[first posted: 1.25.17/most recent edits & additions: 2.28.17]

Preamble: this conjecture relates to aspects of fluid mechanics that are extremely fascinating and far from understood at the fine-scale level of detail in which the cell likely operates. Although the discussion here is schematic only, it is presented because it relates to Topics I: Isotopes in the Cell?, VII: Isotopes, Nuclear Spin & Chirality?, and IV: Asymmetry in the Cell Nucleus as a Means for Driving Torque?. This leads to a much more broad discussion about protein geometry and the advantageous fluid dynamical properties their shape can provide when placed into cell currents. This subject of protein shape and fluid currents will be detailed here in the spring. For now, the subject is best introduced with a short story...

Hypothesis: No specific hypothesis is stated for this topic, but there are a few general points of consideration that are pertinent the hypotheses in other sections. Foremost, is the recognition that when we look through a microscope, the motion we see in the cell - or sometimes the motion we don't see - is the sum of a great many forces acting on the elements under review. Because gravitational forces are weak and change is only noticed over relatively long timeframes, we sometimes forget that underlying the hyperfine balance we see in fluids are properties such as pressure, or velocity, or vorticity, which are each inertial in nature and therefore significantly influenced by gravitation and centrifugal forces. Accordingly, when we view the rotation of a molecule, or the torque that one molecule imposes on another, or even when we view a polypeptide chain that must fold precisely for it to function as a protein properly, we should not exclude the possible action produced by changes in the background acceleration frame that the cell resides in.

December 2016; Oakland, California. We were 7 days into a relatively rainy and cold period (for us, that means temperatures in the low 40 degrees F). It was Christmas time, so the caretaker of our cluster of townhomes had been on vacation. Happening upon the pool (unheated during the winter) we saw this single leaf floating perfectly still in the water about a foot below the surface.

Just sitting there motionless...so calm, so beautiful in the clear water. Totally at peace. We returned to the leaf several times during each of the next three days just to observe - even enjoy - its stillness. On the forth day, when we went for our visit, we found it had sunk to the bottom - to thereafter rest beside the other leaves. We then sat there in the warm sunlight and contemplated what we would do for the rest of the day.

Inspiration for a poet? Perhaps. But it was inspiration for a scientist too as well - here is why.

Why would the leaf float at a point one foot below the surface of the water? We were not there when the leaf arrived, but presumably the leaf started its journey by falling into the pool and initially floating on the surface. And sometime later, after becoming waterlogged and thus slightly heavier, it started to sink. But instead of continuing its one-way trek downwards to position itself beside all the other waterlogged leaves, it stopped at a point only part-way down. Quite probably, this was the result of our weather: the cold dense water likely sank and without the pool's caretaker there to activate the water pump and stir the water, the water density became stratified, and the leaf came to rest at the point were its density matched that of the water. Four days later, when the sun came out, the water warmed up and the density beneath the leaf lessened, and the leaf sank. The phrase 'quite probably' is used here, because no temperature measurements during the 4-day event were taken.

[Note: with respect to cellular evolution, where might we find a similarly stable environment for the external gravitational forces and the local fluid pressure gradients to interact with the inertial forces of objects within the cell in a sufficiently subtle manner that allows small but advantageous alterations in configuration to be explored? A quick observation finds one such environment right beside the pool in the heart of a tall redwood tree. The cells in the trunk of the tree don't have to endure all the rapid pressure changes and tidal chaos experienced during the normal day of animal and insect cells. (See also the discussion in Topic XI about tidal forces in the cell). Indeed, insect and animal cells must have developed methods for managing the physical changes brought about by the wandering life of their hosts. Thus, if we know what to look for, we should be able to see this expressed in structural differences between plants and both animal and insect cells.]

When we look at familiar images of the cell, we typically see organelles shown floating around in the cytosol. Two such examples are shown below. Although, in both of these images, artistic license was taken to not clutter up the illustrations by including the structure of the cytoskelton, one cannot help but notice the similarity between these 'floating' organelles and the floating leaf in the pool. Even the water looks the same.


*[Our apologies to the artists; we have lost track of where these downloaded images came from].

Now, although the cell is roughly 70% water, the cytosol is considered more of a viscous gel. But, the principles in this discussion are independent of viscosity. One other difference between the cell and the pool is the 'sense of down'. When standing by the pool, our sense of down is associated with the direction to our feet - the direction in which a ball falls. But in a closed environment like the cell, the sense of down is not so easily established. In the cytosol, relative density tends to establish the direction in which objects fall. If the cell is still, then objects with a density lighter than the cytosol will 'fall' up - in a direction opposite to the direction to the earth. In fact, it can be argued that the sense of down in the cell seems to always be oriented in the direction of the nucleus; this point will be expanded on later. For the present, let us revisit our leaf and consider its stillness a little more closely.

What is interesting about the stillness of this leaf is that it is a stillness resulting from a perfect balance between the weight and shape of the leaf and the fluid properties of the water (temperature, density, viscosity...). Without diverting into a philosophical discussion, there is an important difference between an object that is still because no forces are acting on it and an object that is still because it is being held still - the latter case being the result of any number of forces perfectly balancing each other. Although it is our general preference to not metaphorically detach an object from its environment, and our further preference to not anthropomorphize inanimate objects, let us break both of those rules here and consider what actions the leaf might take if it wanted to alter its position in the water, and what actions the water might take if it wanted to move the leaf.

