Introduction Imaging using GECIs is a common technique utilized to measure neuronal activity [1]. This method, however, provides a proxy for neuronal activity and extracting the spiking activity from the observed fluorescence remains an open problem [2]. We utilize a set of differential equations to infer the underlying spike train from fluorescence recordings done in mice.
Methods We started from the model for the calcium concentration (c) and fluorescence (p) to estimate the underlying spike trains [3]. We focused on signals averaged over many trials and ignored Brownian noise and baseline fluorescence. The model assumed linear dynamics for c that decays exponentially, but each spike increases c by a fixed fraction. The dynamics of p is a nonlinear function of c with parameters specific to the indicator used. A key parameter is the fluorescent saturation ɣ. It is possible to calculate c(t) by inverting the equations of p. To do so requires that the saturation parameter ɣ is small enough that 1- ɣp is bounded away from 0. From c, the spike train S(t) can be calculated by inverting the linear differential equation.
Results The spike train estimation method was first optimized with ground-truth data simulated across trials and averaged. This method successfully reconstructed c and S(t) from p. We then applied the method to simultaneous recordings, using fiber photometry, of neurons of the deep cerebellar nuclei (DCN) projecting to the substantia nigra pars compacta (SNc) and dopamine neurons in the SNc, in mice performing a simple Pavlovian task [4]. The obtained spike rates were compared to signals obtained from the licking rate of the animals and a rate model of the DCN neurons, in order to estimate how the firing rates are modulated by reward value and sensory stimuli.
Discussion GECI signals provide a proxy for neural activity, but building mechanistic models that represent these signals requires neural activity rates underlying the fluorescent signals to be properly estimated. This is especially useful when the baseline and maximum rates of neural activity in the recorded regions is known and, therefore, the changes in activity due to sensory inputs, movement and extrinsic modulatory signals can be explored using meso-scale mechanistic models. We will use these results to compare different circuit motifs that include distinct feedforward and feedback connections in order to test hypotheses for the role of cerebellum inputs to the midbrain dopamine centers.
References 1. Dana H, et al. (2019). High-performance calcium sensors for imaging activity in neuronal populations and microcompartments. Nature methods, 16(7), 649–657. doi:10.1038/s41592-019-0435-6 2. Rupprecht P, et al. (2025). Spike rate inference from mouse spinal cord calcium imaging data. bioRxiv : the preprint server for biology, 2024.07.17.603957. doi:10.1101/2024.07.17.603957 3. Deneux T, et al. (2016). Accurate spike estimation from noisy calcium signals for ultrafast three-dimensional imaging of large neuronal populations in vivo. Nature communications, 7, 12190. doi:10.1038/ncomms12190 4. Washburn S, et al. (2024). The cerebellum directly modulates the substantia nigra dopaminergic activity. Nature neuroscience, 27(3), 497–513. doi:10.1038/s41593-023-01560-9
Acknowledgement This work was conducted at New Jersey Institute of Technology using data collected at Albert Einstein College of Medicine. Financial support was provided by NIH MH060605 (FN) and NSF IOS-2002863 (HGR).
