Fast state-space methods for inferring dendritic synaptic connectivity

Abstract

We present fast methods for filtering voltage measurements and performing optimal inference of the location and strength of synaptic connections in large dendritic trees. Given noisy, subsampled voltage observations we develop fast l 1 -penalized regression methods for Kalman state-space models of the neuron voltage dynamics. The value of the l 1 -penalty parameter is chosen using crossvalidation or, for low signal-to-noise ratio, a Mallows' C p -like criterion. Using low-rank approximations, we reduce the inference runtime from cubic to linear in the number of dendritic compartments. We also present an alternative, fully Bayesian approach to the inference problem using a spike-andslab prior. We illustrate our results with simulations on toy and real neuronal geometries. We consider observation schemes that either scan the dendritic geometry uniformly or measure linear combinations of voltages across several locations with random coefficients. For the latter, we show how to choose the coefficients to offset the correlation between successive measurements imposed by the neuron dynamics. This results in a "compressed sensing" observation scheme, with an important reduction in the number of measurements required to infer the synaptic weights.

Efficient "Shotgun" Inference of Neural Connectivity from Highly Sub-sampled Activity Data

“…As we discussed in the previous section, it relatively straightforward to infer neuronal correlations, given enough observed neural pairs. It is also relatively easy to infer a linear-Gaussian model of the network activity with missing observations [ 44 , 50 ], since we can analytically integrate out any unknown observations. However, as mentioned earlier (section 8) when inferring actual synaptic connectivity from real data, correlation and linear-based methods are inferior to a GLM-based approach.…”

Closed-Loop and Activity-Guided Optogenetic Control

“…At the finest scale, fast light-targeting methods have been developed in dendritic imaging and glutamate uncaging experiments (Branco et al, 2010; Lutz et al, 2008; Nikolenko et al, 2008; Svoboda et al, 1997; Yuste, 2010; Denk et al, 1996; reviewed in Grienberger et al, 2015). At the same time, mathematical and computational machinery necessary for system identification and control on dendrites using observation with optical voltage and calcium sensors has been developed (Pakman et al, 2014; Pnevmatikakis et al, 2012; Huggins and Paninski, 2012; Paninski, 2010), rendering optogenetic system identification and control of dendritic trees a promising area for future investigations. Recently, holographic light shaping and SLM point-scanning optogenetic manipulations have been explored using tools defined at the subcellular and cellular scale (Prakash et al, 2012; Packer et al, 2012; Vaziri and Emiliani, 2012; Anselmi et al, 2011; Yang et al, 2011; Papagiakoumou et al, 2008).…”

Systematic errors in connectivity inferred from activity in strongly coupled recurrent circuits

“…With the total volume of spike data that we collected from the network, the largest value of n for which this was possible is 10. Thus, these distributions are over 2 10 10-neuron binary spike state vectors.…”