Behavior emerges out of the coordinated activity of large neuronal populations. Understanding the neural basis of specific behaviors will require interpretation of the dynamics of this activity and, to address causality, real-time perturbation. Much effort is currently aimed at maximizing the number of neurons that can be optically recorded simultaneously in experimental preparations allowing concurrent behavioral measurement. As the size of data sets grows, so grows the need for methodology facilitating the localization within these sets of neurons relevant to measured behaviors, both during experiments and subsequent off-line data analysis. We have addressed this need by developing a regression-based method for rapidly identifying cells displaying behaviorally correlated neural activity within fluorescence image time series. We applied this method to data collected from a novel preparation allowing simultaneous tracking of eye position and two-photon imaging of optical probes measuring calcium concentration changes in awake, behaving zebrafish larvae. The identification of eye-movement–related activity with cellular resolution using our method enabled targeted electrical recordings and optical ablations that localized the hVPNI in these larvae. We found a broad distribution of cells encoding eye position and ipsiversive velocity that differs markedly from the highly confined distribution in adult goldfish (Aksay et al. 2000
Our identification method succeeded because we were able to formulate a linear regression model that accounted for a substantial degree of the structure of fluorescence fluctuations in the cells we sought. This hinged on two main factors: 1
) a sufficiently good prior expectation of the encryption of behavioral parameters in the firing patterns of our cells of interest and 2
) a sufficiently good approximation of the mapping between firing and calcium-sensitive fluorescence fluctuations. The rapidity of our identification procedure stemmed from the use of a linear model, for which a computationally cheap closed-form solution to the regression problem exists, and the legitimacy of parametric statistical testing, which allowed us to avoid bootstrap-based nonparametric tests. Ultimately, the sensitivity of an approach such as ours depends on how much of the structure of cellular fluorescence fluctuations the regression model is able to capture. Our results show that models assuming approximations to behavior–firing relations and firing–calcium concentration relations can perform well. It is possible that the exponentially decaying CIRF we have used here may not be sufficient for cell identification in other contexts. CIRFs of this form have been useful for firing rate estimation (Yaksi and Friedrich 2006
), but in general CIRF form may need to be estimated uniquely for distinct cell types and more complex functional forms may be necessary for certain applications. It is important to note that the ability to later infer action potential firing from optical measurements alone in identified neurons can be diminished by a lack of biophysical realism in assumed firing–calcium concentration relations.
The determinants of our method's strength also evidence certain limitations. It likely will not always be the case that a linear model captures essentially all the structure in fluorescence fluctuations, particularly for data sets with high temporal resolution. This could result, for example, from a nonlinear dependence of underlying neuronal firing on measured behavioral variables or from temporally structured components of firing that are independent of these variables. Cells whose activity depends nonlinearly on behavior could still be identified if that nonlinearity has a significant linear correlation over the measured range of behavior. However, in these cases an approximately normal residual distribution is not guaranteed and nonparametric statistical testing relying on bootstrap sampling could be used instead, although at a computational cost. Alternately, methods that account for signal structure not captured by regressors, recovering the ability to parametrically test the significance of linear correlations (Leek and Storey 2008
), could be implemented. The general approach taken here would be compatible with the use of nonlinear regression models in cases in which linear models fail to capture a sufficient fraction of the signal structure for the desired purpose. Following the initial application of linear regression models, nonlinear models have been used extensively in analysis of fMRI time series (Buchel et al. 1996
; Friston et al. 1998
; Genovese 2000
). We expect a similar analytical development in the future as the problem of identifying neurons demonstrating behaviorally related activity from cellular resolution optical recordings is progressively addressed by researchers. It is also important to note that our method relies on univariate statistics, testing behavioral correlation at individual pixels separately. Improved detection sensitivity could be achieved using multivariate statistical methods that could account for behavioral dependence on collective fluorescence changes across pixels. Such methods have been successfully applied in the analysis of fMRI data in which researchers are searching for groups of voxels that carry information about cognitive or behavioral variables (Norman et al. 2006
). One caveat to consider here is that when testing the significance of the relationship of groups of pixels with behavior, a null model characterizing the expected correlation between image pixels must be assumed.
Despite its limitations, our approach should fill an important niche among methods for image time series analysis, speeding both on-line and off-line identification of neurons encoding measured behaviors. To date, most reported analyses of in vivo optical recording data have relied on manual ROI definition (Dombeck et al. 2007
; Kerr et al. 2005
; Niell and Smith 2005
), which can be laborious, particularly with imaging of large populations, and may not be tenable for cell identification during experiments. Automated methods for cell identification have been described that make use of cell morphology apparent in image contrast (Dorostkar et al. 2010
; Ohki et al. 2005
; Valmianski et al. 2010
) and/or the correlation structure of image time series (Mukamel et al. 2009
; Ozden et al. 2008
). The former type has been applied to segment cells in cortex, but it remains unclear how well it would perform when confronted with situations where cells are more closely packed, as in the larval zebrafish CNS, or fluorescent labeling provides limited contrast between somata and neuropil. Correlation-based methods require a certain degree of independence between cells to distinguish them. For example, the ICA-based method described by Mukamel et al. (2009)
begins to have trouble separating cells when the pairwise correlation of their calcium-sensitive fluorescence exceeds 0.8. Yet in our data, closely apposed cells commonly had correlations >0.9. Whereas Mukamel and colleagues turn to image segmentation to separate highly correlated cells, the dense packing of highly correlated cells in the zebrafish hindbrain drove us instead to use local maxima and minima in maps of behavior correlation to draw cellular boundaries.
