Optical recording of action potentials and other discrete physiological events: a perspective from signal detection theory

An Ultrasensitive Genetically Encoded Voltage Indicator Uncovers the Electrical Activity of Non-Excitable Cells

Most animal cell types are classified as non-excitable because they do not generate action potentials observed in excitable cells, such as neurons and muscle cells. Thus, resolving voltage signals in non-excitable cells demands sensors with exceptionally high voltage sensitivity. In this study, the ultrabright, ultrasensitive, and calibratable genetically encoded voltage sensor rEstus is developed using structure-guided engineering. rEstus is most sensitive in the resting voltage range of non-excitable cells and offers a 3.6-fold improvement in brightness change for fast voltage spikes over its precursor ASAP3. Using rEstus, it is uncovered that the membrane voltage in several non-excitable cell lines (A375, HEK293T, MCF7) undergoes spontaneous endogenous alterations on a second to millisecond timescale. Correlation analysis of these optically recorded voltage alterations provides a direct, real-time readout of electrical cell-cell coupling, showing that visually connected A375 and HEK293T cells are also largely electrically connected, while MCF7 cells are only weakly coupled. The presented work provides enhanced tools and methods for non-invasive voltage imaging in living cells and demonstrates that spontaneous endogenous membrane voltage alterations are not limited to excitable cells but also occur in a variety of non-excitable cell types.

High-speed low-light in vivo two-photon voltage imaging of large neuronal populations

Monitoring spiking activity across large neuronal populations at behaviorally relevant timescales is critical for understanding neural circuit function. Unlike calcium imaging, voltage imaging requires kilohertz sampling rates that reduce fluorescence detection to near shot-noise levels. High-photon flux excitation can overcome photon-limited shot noise, but photobleaching and photodamage restrict the number and duration of simultaneously imaged neurons. We investigated an alternative approach aimed at low two-photon flux, which is voltage imaging below the shot-noise limit. This framework involved developing positive-going voltage indicators with improved spike detection (SpikeyGi and SpikeyGi2); a two-photon microscope ('SMURF') for kilohertz frame rate imaging across a 0.4 mm × 0.4 mm field of view; and a self-supervised denoising algorithm (DeepVID) for inferring fluorescence from shot-noise-limited signals. Through these combined advances, we achieved simultaneous high-speed deep-tissue imaging of more than 100 densely labeled neurons over 1 hour in awake behaving mice. This demonstrates a scalable approach for voltage imaging across increasing neuronal populations.

Fluorescence imaging of large-scale neural ensemble dynamics

Recent progress in fluorescence imaging allows neuroscientists to observe the dynamics of thousands of individual neurons, identified genetically or by their connectivity, across multiple brain areas and for extended durations in awake behaving mammals. We discuss advances in fluorescent indicators of neural activity, viral and genetic methods to express these indicators, chronic animal preparations for long-term imaging studies, and microscopes to monitor and manipulate the activity of large neural ensembles. Ca²⁺ imaging studies of neural activity can track brain area interactions and distributed information processing at cellular resolution. Across smaller spatial scales, high-speed voltage imaging reveals the distinctive spiking patterns and coding properties of targeted neuron types. Collectively, these innovations will propel studies of brain function and dovetail with ongoing neuroscience initiatives to identify new neuron types and develop widely applicable, non-human primate models. The optical toolkit's growing sophistication also suggests that "brain observatory" facilities would be useful open resources for future brain-imaging studies.

Voltage Imaging with a NIR-Absorbing Phosphine Oxide Rhodamine Voltage Reporter

The development of fluorescent dyes that emit and absorb light at wavelengths greater than 700 nm and that respond to biochemical and biophysical events in living systems remains an outstanding challenge for noninvasive optical imaging. Here, we report the design, synthesis, and application of near-infrared (NIR)-absorbing and -emitting optical voltmeter based on a sulfonated, phosphine-oxide (po) rhodamine for voltage imaging in intact retinas. We find that po-rhodamine based voltage reporters, or poRhoVRs, display NIR excitation and emission profiles at greater than 700 nm, show a range of voltage sensitivities (13 to 43% ΔF/F per 100 mV in HEK cells), and can be combined with existing optical sensors, like Ca2+-sensitive fluorescent proteins (GCaMP), and actuators, like light-activated opsins ChannelRhodopsin-2 (ChR2). Simultaneous voltage and Ca2+ imaging reveals differences in activity dynamics in rat hippocampal neurons, and pairing poRhoVR with blue-light based ChR2 affords all-optical electrophysiology. In ex vivo retinas isolated from a mouse model of retinal degeneration, poRhoVR, together with GCaMP-based Ca2+ imaging and traditional multielectrode array (MEA) recording, can provide a comprehensive physiological activity profile of neuronal activity, revealing differences in voltage and Ca2+ dynamics within hyperactive networks of the mouse retina. Taken together, these experiments establish that poRhoVR will open new horizons in optical interrogation of cellular and neuronal physiology in intact systems.

