µFIX – Enabling Combinations of Concurrent Optogenetics and Lock-in Amplification Fiber Photometry via Removal of Optogenetic Stimulation Crosstalk

9 Simultaneous fiber photometry and optogenetics is a powerful emerging technique for precisely 10 studying the interactions of neuronal brain networks. However, spectral overlap between 11 photometry and optogenetic components has severely limited the application of an all-optical 12 approach. Due to spectral overlap, light from optogenetic stimulation saturates the photosensor 13 and occludes photometry fluorescence, which is especially problematic in physically smaller 14 model organism brains like mice. Here, we demonstrate the Multi-Frequency Interpolation X-15 talk removal algorithm (MuFIX, or µFIX) for recovering crosstalk-contaminated photometry 16 responses recorded with lock-in amplification. µFIX exploits multi-frequency lock-in 17 amplification by modeling the remaining uncontaminated data to interpolate across crosstalk-18 affected segments (R2 ~ 1.0); we found that this approach accurately recovers the original 19 photometry response after demodulation (Pearson’s r ~ 1.0). When applied to crosstalk-20 contaminated data, µFIX recovered a photometry response closely resembling the dynamics of 21 non-crosstalk photometry recorded simultaneously. Upon further verification using simulated 22 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint and empirical data, we demonstrated that µFIX reproduces any signal that underwent simulated 23 crosstalk contamination (r ~ 1.0). We believe adopting µFIX will enable experimental designs 24 using simultaneous fiber photometry and optogenetics that were previously not feasible due to 25 crosstalk. 26

fiber photometry; optogenetics; interference; biosensor; epilepsy; hippocampus 27 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint

28 The human brain is responsible for reason, memory, and emotion, enabling it to control our 29 interaction with the rest of the world. A complex network of diverse and specialized neurons 30 performs the brain’s functions. To understand the brain is, in part, to understand the role each 31 specialized neuron plays in this network. Modern genetic and viral engineering tools allow the 32 targeting of genetically defined neuronal subtypes to manipulate their activity and determine 33 their causal roles in behavior. Optogenetics is one such tool; it employs light to control ion 34 channels (opsins) that activate or inhibit the activity of neurons1–4. Upon exposure to light of a 35 specific range of wavelengths, opsins open to depolarize or hyperpolarize targeted neurons. The 36

of opsin manipulation or other network phenomena can be measured by imaging neuronal 37 activity with fluorescent indicator proteins5,6. Some widely adopted fluorescence indicators are 38 genetically encoded calcium indicators (GECIs; e.g., GCaMP & RCaMP variants) for monitoring 39 intracellular calcium7 and genetically encoded neurotransmitter & neuromodulator indicators 40 (GENIs)8. Wavelength-specific light exposure causes GECI (calcium) or GENI 41 (neurotransmitter) binding to emit a fluorescence indicative of neural activity or inter-neuronal 42 interaction, respectively. Whereas traditional electrophysiology indiscriminately records and 43 stimulates all types of neurons, opsins and fluorescent indicators can be expressed in chosen cell 44 types. This allows targeted interrogation of the neuronal network of interest, especially in 45 understanding the mechanism underlying their pathological states. 46 Combining optogenetics and fiber photometry5,6 builds a robust methodology for real-time 47 manipulation and simultaneous recording of targeted neurons9–12. However, overlaps in the 48 spectral ranges of the available opsins and fluorescent indicators limit the experimental design of 49 all-optical approaches. With the current GECI toolkit, it is only possible to record two 50 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint fluorescence signals in the same optic fiber: one in the green (GCaMP) and one in the orange/red 51 (RCaMP) spectra. Most readily available optogenetic tools (chiefly ChR2, C1V1, ChRmine, and 52 ChrimsonR) overlap with one or both GECI emission spectra. In applications where 53 multichannel fiber photometry is desired at a site nearby to the site of optogenetic stimulation, 54 such spectral overlaps cause recording artifacts from unavoidable optogenetic stimulation 55 crosstalk, even with high-end optical filtering or spatial separation between the optogenetic and 56 photometry sites. Furthermore, since optogenetic stimulation usually requires at least 1 mW of 57 stimulation power to be effective1,2,9,13,14, optogenetic stimulation inevitably saturates and 58 renders nanowatt-range photometry signals unusable. 59 There is a lack of solutions to address crosstalk interference that still allow lock-in amplification 60 (LIA) to capture the fiber photometry response. LIA is a common approach for recording fiber 61 photometry15 by activating indicator proteins with a sinusoid-modulated excitation light intensity 62 rather than a constant one. This produces an emitted response at the same chosen sinusoidal 63 frequency and improves the signal-to-noise ratio. Most importantly, LIA enables encoding 64 multiple signals in one carrier signal. Multiplexing with LIA can encode a neural signal 65 alongside a reference isosbestic signal on the same photosensor channel, which helps correct 66 non-neural changes in fluorescence16–18. However, optogenetic crosstalk interacts detrimentally 67 with LIA demodulation, producing artifacts that mask out the photometry response during 68 stimulation by disrupting the ability to recover the sinusoidal carrier signal. 69 The ability to compensate for optogenetic crosstalk would enable all-optical experimental 70 designs that had not been previously practical due to physical proximity and spectral overlap of 71 optogenetic and fiber photometry targets, including closed-loop experimental designs. As an 72 example of the power of this approach, we have shown that initiating focal seizures with 73 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint optogenetic stimulation in the hippocampus may involve positive feedback from the contralateral 74 hippocampus19. Our work investigating re-entrant feedback in the hippocampus, under the long-75 standing theory that seizures arise from excitation/inhibition imbalance in neuronal activity20, has 76 required readout of both the excitatory and inhibitory network activity in the contralateral 77 hippocampus while delivering optogenetic stimulation to the ipsilateral hippocampus (see 78 experimental setup illustrated in Fig. 1). Crosstalk has the potential to impede discoveries 79 leveraging the combination of optogenetics and fiber photometry and removing it will open 80 many new possibilities. 81 Here, we describe the Multi-Frequency Interpolation X-talk (µFIX, using the Greek letter Mu) 82 removal algorithm for recovering LIA photometry signals from crosstalk. We validated µFIX 83 using in vivo recording and simulated LIA photometry signals as a ground truth. We 84 demonstrated that µFIX introduces minimal distortion when applied to in vivo recordings from 85 the mouse hippocampus and defined the extent of crosstalk that µFIX can remove. Our results 86 show that µFIX recovers a highly accurate estimate of the underlying photometry response 87 originally corrupted by optogenetic stimulation crosstalk. Extended simulations indicate that 88 µFIX signal recovery is highly accurate over a robust range of stimulus durations commonly 89 employed to activate neural activity, and neural population-level temporal dynamics of 90 fluorescence indicators. 91 92 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint

93 We prepared mice to study the excitation/inhibition imbalance during seizure generation by 94 simultaneously monitoring Ca2+ fiber photometry activity in putative excitatory neurons and 95 parvalbumin-positive (PV+) interneurons in the mouse hippocampus while inducing seizures 96 with optogenetic stimulation. We transduced excitatory neurons in the left hippocampus with a 97 bicistronic viral vector containing ChRmine for optogenetic stimulation and GCaMP for fiber 98 photometry recordings in two PV-Cre mice. In the right hippocampus, we used RCaMP for 99 excitatory neuron photometry and GCaMP for PV+ interneuron photometry. The experimental 100 setup for these two mice is illustrated in Fig. 1. Their setup produces six photometry channels: 101 three primary Ca2+ indicator signals with one corresponding isosbestic signal reference each to 102 correct for non-neural fluorescence21. Optical filtering was employed using Doric mini cubes to 103 converge the excitation light and separate the emission spectra (see Methods for optical filter 104 makeup). We adopted LIA photometry to multiplex all of them simultaneously. Here, we 105 describe the unavoidable optogenetic crosstalk in this experimental setup and the technique used 106 to remove it. 107 Cross-hemispherical optogenetic crosstalk between ChRmine and RCaMP 108 Optogenetic activation of hippocampal putative excitatory neurons induces seizures in freely 109 moving mice 13,14,22. In this study, we delivered 5 ms pulse trains at 10 or 20 Hz for 30 s, 110 observing that optogenetically-induced seizures manifest as an increase from baseline in the Ca2+ 111 fiber photometry response recorded in both the ipsilateral putative excitatory (GCa1, not shown) 112 and contralateral inhibitory neurons (GCa2, Fig. 2A, B). However, we encountered optogenetic 113 stimulation crosstalk in the contralateral hippocampus on the RCaMP channel (RCa2) and its 114 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint isosbestic reference (IRa2) (Fig. 2A, B). This occurred despite advanced optical filtering and as 115 much as a 3.2 mm mediolateral (ML) separation between the recording and the stimulation sites 116 (at the same anteroposterior (AP) axis and dorsoventral (DV) axis coordinates). The 117 demodulated RCaMP signal with crosstalk contamination typically appeared as an oscillating 118 signal pattern or a step increase or decrease from the baseline during stimulation. Artifacts in the 119 Figure 1. Illustration of empirical recording setup with µFIX processing pipeline. (A) Photosensor recordings of lock-in amplified (LIA) Ca2+ photometry signal without crosstalk (i) and with crosstalk (ii). µFIX removes the crosstalk from the LIA signal (iii) to recover the underlying Ca2+ response (iv) shown in (E). (B) Doric Mini Cube input/output optical filter setup converging light sources through a single fiber optic to the tissue and splitting the fluorescent emission into GCaMP and RCaMP spectra for the recording system. (C) Diagram of implanted components in bilateral hippocampi. Ipsilateral hippocampus: Bicistronic transduction of ChRmine and GCaMP in putative excitatory neurons. Contralateral hippocampus: PV-Cre GCaMP and putative excitatory RCaMP transduction from a viral vector cocktail. (D) Histology image of mouse OP275 prepared with the illustrated empirical setup. (E) Zoom-in visualization of the contralateral hippocampus showing the underlying LIA Ca2+ response. