Monte Carlo simulation of single-molecule trapping via electrophoresis

For many biophysical studies, there is a need to observe a molecule for an extended duration without immobilizing it on a surface. The problem of trapping a single fluorescent molecule in solution is examined here via Monte Carlo numerical simulation.~ Optical forces are insufficient for trapping small molecules. Instead, trapping is executed by sensing the position and applying real-time feedback of flow to compensate diffusional displacement. Using a nanochannel as the volume of interest reduces the problem to one dimension, and with such a configuration the position of the molecule can be measured from its fluorescence in the presence of a two-focus irradiance pattern.~ The collected photons are analyzed by an algorithm developed for a field-programmable gate array controller for experimental implementation, and an electrophoretic flow provides the trapping mechanism.~ Trapping is also possible in three dimensions with two-photon excitation of the molecule from a four-focus irradiance pattern arranged as a tetrahedron or with a single focus scanning over a three-dimensional volume.