Ultrafast Two-Photon Imaging of a High-Gain Voltage Indicator in Awake Behaving Mice

Optical interrogation of voltage in deep brain locations with cellular resolution would be immensely useful for understanding how neuronal circuits process information. Here, we report ASAP3, a genetically encoded voltage indicator with 51% fluorescence modulation by physiological voltages, submillisecond activation kinetics, and full responsivity under two-photon excitation. We also introduce an ultrafast local volume excitation (ULoVE) method for kilohertz-rate two-photon sampling in vivo with increased stability and sensitivity. Combining a soma-targeted ASAP3 variant and ULoVE, we show single-trial tracking of spikes and subthreshold events for minutes in deep locations, with subcellular resolution and with repeated sampling over days. In the visual cortex, we use soma-targeted ASAP3 to illustrate cell-type-dependent subthreshold modulation by locomotion. Thus, ASAP3 and ULoVE enable high-speed optical recording of electrical activity in genetically defined neurons at deep locations during awake behavior.

CELLULAR RESOLUTION IMAGING OF NEURONAL ACTIVITY ACROSS SPACE AND TIME IN THE MAMMALIAN BRAIN

While the action potential has long been understood to be the fundamental bit of information in brain, how these spikes encode representations of stimuli and drive behavior remains unclear. Large-scale neuronal recordings with cellular and spike-time resolution spanning multiple brain regions are needed to capture relevant network dynamics that can be sparse and distributed across the population. This review focuses on recent advancements in optical methods that have pushed the boundaries for simultaneous population recordings at increasing volumes, distances, depths, and speeds. The integration of these technologies will be critical for overcoming fundamental limits in the pursuit of whole brain imaging in mammalian species.

Voltage Imaging: Pitfalls and Potential

Optical methods for interrogating membrane potential changes in neurons promise to revolutionize our ability to dissect the activity of individual cells embedded in neural circuits underlying behavior and sensation. A number of voltage imaging strategies have emerged in the past few years. This Perspective discusses developments in both small-molecule and genetically encoded fluorescent indicators of membrane potential. We survey recent advances in small-molecule fluorescent indicators that rely on photoinduced electron transfer to sense voltage as well as refinements of voltage-sensitive fluorescent proteins and new opsin-based strategies for monitoring voltage changes. We compare the requirements of fluorescent voltage indicators to those for more canonical Ca2+ sensing as a way to illuminate the particular challenges associated with voltage imaging.

Genetically encoded indicators of neuronal activity

Experimental efforts to understand how the brain represents, stores and processes information require high-fidelity recordings of multiple different forms of neural activity within functional circuits. Thus, creating improved technologies for large-scale recordings of neural activity in the live brain is a crucial goal in neuroscience. Over the past two decades, the combination of optical microscopy and genetically encoded fluorescent indicators has become a widespread means of recording neural activity in nonmammalian and mammalian nervous systems, transforming brain research in the process. In this review, we describe and assess different classes of fluorescent protein indicators of neural activity. We first discuss general considerations in optical imaging and then present salient characteristics of representative indicators. Our focus is on how indicator characteristics relate to their use in living animals and on likely areas of future progress.

Photoacoustic imaging of voltage responses beyond the optical diffusion limit

Non-invasive optical imaging of neuronal voltage response signals in live brains is constrained in depth by the optical diffusion limit, which is due primarily to optical scattering by brain tissues. Although photoacoustic tomography breaks this limit by exciting the targets with diffused photons and detecting the resulting acoustic responses, it has not been demonstrated as a modality for imaging voltage responses. In this communication, we report the first demonstration of photoacoustic voltage response imaging in both in vitro HEK-293 cell cultures and in vivo mouse brain surfaces. Using spectroscopic photoacoustic tomography at isosbestic wavelengths, we can separate voltage response signals and hemodynamic signals on live brain surfaces. By imaging HEK-293 cell clusters through 4.5 mm thick ex vivo rat brain tissue, we demonstrate photoacoustic tomography of cell membrane voltage responses beyond the optical diffusion limit. Although the current voltage dye does not immediately allow in vivo deep brain voltage response imaging, we believe our method opens up a feasible technical path for deep brain studies in the future.