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint RCaMP response coincide with each episode of stimulation (30s of stimulation every 120s, Fig. 120 2A), where any potential RCaMP response was obfuscated. The 589 nm wavelength laser used to 121 activate ChRmine in the ipsilateral hippocampus overlapped the emission spectrum of RCaMP 122 and was, therefore, picked up by its corresponding optical filter setup. We only needed ~2 mW 123 of light to activate ChRmine in the ipsilateral hippocampus, sufficient to saturate the RCaMP 124 photosensor in the other hippocampus immediately. 125 We explored two techniques to reduce crosstalk unsuccessfully. First, a laser light source did not 126 remove crosstalk compared to an LED light source with the same wavelength (590nm). Although 127 the laser light source had a narrower light beam and spectral band, neither factor was the cause 128 Figure 2. Optogenetic crosstalk and µFIX response recovery. (A) Photometry response before-and-after µFIX processing on a crosstalk recording. Channels RCa2 and IRa2 contain crosstalk and channel GCa2 does not. The corresponding EEG is illustrated. Gray vertical bars indicate delivery of ChRmine optogenetic stimulation, with “S” demarking a seizure response. (B) Zoom-in of a single seizure response epoch showing detail of recovered photometry response and EEG from (A). (C-D) Same as (A-B) for a recording from a mouse prepared for ChR2 stimulation. No crosstalk was observed during ChR2 optogenetic stimulation. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint for the crosstalk. Then, we postulated that light leakage occurred in the semi-translucent acrylic 129 headcap between the dual-fiber cannula, so we adopted opaque black acrylic headcaps. This also 130 did not reduce the crosstalk; we observed optogenetic light leaking out of the temporal side of 131 the animal’s head during stimulation. Our investigation led us to conclude that, due to the small 132 volume of the mouse brain, cross-cannula crosstalk came from optogenetic light reflected and 133 diffused by the animal’s brain and skull tissue. Therefore, crosstalk was inevitable and required 134 post-hoc processing. 135 µFIX: Exploiting LIA signal composition for crosstalk restoration 136 LIA demodulation of the photometry signal requires a continuous sine wave without interruption 137 or clipping; otherwise, the LIA frequency and crosstalk will interact and create artifacts. Thus, 138 we had to address the problem within the raw photosensor recording (i.e., prior to LIA 139 demodulation) to prevent it from disrupting signal extraction. We found that saturation of the 140 raw recording occurred only during the delivery of an optogenetic stimulus to the tissue. 141 Therefore, under a 20 Hz stimulation protocol with 5 ms pulses and 45 ms pauses, there would 142 be an intact response between every pulse for most of the time (~45 ms). We postulated that if 143 we can remove optogenetic artifacts by replacing these short, saturated segments with an 144 appropriate waveform, LIA demodulation would recover the underlying photometry response. 145 Our approach exploited the carrier frequency principle of LIA photometry – we termed it the 146 Multi-Frequency Interpolation of X-talk (µFIX) algorithm. 147 LIA photometry works by driving the temporal profile of the fluorescence emission at the 148 specified carrier frequencies. Our recording used 210, 330, and 530 Hz to excite RCaMP, 149 GCaMP, and the isosbestic reference, respectively. We separated the return fluorescence into the 150 GCaMP and RCaMP spectral ranges through a dichroic mirror and optical filter system (Doric 151 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint mini cube), which are designed for precise spectral separation to ensure minimal crosstalk and to 152 route signals to separate photosensors (Fig. 1). Power spectral analysis of the raw photosensor 153 data from outside the stimulation period in a recording of a mouse with this experimental setup 154 confirmed that 210, 330, and 530 Hz were the main response frequencies (Fig. 3A). However, 155 we surprisingly observed the RCaMP 210 Hz carrier emission at the GCaMP photosensor 156 channel and the GCaMP 330 Hz carrier emission at the RCaMP photosensor channel despite 157 optical filtering. The 530 Hz excitation light produced both GCaMP and RCaMP isosbestic 158 emissions; spectral peaks for all three LIA carrier frequencies were found in both RCaMP and 159 GCaMP photosensor channels. 160 We inferred that the most accurate restoration of the saturated segments would be a composite of 161 all the LIA carrier frequencies. µFIX, therefore, works by filling in the saturated segments with 162 Figure 3. Signal component analysis and crosstalk segment fitting. (A) Spectral analysis of the GCaMP and RCaMP photosensor recording, showing LIA carrier frequencies used for GCaMP (330 Hz), RCaMP (210 Hz) and isosbestic reference (530 Hz). Additional peaks were found at the harmonics and beat frequencies of 210 and 330 Hz. (B) A segment of photosensor recording disrupted by stimulation crosstalk. Inset: same segment in (B) at the full 10 V scale. A 5ms stimulation pulse saturates the photosensor with an after-saturation artifact. A segment of 9 ms was cropped for replacement. (C) The same segment in (B) after µFIX interpolation (red). Interpolation was based on intact data 11 ms before and 11 ms after the cropped segment. (D) A different photosensor recording segment without crosstalk. µFIX was applied in the same way as if there was crosstalk. The recovered signal (dashed red line) closely matched the original (R2 ≈ 1.0). .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint interpolated patches generated using the following model of the LIA fluorescence emission at the 163 photosensor: 164 𝑉̂𝑇(𝑡) = 𝐴210. sin(2𝜋 ∙ 210Hz ∙ 𝑡 + 𝜑210) + 𝐴330. sin(2𝜋 ∙ 330Hz ∙ 𝑡 + 𝜑330)165 + 𝐴530. sin(2𝜋 ∙ 530Hz ∙ 𝑡 + 𝜑530) + 𝑑 166 This is the expanded version of Eq(4) in the Methods for the three carrier frequencies adopted in 167 our recording. Since GCaMP/RCaMP have slow dynamics, we make the critical assumption that 168 the encoded fluorescence signal amplitudes (𝐴210, 𝐴330, 𝐴530) during brief saturated crosstalk 169 segments are constant. The amplitude (𝐴210, 𝐴330, 𝐴530), phase (𝜑210, 𝜑330, 𝜑530), and offset 170 (d) were estimated by fitting the model to the non-contaminated recording just before and after 171 each saturated segment. For 5ms stimulation pulses, as in our experiment, we identified segments 172 of 9 ms for µFIX – from the onset of the stimulus to 4ms after to exclude after-saturation 173 artifacts (Fig. 3B). The model parameters were sufficiently estimated by the raw photosensor 174 recording for 2.5 cycles of the lowest carrier frequency (11.3ms @ 210 Hz) before and after the 175 contaminated segment (5 cycles, 22.6ms altogether). 176 µFIX effectively restores the photometry response from crosstalk 177 We first tested whether µFIX introduces distortions to the underlying photometry response when 178 applied to uncontaminated recordings. We found that it resulted in a perfect match to the original 179 photosensor recording (Fig. 3D). We calculated the R2 value of the µFIX filled-in segments for 180 the uncontaminated GCa2 channel plotted in Fig. 2A, finding that it was between 0.98 and 1.00 181 across the 5990 pulse segments in this recording, with a median of 1.00. Our result implied that 182 LIA demodulation of the complete µFIX response matches the originally demodulated 183 photometry response. We measured the fidelity of the signal recovery by calculating the 184 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint correlation coefficient of the µFIX output to the original across each stimulation epoch, starting 2 185 seconds before to 4 seconds after the 30-second stimulus pulse train. The fidelity of the 10 186 epochs in Fig. 2A ranged from 0.98 to 1.00, with a median of 1.00. 187 We then applied µFIX to our crosstalk-contaminated recordings. µFIX produces interpolated 188 segments that are visually continuous with the unaffected part of the photosensor recording 189 between each segment (Fig. 3B). After LIA demodulation, µFIX-treated output was consistent 190 with the photometry responses from non-contaminated channels (Fig. 2A & B, RCa2 vs GCa2): 191 a slowly evolving Ca2+ signal in the recovered photometry response corresponding to the 192 optogenetically-induced seizure. Crosstalk was successfully removed to reveal the underlying 193 neural seizure and non-seizure responses in all 23 recordings, totaling 210 epochs of stimulation 194 from two mice (OP2718 and OP275; Table 1). More examples of crosstalk-contaminated 195 recordings and the recovered signals are shown in Fig. S1. These recovered responses are part of 196 the empirical data pool used in simulations described later. 