It is of great interest to characterize the spiking activity of individual neurons in a cell ensemble. Many different mechanisms, such as synaptic coupling and the spiking activity of itself and its neighbors, drive a cell's firing properties. Though this is a widely studied modeling problem, there is still room to develop modeling solutions by simplifications embedded in previous models. The first shortcut is that synaptic coupling mechanisms in previous models do not replicate the complex dynamics of the synaptic response. The second is that the number of synaptic connections in these models is an order of magnitude smaller than in an actual neuron. In this research, we push this barrier by incorporating a more accurate model of the synapse and propose a system identification solution that can scale to a network incorporating hundreds of synaptic connections. Although a neuron has hundreds of synaptic connections, only a subset of these connections significantly contributes to its spiking activity. As a result, we assume the synaptic connections are sparse, and to characterize these dynamics, we propose a Bayesian point-process state-space model that lets us incorporate the sparsity of synaptic connections within the regularization technique into our framework. We develop an extended expectation-maximization. algorithm to estimate the free parameters of the proposed model and demonstrate the application of this methodology to the problem of estimating the parameters of many dynamic synaptic connections. We then go through a simulation example consisting of the dynamic synapses across a range of parameter values and show that the model parameters can be estimated using our method. We also show the application of the proposed algorithm in the intracellular data that contains 96 presynaptic connections and assess the estimation accuracy of our method using a combination of goodness-of-fit measures.