A Computationally Efficient Filter for Reducing Shot Noise in Low S/N Data

Functional multineuron calcium imaging (fMCI) provides a useful experimental platform to simultaneously capture the spatiotemporal patterns of neuronal activity from a large cell population in situ. However, fMCI often suffers from low signal-to-noise ratios (S/N). The main factor that causes the low S/N is shot noise that arises from photon detectors. Here, we propose a new denoising procedure, termed the Okada filter, which is designed to reduce shot noise under low S/N conditions, such as fMCI. The core idea of the Okada filter is to replace the fluorescence intensity value of a given frame time with the average of two values at the preceding and following frames unless the focused value is the median among these three values. This process is iterated serially throughout a time-series vector. In fMCI data of hippocampal neurons, the Okada filter rapidly reduces background noise and significantly improves the S/N. The Okada filter is also applicable for reducing shot noise in electrophysiological data and photographs. Finally, the Okada filter can be described using a single continuous differentiable equation based on the logistic function and is thus mathematically tractable.

Multifocal fluorescence microscope for fast optical recordings of neuronal action potentials

In recent years, optical sensors for tracking neural activity have been developed and offer great utility. However, developing microscopy techniques that have several kHz bandwidth necessary to reliably capture optically reported action potentials (APs) at multiple locations in parallel remains a significant challenge. To our knowledge, we describe a novel microscope optimized to measure spatially distributed optical signals with submillisecond and near diffraction-limit resolution. Our design uses a spatial light modulator to generate patterned illumination to simultaneously excite multiple user-defined targets. A galvanometer driven mirror in the emission path streaks the fluorescence emanating from each excitation point during the camera exposure, using unused camera pixels to capture time varying fluorescence at rates that are ∼1000 times faster than the camera's native frame rate. We demonstrate that this approach is capable of recording Ca(2+) transients resulting from APs in neurons labeled with the Ca(2+) sensor Oregon Green Bapta-1 (OGB-1), and can localize the timing of these events with millisecond resolution. Furthermore, optically reported APs can be detected with the voltage sensitive dye DiO-DPA in multiple locations within a neuron with a signal/noise ratio up to ∼40, resolving delays in arrival time along dendrites. Thus, the microscope provides a powerful tool for photometric measurements of dynamics requiring submillisecond sampling at multiple locations.

Red fluorescent proteins (RFPs) and RFP-based biosensors for neuronal imaging applications

The inherent advantages of red-shifted fluorescent proteins and fluorescent protein-based biosensors for the study of signaling processes in neurons and other tissues have motivated the development of a plethora of new tools. Relative to green fluorescent proteins (GFPs) and other blue-shifted alternatives, red fluorescent proteins (RFPs) provide the inherent advantages of lower phototoxicity, lower autofluorescence, and deeper tissue penetration associated with longer wavelength excitation light. All other factors being the same, the multiple benefits of using RFPs make these tools seemingly ideal candidates for use in neurons and, ultimately, the brain. However, for many applications, the practical utility of RFPs still falls short of the preferred GFPs. We present an overview of RFPs and RFP-based biosensors, with an emphasis on their reported applications in neuroscience.

Closed-loop and activity-guided optogenetic control

Advances in optical manipulation and observation of neural activity have set the stage for widespread implementation of closed-loop and activity-guided optical control of neural circuit dynamics. Closing the loop optogenetically (i.e., basing optogenetic stimulation on simultaneously observed dynamics in a principled way) is a powerful strategy for causal investigation of neural circuitry. In particular, observing and feeding back the effects of circuit interventions on physiologically relevant timescales is valuable for directly testing whether inferred models of dynamics, connectivity, and causation are accurate in vivo. Here we highlight technical and theoretical foundations as well as recent advances and opportunities in this area, and we review in detail the known caveats and limitations of optogenetic experimentation in the context of addressing these challenges with closed-loop optogenetic control in behaving animals.

Cellular level brain imaging in behaving mammals: an engineering approach

Fluorescence imaging offers expanding capabilities for recording neural dynamics in behaving mammals, including the means to monitor hundreds of cells targeted by genetic type or connectivity, track cells over weeks, densely sample neurons within local microcircuits, study cells too inactive to isolate in extracellular electrical recordings, and visualize activity in dendrites, axons, or dendritic spines. We discuss recent progress and future directions for imaging in behaving mammals from a systems engineering perspective, which seeks holistic consideration of fluorescent indicators, optical instrumentation, and computational analyses. Today, genetically encoded indicators of neural Ca(2+) dynamics are widely used, and those of trans-membrane voltage are rapidly improving. Two complementary imaging paradigms involve conventional microscopes for studying head-restrained animals and head-mounted miniature microscopes for imaging in freely behaving animals. Overall, the field has attained sufficient sophistication that increased cooperation between those designing new indicators, light sources, microscopes, and computational analyses would greatly benefit future progress.

