Fixed Points of Majority Rule Cellular Automata with Application to Plasticity and Precision of the Immune System

A bstract. Signal processing in the immune syst em is st udied in a t heoretical multilayered network. The elements in th e network have regular conn ectiviti es, with t he level of connectivity reflecti ng t he level of signal (cyto kine) multifunctionality. Each element opera tes by th e same nonlinear majority rule. An exact formul a for t he/ {;umber of fixed points is derived as a fun ction of t he network's size n (n odd) and connect ivity r, as well as a general upper-bound estimate for t he numb er of fixed point s for all n and r. Results show th at increasing connectivity enha nces resilience by st rengthening t he globa l error damping capacity of t he system. It s cost is dimin ished general memory storage space, reflectin g diminished ph enotypic plast icity. Lab oratory experiments are suggeste d for verifying t he implications of the result s for pathogenesis and immunosuppression. The durat ion a nd amplit ude of t he immune resp onse is regu lated by a group of p eptid es called cytokin es t hat bi nd to the cell sur face and ult im ately lea d t o a change in it s phen otypic state , t hat is, it s pro lifer ati ve or fun ct ion al b eh avior. In t he past , ea ch step in t he im mune process was t ho ug ht to b e contro lled by a unique sing le-p urpose m olecul e. Tod ay it is realized t hat cytokine activity is characterized by pleiotropism a nd redundancy: indi vid-ua l cytokines are pleiotropic in having mult ipl e overlapping cell regula tory actions (de no te d a on e/ m any property) , while differen t cytokines can have a sim ila r a ct ion (many/one proper ty). Mo reove r , t he ult im a te resp on se of a cell usually dep ends on two or more differen t messages received concurrent ly a t t he cell surface; t hese are selecte d from a larger rep ertoire of cytokines [1-3]. It thus appe ars that t he pr ocessing rules in t his system , who se state t rans it ions are det ermined by …