Biophysics based models of LTP/LTD

In this chapter we describe some of the main experimental results recently carried out studying learning and memory mechanisms at molecular level and theoretical approaches based on these results. One of the most improving step on understanding brain function is the recognition that neuronal synapses can perform sophisticated computations and convey information throughout neuronal networks. This modality might be synthesised in the synaptic plasticity phenomenon which, among others, include the molecular transition between a synaptic state of permanent (long-term) potentiation (LTP) and one depressed (long-term depression, LTD). The majority of synapses express both LTP and LTD, thus a molecular mechanisms able to drive information toward a potentiated state versus a depressed one is needed. Phosphorylation and dephosphorylation of receptors mediating synaptic transmission is the major mechanisms for LTP/LTD induction and regulation. This knowledge have fuelled new kind of theoretical and experimental researches mainly on the stability versus meta-stability properties as a function of the involved enzymes. Mainly from a biophysical and mathematical point of view, great effort has been done in order to describe the biochemical mechanism underlying LTP and LTD in terms of dynamical equations and to determine sufficient and necessary conditions to ensure bistability and hence long lasting memory properties. An interesting and perhaps new type of approach that we will mention is the description of biochemical cycle in term of stochastic differential equations that are more adherent to the biological reality because the concentration of involved receptors is low and their production is a noisy process. An interesting consequence of this formalization is the possibility to have a constructive role of noise, that can serve to stabilize memory properties.