. M.; Goddard, W. A., III; Kiefer, G. E.; Tomalia, D. A. J. Am. Chem. Soc. 1989, 111, 2339-2341. (b) Tomalia, D. A.; Naylor, A. M.; Goddard, W. A., III Angew. Chem., Int. Ed. 1990, 29, 138-175. (c) Mansfiled, M. L.; Klushin, L. I. Macromolecules 1993, 26, 4262-4268. (d) Murat, M.; Grest, G. S. Macromolecules 1996, 29, 1278-1285. (e) Cai, C.; Chen, Z. Y. Macromolecules 1997, 30, 5104-5117. (f) Scherrenberg, R.; Coussens, B.; van Vliet, P.; Edouard, G.; Brackman, J.; de Brabander, E. Macromolecules 1998, 31, 456-461. (g) Uppuluri, S.; Keinath, S. E.; Tomalia, D. A.; Dvornic, P. R. Macromolecules 1998, 31, 4498-4510. (h) Naidoo, K. J.; Hughes, S. J.; Moss, J. R. Macromolecules 1999, 32, 331-341. (i) Topp, A.; Bauer, B. J.; Tomalia, D. A.; Amis, E. J. Macromolecules 1999, 32, 7232-7237. (j) Cagin, T.; Miklis, P. J.; Wang, G.; Zamanakos, G.; Martin, R.; Li, H.; Mainz, D. T.; Vaidehi, N.; Goddard, W. A., III Mat. Res. Soc. Symp. Proc. 1999, 543, 299-310. (k) Cagin, T.; Wang, G.; Martin, R.; Breen, N.; Goddard, W. A., III Nanotechnology 2000, 11, 77-84. (l) Gorman, C. B.; Smith, J. C. Polymer 2000, 41, 675-683. (m) Cagin, T.; Wang, G.; Martin, R.; Zamanakos, G.; Vaidehi, N.; Mainz, D. T.; Goddard, W. A., III Comp. Theor. Polym. Sci. 2001, 11, 345-356. (n) Lee, I.; Athey, B. A.; Wetzel, A. W.; Meixner, W.; Baker, J. R. Macromolecules 2002, 35, 4510-4520. (o) Mecke, A.; Lee, I.; Baker, J. R.; Banaszak, Holl, M. M.; Orr, B. G. Eur. Phys. J. E 2004, 14, 7-16. (p) Maiti, P. K.; Cagin, T.; Wang, G.; Goddard, W. A., III Macromolecules 2004, 37, 6236-6254. (q) Maiti, P. K.; Cagin, T.; Lin, S. T.; Goddard, W. A. Macromolecules 2005, 38, 979-991. (r) Lin, S. T.; Maiti, P. K.; Goddard, W. A., III J. Phys. Chem. B 2005, 109, 86638672. (24) MacKerrell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, D. L.; Evanseck, J. D.; Field, M. J. J. Phys. Chem. B 1998, 102, 3586-3616. (25) Thompson, D.; Larsson, J. A. J. Phys. Chem. B 2006, 110, 16640-16645. (26) Jorgensen, W.; Chandrasekhar, J.; Madura, J.; Impey, R.; Klein, M. J. Chem. Phys. 1983, 79, 926-935. (27) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 1977, 23, 327-341. (28) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaninathan, S.; Karplus, M. J. Comput. Chem. 1983, 4, 187-217.