Inference of neuronal network spike dynamics and topology from calcium imaging data

Two-photon calcium imaging enables functional analysis of neuronal circuits by inferring action potential (AP) occurrence ("spike trains") from cellular fluorescence signals. It remains unclear how experimental parameters such as signal-to-noise ratio (SNR) and acquisition rate affect spike inference and whether additional information about network structure can be extracted. Here we present a simulation framework for quantitatively assessing how well spike dynamics and network topology can be inferred from noisy calcium imaging data. For simulated AP-evoked calcium transients in neocortical pyramidal cells, we analyzed the quality of spike inference as a function of SNR and data acquisition rate using a recently introduced peeling algorithm. Given experimentally attainable values of SNR and acquisition rate, neural spike trains could be reconstructed accurately and with up to millisecond precision. We then applied statistical neuronal network models to explore how remaining uncertainties in spike inference affect estimates of network connectivity and topological features of network organization. We define the experimental conditions suitable for inferring whether the network has a scale-free structure and determine how well hub neurons can be identified. Our findings provide a benchmark for future calcium imaging studies that aim to reliably infer neuronal network properties.

Confocal imaging of transmembrane voltage by SEER of di-8-ANEPPS

Imaging, optical mapping, and optical multisite recording of transmembrane potential (V_m) are essential for studying excitable cells and systems. The naphthylstyryl voltage-sensitive dyes, including di-8-ANEPPS, shift both their fluorescence excitation and emission spectra upon changes in V_m. Accordingly, they have been used for monitoring V_m in nonratioing and both emission and excitation ratioing modes. Their changes in fluorescence are usually much less than 10% per 100 mV. Conventional ratioing increases sensitivity to between 3 and 15% per 100 mV. Low sensitivity limits the value of these dyes, especially when imaged with low light systems like confocal scanners. Here we demonstrate the improvement afforded by shifted excitation and emission ratioing (SEER) as applied to imaging membrane potential in flexor digitorum brevis muscle fibers of adult mice. SEER—the ratioing of two images of fluorescence, obtained with different excitation wavelengths in different emission bands—was implemented in two commercial confocal systems. A conventional pinhole scanner, affording optimal setting of emission bands but less than ideal excitation wavelengths, achieved a sensitivity of up to 27% per 100 mV, nearly doubling the value found by conventional ratioing of the same data. A better pair of excitation lights should increase the sensitivity further, to 35% per 100 mV. The maximum acquisition rate with this system was 1 kHz. A fast “slit scanner” increased the effective rate to 8 kHz, but sensitivity was lower. In its high-sensitivity implementation, the technique demonstrated progressive deterioration of action potentials upon fatiguing tetani induced by stimulation patterns at >40 Hz, thereby identifying action potential decay as a contributor to fatigue onset. Using the fast implementation, we could image for the first time an action potential simultaneously at multiple locations along the t-tubule system. These images resolved the radially varying lag associated with propagation at a finite velocity.

Measuring membrane voltage with fluorescent proteins

Measuring signal transduction in large numbers of cells with high spatial and temporal resolution is fundamental to studying information processing in the nervous system. DNA-encoded sensors have an advantage in that they can be introduced into an organism noninvasively and targeted to specific brain regions, cell types, or subcellular compartments. A variety of chimeric proteins that report transmembrane voltage have been developed. The prototype sensor, FlaSh, is a green fluorescent protein fused to a voltage-sensitive K(+) channel, where voltage-dependent rearrangements in the channel induce changes in the protein's fluorescence. Subsequent sensors have refined this basic design using a monomeric voltage-sensing phosphatase domain from Ciona intestinalis and pairs of fluorescent proteins to produce a larger fluorescent signal. These sensors and their uses are discussed here.

Optical strategies for sensing neuronal voltage using quantum dots and other semiconductor nanocrystals

Biophysicists have long sought optical methods capable of reporting the electrophysiological dynamics of large-scale neural networks with millisecond-scale temporal resolution. Existing fluorescent sensors of cell membrane voltage can report action potentials in individual cultured neurons, but limitations in brightness and dynamic range of both synthetic organic and genetically encoded voltage sensors have prevented concurrent monitoring of spiking activity across large populations of individual neurons. Here we propose a novel, inorganic class of fluorescent voltage sensors: semiconductor nanoparticles, such as ultrabright quantum dots (qdots). Our calculations revealed that transmembrane electric fields characteristic of neuronal spiking (~10 mV/nm) modulate a qdot's electronic structure and can induce ~5% changes in its fluorescence intensity and ~1 nm shifts in its emission wavelength, depending on the qdot's size, composition, and dielectric environment. Moreover, tailored qdot sensors composed of two different materials can exhibit substantial (~30%) changes in fluorescence intensity during neuronal spiking. Using signal detection theory, we show that conventional qdots should be capable of reporting voltage dynamics with millisecond precision across several tens or more individual neurons over a range of optical and neurophysiological conditions. These results unveil promising avenues for imaging spiking dynamics in neural networks and merit in-depth experimental investigation.

