Neuronal innervation, intracellular signal transduction and intercellular coupling: a model for syncytial tissue responses in the steady state.

A model tissue is proposed in which chemically responsive cells are interconnected by gap junctions and innervated by the autonomic nervous system. The model is explicitly dependent on the following physiologically relevant assumptions: (1) a fraction of the cells are directly innervated, and these cells respond to a periodic neuronal stimulus (i.e. the release of neurotransmitter) by production of an intracellular substance (i.e. second messenger molecule); (2) production of second messenger molecules modulates the amplitude of a cellular response, such as contraction or secretion; (3) intracellular formation of second messenger molecules in innervated cells is proportional to the periodicity of the neuronal stimulus, while the intracellular concentration in non-innervated cells is governed by the half-life of the second messenger molecule and the extent of cell-to-cell coupling; (4) the amplitude of the graded response of the individual cell is related to the intracellular second messenger concentration by a Michaelis-Menten function; (5) the amplitude of the graded tissue response is a function of the innervation density, the frequency of stimulation, and the extent of intercellular coupling. Thus, a stimulus-response relationship was developed, where the magnitude of the tissue response was described as a function of the total tissue stimulus. The predicted stimulus-response curve was encapsulated by two parameters: (1) the Hill-exponent, which reflects the steepness of the stimulus-response curve; and (2) the location of the stimulus-response curve, or the half-maximally effective stimulus. Both random and uniform neuronal innervation patterns were considered in model tissues with various effective dimensions. The simulations were also applied to a realistic model of vascular tissue. The shape of the stimulus-response curve is critically dependent on the geometry of innervation. For physiologically relevant (10-90% over 2-3 orders of magnitude) dose-response curves, the model yields an implicit relationship between three different dimensionless parameters. If, in a system, two of these parameters are known, the model can be used to bracket the possible range of the third parameter.