The so-called lollipop model is a biophysical model, which allows to simulate the behavior of end-tethered DNA-nanolevers on chargeable surfaces. It mathematically simplifies the hydrodynamic properties of DNA nanolevers with attached protein molecules by assuming that the DNA is a charged and rigid cylinder that carries a spherical body on top.
The model predicts the steady state orientation at constant potential as well as the switching motion of the nanolevers in alternating electric fields, based on electrostatics and Smoluchowski’s drift-diffusion equation. Solutions to the model show how the increased hydrodynamic drag caused by a protein bound to the DNA’s distal end affects the molecular dynamics of the DNA−protein complex upon electrical actuation. During switchSENSE®protein size analysis, switchANALYSIS software compares experimental switching motion curves with a library of simulated curves to extract the hydrodynamic protein diameter.
In the following, the underlying effects of the lollipop model are shortly explained.
A detailed mathematical description is published and can be found here.
- Electrostatics: The electric field at the gold-buffer interface decays exponentially from the surface and strongly depends on electrolyte properties, such as ionic strength and viscosity. Additionally, the finite charging time of the electrodes is considered for the time resolved switching curves. Due to the strong buffer dependence and the lack of a unified analytical model for arbitrary electrolytes with multivalent ions, protein sizing with the lollipop model is currently limited to our standard buffer XE40 (10 mM tris/phosphate/hepes at pH7.4, 40 mM NaCl, 50 µM EDTA, 50 µM EGTA, 0.05 % Tween20).
- Electric force: At negative electrode potentials, the negatively charged DNA nanolevers are repelled from the surface while they are attracted at positive potentials, leading to the typical switching curves for alternatingly applied potentials.
- Entropic force: The entropic effect can be visualized as follows: All possible orientations of the nanolever are equally likely. However, as the nanolever can freely rotate around its anchor point, there is only one fully upright orientation (90°), but many possibilities to lie down. This simplified picture translates into a force which pushes the nanolever towards the surface. Consequently, the observed average maximum angle between nanolever and surface typically only reaches about 60°, even at high negative potentials.
- Diffusion: The switching motion upon electric actuation is described by a drift-diffusion equation. While entropic and electric forces are directed, the diffusion term accounts for thermally induced random motion, namely the free rotation of the DNA nanolevers around their anchor point. This random motion depends on the hydrodynamic drag of the nanolever and hence on the DNA length and the hydrodynamic diameter of the attached protein. In switchSENSE protein sizing, this property is exploited for the determination of protein sizes.
- Steric hindrance: For proteins with a diameter larger than the DNA diameter, the nanolevers cannot fully lie down due to steric hindrance. To account for this effect, a potential barrier is introduced which prohibits smaller angles.