Since the mission of combating disease and aging are anchoring research to reality in biophysics much progress is being made as a result, despite limitations of investigative methods adherence to philosophical biases. The difference with the Quixotic quest for an unverifiable unified field theory of everything in physics is stark in contrast.
I contend that much of the brilliant hypothesizing that created the non Euclidean, Riemannian spacetime manifold geometry is just as applicable, if not more so, to biophysics. In the broadest overview within the domain of the biosphere we encounter nested sequences of functional dynamic orderings. To seek to bring these into coherence we must locate the progression of evolutionary sequences in capability of nonlinear improvements in energy flux density of negentropy. The biosphere itself is bounded by the inorganic and human noetic power analogous to Dirichlet's principle in least action bounding dynamics for topology.
Within that biosphere we can investigate how the divisions of life types adhere to the intake and transformation of useful energy. It is the interaction with the inorganic domain that limits the development of both. For example, the organic carbohydrates that comprise the biosphere require for their dynamic life sustaining elements to be incorporated to resolve their ability to reproduce. Thereby the uptake of phosphorus by mitochondria as catalytic in providing energy reduction by the enzymatic framework of ATP was evolved for the different branches of cellular life.
One intriguing direction would be developing a rigorous geometrical framework for the protein "interactome." There exist multiply connected functions within that interactome and there are coherent classes of cases of proteins acting as singularities that bridge them. For example, the scaffolding functions of actin and myosin might be bridged in some cases by multifunctional proteins interacting with signaling entities like sonic hedgehog. There appears to be a scale of closer integrated cellular functions enmeshed with these multifunctional proteins with some that are referred to as moonlighting seemingly unrelated such functions. Topologically, these disparate states might be thought as Riemannian non deformable surfaces of higher ordered connectedness.
However within such extended topologies there also exist the equivalence of multi sheeted polarities whereby the multifunctional proteins exhibit the characteristic of operating as branch points. This physical geometric framework was supplied toward the end of 19th century by Riemann and Abel among others. The problem is that the further development of this physical geometry was vitiated by the usage of the statistics of entropy as a fundamental principle for scientific research.
It should have been apparent that a negentropic higher ordering principle contradicted the materialist assumptions of limited resources. This proceeds from the top down via human creative breakthroughs that reorganize and redefine what constitutes resources for economic survival of society. That principle of moving beyond the relatively fixed limits of reproduction within that economic topology is equivalent to the emergence of life from the fixed limits of the inorganic domain. It is representative of a higher harmonic class of ordering.
In that context, I came across a rather startling bit of brilliant research bearing upon morphogenesis yesterday evening. The apparent random process of cellular reproduction are controlled by "morphogens" that admit self organization in embryogenesis. It is my contention that such agents of self organization apply as a limiting principle to the entirety of the domain of biophysical interactions. Thus we see cohesin and topoisomerase functions operating upon the mitotic DNA reproductive process, for instance. This represents a principle of self similar harmonic ordering that "closes" the boundaries of structure of the biophysical domain that Dirichlet provided for compact manifolds.
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