Fast non-negative temporal deconvolution for laser scanning microscopy

Mechanisms of synapse-to-nucleus calcium signalling in striatal neurons and impairments in Huntington's disease

Huntington's disease (HD) is a monogenic disorder with autosomal dominant inheritance. In HD patients, neurons in the striatum and cortex degenerate, leading to motor, psychiatric and cognitive disorders. Dysregulated synaptic function and calcium handling are common in many neurodegenerative diseases, including HD. N-methyl-D-aspartate (NMDA) receptor function is enhanced in HD at extrasynaptic sites, altering the balance of calcium-dependent neuronal survival versus death signalling pathways. Endoplasmic reticulum (ER) calcium handling is also abnormal in HD. The ER, which is continuous with the nuclear envelope, is purportedly involved in nuclear calcium signalling; based on this, we hypothesised that nuclear calcium signalling is altered in HD. We explored this hypothesis with calcium imaging techniques, including simultaneous epifluorescent imaging of cytosolic and nuclear calcium using jRCaMP1b and GCaMP3 sensors, respectively, in striatal spiny projection neurons in cortical-striatal co-cultures from the YAC128 mouse model of HD. Our data show contributions from a variety of calcium channels to nuclear calcium signalling. NMDA receptors (NMDARs) play an essential role in initiating action potential-dependent calcium signalling to the nucleus, and ryanodine receptors (RyR) contribute to both cytosolic and nuclear calcium signals. Unlike previous reports in glutamatergic hippocampal and cortical neurons, we found that in GABAergic striatal neurons, L-type voltage-gated calcium channels (CaV) contribute to cytosolic, but not nuclear calcium signalling. Calcium imaging also suggests impairments in nuclear calcium signalling in HD striatal neurons, where spontaneous action potential-dependent calcium transients in the nucleus were smaller in YAC128 striatal neurons compared to those of wild-type (WT). Our results elucidate mechanisms involved in action potential-dependent nuclear calcium signalling in GABAergic striatal neurons, and have revealed a clear deficit in this signalling in HD.

Two-photon imaging with silicon photomultipliers

We compared performance of recently developed silicon photomultipliers (SiPMs) to GaAsP photomultiplier tubes (PMTs) for two-photon imaging of neural activity. Despite higher dark counts, SiPMs match or exceed the signal-to-noise ratio of PMTs at photon rates encountered in typical calcium imaging experiments due to their low pulse height variability. At higher photon rates encountered during high-speed voltage imaging, SiPMs substantially outperform PMTs.

Kilohertz frame-rate two-photon tomography

Point-scanning two-photon microscopy enables high-resolution imaging within scattering specimens such as the mammalian brain, but sequential acquisition of voxels fundamentally limits its speed. We developed a two-photon imaging technique that scans lines of excitation across a focal plane at multiple angles and computationally recovers high-resolution images, attaining voxel rates of over 1 billion Hz in structured samples. Using a static image as a prior for recording neural activity, we imaged visually evoked and spontaneous glutamate release across hundreds of dendritic spines in mice at depths over 250 µm and frame rates over 1 kHz. Dendritic glutamate transients in anesthetized mice are synchronized within spatially contiguous domains spanning tens of micrometers at frequencies ranging from 1-100 Hz. We demonstrate millisecond-resolved recordings of acetylcholine and voltage indicators, three-dimensional single-particle tracking and imaging in densely labeled cortex. Our method surpasses limits on the speed of raster-scanned imaging imposed by fluorescence lifetime.

Information-Theoretic Approach and Fundamental Limits of Resolving Two Closely Timed Neuronal Spikes in Mouse Brain Calcium Imaging

OBJECTIVE

Although optical imaging of neurons using fluorescent genetically encoded calcium sensors has enabled large-scale in vivo experiments, the sensors' slow dynamics often blur closely timed action potentials into indistinguishable transients. While several previous approaches have been proposed to estimate the timing of individual spikes, they have overlooked the important and practical problem of estimating interspike interval (ISI) for overlapping transients.

METHODS

We use statistical detection theory to find the minimum detectable ISI under different levels of signal-to-noise ratio (SNR), model complexity, and recording speed. We also derive the Cramer-Rao lower bounds (CRBs) for the problem of ISI estimation. We use Monte-Carlo simulations with biologically derived parameters to numerically obtain the minimum detectable ISI and evaluate the performance of our estimators. Furthermore, we apply our detector to distinguish overlapping transients from experimentally obtained calcium imaging data.

RESULTS

Experiments based on simulated and real data across different SNR levels and recording speeds show that our algorithms can accurately distinguish two fluorescence signals with ISI on the order of tens of milliseconds, shorter than the waveform's rise time. Our study shows that the statistically optimal ISI estimators closely approached the CRBs.

CONCLUSION

Our work suggests that full analysis using recording speed, sensor kinetics, SNR, and the sensor's stochastically distributed response to action potentials can accurately resolve ISIs much smaller than the fluorescence waveform's rise time in modern calcium imaging experiments.

SIGNIFICANCE

Such analysis aids not only in future spike detection methods, but also in future experimental design when choosing sensors of neuronal activity.

