Discussion
Determining the characteristic time of diffusion of MPs is of great
value in biochemical engineering, and, specifically, it could help
defining the limiting step in the hybridization process in FISH,
establishing the problematic of the hybridization efficiency either as
an equilibrium problem or a kinetic problem. In here, the characteristic
time spent crossing each barrier in the cell by the MPs in a FISH
procedure, from the bulk solution to the reaction site, was determined,
taking into account the chemical and physical differences between
bacterial and animal cells. The obtained diffusional characteristic
times are summarized in Table 2.
Overall, the limiting step for the diffusion in bacterial cells seems to
be the peptidoglycan layer. In animal cells, the cytoplasmic membrane
does not impose a significant barrier for diffusion and, therefore, the
limiting step for the diffusion of MPs is more likely to be in the bulk
solution or in the hybridization reaction step.
There are very few studies regarding the diffusion of nucleic acids
through bacterial and animal cells, and, for that reason, several
adjustments were made to simplify the model here presented. For
instance, the gram-negative outer membrane is considered an asymmetric
lipid bilayer, whose inner side is composed of phospholipids and whose
outer side is a LPS layer. The LPS net negative charge is higher than
the negatively charged phospholipids, and it is known to decrease the
permeability of the outer membrane to hydrophobic compounds. In E.
coli , studies show that the outer membrane limits the penetration of
PNA, with the LPSs as the major accountable factors52.
The neutral charge of PNA and its relatively high hydrophobicity
compared to charged oligonucleotides was pinpointed as the probable
cause for the PNA’s limited diffusion in the E. coli ’s outer
membrane. After passing this initial barrier, the molecules face the
peptidoglycan layer, which in E. coli , due to the thickness of
the layer, was shown to not impose a significant barrier to PNA
passage52. This might not be true for gram-positive
bacteria, which, due to the lack of an outer membrane with LPSs as the
first protection barrier, instead present teichoic acids that limit the
permeability to hydrophobic compounds, and a thicker peptidoglycan layer
that may significantly retard the penetration of PNA. In the case of
negatively charged nucleic acids, such as DNA and LNA, they need to
overcome the electrostatic repulsion of the LPSs, also negatively
charged, in order to cross the outer membrane. Moreover, the outer
membrane also presents channel-forming proteins, called porins, which
allow the passage of hydrophilic compounds and large
molecules53. The passage of most nucleic acids with
around 2–4 kDa in size across the outer membrane is very unlikely
because porins are only permeable to molecules with 0.7–0.8 nm in
diameter and 600 Da in molecular weight 54.
In the peptidoglycan layer, measurements of the penetration of
polysaccharides show that the peptidoglycan and its associated anionic
polymers provide an open network which is accessible to molecules of
molecular weights in the range 30 KDa to 57 KDa. The molecular weight of
the MPs used in here is smaller than this range (3 KDa and 12 KDa for 10
bp and 40 bp, respectively), and probably because of the small MP size
the diffusion of these molecules is facilitated. The permeability
properties of gram-positive cell wall may be dependent upon the nature
of the peptidoglycan, particularly its degree of cross-linking and the
glycan chain length36. Moreover, the fixation and
permeabilization steps, typically performed in FISH/FIVH, may lead to
altered membrane structures, facilitating the diffusion through this
barrier.
All of these particular specifications at the bacterial cell envelope
level were not taken into account in the model, and therefore the
characteristic times showed in Table 2 caress from further optimization,
since they might be underestimated specially for the diffusion in the
outer membrane of gram-negative bacteria, and overestimated in the case
of the diffusion in the peptidoglycan layer.
For animal cells, passive diffusion of nucleic acid mimics is very
unlikely because the phospholipid bilayer only allows the passage of
small, relatively hydrophobic and uncharged molecules, limiting the
uptake of charged molecules of any size55. However,
there are studies indicating that antisense oligonucleotides may be
easily and rapidly internalized by endocytosis, and then transported
through multiple membrane-bound intracellular compartments, which may
retard cytoplasmic diffusion56. Therefore, the
diffusion of molecular probes might not be limited by the phospholipid
membrane of mammalian cells, yet it might be compromised in the
cytoplasm and/or bulk solution.
Considering the hybridization reaction of the MPs, the values presented
in Table 2 were obtained assuming a two-state model to simplify the
system. However, during hybridization the MPs and the target RNA can
undergo other configurations (folded or unfolded), as presented in the
work of Yilmaz et al. 57. This way, the
reaction time might be slower than the one presented here. Moreover,
parameters related to probe affinity, such as Gibbs energy, were not
considered, and the model was built only considering the kinetics of the
hybridization. The fluorescence intensity of the cells and, thus. of the
FISH method, is influenced by the accessibility and affinity of the MPs
to their target site, which can be defined thermodynamically by an
overall Gibbs free energy change (ΔGºoverall).
Thermodynamic measurements should be further associated with
hybridization kinetics studies, in order to obtain a more realistic
model of the MPs hybridization in FISH57,58. Also, the
diffusional time for a MP to cross the ribosome and reach the target RNA
was not considered, which may affect the overall time of a FISH
procedure. Ridgway et al. 59, simulated the
diffusion and reaction kinetics in a crowded virtual cytoplasm, usingE. coli as a model. They established that the diffusion time
necessary for the largest particles in the cytoplasm to cross a ribosome
is roughly around 10−7 s and 10−6 s.
FRAP takes advantage of the permanent loss of the fluorescent signal
when exposed to a beam of intense light (bleaching). After bleaching of
the selected region, the photobleached molecules diffuse out of the
bleached area and fluorescent molecules diffuse into it, allowing the
recovery of fluorescence in the same area. Using a low-intensity light
source, it is possible to image and monitor the movement of the
molecules, and, as such, obtain the time necessary to recover the
fluorescence signal in the selected region, or the recovery-rate
constant. Such parameter is related with the diffusion coefficient of
the molecules in that setting60. FRAP has been used to
study the motion of fluorescent molecules in solution, on cell surfaces
and within the cytoplasm39,61,62. The model presented
here could greatly benefit from well-designed FRAP experiments to
determine the diffusion coefficients of the MPs in each diffusional
barrier, ultimately leading to an overall diffusion and uptake rate for
the MPs in FISH, in order to better fit the approximation to the oxygen
transfer model.