Supporting Information
Nanomechanical Motion of Microcantilevers Driven by Ion-Induced DNA Conformational Transitions
Kilho Eom1,2,*, Huihun Jung3, Suho Jung3, Dae Sung Yoon1,3, and Taeyun Kwon1,3,*
1Institute for Molecular Sciences, Seoul 120-752, Republic of Korea
2Department of Mechanical Engineering, Korea University, Seoul 136-701, Republic of Korea
3Department of Biomedical Engineering, Yonsei University, Wonju 220-740, Republic of Korea
*E-mails: (K.E.) and (T.K.)
Physical Principles: Cantilever’s Bending Motion Due to Molecular Interactions
The fundamental principle is the transduction of molecular adsorption (binding) onto a cantilever’s surface into the surface stress change, which results in the bending deflection change. In order to gain an insight into the relationship between molecular adsorption and surface stress change, we have considered the continuum mechanics framework. Specifically, the molecular binding (adsorption) onto a cantilever’s surface induces the intermolecular interactions Ui that depends on the bending curvature (K) of a cantilever, since intermolecular distance is dependent on bending curvature [1-4], i.e. UiUi(K). In the presence of molecular binding (adsorption), the effective potential energy for a cantilever with molecular adsorption becomes U = Uel(K) + Ui(K), where Uel(K) is the strain energy of a cantilever such as
(1)
with E, h, and v being the elastic modulus, thickness, and Poisson’s ratio of a cantilever, respectively. In other words, the molecular adsorption changes the effective potential energy U by the amount of Ui(K) which stems from the change of surface state (i.e. adsorption at surface), indicating that Ui(K) is the adsorption-driven surface energy [3]. We note that
(2)
where ui(K) is the intermolecular interactions per unit length of a cantilever. In a continuum mechanics framework, the surface energy Us is represented in the form
(3)
where is the surface stress change due to adsorption (molecular binding), and u is the strain of an upper surface on which molecular binding occurs (i.e. u = Kh/2). From a relation of Ui = Us, the surface stress change is related to the intermolecular interactions
(4)
This indicates that molecular adsorption (binding) onto a cantilever surface induces the change of surface energy, which results in the surface stress change. This surface stress change leads to the cantilever’s bending deflection change [5].
(5)
Enumeration of DNA Molecules Immobilized on a Cantilever’s Surface
Since the driving force for a cantilever’s bending motion is the conformational transitions of DNA molecules immobilized on a cantilever’s surface, the bending deflection change due to DNA conformational changes significantly depends on the number of immobilized DNA molecules. In order to ensure that our experiment may be reproducible (particularly, the amount of bending deflection), it is necessary to confirm that the number of immobilized DNA molecules is invariant between experiments. For such a confirmation, we have measured the surface density of immobilized DNA molecules, and made comparison between surface densities obtained from our experiments and available from literatures.
We have considered fluorescence probe in order to measure the surface density of immobilized DNA molecules. The details of enumeration of molecules immobilized on a surface are well described in a literature [6]. Here, we briefly describe the experimental procedure to measure the surface density of immobilized DNA molecules. First, we have immobilized DNA molecules onto a cantilever surface based on chemical conjugation between thiol (for thiol-modified DNA) and gold-coated cantilever surface. Then, the cantilever functionalized with DNA molecules (based on gold-thiol bond) was treated with -mercaptoethanol (ME) for 24 hrs, which results in the cleavage of chemical bond between thiol and gold. Subsequently, we have measured the fluorescence intensity of DNA molecules that were displaced from a cantilever due to ME-driven breakage of thiol-gold bonds using Spectrophotometers. In order to compute the density of displaced DNA molecules, we have made a calibration curve that shows the relationship between the fluorescence intensity and the number of DNA molecules. To obtain such a calibration curve, we have prepared a buffer solution (containing ME), in which DNA molecules with known concentrations were dissolved, and then fluorescence intensity was measured. Based on the calibration curve (see Fig. S1), we compute the surface density of DNA molecules immobilized on a cantilever surface. The surface density was given as 1.89 1012 molecules/cm2, which is consistent with previous study [7] showing that the surface density of immobilized DNA molecules is given as 5.7 1012 molecules/cm2. This clearly suggests that the surface density of immobilized DNA molecules is consistent regardless of different experimental setup. This has been written in the Supporting Information.
Figure S1. Calibration curves that show the relationship between amount of DNA molecules and fluorescence intensity. Black square dots indicate the experimental data obtained from a priori knowledge of amount of DNA molecules. Blue circle dot represents the experimental data obtained from ME-driven breakage of thiol bond between DNA molecules and a surface.
References
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[3]X. Yi and H. L. Duan, J. Mech. Phys. Solids 57 (2009) 1254.
[4]K. Eom, H. S. Park, D. S. Yoon, and T. Kwon, Phys. Rep. 503 (2011) 115.
[5]G. G. Stoney, Proc. R. Soc. Lond. A 82 (1909) 172.
[6]K. Castelino, B. Kannan, and A. Majumdar, Langmuir 21 (2005) 1956.
[7]T. M. Herne and M. J. Tarlov, J. Am. Chem. Soc. 119 (1997) 8916.
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