Quantifying bursting neuron activity from calcium signals using blind deconvolution

Advances in calcium imaging have enabled studies of the dynamic activity of both individual neurons and neuronal assemblies. However, challenges, such as unknown nonlinearities in the spike-calcium relationship, noise, and the often relatively low temporal resolution of the calcium signal compared to the time-scale of spike generation, restrict the accurate estimation of action potentials from the calcium signal. Complex neuronal discharge, such as the activity demonstrated by bursting and rhythmically active neurons, represents an even greater challenge for reconstructing spike trains based on calcium signals. We propose a method using blind calcium signal deconvolution based on an information-theoretic approach. This model is meant to maximise the output entropy of a nonlinear filter where the nonlinearity is defined by the cumulative distribution function of the spike signal. We tested our maximum entropy (ME) algorithm using bursting olfactory receptor neurons (bORNs) of the lobster olfactory organ. The advantage of the ME algorithm is that the filter can be trained online based only on the statistics of the spike signal, without any assumptions regarding the unknown transfer function characterizing the relation between the spike and calcium signal. We show that the ME method is able to more accurately reconstruct the timing of the first and last spikes of a burst compared to other methods and that it improves the temporal precision fivefold compared to direct timing resolution of calcium signal.

Photon shot noise limits on optical detection of neuronal spikes and estimation of spike timing

Optical approaches for tracking neural dynamics are of widespread interest, but a theoretical framework quantifying the physical limits of these techniques has been lacking. We formulate such a framework by using signal detection and estimation theory to obtain physical bounds on the detection of neural spikes and the estimation of their occurrence times as set by photon counting statistics (shot noise). These bounds are succinctly expressed via a discriminability index that depends on the kinetics of the optical indicator and the relative fluxes of signal and background photons. This approach facilitates quantitative evaluations of different indicators, detector technologies, and data analyses. Our treatment also provides optimal filtering techniques for optical detection of spikes. We compare various types of Ca(2+) indicators and show that background photons are a chief impediment to voltage sensing. Thus, voltage indicators that change color in response to membrane depolarization may offer a key advantage over those that change intensity. We also examine fluorescence resonance energy transfer indicators and identify the regimes in which the widely used ratiometric analysis of signals is substantially suboptimal. Overall, by showing how different optical factors interact to affect signal quality, our treatment offers a valuable guide to experimental design and provides measures of confidence to assess optically extracted traces of neural activity.

Two-photon compatibility and single-voxel, single-trial detection of subthreshold neuronal activity by a two-component optical voltage sensor

Minimally invasive measurements of neuronal activity are essential for understanding how signal processing is performed by neuronal networks. While optical strategies for making such measurements hold great promise, optical sensors generally lack the speed and sensitivity necessary to record neuronal activity on a single-trial, single-neuron basis. Here we present additional biophysical characterization and practical improvements of a two-component optical voltage sensor (2cVoS), comprised of the neuronal tracer dye, DiO, and dipicrylamine (DiO/DPA). Using laser spot illumination we demonstrate that membrane potential-dependent fluorescence changes can be obtained in a wide variety of cell types within brain slices. We show a correlation between membrane labeling and the sensitivity of the magnitude of fluorescence signal, such that neurons with the brightest membrane labeling yield the largest ΔF/F values per action potential (AP; ∼40%). By substituting a blue-shifted donor for DiO we confirm that DiO/DPA works, at least in part, via a Förster resonance energy transfer (FRET) mechanism. We also describe a straightforward iontophoretic method for labeling multiple neurons with DiO and show that DiO/DPA is compatible with two-photon (2P) imaging. Finally, exploiting the high sensitivity of DiO/DPA, we demonstrate AP-induced fluorescence transients (fAPs) recorded from single spines of hippocampal pyramidal neurons and single-trial measurements of subthreshold synaptic inputs to granule cell dendrites. Our findings suggest that the 2cVoS, DiO/DPA, enables optical measurements of trial-to-trial voltage fluctuations with very high spatial and temporal resolution, properties well suited for monitoring electrical signals from multiple neurons within intact neuronal networks.

Optically monitoring voltage in neurons by photo-induced electron transfer through molecular wires

Fluorescence imaging is an attractive method for monitoring neuronal activity. A key challenge for optically monitoring voltage is development of sensors that can give large and fast responses to changes in transmembrane potential. We now present fluorescent sensors that detect voltage changes in neurons by modulation of photo-induced electron transfer (PeT) from an electron donor through a synthetic molecular wire to a fluorophore. These dyes give bigger responses to voltage than electrochromic dyes, yet have much faster kinetics and much less added capacitance than existing sensors based on hydrophobic anions or voltage-sensitive ion channels. These features enable single-trial detection of synaptic and action potentials in cultured hippocampal neurons and intact leech ganglia. Voltage-dependent PeT should be amenable to much further optimization, but the existing probes are already valuable indicators of neuronal activity.

