Optical Trapping and Accumulation Of Nanoparticles

A recent paper in Nature Biotechnologl has pointed out an unexplained discrepancy in miniature biosensors between theoretical binding rates and experimental results. 1,7 For extremely dilute (sub-femtomolar) solutions the binding delay time calculated based on diffusive and convective transport of target molecules to miniature sensors are impractically long in contrast to recently measured experimental times. A particular example of this discrepancy is the large binding rates (one hundred times larger than estimated in Ref. (6)) of bioparticles to an optical Whispering Gallery Mode (WGM) micro-toroidal bio-sensor.7 After discussing their convectionreaction- diffusion theory, the authors of Ref. (6) conclude "that additional, yet undetermined ingredients (beyond what we have incorporated here) must be present in the experiments". We have made an observationS in the case of spherical and toroidal WGM sensors that an optical mechanism, not discussed in Ref. (6), considerably enhances binding rates. Nanoparticles suspended in aqueous solution are normally in Brownian motion. However, within the reach of the WGM's evanescent field (~200 nm) nanoparticles are drawn toward the surface by gradient forces, similar to those present in optical tweezers. The gradient forces draw the nanoparticles towards the high-intensity region of the evanescent field from where they tend to adsorb and accumulate on the surface of the resonator (Fig. 1, example for a toroidal resonator).

In the case of a low binding-affinity or a low density of binding sites, the nanoparticles are propelled around the orbit by radiation pressures. Within this orbital trap, radial stochastic motion is induced by thermal energy within the exponential-potential-well setup by the evanescent field, forcing a nanoparticle to visit the surface many times per micron during its circumnavigation. As a result binding is essentially assured once the nanoparticle is pulled into this stochastic orbit. This considerably increases the binding rate even in the presence of very few binding sites and at extremely low nanoparticle concentrations (fM). In addition the nanoparticle is drawn to the highest intensity of the WGM where its presence produces the largest sensing signal (i.e. wavelength shift). We have been able to successfully model the particles drift speed around the circumference, and the minimum threshold laser power required for orbital trappings. We find that the binding energy W b is proportion to the product of the resonant quality factor Q and the laser power P. Surprisingly, the threshold power for virus-sized particles is in the one hundred microwatt range due to the build up in intensity caused by the high Q of our WGMs (~106 - 107). Thermal energy plays the major combative role in trapping. The trap is secured by raising the binding energy Wb associated with the radial gradient force by a few times the Boltzman energy, kBT. In the presence of appropriate antibodies at low densities on the surface, the bio-particle binding probability is extremely high. The advantage of this mechanism is that it attracts the particles to the largest intensity within the WGM orbit, which increases their concentration at the place of maximum sensitivity on the resonator surface. The results of this workS can add understanding to single molecule detection limits and are applicable for quantitative analysis of the WGM bio-sensor measurements at ultra-low concentrations. The orbital trapping mechanism with high Q WGM sensors is unavoidable considering the low power level at which this opto-mechanical effect occurs. Opto-mechanical forces have already been demonstrated above optical waveguides for the transport of particles (diameter> 500 nm)8 at considerable higher laser power levels (~ 50 mW). For WGM biosensors having a Q ~ 107 this power level can be reduced by more than 1,000 times, which is expected to make the phenomenon we have described here difficult to avoid.

 

 

A: Scanning electron microscope image of a ~ 80 ?m diameter toroidal resonator. B: Fluorescence image of the same resonator immersed in a solution with 200 nmdiameter polystyrene particles. The nanoparticles are found to bind and accumulated predominantly at the equatorial region of the WGM light orbit. The inset shows greyscale values averaged for several line-scans taken across the center of the toroid.