197 We further verified the dynamics of the recovered photometry response by preparing two 198 additional mice with viral combinations that did not lead to optogenetic crosstalk. These mice 199 were transduced with ChR2 (instead of ChRmine) for excitatory neuron optogenetics in the left 200 hippocampus, and RCaMP on its own for Ca2+ photometry of the right hippocampus, transduced 201 in excitatory neurons in one mouse and PV+ interneurons in the other (Table 1). The photometry 202 Table 1. Mouse experiment parameters. Data was collected from four mice in total. Note that OP27x mice have identical setups, while the OP19x mice are identical except for right hippocampal injections. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint response of a recording from the latter was plotted in Fig. 2C and D. We found that the µFIX 203 recovered RCa2 response in Fig. 2A & B exhibited similar dynamics as the uncontaminated 204 response from the same group of neurons captured via RCa1 in Fig. 2C & D. 205 µFIX recovery of artificially generated crosstalk data with high fidelity 206 Given the recovery fidelity of uncontaminated recordings, we inferred that the missing LIA 207 fluorescence signal was correctly recovered for each crosstalk-saturated segment. However, 208 since the crosstalk overwrote the original fluorescence emission signals of contaminated 209 recordings, quantifying the effectiveness of µFIX recovery with true crosstalk was impossible. 210 Therefore, we validated µFIX against artificially generated data via a simulated LIA photometry 211 pipeline. 212 In our tests, ground truth data we assigned to our testing pipeline (the first step in Fig. 4A) served 213 in place of unknown physiological signaling values that we sought to recover from recordings 214 with crosstalk (starting from ii. in Fig. 1A). Unlike physiological signaling values, which were 215 not known prior to LIA-encoded photosensor pickup and therefore lost to crosstalk, the initial 216 value of ground truth assigned to testing was saved prior to LIA encoding and crosstalk 217 contamination. Therefore, ground truth in our testing algorithm could be quantifiably compared 218 before and after decoding to determine recovery fidelity. 219 We contaminated ground truth data with artificial crosstalk and tested the effectiveness of µFIX 220 recovery of the ground truth (Fig. 4A). We performed this validation first with artificially 221 generated ground truth. Then, we verified it further using empirical data as the ground truth 222 derived from a combination of uncontaminated and contaminated, µFIX-recovered recordings. 223 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint LIA photometry was generated by modulating the excitation light intensity in a sinusoidal profile 224 (𝐸𝑋𝑓(𝑡)) with a baseline offset. The excitation light probes the underlying Ca2+ indicator signal 225 (𝑉𝑠(𝑡)) multiplicatively, producing a fluorescence emission (𝑉𝑒(𝑡)), modelled as (see also Eq(1) 226 in methods): 227 𝑉𝑒(𝑡) = 𝑉𝑠(𝑡). 𝐸𝑋𝑓(𝑡), 𝐸𝑋𝑓(𝑡) = 1 2 (sin(2𝜋𝑓𝑡+ 𝜑) + 1) 228 Here, we modeled the excitation light (𝐸𝑋𝑓(𝑡)) as a sinusoid oscillating between zero and one at 229 the carrier frequency f. For simplicity, we omitted the baseline offset in the excitation light. 230 Figure 4. µFIX validation using simulated LIA with artificial ground truth. (A) Flowchart illustrating LIA photometry simulation pipeline. The ground truth signals (i) were LIA modulated (ii) and multiplexed into a single composite carrier wave (iii). Crosstalk was added to the composite carrier wave (iv). (B) Pearson correlation was used to compare the original ground truth to the LIA demodulated responses before simulated crosstalk (CT−), after simulated crosstalk (CT+), and simulated crosstalk with µFIX applied (CT+µFIX). Results show 120 runs of the artificial ground truth simulation in (A). In each run, three ground truth signals were generated, and the simulation was run three times with signals rotated through all three carrier frequencies. Altogether, there are n = 360 matched data points for each group. (C) An example epoch of demodulated response CT+ (blue) compared against CT− (dashed black line). The fidelity of demodulation was measured using Pearson’s correlation coefficient over a period from 2 s before the start of stimulation to 4 s after the end of stimulation (gray lines). Right: Scatter plot showing lack of correlation between CT+ from (C, blue) and its corresponding ground truth. By contrast, CT− strongly correlates to the ground truth (black line). (D) The demodulated response CT+µFIX for the same epoch as (C). Right: Scatter plot demonstrating r ≈ 1.00 correlation between CT+µFIX in (D, red) and its corresponding ground truth. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint When multiple LIA light sources are combined (multiplexed) into a single optic fiber, it can be 231 modeled as a summation of the individual emissions (also see Eq(2) of Methods): 232 𝑉𝑇(𝑡) = 𝑉𝑒1(𝑡) + 𝑉𝑒2(𝑡) + 𝑉𝑒3(𝑡) + ⋯ 233 Our artificial known ground truth signals were generated with distinct amplitudes and dynamics, 234 like empirical recordings (see Methods). We randomly generated three source signals for each 235 simulation run, LIA-modulated them at the same carrier frequencies as our experiments (210, 236 330, and 530 Hz), and summed them to simulate the raw photosensor recording with all three 237 signals multiplexed together (Fig. 4A). Rotating each triplet of generated source signals through 238 different assignments to the three carrier frequencies allowed us to isolate source-specific effects 239 from frequency effects; this created three data points per trial. For each trial, we first 240 demodulated the summed emission without added crosstalk, referring to this as the CT– result. 241 This created a baseline measure of recovery by calculating the Pearson r correlation coefficient 242 between the demodulation output and the known ground truth—a measure referred to as just 243 fidelity from here forward. As expected, the CT– output perfectly reconstructed the ground truth 244 with a median fidelity of 1.00 and a 95th percentile range of 1.00 to 1.00 (Fig. 4B). 245 Therefore, we added simulated crosstalk by overwriting the ground truth carrier wave with a 246 pulse pattern matching real crosstalk. Each stimulation pulse time was set to the saturation point 247 of the photosensor at 10V, followed by a rebound to -1V (Fig. 3B). We added stimulation pulse 248 crosstalk at the regular 20 Hz interval in our real recordings. This closely replicates the pattern 249 that real crosstalk interference created in the carrier wave. 250 Introducing simulated crosstalk created illegible interruptions to the resultant demodulated signal 251 (CT+), akin to the effect of crosstalk from empirical experiments (Fig. 4C). Crosstalk corrupted 252 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint LIA demodulation, resulting in a low fidelity of 0.45 [0.06–0.94] (Fig 4B), significantly lower 253 than CT– (p < 0.001, ANOVA, Tukey’s post-hoc test). Notably, the 530 Hz frequency fidelity 254 (0.80 [0.64–0.94]) was significantly more resistant to crosstalk than 210 Hz (0.21 [0.02–0.56], p 255 < 0.001 against 530Hz) and 330 Hz (0.28 [0.11–0.66], p < 0.001 against 530Hz), with 330 Hz 256 being the least resistant (p < 0.001 against 210Hz, ANOVA, Tukey’s post-hoc test). 257 Applying µFIX (CT+µFIX) accurately restored the crosstalk-contaminated signal (Fig. 4D), 258 achieving perfect 1.00 [1.00–1.00] fidelity for all three component frequencies (Fig 4B). This 259 was significantly better than demodulation without removal (p < 0.001 against CT+, ANOVA, 260 Tukey’s post-hoc test). 261 The distinct amplitude limits for our randomly generated ground truth data were chosen 262 deliberately to test how multiplexed data of different sources might be affected by crosstalk 263 differently. The fidelity of signal recovery appears to depend on the range of the signals rather 264 than the magnitude of the signal. Ground truths with a signal range of 15–20 mV produced 265 similar CT+µFIX fidelity (6.3 [5.5–6.5]) in Fisher Z units as signals of 5–10 mV (6.2 [5.8–7.2]), 266 where the signal magnitude was reduced while the range was maintained. By contrast, ground 267 truths with the same minimum magnitude but a larger signal range of 15–30 mV produced higher 268 CT+µFIX fidelity (7.2 [7.3–7.5]). These minor differences translated to r = 1.00 fidelity in 269 Pearson correlation units. 270 We further altered the dynamics of our artificial ground truth values to examine the limits of LIA 271 and µFIX recovery (Fig. 5A). Signal dynamics of the encoded fiber photometry data determine 272 how slowly or quickly the value changes up or down. For bulk neural activity recordings, such as 273 fiber photometry, signals are usually slow changing (< 8 Hz). Signal dynamics is implemented in 274 our artificial ground truth signals in nodes per second (nps), i.e., the number of randomly 275 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint generated values per second from which the higher-sampling rate signal was smoothly 276 interpolated. For the preceding µFIX fidelity validation with artificial ground truth, signals were 277 generated at 3 nps based on our intended signal of interest from empirical recordings (Fig. S2A 278 and C). The larger research community may be interested in faster signal content, so we repeated 279 our simulations for artificial ground truth signals generated at higher nps. We found that LIA 280 modulation (CT–) of 210 and 330 Hz began to fall below 0.99 recovery fidelity above 100 nps, 281 and 530 Hz modulation maintained 0.99 fidelity to > 100 nps (Fig. 5B). CT+µFIX fidelity fell 282 below 0.99 sooner, at 50 nps for 210 and 330 Hz modulation and 70 nps for 530 Hz modulation 283 (Fig. 5C). By examining the power spectrum of the generated signals at these nps, we estimate 284 µFIX can recover signal dynamics up to 20 Hz from crosstalk contamination (Fig. S2F). This is 285 much higher than the signal content of our empirical recording (Fig. S2) and for bulk 286 fluorescence indicator recordings at large. 