Thompson 2.2. Molecular Dynamics (MD) Simulations. Two nanoseconds of molecular dynamics were performed (for each system) at constant, room temperature and pressure with a Nose´-Hoover algorithm, following 100 ps of thermalization. The G0-PAMAM-(Fc)4 and G1-PPI-(Fc)4 dendrimers were simulated in solution under low-pH conditions: (a) with no constraints, (b) with two or more of the anchor groups fixed to positions corresponding to (implicit) printboard binding sites, and (c) bound explicitly in printboard cavities. For the “free” simulations, (a) we also modeled the dendrimers at pH-neutral conditions and show the importance of accurate treatment of the low-pH environment. The “implicit printboard” model (b) has “bound” anchor groups fixed at positions 20.6 Å apart (see the molecular printboard model in Figure 1(III)sbased on AFM data from ref 2) to model bound-to-printboard geometries, while model (c) explicitly includes the β-cyclodextrin binding sites. Degrees of multivalency deduced from the “free” simulations (a) were tested using the more sophisticated “bound” (to implicit printboard) simulations (b) and finally by simulations of the dendrimers explicitly attached to the printboard surface (c), showing multivalency in line with experimental titrations.15 We then predict the multivalent binding of novel two- and four-legged adamantane-terminated fluorophore ink molecules to the printboard, previously studied qualitatively using confocal microscopy,14 using the MD protocol (a) described above for the ferrocene-terminated dendrimers. In all, over 40 ns of dynamics were produced. Given the large water boxes required for accurate treatment of solvation, multinanosecond sampling times needed for extensive conformational space searching and the large number of different free and bound conditions to be considered, we did not explicitly include the printboard in simulation cells for protocols (a) and (b). Protocol (c) involved 1 ns simulations of G0-PAMAM-(Fc)4 and G1-PPI-(Fc)4 explicit binding to the surface of the printboard, and we observed the binding/unbinding behavior predicted from the solution simulations (a) and (b) above, illustrating the validity of the implicit printboard model approximation for predicting dendrimer binding multivalency.

3. Results and Discussion First, the pH-dependence of dendrimer conformations is briefly described. Then, low-pH MD structures for PAMAM and PPI four-legged dendrimers are analyzed, both in “free” and “bound” conformations. These data are used to describe the multivalent binding of dendrimers to the molecular printboard as a function of their maximum interanchor separations, henceforth termed their “stretchability”, and the energetic cost of binding small dendrimer inks with artificially high multivalency is also computed. The predicted behavior is tested by explicit binding simulations to the printboard surface, and we find good agreement with known binding modes.15 Finally, the conformational space available to fluorophore ink molecules is described and used to predict their binding multivalencies at the printboard.14 3.1. Dendrimer Stretchability under Low-pH Conditions. The degree of multivalent binding between the four-anchor PAMAM and PPI dendrimers was measured experimentally under low-pH conditions.15 As described in section SM2 of the Supporting Information and below, pH-neutral and low-pH dendrimers have very similar overall shapes. The main effect of lowering pH is an increase in average interanchor distancessthe compactness of the low-generation dendrimers at neutral conditions impairs multivalent binding. At low pH, the core amines are protonated, changing the charge distribution in the dendrimer core; see section SM1 of the Supporting Information for atomic charges as a function of pH. Low-pH dendrimer conformational properties in bulk solution are shown in Figure 2. Figures 3 and 4 show dendrimer conformational properties when bound to the printboard using two anchor groups, together with distances between the remaining

Dendrimer Binding MultiValency at Molecular Printboards

Langmuir, Vol. 23, No. 16, 2007 8443

Figure 1. I. (a) G0-PAMAM-(Fc)4 and (b) G1-PPI-(Fc)4 dendrimer structures are shown, with core and anchor groups as markedsthe remaining atoms are grouped as “legs”. II. (a) G0-PAMAM-(Fc)4 and (b) G1-PPI-(Fc)4 dendrimer molecules are shown, along with a schematic for the different inter-anchor distances. Vertical arrows mark distance between anchors on the same branch; the horizontal and diagonal arrows mark distance between anchors on opposite branches. III. Plan view of the molecular printboard, with β-CD anchored using disulfide chains. Hydrogens are omitted for clarity. The 20.6 Å inter-β-CD lattice constant2 is marked by arrows.

unbound ferrocene anchors and available β-CD cavities, for both divalent and trivalent dendrimer binding. Figure 1(II) shows starting dendrimer structures, and Figure 2(I) illustrates the extensive conformational sampling of possible anchor positions for each dendrimer, over 2 ns of free dynamics.

