Thanks for that. I look forward to the next episode.
Here then is episode 2.
In general then, the prime question is, how and why do cell's move?
Coming on then to your question two, "what is the evidence for the "Wave Model" that distinguishes this from any other model?" I am slightly unclear about what you mean by that question.
You could be asking
2a. What features of the model distinguish the wave model from alternative theories?
2b. What observational evidence supports the wave model over the alternatives?
2c. What observational evidence tends to falsify the alternatives?
In themselves all of those questions are perfectly reasonable but one could give a fairly extended answer to each of them. Such extension is already available on my web site so I won't attempt major detail here.
On that basis my replies to your question 2 are as follows.
2a. The three theories are the "cytoskeletal model," the "flow model" and the "wave model." The cytoskeletal model is currently held to be "correct." The word "cytoskeleton" literally means "cell skeleton" but it is something of a misnomer – these cells have no skeleton but, nonetheless, the cytoskeleton is a real organelle and does determine the cell's shape. The cytoskeleton is actually made from muscle type proteins, so one might think of the cell's shape as being determined by a kind of internal muscle, much as is that of many invertebrates. An actual statement of the cytoskeletal model is difficult to find but the general idea is that, in some way, the cytoskeleton becomes directly linked, through the cell's outer membrane, with external objects which are, in some way, directly transported by cytoskeletal action. A whole variety of actual mechanisms have been proposed for this, many of which actually imply some kind of computational capacity on the part of the cytoskeleton. I have never found any clarity as to which exact mechanism is currently believed and, indeed, it seems to vary from person to person. The clearest evidence against the cytoskeletal is that some membrane components, that clearly do not traverse the membrane, can be aggregated into patches that behave like external particles and move, even though they clearly cannot be in direct contact with an internal cytoskeleton.
In a manner of speaking, I do agree with the cytoskeletal model because the wave model does postulate that the cytoskeleton is producing contractile waves that on the outer membrane. However, that possibility seems to be universally rejected. I have no idea why.
The membrane flow model is quite different. The outer membrane of a cell is a liquid crystal - the membrane is based on lipds which are fluid in the horizontal plane but ordered in the vertical plane. The membrane or lipid flow suggests that the entire outer membrane of the cell is flowing it is internalized at the back, transported through the cell as vesicles and it reformed as membrane at the front. This flow, it is claimed, is sufficient to carry external particles along with it, rather like twigs in a stream.
There is direct, published, observational evidence that the membrane does not flow at the rates required by this model and it is now generally rejected. Nonetheless, some people, notably Bretscher, still profess to believe it.
The mechanism and meaning of this theory seems clear enough. However, to me, it always seemed thermodynamically and evolutionarily unreasonable. It seems t me that membrane flow would require a high energy turnover for the cell and, to my knowledge, such mechanisms of transport do not exist anywhere else in nature.
Those are the two models that received serious attention in the journals - including and influentially in "Nature" under the auspices of John Maddox.
2b. The evidence and arguments favouring the wave model are summarized in chapter 7 of my web site. Aside from direct observations, the most obvious arguments in favour of the wave model are that wave motility recurs throughout the biosphere and does seem to be an energy efficient process. I do not know any serious arguments that falsifies the wave model. However, John Maddox, then editor in Chief of "Nature," did see fit to compare it with the suggestion that the moon is made of green cheese! (Yes, dear reader, he really did.) I presume, therefore, that I am regarded as so ignorant of science that I cannot understand the blindingly obvious, so perhaps some reader here might like to fill me in - metaphorically speaking that is.
2c. The observational evidence tending to falsify the cytoskeletal and membrane flow was given above and is given in more detail on my web site.
I will come back to your question 3 later.