An optically stabilized fast-switching light emitting diode as a light source for functional neuroimaging

Neuroscience research increasingly relies on optical methods for evoking neuronal activity as well as for measuring it, making bright and stable light sources critical building blocks of modern experimental setups. This paper presents a method to control the brightness of a high-power light emitting diode (LED) light source to an unprecedented level of stability. By continuously monitoring the actual light output of the LED with a photodiode and feeding the result back to the LED's driver by way of a proportional-integral controller, drift was reduced to as little as 0.007% per hour over a 12-h period, and short-term fluctuations to 0.005% root-mean-square over 10 seconds. The LED can be switched on and off completely within 100 s, a feature that is crucial when visual stimuli and light for optical recording need to be interleaved to obtain artifact-free recordings. The utility of the system is demonstrated by recording visual responses in the central nervous system of the medicinal leech Hirudo verbana using voltage-sensitive dyes.

Visualization and manipulation of neural activity in the developing vertebrate nervous system

Neural activity during vertebrate development has been unambiguously shown to play a critical role in sculpting circuit formation and function. Patterned neural activity in various parts of the developing nervous system is thought to modulate neurite outgrowth, axon targeting, and synapse refinement. The nature and role of patterned neural activity during development has been classically studied with in vitro preparations using pharmacological manipulations. In this review we discuss newly available and developing molecular-genetic tools for the visualization and manipulation of neural activity patterns specifically during development.

Denoising two-photon calcium imaging data

Two-photon calcium imaging is now an important tool for in vivo imaging of biological systems. By enabling neuronal population imaging with subcellular resolution, this modality offers an approach for gaining a fundamental understanding of brain anatomy and physiology. Proper analysis of calcium imaging data requires denoising, that is separating the signal from complex physiological noise. To analyze two-photon brain imaging data, we present a signal plus colored noise model in which the signal is represented as harmonic regression and the correlated noise is represented as an order autoregressive process. We provide an efficient cyclic descent algorithm to compute approximate maximum likelihood parameter estimates by combing a weighted least-squares procedure with the Burg algorithm. We use Akaike information criterion to guide selection of the harmonic regression and the autoregressive model orders. Our flexible yet parsimonious modeling approach reliably separates stimulus-evoked fluorescence response from background activity and noise, assesses goodness of fit, and estimates confidence intervals and signal-to-noise ratio. This refined separation leads to appreciably enhanced image contrast for individual cells including clear delineation of subcellular details and network activity. The application of our approach to in vivo imaging data recorded in the ferret primary visual cortex demonstrates that our method yields substantially denoised signal estimates. We also provide a general Volterra series framework for deriving this and other signal plus correlated noise models for imaging. This approach to analyzing two-photon calcium imaging data may be readily adapted to other computational biology problems which apply correlated noise models.

Optical recording of neuronal spiking activity from unbiased populations of neurons with high spike detection efficiency and high temporal precision

Activity in populations of neurons is essential for cortical function including signaling of information and signal transport. Previous methods have made advances in recording activity from many neurons but have both technical and analytical limitations. Here we present an optical method, dithered random-access functional calcium imaging, to record somatic calcium signals from up to 100 neurons, in vitro and in vivo. We further developed a maximum-likelihood deconvolution algorithm to detect spikes and precise spike timings from the recorded calcium fluorescence signals. Spike detection efficiency and spike timing detection was determined in acute slices of juvenile mice. The results indicate that the combination of the two methods detected precise spiking activity from unbiased and spatially distributed populations of neurons in acute slices with high efficiency of spike detection (>97%), low rate of false positives (0.0023 spikes/s), and high temporal precision. The results further indicate that there is only a small window of excitation intensities where high spike detection can be achieved consistently.

Fast nonnegative deconvolution for spike train inference from population calcium imaging

Fluorescent calcium indicators are becoming increasingly popular as a means for observing the spiking activity of large neuronal populations. Unfortunately, extracting the spike train of each neuron from a raw fluorescence movie is a nontrivial problem. This work presents a fast nonnegative deconvolution filter to infer the approximately most likely spike train of each neuron, given the fluorescence observations. This algorithm outperforms optimal linear deconvolution (Wiener filtering) on both simulated and biological data. The performance gains come from restricting the inferred spike trains to be positive (using an interior-point method), unlike the Wiener filter. The algorithm runs in linear time, and is fast enough that even when simultaneously imaging >100 neurons, inference can be performed on the set of all observed traces faster than real time. Performing optimal spatial filtering on the images further refines the inferred spike train estimates. Importantly, all the parameters required to perform the inference can be estimated using only the fluorescence data, obviating the need to perform joint electrophysiological and imaging calibration experiments.