The corresponding timelines of maximum interanchor separations in Figure 2(II) show no net drift with time and indicate that both the PAMAM and PPI dendrimers can engage in divalent binding with the printboard using two ferrocene anchors on opposite branches, their separations comparable to the measured2 inter-

8444 Langmuir, Vol. 23, No. 16, 2007

Thompson

Figure 2. Conformational properties of ferrocene-terminated dendrimers in solution. I. One representative MD structure is shown for (a) G0-PAMAM-(Fc)4 dendrimer and (b) G1-PPI-(Fc)4 dendrimer, with gray lines mapping the space occupied by the ferrocene terminal groups over 2 ns. II. The bottom panels show timelines of maximum interanchor distances for (a) G0-PAMAM-(Fc)4 dendrimer and (b) G1-PPI-(Fc)4 dendrimer. Time-averaged maximum interanchor distances, radii of gyration (Rg), aspect ratios, and shape anisotropies (κ2) are averaged over 5000 MD structures and quantify the size of the dendrimers.

β-CD spacing (20.6 Å) at the printboard. The larger PAMAM dendrimer may also bind simultaneously to a third printboard site, as indicated by the simultaneous >20.6 Å separations of both opposite-branch and same-branch ferrocenes. To test this prediction of PAMAM but not PPI trivalency, based on unconstrained solution MD simulations, we performed additional simulations, fixing one, two, and three ferrocene anchors to positions corresponding to (implicit) printboard binding sites. For divalent binding, the resulting conformational space sampling of the two remaining unbound ferrocenes is shown in panels (a) and (b) of Figures 3 and 4. Together with the |unbound ferrocene - empty β-CD cavity| distance timelines in panel (c) of Figures 3 and 4, these structures show the feasibility of trivalent binding for PAMAM. The separation between one of the unbound ferrocenes and an empty β-CD cavity drops as low as only 3 Å when PAMAM is divalently bound. Divalently bound PPI, on the other hand, has its remaining ferrocenes always at least 5 Å from an empty printboard β-CD cavity, and so trivalent binding is not available for PPI. As shown in panel (c) of Figures 3 and 4, trivalently bound dendrimers are incapable of forming a fourth interaction; the remaining ferrocene is kept at least 10 Å (PAMAM) and 15 Å (PPI) away from the printboard. Conformational energies given

in section SM3 of the Supporting Information are combined with experimental measures of ferrocene/β-CD binding strengths3 in section 3.2 below, showing that the free energy balance between nonequilibrium dendrimer conformations and binding energy permits PAMAM but not PPI to engage in trivalent binding to the printboard. 3.2. Energy Penalty for Binding Small Dendrimers in Frustrated Conformations. Table 1 gives averages for the external and internal conformational energy timelines shown in section SM3 of the Supporting Information, together with constraint energies necessary to enforce divalent and trivalent binding geometries in the multivalently bound PAMAM and PPI dendrimers. Highlighted are multivalent orientations entailing a significant destabilization in conformational energy relative to the reference monovalent systems. These monovalently bound structures are equivalent in conformation energy to unconstrained “free” solution structures. Significant penalties are found, in order of magnitude, for PPI trivalent binding, PPI same-branch divalent binding, and PAMAM trivalent binding. The measured binding free energy of ferrocene to β-CD complexation is -5.4 kcal/mol,3 in line with theoretical predictions of a ferrocene vs ferrocenium cation binding free energy difference of g7 kcal/mol;25 i.e., the binding free energy

Dendrimer Binding MultiValency at Molecular Printboards

Langmuir, Vol. 23, No. 16, 2007 8445

Figure 3. Conformational properties of G0-PAMAM-(Fc)4 dendrimer bound to the (implicit) molecular printboard using divalent binding of ferrocenes (a) on the same branch and (b) on opposite branches. Black spheres mark the centers of the hexagonally packed CD cavities at the surface of the printboard. One representative MD structure is shown, with gray lines mapping the space occupied by the unbound ferrocenes over 2 ns. (c) Timeline of minimum distances between an unbound ferrocene and an unoccupied β-CD cavity. Curves correspond to dendrimer bound to the molecular printboard using divalent binding of ferrocenes on the same branch (black line) and opposite branches (dark gray line), and trivalent binding (light gray line).

