The following two subsections are included as a discussion of other ideas, ways of asking and answering similar questions, and questioning what else might be important for a sound physical understanding of fluid flow at the nanoscopic scale. The first subsection discusses in more depth what role thermal fluctuations might be playing in the conductance properties of the channel. The second section suggests additional classes of experiments and complementary in vivo studies for assaying channel flow and the physiological role of osmoregulation.
3.5.1 Possible Effects of Temperature
Clearly, temperature plays an important role in regulating the transitions between the closed and open states of any channel, and in particular this channel, since it adjusts the relative importance of the free energy difference between possible conformations, as seen in eqn. 3.1. Then consider a channel, subject to a membrane tension higher than the gating tension, such that the open-channel probability is essentially unity; this is particularly easy to imagine for the gain-of-function mutants of MscL that gate at lower tensions than wild-type MscL. The pressure drop across the membrane acts to push water and osmolytes from regions of high pressure to regions of low pressure, performing thermodynamic work in the typical P V fashion. Unlike a macroscopic pipe or orifice, where the pressure drop across and volume of the pore results in work with an energy scale much larger than kBT, as we demonstrate below, the channel pore volume and relevant pressures result in work with an upper bound energy scale on the order of kBT, suggesting that the pressure driven fluid movement through the pore must compete with fluctuations in fluid flux in the pore produced by thermal fluctuations. Our estimates of the channel volumetric flux using Aristotelian dynamics is flavored with the notion of variability in fluid flow due to thermal fluctuations, because it expressly acknowledges that the driving force is acting in concert with diffusion.
As mentioned earlier, the pore diameter of MscL is approximately 3 nm, and spans a thickness of ∼2.5 nm, giving the pore a total volume of '18 nm3. The pressure drop across the membrane spans a large range, depending on whether we are considering micropipette aspiration experiments, with pressure gradients on the order of 1/100th of an atmosphere, or pressure gradients experienced by living microbes which can be as high as ∼ 3 atmospheres [157]. Given that at any one time the pore contains∼18 nm3 of fluid volume, this means moving that volume across the membrane corresponds to a change in free energy of∼0.005kBT at lower pressures up to∼1kBT at higher pressures seen in the real physiological setting. In either case, though especially in the lower pressure scenario, this estimate suggests that fluctuations in the movement of fluid through the pore, caused by temperature, might play an important role in the channel’s flow properties. For instance, thermal fluctuations have been theoretically predicted to affect the conductance of other, lower conductance channels [168]. Even the physical state of water in a nanoscopic pore is thought to be variable [169]. Likewise, our own estimates point towards fluctuation playing an important role, where we estimated the diffusive root-mean-square velocity of water through the channel pore was 100 times faster than the drift velocity of water through the pore due to a pressure gradient. To put this fluctuation in more biologically familiar terms, this is querying the processivity of volume movement through the channel. This is analogous to querying the processivity of forward motion of a molecular motor [170,171], where the free energy difference between motor steps is often small enough that thermal fluctuations cause the motion of the motors to be less than fully rectified, hence effectively slowing down the processive motion of the motors. By analogy, we would expect this fluctuation in fluid movement to cause a generic decrease in the rate of volume flux, though this qualitative prediction certainly does not account for all the effects in play, and awaits experimental
verification.
For purposes of comparison, consider the free energy change of a typical mono-valent ion mov- ing down an electrochemical gradient. A typical transmembrane potential is ∼ 50 mV [1], which translates into a free energy change for an ion moving from one side of the membrane to the other of ∼ 0.05 eV ' 2kBT. Typically, ion channels hold multiple such ions in their pore at any one time, and hence to make the analogy complete, the free energy to move the entire chain of ions through the channel pore, down the electrochemical gradient, is closer to∼20kBT. This is simply to say that for two classes of channels whose function on the coarsest level is similar, that is, to move ‘things’ across the membrane, their detailed mechanisms may be quite different. Likewise, the entire interesting and pertinent realm of physics concerned with electro-diffusion and electro- chemical flows [172] lies well outside this author’s range of expertise, but given that life exists in, and crucially depends on high ionic concentrations, these physics of material transport may yet be an important piece of the nanoscopic fluid flow puzzle.
3.5.2 Interesting Possibilities
While designing, modeling and obtaining preliminary results for this experiment, other interesting ideas for future experiments were generated. We will briefly discuss a few of them here, to keep a record of some possible future directions. The first, and probably simplest extension of this experiment would be to employ fluorescent dyes as an additional readout of material transport across the membrane. For instance, GUVs could be formed that contain ionic calcium at the millimolar level, and after formation could be transferred to a solution containing calcium sensitive dye [173]. Given that the MscL channels are not ion selective [147], the calcium would exit the vesicle and light up the solution around the vesicle. In principle, one could measure the rate of increase of fluorescence, properly corrected for photobleaching, and ascertain the rate at which dye, presumably at a controlled concentration, must have exited the vesicle. Or alternatively, one could use fluorescence correlation spectroscopy to measure the in situ change in concentration of dilute dye molecules in the vesicle to get the same generic readout [174,154].
In the microbial setting, cells that express GFP, or a similar large fluorescent genetic marker, could be loaded with a small organic dye of a different color. Cells could be adhered in a flow chamber where the osmolarity can be quickly and precisely changed. Prior to osmotic down shock, a wild-type cell or cell line expressing MscL would be two colors from the two different markers, and then after down shock, only the protein marker would remain in the cell, hence a large color shift upon hypo-osmotic shock. In a mutant strain missing the genes encoding for mechanosensitive channels, the osmotic down shock should burst the cells allowing both fluorescent markers to escape and hence the mutant cells would go dark under hypo-osmotic shock. In both cases, high speed video microscopy could be used to track the fluorescence changes over time to estimate reaction time of the osmoregulation proteins and rate of passage of the osmolytes.