The expanding reach of the GAL4/UAS system into the behavioral neurobiology of Drosophila

Our understanding of the relationships between genes, brains, and behaviors has changed a lot since the first behavioral mutants were isolated in the fly bottles of the Benzer lab at Caltech (1), but Drosophila is still an excellent model system for studying the neurobiology of behavior. Recent advances provide an unprecedented level of control over fly neural circuits. Efforts are underway to add to existing GAL4-driver lines that permit exogenous expression of genetic tools in small populations of neurons. Combining these driver lines with a variety of inducible UAS lines permits the visualization of neuronal morphology, connectivity, and activity. These driver lines also make it possible to specifically ablate, inhibit, or activate subsets of neurons and assess their roles in the generation of behavioral responses. Here, I will briefly review the extensive arsenal now available to drosophilists for investigating the neuronal control of behavior.

Electrophysiology in the age of light

Electrophysiology, the 'gold standard' for investigating neuronal signalling, is being challenged by a new generation of optical probes. Together with new forms of microscopy, these probes allow us to measure and control neuronal signals with spatial resolution and genetic specificity that already greatly surpass those of electrophysiology. We predict that the photon will progressively replace the electron for probing neuronal function, particularly for targeted stimulation and silencing of neuronal populations. Although electrophysiological characterization of channels, cells and neural circuits will remain necessary, new combinations of electrophysiology and imaging should lead to transformational discoveries in neuroscience.

The optogenetic catechism

An emerging set of methods enables an experimental dialogue with biological systems composed of many interacting cell types--in particular, with neural circuits in the brain. These methods are sometimes called "optogenetic" because they use light-responsive proteins ("opto-") encoded in DNA ("-genetic"). Optogenetic devices can be introduced into tissues or whole organisms by genetic manipulation and be expressed in anatomically or functionally defined groups of cells. Two kinds of devices perform complementary functions: Light-driven actuators control electrochemical signals, while light-emitting sensors report them. Actuators pose questions by delivering targeted perturbations; sensors (and other measurements) signal answers. These catechisms are beginning to yield previously unattainable insight into the organization of neural circuits, the regulation of their collective dynamics, and the causal relationships between cellular activity patterns and behavior.

Spike inference from calcium imaging using sequential Monte Carlo methods

As recent advances in calcium sensing technologies facilitate simultaneously imaging action potentials in neuronal populations, complementary analytical tools must also be developed to maximize the utility of this experimental paradigm. Although the observations here are fluorescence movies, the signals of interest--spike trains and/or time varying intracellular calcium concentrations--are hidden. Inferring these hidden signals is often problematic due to noise, nonlinearities, slow imaging rate, and unknown biophysical parameters. We overcome these difficulties by developing sequential Monte Carlo methods (particle filters) based on biophysical models of spiking, calcium dynamics, and fluorescence. We show that even in simple cases, the particle filters outperform the optimal linear (i.e., Wiener) filter, both by obtaining better estimates and by providing error bars. We then relax a number of our model assumptions to incorporate nonlinear saturation of the fluorescence signal, as well external stimulus and spike history dependence (e.g., refractoriness) of the spike trains. Using both simulations and in vitro fluorescence observations, we demonstrate temporal superresolution by inferring when within a frame each spike occurs. Furthermore, the model parameters may be estimated using expectation maximization with only a very limited amount of data (e.g., approximately 5-10 s or 5-40 spikes), without the requirement of any simultaneous electrophysiology or imaging experiments.

Submillisecond optical reporting of membrane potential in situ using a neuronal tracer dye

A major goal in neuroscience is the development of optical reporters of membrane potential that are easy to use, have limited phototoxicity, and achieve the speed and sensitivity necessary for detection of individual action potentials in single neurons. Here we present a novel, two-component optical approach that attains these goals. By combining DiO, a fluorescent neuronal tracer dye, with dipicrylamine (DPA), a molecule whose membrane partitioning is voltage-sensitive, optical signals related to changes in membrane potential based on FRET (Förster resonance energy transfer) are reported. Using DiO/DPA in HEK-293 cells with diffraction-limited laser spot illumination, depolarization-induced fluorescence changes of 56% per 100 mV (tau approximately 0.1 ms) were obtained, while in neuronal cultures and brain slices, action potentials (APs) generated a Delta F/F per 100 mV of >25%. The high sensitivity provided by DiO/DPA enabled the detection of subthreshold activity and high-frequency APs in single trials from somatic, axonal, or dendritic membrane compartments. Recognizing that DPA can depress excitability, we assayed the amplitude and duration of single APs, burst properties, and spontaneous firing in neurons of primary cultures and brain slices and found that they are undetectably altered by up to 2 microm DPA and only slightly perturbed by 5 microm DPA. These findings substantiate a simple, noninvasive method that relies on a neuronal tracer dye for monitoring electrical signal flow, and offers unique flexibility for the study of signaling within intact neuronal circuits.

