Methods for neural circuit inference from population calcium imaging data

• ¹ Johns Hopkins University, United States
• ² Columbia University, United States

Calcium imaging techniques have become an important and ubiquitous tool for studying neural circuits. Advances in fluorescence microscopy and calcium sensors allow researchers to obtain data with increasingly better spatial and temporal resolution - and provide them with the ability to observe ever finer details of population dynamics. However, many fundamental questions about neural coding and circuit connectivity are not directly approachable with raw fluorescence data. Here we present results from the application of inference techniques to calcium imaging data: a fast spike inference algorithm [1], and a Monte Carlo expectation maximization algorithm for inferring neural connectivity [2]. We have developed a faster than real time algorithm that infers the approximately most likely spike train for each neuron in an imaged population. A simple generative model of calcium dynamics was used to formulate a concave objective function. We imposed a log-barrier penalty using interior-point methods to ensure non-negativity of the spike trains. Since the Hessian term in our objective function is a tridiagonal matrix, we can implement the Newton-Raphson method in linear time by using standard banded Gaussian elimination methods. By generalizing our model of calcium dynamics to an entire population, we can infer the probability of a single neuron spiking given the fluorescence activity of the entire network. A maximum a posteriori estimate of the model parameters is fit to the observed data through the use of a Monte Carlo expectation maximization algorithm. The sufficient statistics are computed using a spike inference algorithm [1,3] and a hybrid blockwise Gibbs sampler. On simulated noisy calcium data, connectivity matrices (even for more than 100 neurons) can be accurately reconstructed using this approach. In order to refine these methods for use on real data, we used calcium indicators in vitro to image spontaneous neural activity in mouse cerebral cortex. To verify the accuracy of our spike inference methods, we recorded from individual neurons intracellularly during imaging. Across a variety of preparations, our fast spike inference algorithm outperformed the optimal linear deconvolution method (aka, a Wiener filter) and also accurately inferred the timing of most action potentials detected intracellularly. These data are now being used to test our connectivity inference algorithm. We can validate our model by comparing the neurons that were inferred to create negative connections with genetically labeled inhibitory interneurons present in the tissue. Inferred synaptic connections can also be directly verified using paired whole cell recordings. See Supplementary Materials for model details, inference algorithm pseudocode, and figures.