volumes as low as a few microliters. The measurements can be performed in a
solution and in living cells.
When considering the spreading ordiffusionof ions and molecules in solutions,
often it is important to estimate the time required for the molecule to diffuse over a
given distance. A key parameter for such an estimate is thediffusion coefficientD,
which has a unique value for each type of molecule and must be determined
experimentally. The diffusion coefficient typically is expressed in units of cm^2 /s and
is a function of factors such as the molecular weight of the diffusing species,
temperature, and viscosity of the medium in which diffusion takes place. The
diffusion timet is inversely proportional to the diffusion coefficient and can be
approximated by
tx^2
2Dð 9 : 4 Þwhere x is the mean distance traveled by the diffusing molecule in one direction
along one axis after an elapsed time t.
Example 9.5Consider the following diffusion coefficients for CO 2 ,glucose,and
hemoglobin for diffusion in water at 25 °C: (a) D(CO 2 )=1.97× 10 −^5 cm^2 /s,
(b) D(glucose) = 5.0× 10 −^6 cm^2 /s, and (c) D(hemoglobin) = 6.9× 10 −^7 cm^2 /s
What is the time required for these molecules to diffuse 50 nm in water?
Solution: From Eq. (9.4) the diffusion times are (a) 635 ns, (b) 2.5μs,
(c) 18.1μs.Parameters that can be examined readily with FCS include local molecular
concentrations, molecular mobility coefficients (which describe the rate at which
molecules diffuse), and chemical and photophysical rate constants (which describe
the rate at which intermolecular or intramolecular reactions offluorescently labeled
biomolecules take place). One important application of FCS is the measurement of
lipid and protein diffusions in planar lipid membranes to study the factors
influencing membrane dynamics, such as membrane composition, ionic strength,
the presence of membrane proteins, or frictional coupling between molecules.
As Fig.9.9shows, the detection volume normally is a spheroid with equatorial
axis and polar axis radii of approximatelya = 0.3μm andc = 2.0μm, respectively.
This yields a volume of around 1μm^3 or one femtoliter (fL), which is about the
volume of anE .colibacterial cell. The solutions have concentrations in the
nanomolar range for the molecules of interest. In such a case, only a few molecules
are detected simultaneously, which allows good signal-to-noise ratios for making
precise measurements on small biological units.
270 9 Spectroscopic Methodologies