Effect of voltage sensitive fluorescent proteins on neuronal excitability

Fluorescent protein voltage sensors are recombinant proteins that are designed as genetically encoded cellular probes of membrane potential using mechanisms of voltage-dependent modulation of fluorescence. Several such proteins, including VSFP2.3 and VSFP3.1, were recently reported with reliable function in mammalian cells. They were designed as molecular fusions of the voltage sensor of Ciona intestinalis voltage sensor containing phosphatase with a fluorescence reporter domain. Expression of these proteins in cell membranes is accompanied by additional dynamic membrane capacitance, or "sensing capacitance", with feedback effect on the native electro-responsiveness of targeted cells. We used recordings of sensing currents and fluorescence responses of VSFP2.3 and of VSFP3.1 to derive kinetic models of the voltage-dependent signaling of these proteins. Using computational neuron simulations, we quantitatively investigated the perturbing effects of sensing capacitance on the input/output relationship in two central neuron models, a cerebellar Purkinje and a layer 5 pyramidal neuron. Probe-induced sensing capacitance manifested as time shifts of action potentials and increased synaptic input thresholds for somatic action potential initiation with linear dependence on the membrane density of the probe. Whereas the fluorescence signal/noise grows with the square root of the surface density of the probe, the growth of sensing capacitance is linear. We analyzed the trade-off between minimization of sensing capacitance and signal/noise of the optical read-out depending on kinetic properties and cellular distribution of the probe. The simulation results suggest ways to reduce capacitive effects at a given level of signal/noise. Yet, the simulations indicate that significant improvement of existing probes will still be required to report action potentials in individual neurons in mammalian brain tissue in single trials.

Genetically encoded fluorescent sensors of membrane potential

Imaging activity of neurons in intact brain tissue was conceived several decades ago and, after many years of development, voltage-sensitive dyes now offer the highest spatial and temporal resolution for imaging neuronal functions in the living brain. Further progress in this field is expected from the emergent development of genetically encoded fluorescent sensors of membrane potential. These fluorescent protein (FP) voltage sensors overcome the drawbacks of organic voltage sensitive dyes such as non-specificity of cell staining and the low accessibility of the dye to some cell types. In a transgenic animal, a genetically encoded sensor could in principle be expressed specifically in any cell type and would have the advantage of staining only the cell population determined by the specificity of the promoter used to drive expression. Here we critically review the current status of these developments.

Rational optimization and imaging in vivo of a genetically encoded optical voltage reporter

The hybrid voltage sensor (hVOS) combines membrane-targeted green fluorescent protein and the hydrophobic anion dipicrylamine (DPA) to provide a promising tool for optical recording of electrical activity from genetically defined populations of neurons. However, large fluorescence signals are obtained only at high DPA concentrations (>3 mum) that increase membrane capacitance to a level that suppresses neural activity. Here, we develop a quantitative model of the sensor to guide its optimization and achieved an approximate threefold increase in fractional fluorescence change at a lower DPA concentration of 2 mum. Using this optimized voltage reporter, we perform optical recordings of evoked activity in the Drosophila antennal lobe with millisecond temporal resolution but fail to detect action potentials, presumably because spike initiation and/or propagation are inhibited by the capacitive load added even at reduced DPA membrane densities. We evaluate strategies for potential further improvement of hVOS quantitatively and derive theoretical performance limits for optical voltage reporters in general.

Two-photon excitation of potentiometric probes enables optical recording of action potentials from mammalian nerve terminals in situ

We report the first optical recordings of action potentials, in single trials, from one or a few (approximately 1-2 microm) mammalian nerve terminals in an intact in vitro preparation, the mouse neurohypophysis. The measurements used two-photon excitation along the "blue" edge of the two-photon absorption spectrum of di-3-ANEPPDHQ (a fluorescent voltage-sensitive naphthyl styryl-pyridinium dye), and epifluorescence detection, a configuration that is critical for noninvasive recording of electrical activity from intact brains. Single-trial recordings of action potentials exhibited signal-to-noise ratios of approximately 5:1 and fractional fluorescence changes of up to approximately 10%. This method, by virtue of its optical sectioning capability, deep tissue penetration, and efficient epifluorescence detection, offers clear advantages over linear, as well as other nonlinear optical techniques used to monitor voltage changes in localized neuronal regions, and provides an alternative to invasive electrode arrays for studying neuronal systems in vivo.