Positive feedback circuits and memory.

The concept of regulatory feedback circuit refers to oriented cyclic interactions between elements of a system. There are two classes of circuits, positive and negative, whose properties are in striking contrast. Positive circuits are a prerequisite for the occurrence of multiple steady states (multistationarity), and hence, they are involved in all processes showing hysteresis or memory. Endogenous or exogenous perturbations can lead the system to exhibit or to evoke one particular stable regime. The role of positive circuits in cell differentiation and in immunology is well documented. Negative circuits are involved in homeostatic regulation, with or without oscillations. The aim of this paper is to show: a) that positive circuits account for many features of memory stricto sensu (i.e., neural memory and mnesic evocation) as well as largo sensu (e.g. differentiation or immunological memory); and b) that simple combinations of positive and negative circuits provide powerful regulatory modules, which can also be associated in batteries. These entities have vast dynamical possibilities in the field of neurobiology, as well as in the fields of differentiation and immunology. Here we consider a universal minimal regulatory module, for which we suggest to adopt the term 'logical regulon', which can be considered as an atom of Jacob's integron. It comprises a positive and a negative circuit in its interaction matrix, and we recall the main results related to the simultaneous presence of these circuits. Finally, we give three applications of this type of interaction matrix. The first two deal with the coexistence of multiple stable steady states and periodicity in differentiation and in an immunological system showing hysteretic properties. The third deals with the dual problems of synchronization and desynchronization of a neural model for hippocampus memory evocation processes.