Using our method, we were able to find many somata demonstrating fluorescence fluctuations consistent with an underlying firing rate encoding eye position and/or ipsiversive velocity. The firing of hVPNI neurons in adult vertebrate preparations encodes mixtures of these two variables. Strictly speaking, cells belonging to the hVPNI have at least some position-sensitive firing, yet some of the cells we have found could be exclusively velocity sensitive. These cells could represent developmentally immature neurons that will later encode eye position or saccadic burst neurons that encode ipsiversive velocity and drive saccades.
Our observation of a broad distribution of putative hVPNI neurons across space provides an important snapshot of hVPNI development. Based on the spatial extent of goldfish Area I (Aksay et al. 2000
), we might expect to find such neurons in a more confined region of the hindbrain. The rostrocaudal extent of goldfish Area I represents roughly 10% of the length of the brain stem from the abducens nucleus to the rostral end of the spinal cord, whereas our imaging window represents about 50% of the equivalent extent in zebrafish larvae. Goldfish Area I is also confined to proportionally smaller extents along the mediolateral and dorsoventral axes. Because the gross morphology of the developing hindbrain at the stage we imaged differs from that of the mature brain stem, we expect that the broad distribution reflects the structure of the hVPNI early in development rather than an interspecies difference. The methods we demonstrate should provide a straightforward means to study the development of the spatial organization and dynamics of the hVPNI.
Our preparation and regression-based method will be useful for further study of the mechanisms underlying persistent neural activity within the hVPNI, complementing previous investigations using electrical recording. Two-photon excitation is minimally invasive, limiting not only damage to the microcircuitry under examination but also disturbance of behavior. The use of optical recording is free from certain biases inherent in searching for putative integrator cells with microelectrodes, such as the confinement to isolatable units and the experimenter's arbitration in selecting cells for recording. Emerging techniques for connectivity mapping and subcellular activation measurements among optically identified neuronal populations on short spatial scales should be compatible with the preparation. This would enable a more direct assessment of the extent to which recurrent connections among hVPNI neurons and bistability/multistability within their dendrites subserve firing persistence (Aksay et al. 2001
; Goldman et al. 2003
) than has been feasible to date.
Beyond our preparation, a regression-based cell identification approach should be broadly useful, facilitating experiments aimed at elucidating the logic of microcircuits subserving behavior. Rapid cell identification of behaviorally correlated neurons will enable subsequent cell-specific activity perturbation using laser ablation, juxtacellular stimulation, or the excitation of optogenetic probes. Although we did not use it here to demonstrate hVPNI functionality, we have successfully laser ablated individual identified position-encoding neurons (data not shown). Fast identification may at times be critical in testing ideas about microcircuit function and collective dynamics among component neurons, since this could require not just activity perturbation in arbitrary cells, but in cells with specific activity patterns. The cells identified by our method could also be targeted for neuroanatomical assessment via, for example, electrode-based electroporation of fluorescent probes revealing morphology or synaptic connections, allowing activity measurements to be interpreted vis-à-vis network architecture. Since the subcellular spatial resolution optical recording affords does come with reduced temporal resolution, the identification of cells of interest during an experiment would allow subsequent targeted scanning of these cells at high sampling frequencies or targeted electrical recording. This would speed the collection of high temporal resolution activity measurements from large numbers of behaviorally relevant neurons. Coupling our identification method with emerging techniques for fast random access scanning could allow such measurements to be made simultaneously.
A regression-based approach could be useful for the identification of other cell types functionally imaged simultaneous to behavioral measurement. For example, place or head direction cells typically show firing rate tuning curves relative to an animal's position in one dimension (McNaughton et al. 1983
) or head direction (Taube and Bassett 2003
), respectively, that could be approximated by piecewise linear functions. The same should hold for tuning curves in terms of calcium-sensitive fluorescence. Regression of pixel fluorescence on position or head direction using a piecewise linear model and subsequent significance testing of regression coefficients could be used to identify pixels comprising cells with distinct position or head direction sensitivity. A closed-form solution to the regression problem using a piecewise linear model can be derived for the case in which the x
coordinates of connection points between linear pieces are known and these connection points could be estimated from data prior to model fitting. For head direction cells, firing rate is well described as a piecewise linear function of head direction and the same may be true for fluorescence, such that normally distributed residuals would result from the regression and significance testing would be fast. More generally, our method, when coupled with targeted recording to validate activity–parameter correlations and laser ablation to validate predicted functionality represents a promising framework for optically guided mapping of neuronal populations underlying behavior.