The influence of a neuronal cell on another neuron to which it is connected varies with time in a process called « synaptic plasticity ». This process, the main cellular mechanism underlying learning and memory, has thoroughly been studied by neurobiologists at the cellular level (electrical activity of the cells). However, albeit experimental results in the past decade have identified a large set of signal transduction proteins involved in synaptic plasticity, we still do not understand its operation at the molecular level nor how to explain cellular responses on the basis of the molecular levels. For this purpose, one needs to build computational and mathematical models of the implied signal transduction networks thus effectively developing computational systems biology of synaptic plasticity. In collaboration with the experimental biology lab led by L. Venance at College de France, Paris (CNRS/ UMR 7241 --? INSERM U1050), we are studying the molecular bases of synaptic plasticity (spike--?timing dependent plasticity) in a part of the brain called the basal ganglia (involved in procedural learning). Using a joint experimental--?modeling approach, we have developed a computational model of the implicated molecular networks at play (glutamate receptors, CaMKII, endocannabinoids, PKA...), that precisely allows understanding cellular responses based on the molecular levels for a restricted set of experimental conditions. The objective of this thesis is to extend this model in order to account for further experimental conditions of interest. This will necessitate the extension of the model along three lines (ranked by priority): i) account for STDP regulation by astrocytes via modulation of glutamate removal form the synaptic cleft. ii) improve the description of the presynaptic part of the model, that describes signal transduction by the endocannabinoid system. This will in particular involve the detailed modeling of CB1R signaling and traffic between synaptic and extrasynaptic compartments, iii) add a description of dopamine signaling and in particular the intricacy related to DARPP--?32.