of the ferrocenium cation is positive, and so unbinding may be initiated electrochemically.11,15,19 The experimental ∆G is composed of ∆H ) -6.1 kcal/mol and T∆S ) -0.7 kcal/mol.3 We can thus estimate the “net energy” of bound dendrimers as

the sum of the (additive) binding enthalpy per bound ferrocene and the conformational penalty, if present, associated with the corresponding bound geometry. Figure 5 gives the results of this analysis and shows how the experimentally observed binding

8446 Langmuir, Vol. 23, No. 16, 2007

Thompson

Figure 4. Conformational properties of G1-PPI-(Fc)4 dendrimer bound to the (implicit) molecular printboard using divalent binding of ferrocenes (a) on the same branch and (b) on opposite branches. Black spheres mark the centers of the hexagonally packed CD cavities at the surface of the printboard. One representative MD structure is shown, with gray lines mapping the space occupied by the unbound ferrocenes over 2 ns. (c) Timeline of minimum distances between an unbound ferrocene and an unoccupied β-CD cavity. Curves correspond to dendrimer bound to the molecular printboard using divalent binding of ferrocenes on the same branch (black line) and opposite branches (dark gray line), and trivalent binding (light gray line).

modes15 are significantly stabilized relative to the nonobserved PPI trivalent binding mode. The same-branch PPI divalent binding mode also has a high positive net energy, consistent with the availability of divalent (using opposite-branch anchors) but not trivalent (using opposite-branch and same-branch anchors simultaneously) binding modes. Given the noise in the energy data (Table 1) and the rather ad hoc means of estimating the

conformational strain, it is gratifying that all the experimentally observed15 binding modes have net negative energies (Figure 5), while the nonobserved modes have net positive energies. Hence, binding multivalency involves a balance between increasing number of binding interactions and strained dendrimer orientations. Decomposition of the overall internal energy term into its bond, angle, Urey-Bradley, and dihedral constituents

Dendrimer Binding MultiValency at Molecular Printboards

Langmuir, Vol. 23, No. 16, 2007 8447

Table 1. Energetics of G0-PAMAM-(Fc)4 and G0-PPI-(Fc)4 Four-Legged Dendrimersa external

internal

constraint

Solution/Monovalent binding +525 0 +503 0

PAMAM PPI

-93 994 -93 863

PAMAM PPI

-93 976 (+19, 0%) -93 914 (-50, 0%)

PAMAM PPI

-93 965 (+30, 0%) -93 868 (-5, 0%)

PAMAM PPI

-93 969 (+26, 0%) -93 933 (-70, 0%)

Trivalent Binding +537 (+12, 2%) +520 (+17, 3%)

PAMAM PPI

213 205

10 9

Divalent Same-Branch Binding +524 (0, 0%) +2 (+2, 100%) +520 (+17, 3%) +13 (+13, 100%) Divalent Opposite-Branch Binding +528 (+3, 0%) +2 (+2, 100%) +498 (-5, 1%) +2 (+2, 100%)

total energy -93 470 -93 360 -93 450 (+20 0%) -93 381 (-20, 0%) -93 435 (+34, 0%) -93 368 (-8, 0%)

+3 (+3, 100%) +16 (+16, 100%)

-93 427 (+43, 0%) -93 397 (-37, 0%)

1 3

152 147

Standard Deviations

a All energies (kcal/mol) are averaged over 5000 structures, sampling every 0.4 ps from 2 ns of dynamics. Standard deviations given in the final two rows are the maximum deviations calculated across all data sets. In each case, zero, one, two, or three ferrocene anchors were constrained to (implicit) printboard binding sites. Zero corresponds to the reference solution state and has the same conformational energies as the monovalent (one ferrocene bound) state. Values in parentheses give the difference in energy between monovalent and multivalent statesspositive values indicate conformational energy penalties upon multivalent binding. The percentage value in parentheses expresses this energy difference relative to the energy in the reference monovalent state. For divalent binding, only PPI binding using same-branch ferrocenes is significantly penalized relative to solution (see energetic costs highlighted in bold in the tablesenergy plots in section SM3 of Supporting Information further illustrate how only PPI same-branch binding has a conformational energy cost significantly larger than the sampling error). Trivalent binding is penalized for both dendrimers, most strongly for PPI.

