Diffusion of the MPs through the cell membrane/envelope

In this section, the diffusional path of the MPs through the cell membrane/envelope of the bacterial and mammalian cells, as they move from the bulk to the cytoplasm, is explored. In addition to differing in shape and size, the boundaries of the cells are constituted by structures with different layers and composition (Fig. 4). For instance, animal cells only possess a phospholipidic barrier, the cytoplasmic membrane. Bacterial cells possess an added barrier, the cell envelope, which by its turn has several layers, which differ between gram-positive and gram-negative microorganisms. The gram-negative bacterial cell envelope is constituted by an outer membrane, followed by the periplasmic space which comprises a thin peptidoglycan layer, and the inner cytoplasmic membrane, a phospholipid bilayer (Fig. 4). The periplasmic space normally presents a higher viscosity compared to the cytoplasm due to the presence of small molecules and it is often considered a “crowded” space22. The gram-positive bacterial cell envelope does not have an outer membrane and the peptidoglycan layer is thicker than the one present in gram-negative bacteria, followed by the cytoplasmic membrane (Fig. 4).
Moreover, both bacterial and mammalian cells have proteins channels and other components in their membranes that are responsible for the transport of molecules (Fig. 4). It is a complex structural and functional system, and a comprehensive review about this subject can be found in Santos et al. 23. The structural and chemical differences at the membrane level affect the diffusion of the MPs in the different organisms. Table 1 summarizes the average dimensions of each barrier for the different cell models here defined. For bacterial cells the capsule was not considered and the dimensions displayed for the other barriers are purely reference values, since r and L depend on the growth phase, temperature and available nutrients, among other variables24. The thickness of each layer was set based on the average of available experimental values. In theory, a lipid bilayer has a thickness of around 4 nm25. However, and most likely due to the extra constituents of the outer membrane, such as proteins and lipopolysaccharides (LPS)26, the outer membrane of gram-negative cells is sometimes considered to be thicker than the cytoplasmic membrane. In here, the core size of the bilayer was considered, keeping in mind that the diffusion in this layer may be slower than in the inner membrane.
To facilitate the interpretation, the different layers were grouped in terms of composition. The first barrier discussed here is the lipidic membrane or cytoplasmic membrane, which is the first barrier that the MPs encounter in animal cells. The outer membrane of gram-negative bacteria is also included in the lipid membranes section. The next barriers discussed are the periplasm of gram-negative bacteria followed by the peptidoglycan layers of both gram-positive and gram-negative bacteria. The latter is the first physical barrier for the MP in gram-positive bacteria, and is similar in terms of structure and chemical composition in both grams, varying mainly in thickness26.

Molecular diffusion in lipid membranes

As mentioned above, and in spite of composition differences that might affect the MP’s diffusion, the cytoplasmic membrane of gram-positive bacteria, both membranes (outer and inner membrane) of gram-negative bacteria, and the cytoplasmic membrane of animal cells are approached in the same manner.
Considering the importance of nucleic acids diffusion in lipid membranes, there is a remarkable lack of studies for modelling this process, both in bacterial and animal cells. In one of the few existing studies regarding this issue, the diffusion time of DNA probes in lipid membranes has been estimated by tracking the formation of endosomes after injecting DNA into the outer side of a liposome. For an oligonucleotide of 21 bp, the process takes around 1 s35. For in vivo hybridization, this value should be considered the lowest possible diffusion time, because it is well known that proteins and other molecules can obstruct and bind to MPs, decreasing the diffusion coefficient36. Although no exact equation is available to model this process for the probe of 10 and 40 bp, this information can be used as an indication of the characteristic time a MP takes to go through a lipid membrane.

Molecular diffusion in the periplasm of gram-negative bacteria

In gram-negative bacteria, the periplasm is located between the outer and the cytoplasmic membranes and is about 13-25 nm thick37. In addition to the peptidoglycan layer, the periplasmic space contains a high concentration of other small molecules like amino acids and peptides that contribute to the increase of viscosity in this interface38. As a result, the periplasm seems to be a gel-like matrix, which makes each molecule experience an effective viscosity during movement and, as such, the molecular diffusion in this “crowded” system diverges from a normal Brownian motion (as described in the bulk). There is limited information on particle diffusion through the periplasm, especially for nucleic acids. Most studies report lateral diffusion of proteins in different membrane layers. Such is the case of the work of Mullineaux et al. 39, which explores the lateral diffusion of the globular Green Fluorescence Protein (GFP) in the cytoplasm, periplasm, and plasma membrane of E. coli . They established that the diffusion in the periplasm (Dperi) is about three times smaller than in the cytoplasm (Dcyto), but highlighted that, in terms of physical properties, the periplasm is a relatively fluid environment, in comparison to the cytoplasm. For these reasons, it was assumed that is in the same order of magnitude as . values are provided in the section concerning the diffusion of the MP in the cytoplasm. Using the values and Eq. 1, a 10 bp probe takes 3.8 x10-7 s to diffuse through the periplasm, while a 40 bp probe, with a larger radius, takes 1.8 x10-6 s.

Molecular diffusion in the peptidoglycan

The peptidoglycan layer is structurally similar in gram-negative and -positive bacteria, mostly varying in thickness. In FISH, the diffusion of MPs through the peptidoglycan layer most likely represents the limiting step in both Grams. This is true even for gram-negative bacteria despite of their severally restrictive outer membrane, because of the fixation steps prior to the addition of the MPs, which create pores in the outer membrane, allowing the MPs to directly cross from the extracellular space to the peptidoglycan layer. Gram-negative bacteria have a thin peptidoglycan layer, whereas the peptidoglycan of gram-positive bacteria can be up to 100 nm thick26. Overcoming this layer is crucial for a successful FISH procedure, especially in gram-positive bacteria, where longer hybridization times are required compared to gram-negative bacteria (normally the FISH procedure takes approximately 120 min for the detection of gram-positive bacteria and 60 min for gram-negative)16, most likely due to the differences in thickness. The thickness of the peptidoglycan makes it particularly important to proceed with the permeabilization of fixed gram-positive bacteria, or with the enzymatic hydrolysis of the peptidoglycan prior to the hybridization of large MPs, in order to have a detectable fluorescence signal40.
Since there is no data in the literature related to the diffusion coefficient of the MPs in the peptidoglycan barrier, the difference between the commonly used experimental hybridization times in FISH for gram-negative and gram-positive bacteria was used to calculate the diffusion coefficient of the MP in the layer for both grams. For gram-positive bacteria, a diffusion coefficient of 3.5x10-19 m2/s was obtained, which corresponds to a characteristic diffusion time of 4524 s (75 min). This in agreement with the general concept that the peptidoglycan layer of gram-positive bacteria is one of the most relevant barriers in microbial FISH experiments40.