Leaf. If the leaf were to tuck in its extremities, then its density and sedimentation coefficient would increase and thus, won't this cause the leaf to start to sink? And if the leaf were to fold itself up even tighter, then wouldn't that increase its rate of fall? Isn't this exactly what the skydivers above learned? And, once the leaf is falling, then can't it produce a rotation by only folding in one side and leaving the other side extended to cause an asymmetry in the drag? While it may be peculiar to think about accelerations and drag forces on an object that is barely moving, its speed and orientation should always be thought of in terms of a balance between these two opposing actions. Another means for the leaf to move is by inducing a chemical reaction that changes its mean density. This is much like the 'tuck' method, for it also results in a change in buoyancy (the method of submarines) but it occurs on the molecular level. We might imagine how, if the leaf could controllably release internal oxygen in the form of air bubbles and keep them attached to its surface line a fine layer of buoyant fur, the leave could make itself rise.
[See an interesting article about the size limit on the formation of liquid jets during bubble bursting at: http://www.nature.com/articles/ncomms1369]

Water. The water may cause the leaf to fall by warming its temperature, and/or by altering its viscosity. If the water knows when the leave begins its journey, it may cause the leaf to come to rest at a higher position by cooling its temperature below the temperature it finds itself at now, or by increasing its viscosity. The water may also cause the leaf to move or rotate if it can generate water currents on the large scale or possibly H-bond water manifolds on the small small scale. (See Topic IX.)

Note that more options remain open to both the leaf and the water if the actions are taken when the leaf is still falling and located as high in the water as possible. This is because motion represents kinetic energy, and height provides potential energy - both of which are resources that can be tapped to perform work. Once the leaf comes to rest on the bottom of the pool, no gravitational potential energy is available to it and motion can only be induced by tapping internal potential energy. See the 'popcorn' discussion in Topic 2, and the reference to it further below.

[What is also relevant to this discussion is that options are provided to both the leaf and the water if they have the means to tap into changes that occur to their external environment. And, while these changes are typically perceived as inconsequential, the changing positions of the sun and moon relative to the pool, and the small changes in acceleration they introduce can play a role here. See Topics III, IV, and X.]

If we borrow our leaf again and conceptually reform it into both the large and small sub-units associated with a ribosome, then their images in the water would look schematically like that pictured below. To note is the imagined likely relative heights of the small and large sub-units. With their sedimentation coefficients given by 40S and 60S, respectively, then when falling in a hyperfine density or temperature stratified medium, the less dense 40S sub-unit may be expected to settle into its functional, 'still' position slightly above the 60S sub-unit. It is worth considering how - if the two sub-units come to rest in positions separate from each other - the water might bring these two units closer together? One means relevant to Topic IX (H-Bond Water Manifolds in the Cell) would be for the water to initiate a local rotation about the vertical axis and position that rotation between the two bodies. This would throw the more dense water outwards and leave a less dense region in the between the sub-units - thus, drawing the two parts together. [This notion will be developed later.]

....

[See also Topic IX: H-bond Water Manifolds in the Cell.]
[Note: the sedimentation coefficients in the above diagrammed 'ribosome' sub-units reflect values for eukaryotic ribosomes, prokaryotic cells have somewhat different values. Interestingly, when the two eukaryotic sub-units are combined, their new form has a coefficient of 80S.]

[Additional notes to be transferred in late February.]

When we look at the cell - we see organelles, proteins, and particles being jostled about by pressure gradients and thermal activity. But it is sometimes forgotten how these motions also occur within a gravitational environment - an accelerating environment that always resides in the background, but one which governs all long-term motion. Accordingly, the diagram below may help provide a sense of scale associated with the size of proteins relative to the size of a typical mammalian cell. If we associate the diameter of a pearl (~ 1/4") with the diameter of a typical protein (~ 20 angstroms), then the distance the protein would fall if it traversed the full 'height' of a cell would be equivalent to the pearl falling the height of a 10-story office building. If we were to fill that 10-story building with shampoo (much more viscous than air) the time required for the pearl and the protein to fall the height of their respective containers would be roughly the same.

The terminal velocity of a falling body is established when the force of gravity pulling the mass of the object downwards is balanced by the drag force acting on the object's surface. When the object is subjected to either a gravitation or centrifugal acceleration - the terminal velocity is an expression of the sedimentation speed, or the Svedberg coefficient. The terminal velocity of a falling sphere is relatively simple to calculate using Stoke's formula, shown below. However, in general, the speed is a nonlinear function depended on the mass, geometry, the frictional characteristics of the object, and, of course, the properties of the fluid.

Fluid mechanics within contained environments looks very different from the familiar Newtonian mechanics of free space. Reference was made earlier to travel within a car filled with helium balloons. Quite surprising is how, when you accelerate the car in a forward direction, the balloons also move forward. This is, of course, a result of the balloons getting shoved out of the way (forward) by the heavier air that slides to the back of the car cab as a result of the resistance the air has to acceleration, i.e., inertia.

[Additional notes to be transferred in late February.]

[Volume change and the Sedimentation Coefficient]

[The nucleus is less viscous that the cytoplasm in the main body of the cell. A link to a discussion about their relative viscosities may be found at: http://www.tiem.utk.edu/~gross/bioed/webmodules/nuclearviscosity.htm]

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