287 µFIX recovery of empirically based ground truth with high fidelity 288 To verify that µFIX minimally distorts real photometry recordings, we assigned them as ground 289 truth in the crosstalk simulation pipeline. We pooled 206 seizure epochs and 329 non-seizure 290 Figure 5. µFIX crosstalk recovery with variable source signal dynamics. (A) Illustration of increasing artificial ground truth signal dynamics with higher nodes per second (nps) values. (B) Pearson correlations by carrier frequency between the demodulated, uncontaminated response CT- (as described in Figure 4A) and the ground truth. Besides change in nps values, simulations ran as described in Figure 4. Altogether, there are n = 600 matched data points for each group. (C) Same approach as (B) with crosstalk added and removed (CT+µFIX). .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint epochs across 45 optogenetic seizure induction recordings from four mice. Simulations were 291 performed using the same approach for artificial ground truth and were substituted with 292 empirical photometry epochs. We intentionally included in this pool some epochs from 293 crosstalk-contaminated experiments to compare the result of removal of real and artificial 294 crosstalk. All source recordings were treated with µFIX prior to use in testing for consistency. 295 Therefore, no original crosstalk remained in the ground truth assigned to the pipeline. As with 296 artificial ground truth, we multiplexed three empirical ground truth signals into a signal LIA 297 simulated photosensor recording, then performed demodulation to re-extract them. 298 Our test indicated that without crosstalk (CT–), LIA photometry accurately captures the 299 empirical response for all three frequencies (1.00 [0.88–1.00]) (Fig. 6C). With the addition of 300 simulated crosstalk (CT+), the signal is unrecognizable after LIA demodulation (Fig. 6A) with 301 low fidelity to the ground truth (0.06 [-0.28–0.88]). CT+ results were significantly lower than 302 CT– for all frequencies (p < 0.001, ANOVA, Tukey’s post-hoc test). 530 Hz was significantly 303 Table 2. ANOVA for multi-variable influence on the recoverability of data from crosstalk. Data Source = Seizure response, flat response, or isosbestic data. Encoding Frequency = 210, 330, or 530 Hz encoding. Crosstalk Status = No crosstalk added (CT-), crosstalk added and not removed (CT+), or crosstalk added and removed (CT+µFIX). .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint more resistant to simulated crosstalk than the other frequencies in our artificial ground truth 304 testing (p < 0.001, ANOVA, Tukey’s post-hoc test vs. 210 and 330 Hz). After crosstalk removal 305 with µFIX, the demodulated response (CT+µFIX) closely resembles the ground truth (1.00 306 [0.88–1.00]) (Fig. 6B). This significantly improved over CT+ (p < 0.001, ANOVA, Tukey’s 307 Figure 6. µFIX validation using simulated LIA with empirical responses as ground truth. (A) An example epoch of demodulated response CT+. (B) The demodulated response CT+µFIX for the same epoch as (C). (C) Pearson correlations between the ground truth and the LIA demodulated responses as described in Figure 4A. Results show simulation runs using 473 empirical recording epochs. We extracted up to three photometry responses from each epoch and ran the simulation three times with all responses rotated through the three carrier frequencies (210, 330 and 530 Hz). Altogether, there are 1605 matched data points for each group. (D) Grouping of data in (C) based on source channel, where RCaMP encodes the slowest-moving dynamics, GCaMP is faster with lower amplitudes, and Isosbestic-RCaMP encodes baseline noise without responses to stimulation. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint post-hoc test). Frequency contributed a much smaller effect on the outcome for empirical 308 recordings than in our simulated tests, based on ANOVA (Table 2, F = 3.1633, p = 0.043). 309 The source of ground truth data significantly affected recovery fidelity (Table 2 ANOVA, F = 310 1205.28, p < 0.001). The signal source effect was most pronounced in CT+ results. Although the 311 effect is still apparent on CT+µFIX in the Fisher Z-transformed fidelity scores, it translated to 312 minor separation in group-wise medians (0.995 to 1.000). In particular, we note that signal 313 recovery is practically equivalent regardless of the Ca2+ photometry variant (RCaMP or 314 GCaMP), targeted neural population (excitatory or PV+), or whether the signal contained only a 315 single active photometry source (RCa1) versus two simultaneous active sources (RCa2 and 316 GCa2). Most of the effect between signal sources can be explained by a linear relationship 317 between the fidelity score (Fisher z correlation coefficients) and the logarithm of the signal 318 standard deviation (SD). Signals sourced from isosbestic channels typically had lower signal SD, 319 which resulted in lower fidelity scores. For RCaMP and GCaMP sources, seizures often drive 320 major changes in the source signals, leading to larger signal SD, resulting in high recovery 321 fidelity. Based on our results, a signal SD of about 0.18 mV is required for signal restoration 322 fidelity greater than 0.99 (Fig. S3). 323 While it is impossible to verify whether µFIX has accurately recovered the unknown 324 physiological signaling values of empirical photometry from experimental recordings with real 325 crosstalk, the present data strongly indicate that µFIX recovers data following similar simulated 326 crosstalk. Further, our simulated results are likely generalizable since the result is identical when 327 ground truth data are recovered from real or simulated crosstalk. Thus, we infer that, in most 328 cases, µFIX can accurately recover photometry recordings when real optogenetic crosstalk is 329 present. 330 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint Computational cost and accuracy of µFIX compared to alternative approaches 331 Next, using our simulated LIA photometry pipeline and artificial ground truth, we compared 332 µFIX with more uncomplicated crosstalk interpolation strategies to demonstrate its superior 333 effectiveness in recovering the LIA photometry signal and assess its relative computational cost. 334 We examined whether linear interpolation, spline interpolation, and single-frequency (1-Freq) 335 interpolation are sufficient to recover the LIA photometry signal. Linear interpolation tests the 336 approach of a straight line connecting across the ends of the saturated segment (Fig. 7D). Spline 337 interpolation avoids demodulation artifacts arising from sharp transitions at the ends of the 338 linearly interpolated segment (Fig. 7E). Lastly, we test if a single-frequency sinusoid using the 339 lowest component carrier frequency (210 Hz) is sufficient to recover the photometry signal 340 rather than the complete multi-frequency set (Fig. 7F). 341 Our results show that linear, spline, and 1-Freq approaches are ineffective in removing all the 342 artifacts from crosstalk contamination. The LIA-demodulated response from the linear and spline 343 interpolation illustrated a significant step change in the output but did succeed in removing the 344 major unrecognizable segment of noise (Fig. 7D & 7E). This reflects the loss of signal at the 345 carrier frequencies that were not replaced by these crosstalk interpolating methods. Overall, the 346 fidelity of the demodulated output is 0.88 [0.64–0.92] for linear interpolation, 0.84 [0.61–0.92] 347 for spline, and 0.91 [0.66–1.00] for 1-Freq interpolation; all were significantly lower than 1.00 348 [1.00–1.00] for µFIX (p < 0.001, ANOVA, Tukey’s post-hoc test). 349 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint Further, we wanted to see if the LIA encoding frequency of a signal makes simpler interpolation 350

comparable to µFIX. Differences in fidelity score for µFIX in correlation units are 351 indistinguishable (~1.00), but the simpler approaches had significant variation. For 1-Freq 352 Figure 7. Alternative interpolation approaches for crosstalk snippet removal. (A) Pearson correlation by carrier frequency between the ground truth and the LIA demodulated response with simulated crosstalk (CT+), crosstalk segment interpolated with a straight-line (Linear), cubic Spline, single- frequency sinusoid (1-Freq), and µFIX. Results from simulation on the same artificial ground truths as in Figure 4. (B) Comparison of processing time for each interpolation approach expressed in milliseconds to process each cropped millisecond of crosstalk. (C) An example stimulation epoch of the demodulated response with simulated crosstalk (CT+). (D) The demodulated response after Linear interpolation for the same epoch as (C). (E) The demodulated response after Spline interpolation for the same epoch as (C). (F) The demodulated response after 1-Freq interpolation for the same epoch as (C). (G) The demodulated response after µFIX interpolation for the same epoch as (C). .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint interpolation, as expected, high recovery fidelity was found only for signals modulated on the 353 fitted carrier frequency (210 Hz, 0.99 [0.95–1.00]), but not for signals on 330 Hz (0.90 [0.65–354 0.92]) or 530 Hz (0.87 [0.64–0.92]). For all other interpolation methods, signals on 530 Hz (0.90 355 [0.64–0.92]) and 330 Hz modulation (0.87 [0.64–0.92]) were restored much with higher fidelity 356 than for 210 Hz (0.79 [0.59–0.95]) (p < 0.001, ANOVA, Tukey’s post-hoc test). 