In my opinion, this is a fascinating piece of work that provides a mathematician viewpoint on the impact of Mathematics on Life Sciences, a subject which is widely acknowledged to be one of the major scientific challenges of the XXI century.
The title of [1] explicitly refers to a mathematical theory of living systems. A natural question is whether there is any real need for such a theory. As a matter of fact, many biomedical scientists will adamantly reject the interference of Mathematics in Biology, two fields considered for many centuries as strange to each other. It is beyond the scope of this short comment to go in detail into the reasons for this deep mistrust. Let me just quote, as an example, some remarks due to a pioneer in the introduction of mathematical models in Biology:
. . . Why do models have only a limited reputation? My own experience is that (in Biology) experimentalists are not very enthusiastic if it turns out that a process was correctly predicted. They worked hard to find the basic principles by themselves. Frequently the prediction is then handled more as a speculation, if not completely ignored. This is very different to the habit in physics where an experimental observation would be in no way diminished if it is preceded by a theoretical prediction, on the contrary. . . The reception of some of my models had a strange history. First they were regarded as unrealistic or misleading: "cannot be". More or less abruptly this changed later into: "that is trivial, how else should it be?". This switch had different time constants in different communities. Both attitudes provide the freedom to ignore the theoretical work. . . .
At the technical level, a widely used argument to disregard the use of Mathematics in Biology is that living beings are too complex to allow for any meaningful mathematical treatment. However, the main difficulty in dealing with biological complexity seems to be not so much the large number of components, but the nature of the interactions among them. For instance, in [3] engineering and biological design are compared, using aircraft production as an example. It is there observed that:
. . . A Boeing 777 is a flying circuit, with over 150.000 different modular subsystems, organized by non-trivial protocols, which give raise to complex control networks, including about 1000 computers that can govern all vehicle