Bayesian target optimisation for high-precision holographic optogenetics

Abstract

Two-photon optogenetics has transformed our ability to probe the structure and function of neural circuits. However, achieving precise optogenetic control of neural ensemble activity has remained fundamentally constrained by the problem of off-target stimulation (OTS): the inadvertent activation of nearby non-target neurons due to imperfect confinement of light onto target neurons. Here we propose a novel computational approach to this problem called Bayesian target optimisation. Our approach uses nonparametric Bayesian inference to model neural responses to optogenetic stimulation, and then optimises the laser powers and optical target locations needed to achieve a desired activity pattern with minimal OTS. We validate our approach in simulations and using data from in vitro experiments, showing that Bayesian target optimisation considerably reduces OTS across all conditions we test. Together, these results establish our ability to overcome OTS, enabling optogenetic stimulation with substantially improved precision.

Figure 1:

Off-target stimulation with two-photon optogenetics. (a) Two-photon holographic opto-genetics can be used to elicit spikes in specific ensembles of experimenter-selected neurons. (b) OTS arises due to an inability to confine two-photon excitation to the soma of a target neuron. By repositioning the hologram away from the soma, OTS could be avoided while still activating the target neuron. (c) Data from real two-photon optogenetics experiment showing that at high power (e.g. 40 mW) a neuron can be activated from 15-20 μm away, though this depends on the specific pattern of opsin expression at the soma and proximal dendrites. Red and gray circles indicate locations where stimulation resulted in successful or unsuccessful spikes. Colour map shows the inferred probability of spiking (i.e., the ORF) using the log-barrier Newton method from Subsection 3.2. As the number of sampled locations and laser powers increases, the GP model adapts to the particular ORF shape (see supplementary material for the prior mean). This shape can then be exploited to precisely optimise holographic stimuli. Data from PV-neuron in L2/3 of V1 expressing the soma-targeted, excitatory opsin ChroME2f [44].

Figure 2:

Minimising off-target stimulation using Bayesian target optimisation. (a) Direct nuclear stimulation at 70 mW successfully activates the target neurons with high probability, but also activates nearby non-target neurons due to OTS. Triangles indicate target neurons. Shading indicates probability of spiking. Optical write-in error (bottom) given as the sum of squared errors between the evoked and desired activity patterns. (b) Optimised stimulation using Algorithm 1 repositions the hologram locations away from the nuclei of non-target neurons, resulting in a substantial reduction in off-target activation. (c) Optimisation trajectory of the 6 different target laser powers. Initial laser powers selected randomly between 50 and 70 mW. (d) Optimising holographic targets for 20 different random ensembles shows a robust reduction of optical write-in error (average reduction, 75%).

Figure 3:

Performance of Bayesian target optimisation in increasingly difficult contexts. (a) Two example scenarios with low (left) and high (right) density of opsin-expressing neurons. Triangles indicate example 5-target ensemble to be stimulated. At low density, the risk of OTS is low because neurons are often spaced far apart. However, at high density, OTS arising from direct nuclear stimulation at high power is unavoidable. (b) Optical write-in error for nuclear and optimised stimulation of 5-target ensembles. Error bars show the mean error ± 1 s.d. over 10 different simulations. For each simulation we averaged the write-in error over 20 random ensembles. (c) Same as (b), but for a fixed population size of 50 and varying ensemble size.

Figure 4:

Performance of Bayesian target optimisation using simulations based on two-photon holographic optogenetics data. (a) Left: field of view from a real in vitro optogenetics experiment showing every optimised single-target hologram. Opsin fused to red fluorescent protein mRuby3 so that opsin-expressing neurons can be visualised. Unfilled white circles represent putative neurons detected by automated cell segmentation method. Smaller filled white circles represent optimised holographic targets, shown in relation to the cell nucleus by a straight white line. Right: zoomed view of optimised targets, corresponding to dashed region in the left panel. (b) Optimised laser powers relative to their initialised values show how Bataro exploits differences in photosensitivity to avoid OTS. Each circle represents the power delivered to a single holographic target. (c) Reduction of optical write-in error using optimised holographic targets. Each circle represents the error when attempting to stimulate a single neuron.

Figure 5:

Optimisation of holographic targets in three-dimensional space. (a) Example target neuron and optimised holographic stimulus (plane 3, 25 μm). By repositioning the hologram (primarily in the x/y dimensions), off-target activation is entirely eliminated (bottom spike probability plots, inset numbers show write-in error). Deepest plane labelled as 0 μm by convention. Solid white circle indicates target neuron. Dashed white circles indicate nearby non-target neurons that must be avoided. (b) Similar to (a), but for a neuron in plane 2 (50 μm) and with repositioning of the hologram primarily in the z dimension. (c) All optimised single-target holograms over four stimulation planes. Targets shown at their original depth for visualisation. Average displacement of optimised holographic targets relative to nuclei, 8.3 μm. Scale bar, 20 μm. (d) Max-projection over z-planes simultaneously showing locations of all segmented opsin-expressing neurons. (e) Optimised depths of holographic targets corresponding to neurons in (c). Depths are shown in comparison to one of four depths that the target neuron was segmented at during the experiment. (f) Optimised laser powers relative to their initialised values. (g) Reduction of optical write-in error for all neurons, across multiple depths.