class="head no_bottom_margin" id="sec1title">IntroductionRecent advances in optical imaging techniques and genetically encoded Ca2+ indicators allow researchers to chronically record the activity of hundreds to thousands of neurons simultaneously in behaving animals (, , , , , ). This is typically done using two-photon imaging in head-fixed rodents (, , , ) or one-photon imaging with miniature microscopes in freely behaving rodents (, , , , , href="#bib5" rid="bib5" class=" bibr popnode">Cai et al., 2016). These techniques facilitate within-subject analyses that quantify changes in neuronal activity under different experimental conditions and over extended periods of time (reviewed in href="#bib52" rid="bib52" class=" bibr popnode">Ziv and Ghosh, 2015). However, without identifying the same individual neurons across imaging sessions, the analysis of time-lapse imaging data becomes limited to population-level statistics, thus losing a critical advantage offered by optical imaging relative to dense electrophysiological recordings. Following the activity of the same neurons over time can uncover the changes in the coding properties of individual cells and in the joint activity patterns that underlie the population-level statistics (href="#bib17" rid="bib17" class=" bibr popnode">Huber et al., 2012, href="#bib53" rid="bib53" class=" bibr popnode">Ziv et al., 2013, href="#bib24" rid="bib24" class=" bibr popnode">Lütcke et al., 2013, href="#bib18" rid="bib18" class=" bibr popnode">Jennings et al., 2015, href="#bib37" rid="bib37" class=" bibr popnode">Rubin et al., 2015, href="#bib4" rid="bib4" class=" bibr popnode">Burgess et al., 2016, href="#bib5" rid="bib5" class=" bibr popnode">Cai et al., 2016, href="#bib23" rid="bib23" class=" bibr popnode">Liberti et al., 2016, href="#bib36" rid="bib36" class=" bibr popnode">Rose et al., 2016, href="#bib10" rid="bib10" class=" bibr popnode">Driscoll et al., 2017, href="#bib13" rid="bib13" class=" bibr popnode">Grewe et al., 2017). Such accounts of long-term dynamics are crucially absent in many fields of neuroscience, including the study of learning and long-term memory, where understanding how information is represented, stored, and changes with time is key.To longitudinally follow the activity of individual neurons, the same cells need to be reliably identified (registered) across all time points in the experiment. Registration of the same neurons becomes challenging as the number of detected cells in a session, the number of sessions, and the intervals between them increase. Cell registration is further complicated in data from one-photon Ca2+ imaging, in comparison to two-photon imaging, due to light scattering and lack of optical sectioning (href="#bib48" rid="bib48" class=" bibr popnode">Wilt et al., 2009, href="#bib50" rid="bib50" class=" bibr popnode">Yang and Yuste, 2017), both of which increase the crosstalk between the signals of neighboring neurons in the two-dimensional field of view (FOV). Furthermore, since one-photon microscopy mostly reveals transient and localized changes in fluorescence that exceed the background noise, a cell must be active to be detected. Thus, the set of detected cells can differ between sessions (href="#bib53" rid="bib53" class=" bibr popnode">Ziv et al., 2013, href="#bib35" rid="bib35" class=" bibr popnode">Resendez et al., 2016, href="#bib13" rid="bib13" class=" bibr popnode">Grewe et al., 2017, href="#bib49" rid="bib49" class=" bibr popnode">Xia et al., 2017), and a one-to-one mapping of neural identity across sessions is typically not attainable. Taken together, these factors introduce uncertainty and, consequently, potential errors to the cell registration procedure.While numerous methods for detecting cells and extracting their activity from Ca2+ imaging data have been developed (href="#bib34" rid="bib34" class=" bibr popnode">Reidl et al., 2007, href="#bib45" rid="bib45" class=" bibr popnode">Vogelstein et al., 2009, href="#bib46" rid="bib46" class=" bibr popnode">Vogelstein et al., 2010, href="#bib27" rid="bib27" class=" bibr popnode">Mukamel et al., 2009, href="#bib12" rid="bib12" class=" bibr popnode">Grewe et al., 2010, href="#bib39" rid="bib39" class=" bibr popnode">Smith and Häusser, 2010, href="#bib29" rid="bib29" class=" bibr popnode">Oñativia et al., 2013, href="#bib30" rid="bib30" class=" bibr popnode">Pachitariu et al., 2013, href="#bib26" rid="bib26" class=" bibr popnode">Maruyama et al., 2014, href="#bib33" rid="bib33" class=" bibr popnode">Pnevmatikakis et al., 2016, href="#bib43" rid="bib43" class=" bibr popnode">Theis et al., 2016), relatively little effort has been devoted to the issue of cell registration across sessions. Previous studies that registered cells across sessions (href="#bib53" rid="bib53" class=" bibr popnode">Ziv et al., 2013, href="#bib18" rid="bib18" class=" bibr popnode">Jennings et al., 2015, href="#bib37" rid="bib37" class=" bibr popnode">Rubin et al., 2015, href="#bib5" rid="bib5" class=" bibr popnode">Cai et al., 2016, href="#bib23" rid="bib23" class=" bibr popnode">Liberti et al., 2016, href="#bib22" rid="bib22" class=" bibr popnode">Kitamura et al., 2017), regardless of whether using manual or automatic routines, did not provide a quantitative evaluation of registration accuracy in terms of false-positive errors (different cells falsely registered as the same cells) and false-negative errors (the same cells falsely registered as different cells). The lack of such quantitative evaluation could be detrimental in cases where the acquired data are inadequate for longitudinal analysis and may lead to misinterpretation of the data (href="#bib15" rid="bib15" class=" bibr popnode">Harris et al., 2016). For example, either falsely identifying two different cells as the same or falsely identifying the same cell as two different cells can lead to false conclusions about the dynamics of the neuronal activity. Moreover, previous work has used fixed registration decision parameters (e.g., distance threshold), which were not optimized to the specific data.To address these problems, we adopted a probabilistic approach to devise a method for automated cell registration across sessions. By modeling the distribution of similarities between neighboring cells across sessions, our method estimates the confidence of registration associated with each cell in the data. Moreover, it estimates the overall rates of false-positive and false-negative errors for different registration decision parameters. This approach enables cell registration that is adaptive and optimized to different datasets. Applying our method to data recorded from the hippocampus and cortex of behaving mice, we show that the same cells can be tracked over multiple weeks with estimated false-positive and false-negative rates <5%, yielding more accurate registration than the routines utilized in previous studies. Moreover, we find that registration accuracy remains high with increased numbers of sessions, demonstrating the method’s suitability for longitudinal studies. We provide an open source MATLAB code for cell registration that implements the approach presented in this paper (see href="#sec4" rid="sec4" class=" sec">Experimental Procedures).
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