Transport through the cell cytoplasm until the reaction
site
Not unlike the periplasm, the cytoplasm is considered a crowded system
due to the high concentration of molecules in the medium. In fact, it is
estimated that the macromolecular concentration in the cytoplasm is
about 400 mg/mL, 30-40 % of its total weight41,42.
The presence of these molecules increases the viscosity of the medium,
slowing down the diffusion of small molecules (Mw~ 170 -5,500 KDa) by approximately 20-50% when compared
to the diffusion in water (Dcytoplasm <
Dwater)43.
Golding and Cox44 were the first to introduce the
notion that in crowded environments, particles are subjected to a
sub-diffusing motion, by examining the motion of fluorescently-labelled
mRNA molecules inside E. coli cells. They have demonstrated that
RNA molecules move discontinuously in such cells, with periods of almost
localized motion, separated by fast “jumps” to a new position. This
type of diffusion in the cytoplasm is anomalous, due to the molecular
crowding, contrasting with the normal Brownian diffusion.
In this situation, the diffusion coefficients can be determined by
applying Eq. 3:
\(\ln\left(\frac{D_{0}}{D_{\text{cyto}}}\right)=\ln\left(\frac{\eta}{\eta_{0}}\right)=\ln\left(A\right)+\left(\frac{\xi^{2}}{R_{h}^{2}}+\frac{\xi^{2}}{r_{p}^{2}}\right)^{\frac{-a}{2}}\)(Eq. 3)
where D0 is the diffusion coefficient of a macromolecule
in water with a viscosity of η0, Dcytois the diffusion coefficient of the same macromolecule in the cytoplasm,
η is the effective viscosity experienced by the macromolecule when
crossing the cytoplasm, rp is the hydrodynamic radius of the MP, and ξ,
Rh, A, and a, are fitting parameters. ξ is an average distance
between the surfaces of proteins, Rh is an average hydrodynamic radius
of the biggest crowders, A and a is a constant of the order of 1.
D0 can be calculated using Eq. 1, and the diffusion
coefficient in the cytoplasm for any particle of interest can be
obtained by applying Eq.3. The fitting parameters for the cytoplasm ofE. coli cells are as follows: ξ = 0.51 ± 0.09 nm, rp = 42 ± 9 nm,
ln(A) = 0, and a = 0.53 ± 0.0445. Regarding animal
cells, the fitting parameters obtained for HeLa cells are ξ = 5 ± 4 nm,
Rh = 86 nm, A= 0.9 mPa.s and a = 0.49 ±
0.2246.
By applying Eq. 3 it is possible to determine the for 10 bp and 40 bp
MPs, which are respectively equal to 7.3x10-11 and
1.6x10-11 in bacteria, and 1.5x10-10and 5.6x10-11 m2/s in animal cells.
Using these values, and applying the MSD equation, the correspondent
characteristic times for diffusion of the MPs in the cytoplasm are
2.14x10-3 and 1.01x10-2 s for
bacteria, and 2.79x10-2 and
7.65x10-2 s for animal cells.
These values were obtained assuming that the RNA is located in the
center of the cells, and, as such, the maximum distance taken by the MPs
is the radius in the case of HeLa cells or half of the total length of
the cell in the case of the E. coli and B. subtilis cells(Table 1). As it can be observed, the Dcyto is higher in
animal cells than in bacteria, which is in agreement with the evidence
that bacteria have a more crowded cytoplasm than animal cells
do47.