Since the Principle of Biological Relativity was formulated and developed there have been many implementations in a wide range of biological fields. The purpose of this article is to assess the status of the applications of the principle and to clarify some misunderstandings. The principle requires circular causality between levels of organization. But the forms of causality are also necessarily different. They contribute in asymmetric ways. Upward causation can be represented by the differential or similar equations describing the mechanics of lower level processes. Downward causation is then best represented as determining initial and boundary conditions. The questions tackled in this article are: (1) where and when do these boundaries exist? and (2) how do they convey the influences between levels? We show that not all boundary conditions arise from higher-level organization. It is important to distinguish those that do from those that don’t. Both forms play functional roles in organisms, particularly in their responses to novel challenges. The forms of causation also change according to the levels concerned. These principles are illustrated with specific examples.

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The fine structure of the visual and the supporting cells and of the blood capillaries in the octopus retina is described. Lamellatcd structures contained in the proximal segment of the visual cell consist of compact arrays of dense membranes each of which is quintuplelayered and divides at its margins into two thinner sheets or membranes which are connected directly with the agranular or granular cndoplasmic reticulum. Proximal to the deeper extremitics of the rhabdomcres, the lateral plasma membranes of two adjoining visual cells contact each other forming a quintuple-layered compound membrane, which results in occlusion of the intercellular space. The central layer of the compound membrane is of high density, so that thc membrane, as a whole, appears to be a single thick layer at low magnifications. The supporting cells are connccted with the neighboring visual cells by two typcs of junctions. Long slender processes extend from the supporting cells to the surface of the retina through narrow spaccs among the distal segments of the visual cells. The capillary cndothclial cclls are charactcrized by luminal surfaces irregularly contoured and by lateral surfaccs clahorately interdigitatcd. The functional significancc of the close contact between adjoining visual cclls is discussed.

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We describe a major development of the Shorten et al. (Shorten et al., 2007) model of skeletal muscle electrophysiology, biochemistry, and mechanics. The model was developed by incorporating equations for sarcolemmal transport of calcium ions, including L-type calcium channel, sodium-calcium exchange, calcium pump, and background calcium channel. The extended model also includes an addition to the equations for extracellular potassium ion movements to enable the exchange of potassium ions between bulk (plasma) concentration and the interstitial and tubular compartments to be modeled. In further research in an accompanying paper (Tasaki et al, 2019), we succeeded in reproducing muscle cramp, as well as its prevention and reversal, by investigating muscle contraction and cramp using this extended model in comparison with the original model.

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