Statistical models of effective connectivity in neural microcircuits

To appreciate how neural circuits in the brain control behaviors, we must identify how the neurons comprising the circuit are connected. Neuronal connectivity is difficult to determine experimentally, whereas neuronal activity can often be readily measured. I describe a statistical framework to estimate circuit connectivity directly from measured activity patterns. Because we usually only have access to a small subset of neurons of a circuit, the estimated connectivity reflects an effective coupling, that is, how spiking activity in one neuron effectively modulates the activity of other neurons. For small circuits, like the nervous system of the crab that controls gut muscle activity, we could show that it is possible to derive the actual physiological connectivity from observing neural activity alone. This was achieved with a regression model adapted to the spike train structure of the data (Generalized Linear Model, GLM). This is the first successful demonstration of a network inference algorithm on a physiological circuit for which the connections are known. For larger networks, like cortical networks, the concept of effective connectivity - though not equivalent to structural connectivity - is useful to characterize the functional properties of the network. For example, we may assess whether networks have small-world or scale-free properties that are important for information processing. We find that cortical networks show a small, but significant small-world structure by applying our estimation framework on multi-electrode recordings from the visual system of the awake monkey. Finally, we study how well spike dynamics and network topology can be inferred from noisy calcium imaging data. We applied our framework on simulated data to explore how uncertainties in spike inference due to experimental parameters affect estimates of network connectivity and their topological features. We find that considerable information about the connectivity can be extracted from the neural activity, but only if spikes are reconstructed with high temporal precision. We then study how errors in the network reconstruction affect the estimation of a number of graph-theoretic measures. Our findings provide a benchmark for future experiments that aim to reliably infer neuronal network properties.