The mammalian brain is best understood as a multi-scale hierarchical neural system, in the sense that connection and function occur on multiple scales from micro to macro. Modern genomic-scale expression profiling can provide insight into methodologies that elucidate this architecture. We present a methodology for understanding the relationship of gene expression and neuroanatomy based on correlation between gene expression profiles across tissue samples. A resulting tool, NeuroBlast, can identify networks of genes co-expressed within or across neuroanatomic structures. The method applies to any data modality that can be mapped with sufficient spatial resolution, and provides a computation technique to elucidate neuroanatomy via patterns of gene expression on spatial and temporal scales. In addition, from the perspective of spatial location, we discuss a complementary technique that identifies gene classes that contribute to defining anatomic patterns.

The manner in which different distributions of synaptic weights onto cortical neurons shape their spiking activity remains open. To characterize a homogeneous neuronal population, we use the master equation for generalized leaky integrate-and-fire neurons with shot-noise synapses. We develop fast semi-analytic numerical methods to solve this equation for either current or conductance synapses, with and without synaptic depression. We show that its solutions match simulations of equivalent neuronal networks better than those of the Fokker-Planck equation and we compute bounds on the network response to non-instantaneous synapses. We apply these methods to study different synaptic weight distributions in feed-forward networks. We characterize the synaptic amplitude distributions using a set of measures, called tail weight numbers, designed to quantify the preponderance of very strong synapses. Even if synaptic amplitude distributions are equated for both the total current and average synaptic weight, distributions with sparse but strong synapses produce higher responses for small inputs, leading to a larger operating range. Furthermore, despite their small number, such synapses enable the network to respond faster and with more stability in the face of external fluctuations.