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Molecular Interactions in Surface-Assembled Monolayers of Short Double-Stranded DNA Ling Huang,†,^ Erkin Seker,†,‡,@ James P. Landers,†,‡ Matthew R. Begley,‡ and Marcel Utz*,†,§,
Center for Microsystems for the Life Sciences, ‡Department of Mechanical Engineering, University of California, Santa Barbara, California 93117, §Department of Chemistry, and Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, Virginia 22904, and ^Department of Chemistry, Hofstra University, Hempstead, New York 11549. @Present address: Center for Engineering in Medicine, Harvard Medical School, Boston, MA 02115. )
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Received March 2, 2010. Revised Manuscript Received May 18, 2010 We present an experimental study of the energetics of repulsion between end-grafted fragments of double-stranded DNA. The absorption isotherm of thiolated DNA fragments has been measured as a function of DNA chain length as well as the salinity of the surrounding solution. The results are consistent with a simple excluded-volume model of the interaction between neighboring DNA strands.
Introduction Monolayers of surface-grafted DNA molecules form the basis of genomic detection approaches, including microarrays,1 functionalized beads,2 and microcantilevers.3 The achievable grafting density, as well as the surface stress driving microcantilever sensors, is controlled by the repulsive interaction between adsorbed DNA molecules. Quantitative understanding of this interaction is therefore a prerequisite for the optimization of genomic techniques that rely on self-assembled monolayers of DNA fragments (e.g., end-thiolated DNA on gold). Here, we outline a straightforward theory without fitting parameters that quantifies the grafting density as a function of chain length and salt concentration, as well as the surface stress caused by such films. This framework is validated with both surface density measurements of double-stranded DNA of various lengths on gold surfaces and chemo-mechanical measurements of surface stress. The fragments used for genomic recognition are typically in the range of 20-50 base pairs (bp), which is much shorter than the persistence length of double-stranded DNA (dsDNA) of ∼40 nm, corresponding to more than 100 bp. At the mesoscopic scale, such molecules behave as slightly flexible cylinders, with aspect ratios between 1 and 6, as shown in Figure 1. While solutions of long dsDNA form nematic liquid crystals,4 two-dimensional arrays of grafted, short DNA molecules are not expected to undergo a nematic phase transition, since grafted hard rods do not do so.5 Instead, they align gradually with increasing grafting density because of the steric interference of neighboring rods, as shown in Figure 1A. The loss of orientational entropy and the free energy of formation of the grafting bond are therefore the dominant contributions to the free energy of the grafted film. The loss of entropy is described here in terms of the packing of slightly flexible, *To whom correspondence should be addressed. E-mail: marcel_utz@ virginia.edu.
(1) Peterson, A.; Heaton, A.; Georgiadis, R. Nucleic Acids Res. 2001, 29, 5163– 5168. (2) Mirkin, C.; Letsinger, R.; Mucic, R.; Storhoff, J. Nature 1996, 382, 607–609. (3) Marie, R.; Jensenius, H.; Thaysen, J.; Christensen, C.; Boisen, A. Ultramicroscopy 2002, 91, 29–36. (4) Strey, H.; Parsegian, V.; Podgornik, R. Phys. Rev. E 1999, 59, 999–1008. (5) Chen, Z.-Y.; Talbot, J.; Gelbart, W. M.; Ben-Shaul, A. Phys. Rev. Lett. 1988, 61, 1376–1379.
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nonoverlapping cylinders: the size of the cylinders is adjusted to reflect screened electrostatic interactions (e.g., diameters roughly scaling with the Debye length) and slight bending arising from thermal fluctuations. The latter effect is critical in accurately capturing the length dependence of surface adsorption density.
