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.