Fluorescence Fluctuation Spectroscopic Approaches to the Study of a Single Molecule Diffusing in Solution and a Live Cell without Systemic Drift or Convection: A Theoretical Study

Abstract

Reentries of a single molecule in the confocal, femtoliter-sized probe region (about 10(-16) L and less) are significant because during measurement times they give rise to fluctuation phenomena such as molecule number fluctuations at the single-molecule level in solution without immobilization or hydrodynamic focusing. These fluctuations are the fundamental physical process on which, for example, fluorescence correlation spectroscopy and two-color fluorescence cross-correlation spectroscopy are based. The reentries of just one molecule in the confocal probe region are theoretically examined in this original article using a hidden, continuous-time Markov model. The system is not set up to have systemic drift or convection. It is found that the reentries obey certain conditions and analytical expressions for the reentry probabilities are obtained first. In particular, the time constant of the mean value and the variance of the reentry probabilities are obtained. The fractions of non-meaningful reentries and meaningful reentries are found for these experimental situations. Therewith, the concentration dependence of the meaningful time that one can study bimolecular reactions of the selfsame molecule in the confocal probe region is derived for the first time. The meaningful time in the probe volume is proportional to the diffusion time of the selfsame molecule and related inversely to the size of the given confocal probe volume. For small molecules, i.e. small diffusion times at a given size of the confocal probe region, one needs lower concentrations of molecules of the same kind in the bulk phase, whereas large molecules can be studied at higher concentrations. The selfsame molecule scenario is compared with the molecular scenario that a second molecule enters the probe volume at random as a function of the meaningful time. The analytical solutions of the physical reentry model (mechanism) hold for the one-, two- (membrane), or three- (solution, live cell) dimensional Brownian motion.

Reducing Background Contributions in Fluorescence Fluctuation Time- Traces for Single-Molecule Measurements in Solution

“…Our obtained results pave the way for single-molecule detection in solution at longer observation times that are currently not available [12][13][14]. The concentration of the liquid by dilution is so small that the detection volume contains a single molecule or two or three single but different molecules.…”

“…Their random motions in a liquid solution are detected by recording the fluorescence fluctuations. The time that a single molecule is in the observation volume and the second and third are not can be precisely calculated under such experimental conditions from first physical principles [12]. To study it definitely at the level of single molecule interactions has, up to now, surpassed the capabilities of modern instrumentation.…”

“…In order to achieve detection sensitivity at the 'single-molecule level', the count rate per molecule per second (CPM) is an important parameter [9][10][11] as well, but background rejection influences the amplitude of the correlation function [9][10][11][12]. For example, the 'background' of high concentrations of autofluorescent molecules can easily hide the low signal from the specific fluorescent molecules and makes weak fluorescence signals extremely difficult to detect.…”

“…A lack of diffraction limited optics is usually not a problem in normal FCS; the detection volumes are often enlarged in order to have time for studying different biophysical and biochemical reactions. However, an enlarged detection volume hampers the observation of just one single molecule in solution [12][13][14][15].…”

Quantitative fluorescence nanospectroscopy of nucleotide excision repair : from single molecules to cells

“…FCS provides information about the translational Brownian motion of fluorescent molecules in solution. Since it was invented in the beginning of 1970s, booming applications has been proposed and developed in FCS [88,89,91,[219][220][221]. Recently, we reported an on-line quantitative FCS technique for the study of soluble protein stability [69].…”