Non-locality in biological systems results from hierarchy. Application to the nervous system.

The concept of non-locality is deduced from a new concept for biological systems, the "functional interaction." It is shown that a biological system, which is expressed in terms of functional interactions, can be constructed as a hierarchical system, the dynamics of which are represented by a non-local field at each level of organization. The two following constraints: continuous representation of state variables and hierarchy of the system, result in non-locality, i.e., a space property according to which the system depends on mechanisms that are located elsewhere in the space. Concepts and theory are illustrated in the case of the nervous system, where two levels of organization are considered, the level of neurons and the level of synapses. Non-local versus local field operators are discussed, and an interpretation of the field equation terms is proposed. A general formulation of non-local operators for hierarchical systems is given.