Fixed Points of Majority Rule Cellular Automata with Application to Plasticity and Precision of the Immune System
Zvia Agur
Department of Applied Mathematics and Computer Science,
The Weizmann Institute of Science, Rehovot 76100, Israel
Abstract
Signal processing in the immune system is studied in a theoretical multilayered network. The elements in the network have regular connectivities, with the level of connectivity reflecting the level of signal (cytokine) multifunctionality. Each element operates by the same nonlinear majority rule. An exact formula for the number of fixed points is derived as a function of the network's size n (n odd) and connectivity r, as well as a general upper-bound estimate for the number of fixed points for all n and r. Results show that increasing connectivity enhances resilience by strengthening the global error damping capacity of the system. Its cost is diminished general memory storage space, reflecting diminished phenotypic plasticity. Laboratory experiments are suggest for verifying the implications of the results for pathogenesis and immunosuppression.