Figure 5. Net energies of bound G0-PAMAM-(Fc)4 and G1-PPI-(Fc)4 dendrimers. Net energy is the sum of the experimental Fc to β-CD binding strengths (∆H ) -6.1 kcal/mol, from ref 3) plus the internal and restraint conformational energies relative to the reference solution state (Table 1). Shown in gray are the energetically inaccessible states, not observed experimentally (ref 15). The experimentally observed states are shown in black, and all have negative net energies.

(see section SM3 of Supporting Information), shows that strained, nonoptimum dendrimer bond lengths are largely responsible for the conformational energy penalties identified in Table 1. Comparison of PAMAM bond lengths in monovalent and multivalent structures indicates that trivalently bound PAMAM has core C-C and N-C bond lengths and core-leg N-C bond lengths on average 0.04 Å greater than target force field values. All other bonds have the same average values in both monovalent and multivalent simulations. Divalently bound PAMAM, on the other hand, has all bond lengths within (0.01 Å of monovalent PAMAM and so the same conformational energy (see Figure SM3 in Supporting Information). Thus, the core of PAMAM becomes strained upon trivalent binding, and as shown in Figure 5, this small conformational penalty (Table 1) is offset by the (3 × -6.1 ) -18.3 kcal/mol) ferrocene/β-CD binding energy, and so the net energy is raised only slightly above that of divalently bound PAMAM. For PPI, both same-branch divalent binding and trivalent binding (Table 1 and Figure 5) entail a significant conformational penalty, and so trivalent binding is not observed experimentally.

Due to the enhanced ferrocene/β-CD complexation energy of trivalent PPI, the same-branch divalently bound PPI dendrimer is the least stable binding mode (Table 1 and Figure 5). As shown in Figure SM4 of Supporting Information, strained bond lengths are again largely responsible. Structure inspection indicates that, in both same-branch divalent and trivalent bound PPI, core bond lengths again stretch by an average of 0.04 Å beyond target force field values, so incurring a significant conformational penalty. The PPI core thus hampers all but the opposite-branch divalent multisite binding modes. Core bond stretching accounts for most of the conformational penalty associated with forcing ferrocene anchors to stretch beyond their preferred “natural” extension. 3.3. Explicit Dendrimer/Printboard Binding Simulations. One nanosecond runs were initiated from a typical snapshot along the “bound” dendrimer (implicit printboard) simulations described in sections 3.2 and 3.3 above. The two (divalently bound dendrimers) or three (trivalently bound dendrimers) β-CD hosts were built into the existing solvated dendrimer model and overlapping waters removed. We consider six starting bound

8448 Langmuir, Vol. 23, No. 16, 2007

Thompson

Figure 6. The top panel (left-hand side) shows timelines for ferrocene to β-CD distances in divalently bound G0-PAMAM-(Fc)4 dendrimerprintboard complexes, together with (right-hand side) differences in ferrocene-β-CD complexation energy estimates for monovalent and divalent complexes, ∆∆C. Distance plotted is the separation between each initially bound ferrocene and its β-CD binding cavity in Å, and ∆∆C values are in kcal/mol. Data based on 2500 structures, sampling every 0.4 ps during 1 ns of dynamics. Corresponding data for trivalently bound PAMAM and all binding modes for G1-PPI-(Fc)4 are given in section SM4 of Supporting Information. The middle panel shows starting geometries for runs I-VI; ferrocenes are shown as spheres. See text for details of the complexes corresponding to runs I-VI and A-D. The bottom panel shows complexes after 1 ns of dynamics; run VI has a very flat dendrimer binding geometry and so is shown from above for clarity.

structures: (I) is same-branch divalent PAMAM, (II) oppositebranch divalent PAMAM, (III) trivalent PAMAM, and (IV-VI)

are the corresponding PPI complexes, as shown in Figure 6 below. Ferrocene to β-CD distances in Figure 6(a) show the separation