357 We compared the computational cost among these interpolation methods (Fig. 7B). On our 358 virtual Windows server running on eight 18-core, 36-thread Intel Xeon 6254 processors @ 3.1 359 GHz, we estimated the time for each interpolation to process crosstalk segments from 20 360 simulated experiments. Each experiment was 30 min long and contained 10 epochs, each with 361 600x 5-ms crosstalk segments to process (20 Hz stimulation). Without applying any crosstalk 362 recovery algorithm, each recording took 19.0 ± 0.4 (SD) ms to process each second of the 363 recording. The µFIX algorithm was the most complex and took an average of 67.1 ± 4.5 ms/s, 364 significantly higher than for simpler interpolation approaches (p < 0.001, ANOVA, Tukey’s 365 post-hoc test). On average, µFIX took ~30 s longer to process each recording; dividing this over 366 the 6000 crosstalk segments, we estimate that each 9 ms crosstalk segment required ~5 ms to 367 process on our machine. This processing time may be short enough for deployment in the 368 recording procedure so that Ca2+ photometry can be restored from crosstalk in real time. 369 µFIX is accurately recovers signal from a wide range of stimulation protocols 370 The most effective optogenetic stimulation protocol varies depending on the opsin, target, and 371 response of interest. This includes the duration of stimulation pulses, the frequency of the pulse 372 train, and the length of the pulse train. So far, we have examined using 5 ms pulses at 20 Hz for 373 30 s of stimulation, which is optimal for generating seizures from the hippocampus. µFIX is 374 designed to work with a wider range of stimulation protocols. 375 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint We sought to determine how well µFIX can recover the photometry response with longer 376 durations of optogenetic stimulation. The quality of µFIX recovery was examined using our LIA 377 simulation pipeline from 15 ms to 35 ms of crosstalk driven by a 20 Hz pulse train (Fig. 8A). 378 The fidelity of µFIX recovery was consistently maintained until a precipitous drop from 1.00 379 [0.99–1.00] with a crosstalk duration of 33 ms to 0.15 [-0.11–0.97] with a crosstalk duration of 380 34 ms (Fig. 7B, p < 0.001, ANOVA, Tukey’s post-hoc test). This is consistent with our 381 algorithm’s requirement of ~12 ms (2.5 cycles of 210 Hz) of intact recording preceding and 382 succeeding the crosstalk segment for estimating the interpolation parameters. At 50 ms intervals 383 Figure 8. µFIX crosstalk recovery with longer pulse widths. (A) Illustration of stimulation pulse lengths corresponding to labels in panel (B). (B) Pearson correlations by carrier frequency between the demodulated response CT+µFIX (as described in Figure 4A) and the ground truth. Results from simulation on the same empirical-based ground truths as in Figure 5. Stimulation pulse frequency was at 20Hz (50ms pulse periods). Numeric labels for each group indicate the duration of the stimulation pulse in milliseconds. Insufficient of intact between pulses led to poor µFIX recover for pulses larger than 33 ms. (C) Same as (B), but with pulse frequency of 1 Hz and expanded pulse lengths. µFIX faithfully recovers stimulation pulses as large as 150 ms. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint between pulses (20 Hz), a 34 ms saturated segment with 4 ms of post-stimulation artifact is at the 384 12 ms limit, resulting in defective signal recovery. 385 Beyond the limit of intact data for 20 Hz stimulation, we sought the longest recoverable crosstalk 386 segment by repeating the simulation with longer crosstalk durations using a 1 Hz pulse train 387 (1000 ms intervals). We found that the average recovery fidelity reduced below 1.00 [0.97–1.00] 388 for crosstalk durations longer than 200 ms, to 0.99 [0.88–1.00] at 300 ms, then gradually down to 389 0.95 [0.41–1.00] at 900 ms (Fig. 8C). Signals on the 210 Hz carrier frequency had significantly 390 lower fidelity scores than 330 and 530 Hz (p < 0.001, ANOVA, Tukey’s post-hoc test). 391 However, the reduction in recovery fidelity did not suffer an immediate drop compared to 392 reaching the limit of the intact data (Fig. 8B). The sustained fidelity score with long crosstalk 393 segments reflects the slow dynamics of the photometry response. 394 The highest frequency pulse train that µFIX can recover is limited by the length of intact 395 recording in between pulses as the basis for a good estimate of the signal lost to crosstalk. As 396 described, our standard algorithm requires 2.5 cycles of data at the lowest carrier frequency 397 before and after each crosstalk segment for signal recovery, which is equivalent to ~12 ms using 398 a 210 Hz carrier. With 5 ms pulses, the highest pulse frequency under this setting is ~50 Hz, 399 already approaching the limit for the physiological firing rate of most neurons. Nonetheless, our 400 simulations indicate that this is a very conservative setting. High-fidelity signal recovery can be 401 achieved using as little as 1/4 cycles between pulses (~1.2 ms at 210 Hz, fidelity = 1.00 [1.00–402 1.00], Fig. S4), potentially working with pulse trains up to 100 Hz (with 5 ms pulses). 403 Lastly, as µFIX works on the level of an individual stimulation pulse and its induced crosstalk, 404 we expect that the recovery fidelity would be independent of the length of the stimulation train. 405 To verify this, we performed simulations with longer 5 ms, 20 Hz pulse trains lasting 60 s and 90 406 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint s (Fig. S5). As expected, we found no statistically significant contribution to recovery fidelity 407 from the train duration main factor (p = 0.43, ANOVA). 408 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint

409 The all-optical approach to interrogating neural populations enables cell-type-specific circuitry 410 manipulation and activity read-out using genetic tools. Despite employing state-of-the-art optical 411 spectra filtering (Fig. 1), optogenetic crosstalk contamination hampered our experimentation 412 with multiple optical components, leading to distorted photometry recordings. Consequently, we 413 developed µFIX to recover the underlying LIA fiber photometry signal from crosstalk. µFIX 414 generates signal snippets of LIA-modulated fluorescence emission to replace noise-contaminated 415 segments in the photosensor recording (Fig. 3). Perfect signal recovery fidelity (r ~ 1.00) was 416 achieved on non-crosstalk segments of a recording as well as simulated crosstalk-contaminated 417 LIA photometry with ground truth signals of both artificial and empirical origins. Applying 418 µFIX to our mice recordings effectively recovered photometry responses that resemble the 419 dynamics of the same cell-type response when recorded from a reduced viral preparation that did 420 not suffer from crosstalk. 421 µFIX empowers experimental designs exposed to crosstalk 422 LIA photometry offers the benefits of multiplexing isosbestic reference signals16,21,23–25 and 423 maximizes signal-to-noise ratio in fiber photometry15,25,26, but it is vulnerable to interruptions 424 such as optogenetic crosstalk. In standard setups, a system of dichroic mirrors and advanced 425 optical filters is employed to separate and route the emission spectra to different photosensor 426 light paths (see our system in Fig. 1 as an example). These optical filters typically have a 427 passband of 10-40 nm and an attenuation of OD5 (intensity reduction of five orders of 428 magnitude) outside the passband. Higher OD and narrower passband filters can improve the 429 filtering outcome but are likely to do so at the cost of some signal loss. However, light sources 430 and fluorescent emissions typically have broad and possibly overlapping spectra, therefore, a 431 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint complete signal separation by spectral filtering is not possible (see Fig. 3A). Using an optical 432 filtering system is also insufficient to eliminate optogenetic crosstalk in the fiber photometry 433 light path when the employed opsin and fluorescence indicator have overlapping spectra (e.g., 434 ChRmine and RCaMP). 435 In our recordings, in spite of optical filtering and spatial separation of the fiber photometry 436 cannula from the optogenetic stimulation cannula, optogenetic crosstalk was still evident. It 437 continued to interrupt the carrier signal in square-wave patterns, resulting in characteristic 438 artifacts in the demodulated photometry response. The sharp signal transitions into and out of the 439 stimulation periods produced a large, transient, and ripple-like “ringing artifact” at these time 440 points. During the stimulation period, depending on whether the content at each carrier 441 frequency was boosted or masked out, crosstalk also caused a step-like change in the mean 442 response level. The frequency of stimulation also induced a beat frequency oscillation that can 443 overwhelm the photometry response (Fig. 2A & B). The effect of crosstalk on the demodulated 444 response ranged from severe to subtle, depending on the interaction between the stimulation 445 frequency, LIA carrier frequency, and whether crosstalk saturates the photosensor. Recognizing 446 even the subtle artifacts is imperative, as they can be mistakenly interpreted as stimulus-driven 447 responses. 448 Whether or not optogenetic crosstalk is present, µFIX is a convenient tool that can be applied 449 indiscriminately to any suspected LIA photometry recording without producing adverse effects, 450 providing there is sufficient response amplitude driving the fluorescence signal (0.3 mV standard 451 deviation, Supplemental Fig. 1). µFIX does not distort a response absent of crosstalk (Fig. 2 & 452 3). Where crosstalk is present, we demonstrated that µFIX achieves perfect recovery (r ~ 1.00) 453 for a wide range of stimulation durations (up to 150 ms long, Fig. 7) and signals with slow or fast 454 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint dynamics (up to 20 Hz, Fig. 5 and S2). To our knowledge, this encompasses the majority of 455 experimental designs using optogenetics and fiber photometry. With a processing time of < 1 ms 456 per ms of crosstalk noise (Fig. 6B), µFIX may be deployed in the real-time recording pipeline 457 during experimentation. 