The hydrodynamic problem of Intracellular drug delivery
The problem of intracellular delivery is not only about permeating the outer membrane but also about mixing with the inner ones; when the state matters and when it doesn't.
Following is an excerpt from an email exchange on the topic of why measuring the thermodynamic state is important in violent hydrodynamic forcing (through processes like micro jets ) of drugs into cells and bacteria.
When we use the word “state” we mean knowing the location of the system on scalar function S(x) (a hyperplane), which is at least known locally on (x), where x is a vector with a basis that depends on what quantities you want to follow or observe e.g. energy, volume, charge, ion concentrations. This is the equation of state. The equation of state is essential for solving both the hydrodynamic problem (streaming, jets, cavitation, collapse, shocks, etc.) and physical chemistry problem (reaction, kinetics, permeability, etc.).Every problem in mechanics that concerns us is essentially an optimization problem on entropy with conservation laws as constraints. The equation of state embodies the second law in our calculations. This is the very idea behind Hugoniots in shock theory (an example of a violent hydrodynamic process). I know some don’t prefer such generalist viewpoints, but let me give an example of how the microjet-based concern are implicit and taken care of in the state-based approach.
In a thought simulation, what equation of state should be used to solve the hypothetical jet in the vicinity of a cell? We should remember any assumption we are going to make has a direct bearing on whether our solution satisfies the second law or not. Let say we are willing to violate it a tiny bit ( as we usually do) and assume the water is incompressible and is also not affected by the presence of the membrane. We allow the membrane to be compressible, but again violate the second law a little bit and say the compressibility is constant. Then you will agree that by having cells of different types of same shape and size, the dynamics of the jet is not going to change. Then if the jet is strong enough it will “cut through” any soft material and the state would not matter.
But the story doesn’t end here. You are correct that the state of the membrane doesn’t matter significantly (i.e..we violate the second law only a little bit) if we want to predict the flow patterns of the jet, but it still matters if want to find out if the jet is capable of having any biological effect. The inside and outside of the cell are separate not just because there is membrane in between, the whole inside of the cell also wants to stay away from water. See the picture attached showing how the entire inside is full of membranes. So even if you force a pocket of water containing genes inside the cells using some highly violent nonequilibrium process. It will still just form a new isolated environment inside the cell and not result in a biological action. This is a big problem of “endosomal escape” in the delivery of large molecules. There is no hydrodynamic way around it. If we violently break this pocket you will end up forming more pockets. Now one may argue what if we keep breaking it? First of all, we need to remember there is a whole-cell around which we will scramble completely too in the process, but the problem is more fundamental and similar to that of mixing oil and water hydrodynamically. We can only mix the two macroscopically but not microscopically, to do the latter we need to be able to affect the chemical potential or the partition coefficient of the drug to shift the equilibrium such that it is enriched at the target. From a macroscopic perspective, the chemical potential is also a function of the state, microscopically it can be understood in terms of solvation of the molecule and hence depends on the dielectric of the environment.
Then how physical forces can affect the process? In either case, one needs to understand the change in state (i.e. changes in susceptibilities, which allows changes in — compressibility, heat capacities, and dielectric). This is where soft matter physics is the key. All equations of states are nonlinear when observed for a large enough range of pressure, temperature, etc. In the usual engineering materials, we don’t encounter these nonlinearities easily. They are only important in the so-called “equation of state limited problems” (there might be other names for them too). Therefore, we hardly come across a problem where we can change the solubility in a hydrodynamic problem. In soft material, this is completely different, for example, the compressibility of the material changes significantly even for small pressure or temperature changes. This is further amplified if there is a phase transition. We can not drop the higher-order terms in the equation of state anymore without significantly violating the second law.
But this is not the problem if we directly measure the resulting instantaneous state or measure instantaneous compressibility (S”(x)). So even to decide if a peculiar hydrodynamic field (including microjets) is going to have a desirable bioeffect we either need to measure the effect on the state or predict it. I prefer measuring because then we don’t violate the second law even by mistake, and we make no fits or model assumptions to make predictions. Quasi-static state change experiments give a good initial estimate of how the state has to be changed to have a desirable effect but dynamics add another aspect which is the timescales. You can apply 1MPa to a lipid system but it will roughly take 1ms to have the complete effect, the minimum timescale needed to have a significant effect is of the order of 10us (100kHz). In addition, shear forces can increase diffusion constants while cavitation can reduce it. Small amplitude pressure impulse can reduce it during compression and increase it during rarefaction etc. We have measured and seen this happening in simple membrane now we need to do it in cells, but given the complexity, it will also require new tools, however, this doesn’t change the approach.