Dendrimer Binding MultiValency at Molecular Printboards

Langmuir, Vol. 23, No. 16, 2007 8449

Figure 7. Conformational properties of adamantane-terminated fluorophore dendritic wedges in solution. I. Starting (a) dendritic wedge(Ad)2 and (b) dendritic wedge-(Ad)4 structures are shown along with a schematic (center) for the different interanchor distances in wedge(Ad)4. Vertical arrows mark distance between anchors on the same branch; the horizontal and diagonal arrows mark distance between anchors on opposite branches. II. One representative MD structure is shown for (a) dendritic wedge-(Ad)2 and (b) dendritic wedge-(Ad)4, with gray lines mapping the space occupied by the adamantane center of mass over 2 ns. III. The bottom panels show timelines of maximum interanchor distances in the wedges.

between each initially bound ferrocene and its β-CD binding site in divalently bound PAMAM; also plotted are timelines of

complexation energy estimates, ∆C, of each multivalent binding mode relative to C in the singly bound complex, ∆∆C in kcal/

8450 Langmuir, Vol. 23, No. 16, 2007

mol. Figure SM5 in the Supporting Information gives the corresponding timelines for trivalent PAMAM, plus di- and trivalent PPI, while Figure SM6 in the Supporting Information gives distance timelines for same-branch divalent PAMAM initiated from four alternative starting geometries. The bottom panel of Figure 6 shows final structures for runs I-VI. Distance and complexation energy difference ∆∆C data in Figures 6, SM5, and SM6 show that PAMAM has stable divalent and trivalent binding modes while PPI only has divalent binding using ferrocenes on opposite branches, in agreement with simulations (sections 3.1 and 3.2) using just an implicit printboard model. Irrespective of the starting dendrimer geometry and size of the printboard (see section SM4 of Supporting Information), same-branch divalent PAMAM remains strongly bound for the 1 ns of dynamics; the bound ferrocene to β-CD distances sampled in divalent PAMAM are coincident with those in singly bound PAMAM, as shown in Figure 6 below and Figure SM6 of Supporting Information. Similarly, both the alternative divalent geometry and trivalently bound PAMAM are strongly held complexes, as shown in Figure SM5 of Supporting Information. PPI on the other hand loses one binding interaction when in either trivalent or same-branch divalent geometries; only oppositebranch divalent retains its starting binding mode, as shown in Figure SM5 of the Supporting Information. Highly accurate estimates of binding free energies are difficult to obtain from standard molecular dynamics calculations.29 Indeed, in the present study, we see the expected overestimation of ferrocene/β-CD binding strengths in our MD simulations, approximately -10 to -15 kcal/mol, significantly stronger than the measured -6.1 kcal/mol.3 For prediction of the relative binding strengths of two guests competing for a host site, thermodynamic integration provides a means of obtaining very accurate binding free energy differences.25,30 In the present work, we calculate the relative complexation energy at monovalent vs multivalent binding sites simply by comparing estimates of interaction energies in the singly bound and multibound systems, using the same cell size for each system. We may thus expect the difference in complexation energies ∆∆C to be a good comparator of ferrocene/β-CD binding strengths for singly vs multivalently bound dendrimers. These ∆∆C values are plotted in Figure 6 below and in Figure SM5 of the Supporting Information and show how trivalent and same-branch divalent PPI both lose one binding interaction, a consequence of the conformational penalties quantified in section 3.2 above. Interestingly, retained multivalent binding interactions are each equally strong and of the same strength as monovalent binding, illustrating the “separation” between anchor/host complexation and strain in the main body of the dendrimer. From the MD ∆∆C data, we find no evidence for cooperativity between neighboring printboard β-cyclodextrin binding sites, nor do we find any one preferred ferrocene orientation in the binding site, in agreement with earlier single ferrocene/β-CD interaction studies.25 For same-branch divalent PPI, the second ferrocene unbinds within 0.1 ns but remains near the rim of β-CD for the duration of the 1 ns trajectory due to the strong electrostatic interaction between the carboxylate immediately above the ferrocene anchor and β-CD secondary hydroxyl group(s), reminiscent of the partially bound state sampled by ferrocenium methanol in earlier (29) Wang, J.; Deng, Y.; Roux, B. Biophys. J. 2006, 91, 2798-814. (30) (a) Simonson, T. In Computational Biochemistry and Biophysics; Becker, O. M., MacKerell, A. D., Roux, B., Watanabe, M., Eds.; Marcel Dekker Inc.: New York, 2001. (b) Simonson, T.; Archontis, G.; Karplus, M. Acc. Chem. Res. 2002, 35, 430-437. (c) Thompson, D.; Plateau, P.; Simonson, T. ChemBioChem 2006, 7, 337-344. (d) Thompson, D.; Simonson, T. J. Biol. Chem. 2006, 281, 23792-23803.