458 Fiber photometry is typically only capable of resolving slowly changing bulk signaling from the 459 intended targets5,6,8,27 well within the 20 Hz working limit of the µFIX algorithm. Our empirical 460 signals of interest have the optimal signal-to-noise ratio with a 3 Hz low-pass filter. In a similar 461 application using widefield imaging in monkey V128 , the visually-driven response in GCaMP6 462 diminished sensitivity above 4 Hz stimulation. In two-photon imaging, calcium indicators for 463 capturing single-neuron activity are typically recorded with a frame rate of less than 40 Hz29,30 , 464 i.e. dynamics up to 20 Hz. The working limits of µFIX encompass with the maximum kinetics of 465 the current, commonly used indicators. 466 Adopting µFIX requires short optogenetic stimulation pulses. A non-exhaustive survey within 467 our research interest (seizures and epilepsy) indicated that most researchers are adopting 468 stimulation pulses between 5 to 20 ms 9,14,31–34. Short optogenetic stimulation pulses have also 469 proven successful at eliciting neural activity and are a widely adopted stimulation technique35,36. 470 The effective stimulation pulse duration depends on the specific protocol and opsin, with up to 471 2000 ms reported 37. For stimulation protocols that utilize constant light delivery, such as those 472 typically for activating inhibitory networks, only minimal modification is required to create an 473 equally effective high-duty-cycle pulse-train paradigm compatible with µFIX38,39. 474 As a solution to optogenetic crosstalk, µFIX makes it possible to design experiments with 475 fluorescence photometry sensors whose spectra overlap the spectrum of optogenetic stimulation 476 light. Investigators can simultaneously utilize the blue and red-spectrum fluorescence channels 477 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint (e.g., GCaMP and RCaMP) to monitor the fiber photometry responses of two neural populations 478 or neurotransmitters under optogenetics manipulation. An example of a design with dual 479 photometry and optogenetics is demonstrated in our experimental setup (Fig. 1), which was 480 produced to study the relative excitatory/inhibitory signaling balance leading to a perturbed state 481 of the hippocampus that produces seizures (Fig. 2). In addition, with the use of µFIX, 482 investigators are unrestricted from employing the most suitable optogenetic opsin for their 483 experiment, including the combination of blue and red-spectrum opsins for dual-optogenetic 484 manipulation control (e.g. both ChR2 excitation and NpHR inhibition) alongside simultaneous 485 fiber photometry. 486 µFIX may also combat signal interference wherever LIA (or optical lock-in detection) is used, 487 including other imaging methodologies. Some of the potential use cases are voltage-sensitive-488 dye imaging40, fluorescence-detected multidimensional electronic spectroscopy41, infrared 489 microscopy42, Raman microscopy43, and immunofluorescence microscopy44. 490

and future extensions of µFIX 491 High-fidelity signal recovery with µFIX is built on the fundamental mathematic principles 492 behind multi-frequency LIA photometry. Lesser interpolation approaches (linear, spline, or 493 single-frequency interpolation) did not produce the same fidelity levels (Fig. 7). While µFIX is 494 robust in its current form (see Fig. 5, 8, S4, S5), and more than sufficient for the majority of 495 applications that we are aware of, assumptions were made in the design of the µFIX algorithm 496 may pose constraints on experimental designs using indicators with extremely fast kinetics or 497 uncommon optogenetic pulse train patterns. 498 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint First, to simplify the µFIX formulation, we assumed that the amplitude of the modulated signal is 499 constant during the interpolated segment. This assumption was made because the dynamics of 500 the signal of interest from fiber photometry recordings are generally slow (subsecond scale), and 501 the crosstalk segment is short (milliseconds). While this assumption simplifies µFIX 502 implementation, it has implications for removing crosstalk from stimulation protocols requiring 503 > 150 ms pulse duration (maybe working with inhibitory opsins) or restoring signals with very 504 fast > 20 Hz dynamics (such as voltage-sensitive indicators). For applications working beyond 505 these limits, we believe extending µFIX to model a dynamic amplitude signal profile, such as a 506 cubic spline function or inspiration from deep learning image inpainting approaches45, will allow 507 recovery for more extended pulse widths and faster signal dynamics. 508 Secondly, µFIX requires uncontaminated data to fit its model parameters for reconstructing the 509 signal to crosstalk. We used a conservative 2.5 cycles of the lowest carrier frequency as the 510 required duration of uncontaminated data before and after each contaminated snippet. Our 511 simulation indicates that as little as 1/4 cycles may be used without compromising crosstalk 512 signal recovery (Fig. S4). This imposed a minimum off time between stimulus pulses of ~1.2 ms 513 on the 210 Hz carrier and subsequently limits the duty cycle of the stimulation, a consideration 514 for adapting experiments with constant light delivery to use µFIX. This will also impact 515 experiments requiring a stimulus frequency of >100 Hz. The minimum off time can possibly be 516 reduced by adopting higher LIA carrier frequencies – e.g. with a 530 Hz carrier, which reduces it 517 to 0.47 ms, but we have not tested this setting. 518 Informing the choice of LIA carrier frequency for photometry 519 Carrier frequencies typically used for LIA fiber photometry (and provided as defaults by 520 equipment vendors such as TDT Systems) are 210, 330, and 530 Hz (Fig. 3A). The frequency 521 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint choices are relatively narrow; they must avoid line noise (50 or 60 Hz) and its harmonics as well 522 as not interact with other carriers and their harmonics. In all our simulations, we multiplexed and 523 re-extracted three different signals respectively modulated at 210, 330, and 530 Hz, and our 524

confirmed that these are a suitable mixture of carrier frequencies for LIA photometry. We 525 did not encounter any interference between these carrier frequencies (although we did not 526 specifically test for this). In general, signals were encoded/decoded equally well on all three 527 frequencies (Figs. 4B, 5B, 6C, 8B, 8C). There is evidence that 530 Hz may be better at encoding 528 faster signal dynamics (up to 100 nps or ~50 Hz, Fig. 5), which is generally not required for 529 capturing bulk fluorescence activity from calcium and GRAB sensors but may be helpful in 530 specific experimental scenarios46. While it remained essential to choose the appropriate carrier 531 frequencies in the experimental setup, our results indicated these choices had little impact on 532 encoding quality, immunity from crosstalk, and the performance of µFIX. 533 Spectral analysis of in vivo recordings employing 210, 330, and 530 Hz carrier frequencies 534 indicate that there may be non-linear interactions between them. Spectral peaks other than the 535 carrier frequencies were present (Fig. 3A). Some were observed at the harmonics of the carrier 536 frequency (420Hz and 660Hz). We suspect this originated from the non-linear excitation-537 emission response of our chosen calcium indicators. However, an alternate explanation is an 538 imperfect sinusoidal modulation of the excitation light or non-linear loss in light transmission. 539 We also observed a spectral peak at 120 Hz. We believe this was not a harmonic of the line noise 540 (no corresponding 60 Hz peak); instead, it was the beat frequency between the 210 and 330 Hz 541 carrier frequencies. However, the beat frequency is a time domain manifestation between two 542 sinusoidal signals and does not have a spectral peak; one at the beat frequency indicated a non-543 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint linear mixing of the two fluorescence emissions, either during transmission or at the Ca2+ 544 indicator. The actual source of these spectral peaks requires further investigation. 545 Alternative fiber photometry paradigms to avoid optogenetic crosstalk 546 Time-division multiplexing (TDM) photometry is an alternative to LIA photometry. TDM 547 involves alternating frames of each component light source in the experimental setup so that only 548 one fluorescence is excited and recorded at a time16,47–49. TDM can partition optogenetic 549 stimulation in separate time slots to avoid crosstalk. Although there is evidence that TDM may 550 be more noise-tolerant than LIA photometry16, a more rigorous comparison between these two 551 techniques is required to confirm its advantage. The major disadvantage of TDM is that it 552 requires stimulation to be within pre-determined time divisions, which may hinder the flexibility 553 of the stimulation paradigm. Finally, TDM requires additional specialized hardware and software 554 for researchers who have already adopted LIA photometry systems. 555 Fiber photometry can also be conducted using a constant-level excitation light, i.e., without LIA 556 or TDM modulations. Brief, crosstalk-affected segments at the photosensor can be bridged with 557 simple linear or spline interpolation. However, continuous excitation photometry does not 558 benefit from the improved signal-to-noise ratio of LIA encoding and would suffer greater noise 559 throughout the entire recording. Additionally, this setup would not allow a simultaneous 560 isosbestic reference to be recorded, which is required to correct fluorescence deviations of non-561 neural origins in the photometry response. 562

563 We developed µFIX and showed that it is an effective method to recover LIA-encoded 564 photometry signals contaminated by optogenetic crosstalk. We demonstrated that µFIX allows a 565 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint robust optogenetics stimulation paradigm and is computationally efficient for real-time 566 implementation. µFIX enables extended experimental designs employing multiple simultaneous 567 fiber photometry and optogenetics channels to study the neural circuitry in a previously 568 unfeasible manner due to crosstalk. 569 570 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint

