Optimal experimental design for sampling voltage on dendritic trees in the low-SNR regime

Abstract

Due to the limitations of current voltage sensing techniques, optimal filtering of noisy, undersampled voltage signals on dendritic trees is a key problem in computational cellular neuroscience. These limitations lead to voltage data that is incomplete (in the sense of only capturing a small portion of the full spatiotemporal signal) and often highly noisy. In this paper we use a Kalman filtering framework to develop optimal experimental design methods for voltage sampling. Our approach is to use a simple greedy algorithm with lazy evaluation to minimize the expected square error of the estimated spatiotemporal voltage signal. We take advantage of some particular features of the dendritic filtering problem to efficiently calculate the Kalman estimator's covariance. We test our framework with simulations of real dendritic branching structures and compare the quality of both time-invariant and time-varying sampling schemes. While the benefit of using the experimental design methods was modest in the time-invariant case, improvements of 25-100% over more naïve methods were found when the observation locations were allowed to change with time. We also present a heuristic approximation to the greedy algorithm that is an order of magnitude faster while still providing comparable results.

Fast state-space methods for inferring dendritic synaptic connectivity

“…However, as we show in Appendix C, if S N (i.e., only a minority of compartments are imaged directly, as is typically the case in these experiments) we can perform this operation approximately much more quickly, in O(T N S 2 ) instead of O(T N 3 ) time, using low-rank perturbation techniques similar to those introduced in Paninski (2010); Huggins and Paninski (2012); Pnevmatikakis, Paninski, Rad and Huggins (2012); .…”

“…In the Gaussian case, the first two terms are quadratic in W, and H V V is constant; see Huggins and Paninski (2012) for further details on the evaluation of the log | − H V V | term. For most reasonable concave observation log-likelihoods, the solutionŴ (λ) is continuous in λ, and therefore we use the same path-following idea exploited by LARS to efficiently compute the solution pathŴ (λ).…”

“…The problem is formulated in a state-space model framework and builds on fast Bayesian methods that we have previously developed (Huys et al, 2006;Huys and Paninski, 2009;Paninski and Ferreira, 2008;Paninski, 2010;Huggins and Paninski, 2012;Pnevmatikakis, Paninski, Rad and Huggins, 2012), for performing optimal inference of subthreshold voltage given noisy and incomplete observations. A key contribution of this work is to note that these fast filtering methods can be combined with fast optimization methods from the sparse Bayesian literature to obtain a fast solution to this synaptic estimation problem.…”

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).…”

Using computational theory to constrain statistical models of neural data

“…In our working example, these methods could suggest the combination of stimulus and reward patterns that would be most informative of the underlying learning rate. These methods have been proposed for sampling the voltage on dendritic trees in high-noise settings [65], as well as for designing training regimes for animals [66]. …”