Theoretical Description Molecular Interactions. The change in free energy due to adsorption of a molecule is6 σð1 - cÞ - ΔμB þ Δ μI ðδ, L, dÞ Δμtotal ¼ kT ln ð1Þ cð1 - σÞ The first term represents the ideal gas contribution. ΔμB represents the binding energy. The third term accounts for the moleculeto-molecule interactions on the surface. Thermal equilibrium implies Δμtotal = 0. Here, σ = (d/δ)2 is the area fraction of coverage (referenced to a fully dense surface packing), and c is the volume fraction of DNA in solution, given by " # liter 2 MDNA ð2Þ c 0:16Nbp d mol nm2 where MDNA is the molarity of DNA in solution and d is the effective diameter of the molecule. This expression assumes that the (stacking) height of a single base pair is ∼0.34 nm; that is, the total molecular length L of the double-stranded DNA is ∼0.34 nm Nbp, where Nbp denotes the number of base pairs per molecule. The loss of orientational entropy of a given molecule is determined by the fraction of possible configurations that are eliminated by neighboring molecules invading the space that it could otherwise have occupied. Here, it is assumed that the surfacemolecule bond is free to rotate, such that the configuration space of an isolated molecule is a hemisphere with a radius equal to the molecular length. While the nature of the bond exploited for grafting may eliminate some orientations, such effects are negligible for high packing densities since a far greater range of orientations are (6) Begley, M.; Utz, M.; Komaragiri, U. J. Mech. Phys. Solids 2005, 53, 2119– 2140.
Published on Web 06/15/2010
Langmuir 2010, 26(13), 11574–11580
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Figure 1. (A) Schematic illustration of roughly oriented cylindrical molecules arranged with hexagonal packing, with dashed lines indicating the tip positions that are admissible. (B) Geometry of the interaction at the extreme of admissible positions. (C) To-scale illustration of the actual size (dark green), effective size (determined via isotherm modeling, light green), and adsorption spacing at a salt concentration of 1 M.
eliminated by interactions with the molecule’s nearest neighbors, as shown in Figure 1. In strict terms, when calculating the fraction of possible configurations that are eliminated by interactions, one must account for orientations where the adjacent molecules do not lie in the same plane but rather sqeeze past one another. (That is, there are orientations not shown in Figure 1 in which the molecules can “overlap” through out-of-plane rotations.) To accurately calculate the full range of possible configurations that are eliminated for a given spacing, one can conduct Monte Carlo simulations to map out the possible configuration space. This approach is detailed in the Appendix. In the context presented here, which corresponds to rather high packing densities, it is possible to represent the repulsive interaction with good accuracy by simply assuming that each cylinder is confined in its motion to a cone with an opening angle θmax in such a way that neighboring cones do not overlap. The accuracy of this approach is validated here via comparison of predictions of grafting density to experiments, as well as comparisons of the predicted interaction energy to full Monte Carlo simulations. Elementary trigonometry yields δ-d ð3Þ θmax ¼ arcsin 2L where L is the length of the molecule. Therefore, the solid angle accessible to each spherocylinder is given by 2 3 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Z θmax δ d 5 ð4Þ Ω ¼ 2π sin θ dθ ¼ 2π41 - 1 2l 0 where we have used the identity cos arcsin x=(1 - x2)1/2 for x2 e 1. The resulting interaction potential due to cone exclusion is then, per pair of spherocylinders jCE ¼ - 2kTðln Ω - ln 2πÞ
ð5Þ
The interaction energy prediction implied by eqs 4 and 5 is superimposed over the MC, resulting in Figure 2A,B (solid lines). At large separations, the cone exclusion potential overestimates the repulsion, because it eliminates configurations that are actually possible. However, at small separations, where δ/d < 2, the discrepancy falls below 1kT. We have therefore used the cone exclusion potential, rather than full MC simulations, to fit the experimental results, as discussed in detail below. Langmuir 2010, 26(13), 11574–11580
Figure 2. Free interaction energy of pairs of hard cylinders obtained from Monte Carlo integration (solid dots). The cylinder length is 2.5d. The solid line shows the cone exclusion model (eq 3) fitted to the Monte Carlo data (cf. text).
