This first paper in a series develops a model of structure-function relationships for the oxygen and substrate pathways of oxidative metabolism in working muscle. This will be used in the subsequent experimental papers in asking how biological structures are designed if they serve more than one function and whether one function can be served by more than one structural pathway. We have used the concept of symmorphosis to address this question; in its original form, it postulates that no more structure is built and maintained at each step in a pathway than is required to meet functional demands. The concept of symmorphosis was developed to deal with the problem of modelling the pathway for oxygen from the environment to mitochondria, essentially a single series of interconnected transfer steps. In the present context, the application of this concept is more complex. Both oxygen and substrates are transported directly from the blood to the mitochondria in what appear to be shared steps. The flows along this direct pathway are adjusted during muscular work. However, substrates have an additional option. They can be stored intracellularly as lipid droplets or glycogen, and thus their supply to mitochondria can occur in two steps separated in time: from capillaries to stores during rest, and from stores to mitochondria during work. The integrated pathways have a network structure and the functional flows are partitioned to different branches of the network, and we must ask whether the partitioning of fluxes is related to design constraints. The principle of symmorphosis predicts that the best use is made of the available options and that the design of each step is matched to the specific functional demand in view of a balance to be achieved over the entire network. This will be tested in subsequent papers by determining maximal flows for oxygen, carbohydrates and lipids through each of the transport steps and their respective structural capacities, comparing dogs and goats, animals of the same size whose maximal oxidative capacities differ by more than twofold. Finally, we will ask whether the principle of symmorphosis can be extended to apply to network systems.

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