Monitoring translational diffusion of single molecules in solution or in a living cell, particularly DNA and proteins
brings valuable information unperturbed by interaction with an artificial surface. The article derives theoretical relationships
for time intervals during which just one molecule in the effective probe region can be studied, the time we call
meaningful time. This time is greater than the transit time of the molecule through the detection volume, as a single molecule
will likely reenter the detection volume several times during measurement. From the infinitely stretched molecular
Poisson distribution of single molecules or particles, we select the contribution of the selfsame molecule or particle by applying
rules for choosing appropriate statistics for the single-molecule trajectories. The results point to a useful and sensitive
predictive power of the derived relationships. The meaningful time relationships are the criteria to check the experimental
single molecule data measured under conditions of normal and anomalous Brownian diffusion of the molecules of
interest. At femtomolar bulk concentration, it would be possible to observe an individual molecule over a second time interval
or longer during which biological processes — and not conformational biophysical changes — are just starting.
Keywords: Single molecule, Brownian motion, translational normal diffusion, translational anomalous diffusion, solution, live
cell, theoretical relationships for time intervals during which just one molecule in the effective probe region can be studied,
meaningful time, single molecule spectroscopy, single molecule imaging.
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