Fast online deconvolution of calcium imaging data

Fluorescent calcium indicators are a popular means for observing the spiking activity of large neuronal populations, but extracting the activity of each neuron from raw fluorescence calcium imaging data is a nontrivial problem. We present a fast online active set method to solve this sparse non-negative deconvolution problem. Importantly, the algorithm 3progresses through each time series sequentially from beginning to end, thus enabling real-time online estimation of neural activity during the imaging session. Our algorithm is a generalization of the pool adjacent violators algorithm (PAVA) for isotonic regression and inherits its linear-time computational complexity. We gain remarkable increases in processing speed: more than one order of magnitude compared to currently employed state of the art convex solvers relying on interior point methods. Unlike these approaches, our method can exploit warm starts; therefore optimizing model hyperparameters only requires a handful of passes through the data. A minor modification can further improve the quality of activity inference by imposing a constraint on the minimum spike size. The algorithm enables real-time simultaneous deconvolution of O(10⁵) traces of whole-brain larval zebrafish imaging data on a laptop.

Calcium imaging methods enable simultaneous measurement of the activity of thousands of neighboring neurons, but come with major caveats: the slow decay of the fluorescence signal compared to the time course of the underlying neural activity, limitations in signal quality, and the large scale of the data all complicate the goal of efficiently extracting accurate estimates of neural activity from the observed video data. Further, current activity extraction methods are typically applied to imaging data after the experiment is complete. However, in many cases we would prefer to run closed-loop experiments—analyzing data on-the-fly to guide the next experimental steps or to control feedback—and this requires new methods for accurate real-time processing. Here we present a fast activity extraction algorithm addressing both issues. Our approach follows previous work in casting the activity extraction problem as a sparse nonnegative deconvolution problem. To solve this optimization problem, we introduce a new algorithm that is an order of magnitude faster than previous methods, and progresses through the data sequentially from beginning to end, thus enabling, in principle, real-time online estimation of neural activity during the imaging session. This computational advance thus opens the door to new closed-loop experiments.

Reconstruction of burst activity from calcium imaging of neuronal population via Lq minimization and interval screening

Calcium imaging is becoming an increasingly popular technology to indirectly measure activity patterns in local neuronal networks. Based on the dependence of calcium fluorescence on neuronal spiking, two-photon calcium imaging affords single-cell resolution of neuronal population activity. However, it is still difficult to reconstruct neuronal activity from complex calcium fluorescence traces, particularly for traces contaminated by noise. Here, we describe a robust and efficient neuronal-activity reconstruction method that utilizes Lq minimization and interval screening (IS), which we refer to as LqIS. The simulation results show that LqIS performs satisfactorily in terms of both accuracy and speed of reconstruction. Reconstruction of simulation and experimental data also shows that LqIS has advantages in terms of the recall rate, precision rate, and timing error. Finally, LqIS is demonstrated to effectively reconstruct neuronal burst activity from calcium fluorescence traces recorded from large-size neuronal population.

Error estimation for reconstruction of neuronal spike firing from fast calcium imaging

Calcium imaging is becoming an increasingly popular technology to indirectly measure activity patterns in local neuronal networks. Calcium transients reflect neuronal spike patterns allowing for spike train reconstructed from calcium traces. The key to judging spiking train authenticity is error estimation. However, due to the lack of an appropriate mathematical model to adequately describe this spike-calcium relationship, little attention has been paid to quantifying error ranges of the reconstructed spike results. By turning attention to the data characteristics close to the reconstruction rather than to a complex mathematic model, we have provided an error estimation method for the reconstructed neuronal spiking from calcium imaging. Real false-negative and false-positive rates of 10 experimental Ca(2+) traces were within the estimated error ranges and confirmed that this evaluation method was effective. Estimation performance of the reconstruction of spikes from calcium transients within a neuronal population demonstrated a reasonable evaluation of the reconstructed spikes without having real electrical signals. These results suggest that our method might be valuable for the quantification of research based on reconstructed neuronal activity, such as to affirm communication between different neurons.

Optimized temporally deconvolved Ca²⁺ imaging allows identification of spatiotemporal activity patterns of CA1 hippocampal ensembles

Hippocampal activity is characterized by the coordinated firing of a subset of neurons. Such neuronal ensembles can either be driven by external stimuli to form new memory traces or be reactivated by intrinsic mechanisms to reactivate and consolidate old memories. Hippocampal network oscillations orchestrate this coherent activity. One key question is how the topology, i.e. the functional connectivity of neuronal networks supports their desired function. Recently, this has been addressed by characterizing the intrinsic properties for the highly recurrently connected CA3 region using organotypic slice cultures and Ca(2+) imaging. In the present study, we aimed to determine the properties of CA1 hippocampal ensembles at high temporal and multiple single cell resolution. Thus, we performed Ca(2+) imaging using the chemical fluorescent Ca(2+) indicator Oregon Green BAPTA 1-AM. To achieve most physiological conditions, we used acute hippocampal slices that were recorded in a so-called interface chamber. To faithfully reconstruct firing patterns of multiple neurons in the field of view, we optimized deconvolution-based detection of action potential associated Ca(2+) events. Our approach outperformed currently available detection algorithms by its sensitivity and robustness. In combination with advanced network analysis, we found that acute hippocampal slices contain a median of 11 CA1 neuronal ensembles with a median size of 4 neurons. This apparently low number of neurons is likely due to the confocal imaging acquisition and therefore yields a lower limit. The distribution of ensemble sizes was compatible with a scale-free topology, as far as can be judged from data with small cell numbers. Interestingly, cells were more tightly clustered in large ensembles than in smaller groups. Together, our data show that spatiotemporal activity patterns of hippocampal neuronal ensembles can be reliably detected with deconvolution-based imaging techniques in mouse hippocampal slices. The here presented techniques are fully applicable to similar studies of distributed optical measurements of neuronal activity (in vivo), where signal-to-noise ratio is critical.