571 Animal Preparation 572 Experiments were carried out with adult (20-25 weeks old) male and female inbred homozygous 573 PV-Cre mice (B6.129P2-Pvalb/J – The Jackson Laboratory, Bar Harbor, ME, 574 USA). Mice were reared under social housing and environmental enrichment conditions with ad 575 libitum food and water, standardized 12 h light/12 h dark cycle (lights on at 06:00 AM), 576 temperature, and humidity. All animal studies were conducted via Rutgers IACUC within an 577 AAALAC-accredited facility. IACUC Protocol #PROTO201900218. 578 Data from four animals were used (Table 1). All animals underwent stereotaxic surgeries to 579 receive intrahippocampal adeno-associated viral vector (AAV) injections and a headcap optrode 580 ensemble implantation. AAVs targetting the excitatory pyramidal cells were microinjected in the 581 left dorsal hippocampal CA1 (AP -2.1; ML -1.6; DV -1.4) for optogenetic stimulation. In the 582 right dorsal hippocampal CA1 (AP 2.1; ML 1.6; DV -1.4), a single AAV (mice OP191 & 583 OP193) or an AAV cocktail for dual photometry (OP2718 & OP275) was injected to read out the 584 Ca2+ activity of PV interneurons and the excitatory pyramidal cells. All coordinates are given in 585 millimeters from bregma: anterioposterial (AP), mediolateral (ML), dorsoventral (DV). 586 The exact viral vector combination used varied between mice. Two of the animals, OP275 and 587 OP2718, received 300nL of bicistronic ChRmine (AAV-8-CaMKIIa-GCaMP6m-p2a-ChRmine-588 TS-Kv2.1-HA; GVVC-AAV-180, Gene Vector and Virus Core, Stanford, CA, USA) on the left 589 hippocampus, with 300 nL of Cre-dependent GCaMP6 590 (pAAV.Syn.Flex.GCaMP6m.WPRE.SV40; #100838, Addgene, Watertown, MA, USA) and 100 591 nL of RCaMP (AAV8-CaMKIIa-JRCaMP1b; GVVC-AAV-150, Gene Vector and Virus Core) 592 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint in the right hippocampus. The biscistronic ChRmine vector transfects the same neurons with 593 GCaMP for Ca2+ activity readout. OP191 and OP193 received 300 nL of ChR2 (pAAV-594 CaMKIIa-hChR2(H134R)-EYFP (AAV5); #26969, Addgene) in the left hippocampus with only 595 a single GECI in the right hippocampus. OP193 was targeted for contralateral PV interneurons 596 using Cre-dependent RCaMP (pAAV1.Syn.Flex.NES-jRCaMP1b.WPRE.SV40; #100850, 597 Addgene). OP191 was targeted for contralateral CaMKII cells using RCaMP (AAV8-CaMKIIa-598 JRCaMP1b). Injections were made at a rate of 30 nL/min; the needle was maintained in place for 599 5 minutes after injection to avoid backflow and then slowly retracted. 600 Animals were implanted with a headcap optrode ensemble (Fig. 1C) either in the same surgery 601 (OP191 & OP193) or in a second surgery (2 – 13 weeks after, see Table 1). The head cap 602 ensemble was composed of the two optic fiber cannula (0.66 numerical aperture, 400 um 603 diameter, Doric Lenses, Québec, QC, Canada) sitting just above the bilateral viral vector 604 injection site (AP ±2.1; ML -1.6; DV -1.1), and colocated CA1 (DV -1.4) and DG (DV -1.9mm) 605 recording electrodes (4 altogether, EM6/3/SPC, P1 Technologies, Roanoke, VA, USA). 606 Electrodes were interfaced to a 6-channel connector pedestal (mini6 format, P1 Technologies) 607 with two additional reference electrodes (EM6/96/1.6/SPC or EM6/3/SPC, P1 Technologies) 608 above the prefrontal cortex (AP 1.6; ML ±1.6) or the cerebellum (AP -5.0; ML ±1.6). The 609 ensemble was secured to the skull using dental acrylic cement. 610 Animals were maintained on isoflurane anesthesia (~1.5% isoflurane in pure oxygen) on a 611 heating pad during the surgeries. Sustained-release Buprenorphine (Ethiqa XR, 3.25 mg/kg, s.c.; 612 Ethiqa XR, North Brunswick, NJ, USA) was administered to the animals to alleviate pain and 613 discomfort after recovering from the procedure. After the surgeries, animals were transferred to a 614 clean cage to recover and single-housed. 615 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint Perfusion and Histology 616 After experimentation, the animals were deeply anesthetized with isoflurane and perfused 617 transcardially with 4% paraformaldehyde (PFA) in 1X phosphate buffer (PBS – pH7.4). Brains 618 were extracted and post-fixed for at least 24 hours in 4% PFA and then transferred to 30% 619 sucrose with 0.02% sodium azide in 4% PFA for at least two days at 4°C. Coronal brain sections 620 of 30μm thickness were made on a cryostat (Leica CM3050S, Leica Microsystems, Wetzlar, 621 Germany). Sections were mounted on slides and cover-slipped with DAPI mounting medium. 622 Fluorescent images of the viral expression were acquired on a Leica fluorescent microscope 623 (Leica DM 4B; Leica Microsystems, Wetzlar, Germany). 624 Animal Recording 625 Recordings were performed at least 22 days after the injection surgery to allow time for viral 626 expression. Simultaneous electrophysiological recording, optogenetic stimulation, and Ca2+ fiber 627 photometry were conducted using a TDT system (RZ10x, PZ5, RA16; Tucker Davis 628 Technologies, Alachua, FL, USA). ChRmine optogenetic stimulation was delivered using either 629 the inbuilt RZ10x 590 nm LED (Lx590) or a 589 nm laser (LMS-BY02-GF3-00020-05, 630 Laserglow Technologies, Toronto, ON, Canada). ChR2 optogenetic stimulation was delivered 631 using the inbuilt RZ10x 465 nm LED (Lx465). Excitation light for fiber photometry was 632 delivered with inbuilt RZ10x LEDs: 405 nm for isosbestic signal (Lx405), 465 nm for GCaMP 633 (Lx465), 560 nm for RCaMP (Lx560). 6-port mini cubes (FMC6_IE(400-410)_E1(460-634 490)_F1(500-540)_E2(555-570)_F2(580-680)_S, Doric Lenses) was used to merge and split the 635 light paths (Fig. 1). 636 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint For mice OP2718 and OP275, we interfaced the ChRmine optogenetic light and excitation lights 637 to the left fiber cannula for isosbestic and GCaMP signals. Optogenetic stimulation was 638 delivered through the RCaMP emission port (F2) of the Doric mini cube. We interfaced the 639 excitation lights to the right fiber cannula for isosbestic, GCaMP, and RCaMP signals. The 640 returning emissions from the animal were optically split by the GCaMP and RCaMP spectra and 641 routed to separate photosensors on the TDT system. For OP191 and OP193, the right fiber 642 cannula was similarly interfaced for photometry, while the ChR2 optogenetic light was directly 643 routed to the left fiber cannula without the Doric mini cube. Both electrophysiological and 644 photometry signals were recorded at 6.1 kHz. 645 Optogenetic stimulation was delivered to the left hippocampus to induce seizures in the animals. 646 Each mouse was subjected to an extensive battery of stimulation experiments. This paper 647 includes only experiments using 30-second stimulation trains with 10 Hz or 20 Hz 5 ms pulses. 648 We refer to each 30 s stimulation episode as an epoch. In each experiment, multiple stimulation 649 epochs were delivered, each separated by 90 s non-stimulation time (i.e., 120 s between the start 650 of each epoch). The stimulation power was 2-10 mW, depending on the required power to induce 651 seizures for each mouse in each experiment. This power was measured at the fiber optic tip with 652 a power meter (PM20A, ThorLabs). 653 We collected 45 experiment recordings across four mice (see Table 1). These experiments have 654 at least one seizure response and a demonstrated photometry response on either contralateral 655 channel. Altogether, 535 stimulation epochs were collected, of which 206 resulted in seizures, 656 and 329 did not. 657 658 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint Lock-in Amplification (LIA) Photometry: Encoding, Multiplexing and Demodulation 659 LIA has been adopted in many fiber photometry applications. It is a signal-processing method 660 that encodes the original signal (𝑉𝑠) with a carrier wave of a higher frequency (𝑓1) to increase 661 tolerance to noise in the course of signal transmission16,26: 662 𝑉𝑒1(𝑡) = 1 2 𝑉𝑠1(𝑡). (sin(2𝜋𝑓1𝑡 + 𝜑) + 1) (1) 663 A notable strength of the LIA approach is the ability to multiplex multiple signals into a single 664 transmitted signal (𝑉𝑇). LIA photometry exploits this LIA strength to encode the isosbestic 665 reference21,24 and emission of multiple fluorescence indicators into the same fiber optic 666 channel26. The multiplexing is achieved by encoding all component signals in orthogonal 667 sinusoidal frequencies (Fig.1): 668 𝑉𝑇(𝑡) = 𝑉𝑒1(𝑡) + 𝑉𝑒2(𝑡) + 𝑉𝑒3(𝑡) + ⋯ (2) 669 𝑉𝑒2(𝑡) = 1 2 𝑉𝑠2(𝑡). (sin(2𝜋𝑓2𝑡 + 𝜑) + 1), 670 𝑉𝑒3(𝑡) = 1 2 𝑉𝑠3(𝑡). (sin(2𝜋𝑓3𝑡 + 𝜑) + 1), etc. 671 Leveraging the orthogonality of sinusoidal waves, the encoded signals (𝑉𝑒) can be extracted by 672 isolating the transmitted signal (𝑉𝑇) at the desired encoding frequencies (𝑓1, 𝑓2, etc.) using Euler’s 673 formula. 674 𝑉𝑜1(𝑡) = |𝑉𝑇(𝑡). 𝑒−𝑖2𝜋𝑓1𝑡|, (3) 675 𝑉𝑜2(𝑡) = |𝑉𝑇(𝑡). 𝑒−𝑖2𝜋𝑓2𝑡|, 676 𝑉𝑜3(𝑡) = |𝑉𝑇(𝑡). 𝑒−𝑖2𝜋𝑓3𝑡|, etc. 677 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint Lastly, the original signal (𝑉𝑠) can be demodulated from the extracted signals (𝑉𝑜) by averaging 678 the signal over a sufficiently long time span to remove the carrier frequency. We implemented 679 this using a fifth-order Butterworth low-pass filter with a cut-off frequency of 3 Hz. 680 In our animal experiment, we multiplexed up to three light excitation sources to a single optic 681 fiber to read out both GCaMP (470 nm), RCaMP (560 nm), and their respective isosbestic signal 682 (405 nm). Each light source was modulated with a different LIA carrier frequency from 210 Hz, 683 330 Hz, 450 Hz, or 530 Hz. The exact combination varied slightly between experiments. Our 684 most common configuration was 330 Hz and 530 Hz for ipsilateral GCaMP and isosbestic, with 685 210 Hz, 330 Hz, and 530 Hz for contralateral GCaMP, RCaMP, and isosbestic, respectively. 686 Note that isosbestic references for GCaMP and RCaMP were excited with the same light source 687 (and, by extension, carrier frequency). Their respective isosbestic signals were differentiated by 688 the separate optic filter path for GCaMP and RCaMP and thus from the signal recorded from the 689 separate photosensors. 