Thompson

simulations.25 As shown in Figure SM5, the complexation strength is reduced by up to 10 kcal/mol when the most loosely bound ferrocene is excluded from the β-CD cavity. For trivalent PPI, the third ferrocene unbinds within 0.2 ns and remains at least 10-13 Å outside the β-CD cavity. This stronger unbinding of one ferrocene in trivalent PPI is shown too in the larger reduction in complexation energy of up to 13 kcal/mol. 3.4. Fluorophoric Dendrite Stretchability as Predicator of Multivalent Binding Modes. The adamantane-terminated dendrite wedges used in fluorescence experiments14 were modeled as shown in Figure 7. Section SM5 of the Supporting Information gives details of the force field data used for these molecules. As shown in Figure 7, both the two- and four-legged wedges can undergo divalent binding with the printboard-interanchor separations of >20.6 Å extensively sampled in our 2.0 ns MD simulations. Higher-order multivalent binding, however, is not available. The four-legged wedge is unable to simultaneously place two same-branch adamantane anchors the required 20.6 Å apart. Indeed, as shown in Figure 7, the highest same-branch separation observed is only 12 Å, so both the two- and fourlegged wedges bind to the printboard using two adamantane/ β-CD interactions, in agreement with confocal microscopy images.14

4. Conclusions Molecular dynamics simulations provide support for ongoing experimental efforts to control and fine-tune multivalent binding. Maximizing the number of binding interactions while minimizing internal strain in the bound molecules can provide an energetically favorable complexation. Indeed, nanopatterning experiments have shown that such strongly bound complexes are surprisingly resistant to conventional methods of destabilization or “washing”. Using multiple simulations of ink molecule binding to molecular printboards, we have shown that experimentally inaccessible binding modes involve a significant steric penalty that is not recompensed by multisite binding free energies. These energetically forbidden binding modes stretch the core of small, lowgeneration dendrimers significantly beyond their “natural” geometries, and the free energy balance between this internal stretching and the complexation energy determines the extent of multivalent binding. We observe the predicted binding/unbinding behavior in large simulation cells featuring an explicit representation of the printboard. Given accurate treatment of pH effects and consideration of all possible binding orientations, MD simulations can provide detailed structural, and even energetic, data on multivalent binding. We thus use our experimentally validated model of dendrimer binding here to predict the binding mode of novel fluorophoric dendrites and find behavior consistent with confocal microscopy imaging of pattern formation at molecular printboards. MD simulations, increasingly attractive with advances in hardware and software capability, may provide an alternative to the costly and sometimes very difficult experimental measurements of multivalent binding energetics. This is particularly true of large, many-pronged molecules at interfaces, the control of which is central to next-generation nanopatterning and nanomedical applications. Acknowledgment. This work was partially funded by the EC NaPa project (contract no. NMP4-CT-2003-500120). Andreas Larsson, Jurriaan Huskens, and Jim Greer are thanked for useful discussions. Calculations were performed using in-house clusters provided by Science Foundation Ireland (SFI) and also using the computational facilities at the SFI/HEA Irish Centre for HighEnd Computing (ICHEC).

Dendrimer Binding MultiValency at Molecular Printboards

Supporting Information Available: SM1: Protonation of dendrimer cores at low-pH. SM2: Conformational properties of ferrocene-terminated dendrimers in solution at neutral pH. SM3: Energy landscapes for ferrocene-terminated dendrimers in both monovalent and multivalent conformations. SM4: Ferrocene:printboard distance and complexation energy data for dendrimer multivalent binding.

Langmuir, Vol. 23, No. 16, 2007 8451 SM5: Comparison of conformational properties of adamantaneterminated dendritic wedges obtained with two different atomic charge sets. This information is available free of charge via the Internet at http://pubs.acs.org. LA700878Y