Understanding brain development and function requires unraveling synaptic connectivity in neuronal circuits. Because synaptic connections require physical contacts between axons and dendrites, neuronal arbor morphology may be used for inferring connectivity. We will develop statistical theoretical tools to help infer neuronal connectivity from new light microscopy data. We will focus on the following questions, serving as the specific aims of the proposal, i) Are spatial locations of dendritic and axonal branches correlated or independent? To answer this question we will perform statistical analysis of 3D reconstructions of neuronal pairs, ii) How does potential synaptic connectivity depend on the relative position of cortical neurons belonging to different layers? This question will be addressed by analyzing 3D reconstructions of single neurons from different cortical layers, iii) What rules govern the dynamics of spine remodeling? We will start by analyzing experimental data on spine growth and retraction from in vivo two-photon imaging of transgenic mice. All theoretical work will be carried out in close collaborations with several experimental groups.