The surface density F is related to the molecular spacing via the relation σ=1/(βδ2), where β is a factor that describes the packing geometry. In the following, we assume β=(3)1/2/2, corresponding to hexagonal packing. For a given binding energy, the surface coverage can be predicted for a set of molecular dimensions by solving eqs 1-3 via nonlinear equation solvers. Effective Size of the Molecules. The change in electrostatic screening due to salinity is included by adopting an effective size that incorporates the scaling of the Debye length with salt concentration: rffiffiffiffiffiffiffiffiffiffiffiffi! d0 mol=l 1þ ð6Þ d ¼ M 2 with the reference size d0, which corresponds to a salinity of 1 M NaCl. The scaling of effective diameter d0 with length can be rationalized by assuming that the DNA molecules experience thermally induced bending fluctuations, thus increasing the effective DOI: 10.1021/la100860d
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Figure 3. (A) Surface coverage as a function of DNA concentration at 1 M salt (10, 20, 30, and 40 bp from top to bottom). The shaded regions represent the ranges of effective diameters that span all data points. The lines represent best fits. (B) Surface coverage as a function of salt (NaCl) concentration at 1 μM DNA. Best fits lead to slightly lower binding energies at lower concentrations, with correspondingly slightly larger effective diameters; these curves extrapolate to slightly lower surface coverages at saturation. (C) Effective diameters determined via fitting to experiments. The shaded region represents the predicted diameter of a cylinder that encapsulates bent molecules (with stored energy kT/2) based on computational estimates of effective elastic constants, which range from 50 to 200 MPa.7 The solid black line is for E ≈ 130 MPa, which is the value obtained from a running average of the triplets in the present DNA sequences, using triplet moduli in ref 7.
diameter of the rigid cylinder encapsulating the molecule (Figure 1B). Although the molecules under consideration here are shorter than the persistence length, even a modest amount of bending is shown to account for the results. Assume that the molecule behaves as an elastic rod that bends into an arc (for small deformation, this is quite similar to the first vibration mode), storing an energy of kT/2. The diameter of the cylinder encapsulating the bent rod is then sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi πLEdDNA 4 2 32kT ð7Þ sin d ¼ dDNA þ 8kT πLEdDNA 4 where E is the elastic modulus of the rod. The effective elastic moduli for all trinucleotides have been estimated computationally and range between 50 and 200 MPa.7 Using this range of values, eq 5 predicts an effective size that is shown by the shaded region in Figure 3C, consistent with the experimental results. Surface Stress and Membrane Deflection. The surface stress generated by repulsive interactions described above governs the performance of chemomechanical sensors that translate hybridization into mechanical deformation. This phenomenon provides an alternative experimental pathway for the evaluation of the models described above, since surface stress can be computed from the free energy of interaction.6 That is, one can predict adsorption-induced surface stresses from the model of molecular interactions described above and in turn predict the deformation of a flexible structure through elementary mechanics models. The surface stress can be computed from the molecular description above as γ ¼
1 ∂ΔμI 2βδ ∂δ
ð8Þ
Consider a thin circular membrane whose span is much larger than its thickness, such that bending is negligible. Adsorption generates a repulsive surface stress that causes the membrane to strech and bulge toward the side with the adsorbed molecules. The deformed position of the center of the membrane, defined here as Δ (see Figure 4A), can be related to surface stress by conventional (7) Munteanu, M.; Vlahovicek, K.; Parthasarathy, S.; Simon, I.; Pongor, S. Trends Biol. Sci. 1998, 9, 341–347.
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membrane mechanics: rffiffiffiffiffiffiffiffiffi 3γ Δ ¼ a 2Eh
ð9Þ
where a is the radius of the membrane and E its plane strain modulus.
Experimental Methods Adsorption Studies. Circular wells with gold surfaces at the bottom were created as follows. Holes measuring 6 mm in diameter were punched into a 300 μm thick PDMS sheet with its protective plastic sheet intact: this bilayer was then plasma bonded to a glass slide. The multilayer was then coated with an ∼6.5 nm chrome adhesion layer via sputtering, followed by an ∼30 nm layer of gold. The protective plastic sheet was then removed, such that the gold surface was only on the bottom of the PDMS wells. Prior to the adsorption study, the wells were cleaned with piranha solution, dried with nitrogen, and exposed to oxygen plasma. DNA samples were obtained in lyophilized form, dissolved in deionized water, and stored at -20 C. The sequences are listed in Table 1. Thiolated DNA (LOTxx, where xx = 10, 20, 30, or 40) was treated with 50 mM (2S,3S)-1,4-dimercaptobutane-2,3-diol (DTT, Aldrich) for 30 min to break the disulfide linkage and purified over a PD-10 desalting column (Amersham Biosciences, Uppsala, Sweden) that had been equilibrated with deionized water. After purification, oligonucleotides in all the fractions were quantified using UV-vis spectroscopy in a quartz cuvette. The absorbances at 260 nm (A260) were used to calculate DNA concentrations. The ratio of the absorbance at 260 nm and that at 280 nm (A260/A280) was used to evaluate the purity of each fraction; samples with an A260/A280 of