690 µFIX - Optogenetic Crosstalk Filling-in 691 µFIX (Multi-Frequency Interpolation X-talk removal algorithm) seeks to estimate the signal 692 displaced by crosstalk (𝑉̂𝑇) using the multi-frequency LIA transmission model described in Eq 693 (2): 694 𝑉̂𝑇(𝑡) = ∑ 𝐴𝑛. sin(2𝜋𝑓𝑛𝑡 + 𝜑𝑛)𝑛 (4) 695 The amplitude (𝐴𝑛) and phase (𝜑𝑛) of each carrier sinusoid (𝑓𝑛) were estimated from the intact 696 signals just before and after each contaminated segment. We assumed a static 𝐴𝑛 throughout 697 each short segment filled in. Standard LIA demodulation was applied to the adjusted 698 transmission signal to recover the photometry response. 699 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint For our application, we fitted the model to data representing 2.5 cycles of the lowest carrier 700 frequency (210 Hz) before and after the contaminated segment (i.e., 12 ms or 72 samples at 6.1 701 kHz of data at each end). Model fitting was solved using Matlab's nonlinear, least-squares 702 algorithm (R2023a, MathWorks, Natick, MA, USA). 703 Alternative Interpolation Approaches for Crosstalk Recovery. We investigated simpler 704 alternative approaches for filling in crosstalk segments. (1) A line connecting the ends of the 705 contaminated segment; (2) a smoothed spline interpolating between the ends of the contaminated 706 segment (using Matlab’s inbuild fillmissing() function), and (3) a single-frequency sinusoidal (1-707 Freq) interpolation at the lowest carrier frequency (210 Hz in our experiment). Single-frequency 708 model fitting using the least-squares method in Matlab. These approaches were compared against 709 µFIX for response recovery fidelity and computational time using the simulated LIA photometry 710 pipeline with artificial ground truth. Testing was performed on Matlab R2023a running in 711 Windows Server 2019 Standard (Microsoft, Albuquerque, NM, USA) as a virtual server with 712 eight Intel Xeon Gold 6254 processors (18 cores, 36 threads, 3.1 GHz; Intel, Santa Clara, CA, 713 USA) and 128 Gb of RAM. The time to process all interpolations and demodulation for the 714 entire stimulus train (20 Hz of 5 ms pulses over 30 s, 600 segments altogether) was measured 715 using Matlab’s inbuilt tic/toc functions. 716 Simulated LIA Photometry Pipeline and Artificial Ground-Truth Signal 717 A simulation of the LIA photometry encoding process was devised using Eq (2). The pipeline is 718 illustrated in Fig. 4A. The pipeline starts with the ground truth photometry response and 719 simulates the LIA-encoded fluorescence read-out of the ground truth. Both artificially generated 720 and empirical signals were inputs (ground truth) to the simulation pipeline. 721 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint For artificial ground truth, slow-varying signals were generated starting with 3 random numbers 722 per second (nodes per second, nps) between 0 and 0.1 V. The signal amplitude and nps value 723 were selected to approximate our empirical data. We retested with ground truth signals up to 150 724 nps to simulate faster signaling dynamics. 725 Each sequence of nodes was then interpolated to a smooth 1.0 kHz sampling rate signal (𝑉𝑠). 726 Three independent artificial signals (triplet) were generated for each simulation run and up-727 sampled to 6.1 kHz for LIA encoding according to Eq (1) using carrier frequencies 210 Hz, 330 728 Hz, and 530 Hz, respectively, to match our empirical setup. The three LIA-encoded signals were 729 then multiplexed into a single signal (𝑉𝑇) as described in Eq (2). LIA demodulation was 730 performed on the multiplexed signal and then down-sampled to 1.0 kHz (𝑉𝑜) to match the 1.0 731 kHz ground truth (𝑉𝑠). These sampling rates were chosen to match our empirical recording 732 hardware setup. To assess the effect of the carrier frequency, the modulation/demodulation test 733 pipeline for each artificial ground truth triplet was repeated three times, with each signal 734 assigned to a different carrier frequency in each repeat. 735 Simulating Optogenetic Crosstalk. Crosstalk was simulated by setting the carrier wave equal to 736 10 V for the duration of stimulation—this is the photosensor saturation limit. Real crosstalk 737 exhibits a brief 2 ms post-stimulation rebound up to -1 V, which we also simulated. Crosstalk 738 was inserted into the multiplexed signal (𝑉𝑇) in our simulation pipeline. To match our empirical 739 optogenetic stimulation delivery, segments corresponding to a 30 s train of 5 ms pulses at 20 Hz 740 were saturated to construct a crosstalk contaminated signal (𝑉𝑋𝑇). We refer to the LIA 741 demodulated response from the uncontaminated multiplexed signal as CT-, and the demodulated 742 response from simulated crosstalk as CT+. µFIX was applied to the contaminated signal 𝑉𝑋𝑇. 743 The subsequent demodulated response was named CT+µFIX. The same pipeline was used to 744 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint quantify the effectiveness of photometry signal recovery using alternative crosstalk interpolation 745 approaches (linear, spline, 1-Freq). 746 Measurement of Signal Recovery Fidelity. Output from LIA demodulation was compared 747 using Pearson’s correlation coefficient. This is used to assess the severity of crosstalk-mediated 748 signal distortion and the fidelity of the µFIX recovery. The correlation coefficient was calculated 749 between two demodulated signals from 2 s before each 30 s stimulation train to 4 s after the 750 stimulation (36622 samples at 6.1 kHz), during which we expect the crosstalk to affect their 751 output. Due to its non-normal distribution nature, fidelity scores are reported using the median 752 and [2.5–97.5]% quantile range in correlation units unless otherwise labeled. Statistical 753 calculations were conducted on the Fisher Z-transformed value (z) of the correlation coefficients 754 (r) to improve the normality of the data distribution: 755 𝑧 = 1 2 ln ( 1+𝑟 1−𝑟) = arctanh(𝑟) 756 𝑟 = tanh (𝑧) 757 Empirical Ground Truth Data Pool and Testing 758 We extracted epochs from our empirical recordings to form a pool of empirical ground truth data 759 for the simulated LIA photometry pipeline. We picked three photometry channels from each 760 mouse to form our empirical ground truth triplet in place of the artificial ground truth; otherwise, 761 the same simulation and testing pipeline was used. We include the contralateral GCaMP, 762 RCaMP, and the isosbestic GCaMP responses. We applied µFIX on all signals to obtain non-763 crosstalk contaminated photometry signals as the ground truth. Altogether, from 43 recordings 764 across eight animals, we collected 208 epochs of photometry response triplets. 765 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint The fidelity of µFIX was validated by drawing on this empirical data pool as ground truths for 766 the simulated LIA photometry pipeline. Testing was executed the same way as described for 767 artificial ground truth, here substituted with three photometry responses from each empirical 768 epoch: RCaMP, GCaMP, and GCaMP isosbestic. To isolate differences between carrier 769 frequencies, we repeated the stimulation three times with the carrier frequency assignments 770 rotated through the photometry responses, such that each photometry response was tested once at 771 each of the three carrier frequencies 210, 330, and 530 Hz. This creates 1605 total empirical 772 trials of µFIX. 773 Simulating Longer Duration Crosstalk Segments. The empirical data pool was used as the 774 ground truth signal to assess the fidelity of µFIX recovery with longer crosstalk durations. 775 Simulations were conducted as previously described for empirical ground truth data. In the first 776 batch of simulations, we varied the stimulation pulse duration from 5 to 35 ms using 20 Hz pulse 777 trains. In the second batch of simulations, we reduced the pulse train frequency to 1 Hz to 778 explore longer pulse durations up to 900 ms. 779 Statistical Analysis 780 All Pearson r correlations (fidelity) statistics were conducted using Fisher-transformed values 781 and inverse transformed for plotting. ANOVA was used to evaluate the contribution of data 782 source, channel, encoding frequency, interpolation method, and crosstalk length to fidelity 783 scores. ANOVA and post-hoc tests were performed in Jamovi (v2.4.14.0) using Tukey’s 784 correction for multiple comparisons. Student’s paired t-test was used to compare the difference 785 between means for processing time in our interpolation method pipeline. T-tests and violin plots 786 were created using GraphPad Prism 10. 787 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint Data and Source Code Availability 788 Code and documentation available at: https://github.com/maxbrkstone/mufix. 789 Supporting information 790 PDF: Additional example recordings from two mice of before and after crosstalk removal via 791 µFIX (S1), power spectral analysis of empirical and simulated epochs (S2), signal recovery 792 fidelity vs. source signal standard deviation (S3), µFIX crosstalk removal results with varying 793 length of intact data surrounding crosstalk (S4), µFIX crosstalk removal results in 60 and 90 794 second stimulation compared to the 30 second default (S5). 795 Author Contributions 796 Conceptualization: S.C.C., H.S. Method: M.B., S.C.C. Software: M.B., S.C.C. Data curation: 797 M.B., S.C.C., S.V., E.C., L.S.P., F.T. Investigation: M.B., S.C.C., S.V., E.C., F.T. Validation: 798 M.B., S.C.C. Formal analysis: M.B., S.C.C. Supervision: D.J.B., H.S. Funding: R.E.G., H.S. 799 Visualization: M.B., S.C.C., L.S.P., F.T. Project admin: S.C.C., R.E.G., H.S. Writing: M.B., 800 S.C.C. Review: M.B., S.C.C., D.J.B., H.S. 801 Acknowledgments: none 802 Funding: none 803 Conflicts of interest: none 804 805 806 807 808 809 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 25, 2025. ; https://doi.org/10.1101/2025.02.23.639738doi: bioRxiv preprint 810

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