The journey: from the bulk solution to the target RNA
site
As stated above, the transport of chemical species within physical
systems is ubiquitous on different engineering disciplines, such as
chemical and biological engineering. Taking as an example the oxygen
transport in bioreactors, it is possible to make an analogy with the
transport of the MP from the bulk solution to the reaction site within
the cells (Fig. 1).
In bioreactors, the oxygen is transferred from the gas bubbles through
different interfaces, until it reaches the cells for uptake (Fig. 1A)9,10. This way, the first interfaces involve the
transfer of oxygen from the gas bubbles to the liquid phase (gas-liquid
interface), and the diffusion of oxygen through the bulk liquid
(liquid-cell interface). The subsequent interfaces involve the cellular
uptake of oxygen from the bulk to and within the cytoplasm to the
reaction site. In this model, the variation of the dissolved oxygen’s
concentration in time within the bioreactor depends on the oxygen
transfer rate (OTR) and on the oxygen uptake rate (OUR).
Analogously to oxygen transfer, for the MP to reach its target, it first
has to diffuse from the bulk solution, and cross the cellular
membrane/envelope and the cytoplasm until it reaches the RNA site for
hybridization. The diffusion process is based on a concentration
gradient over time (Fig. 1B). It is important to notice that, in
contrast to oxygen in aerobic bioreactors, the MPs are not continuously
added to the system. Instead, the quantity of the MP applied is
significantly higher than the number of cells/RNA available for the
reaction, in order to ensure a high concentration gradient throughout
the entire process. In fact, in a standard in vitro FISH
procedure there are around 200 MPs per ribosome. It is important to
notice that the steps regarding oxygen transfer from the interior of the
bubble to the gas-liquid interface and then to the bulk (Fig. 1A, step
1-3) are not applicable in a probe diffusion scenario, as the MPs are
already in suspension.
Additionally, in the oxygen transport models, a liquid film around the
cells/solid particle is considered (Fig. 1A step 5 and Fig. 1B step 2).
The film theory is the simplest premise for interfacial mass transfer,
and assumes the existence of a stagnant film, also called unstirred
layer, near every interface. It represents the resistance to mass
transfer that might occur near an interface, and is almost always
hypothetical since the motion of the fluid occurs even in a solid
interface12. Due to the lack of available data for the
MP’s concentrations in the interface, an overall process, where the
cellular membrane/envelope is the first barrier for the MP’s diffusion
from the bulk solution to the cytoplasm of the cells, can be considered
instead (Fig. 1B, step 2).
The characteristic time is defined as an estimation of the order of
magnitude of the time required for a process to reach equilibrium. In
chemical engineering, it describes the dynamics of a system, for
instance the residence time in well-stirred tanks13.
In here, the characteristic time will give an estimation of the limiting
step for diffusion and provide further insights on the circumstances
under which FISH needs to be approached as a diffusional problem or a
reaction kinetics problem.
In the following sections, the characteristic times associated with the
transport through the bulk liquid, the diffusion across the cell
membrane/envelope and in the cytoplasm, and, finally, the reaction of
the MPs with their target RNA will be estimated for 10 and 40 base pairs
(bp) DNA-MPs. The diffusion of the MPs through the cell
membrane/envelope is further characterized taking into account the
cellular differences between E. coli , Bacillus subtilis(B. subtilis ) and HeLa cells, as respective models of
gram-negative bacteria, gram-positive bacteria and animal cells.