Frequency-independent biological signal identification (FIBSI): A free program that simplifies intensive analysis of non-stationary time series data

Extracting biological signals from non-linear, dynamic and stochastic experimental data can be challenging, especially when the signal is non-stationary. Many currently available methods make assumptions about the data structure (e.g., signal is periodic, sufficient recording time) and modify the raw data in pre-processing using filters and/or transformations. With an agnostic approach to biological data analysis as a goal, we implemented a signal detection algorithm in Python that quantifies the dimensional properties of waveform deviations from baseline via a running fit function. We call the resulting free program frequency-independent biological signal identification (FIBSI). We demonstrate the utility of FIBSI on two disparate types of experimental data: in vitro whole-cell current-clamp electrophysiological recordings of rodent sensory neurons (i.e., nociceptors) and in vivo fluorescence image time-lapse movies capturing gastrointestinal motility in larval zebrafish. In rodent nociceptors, depolarizing fluctuations in membrane potential are irregular in shape and difficult to distinguish from noise. Using FIBSI, we determined that nociceptors from naïve mice generate larger, more frequent fluctuations compared to naïve rats, suggesting species-specific specializations in rodent nociceptors. In zebrafish, measuring gut motility is a useful tool for addressing developmental and disease-related mechanisms associated with gut function. However, available methods are laborious, technically complex, and/or not cost-effective. We developed and tested a novel assay that can characterize intestinal peristalsis using imaging time series datasets. We used FIBSI to identify muscle contractions in the fluorescence signals and compared their frequencies in unfed and fed larvae. Additionally, FIBSI allowed us to discriminate between peristalsis and oscillatory sphincter-like movements in functionally distinct gut segments (foregut, midgut, and cloaca). We conclude that FIBSI, which is freely available via GitHub, is widely useful for the unbiased analysis of non-stationary signals and extraction of biologically meaningful information from experimental time series data and can be employed for both descriptive and hypothesis-driven investigations. Author Summary Biologists increasingly work with large, complex experimental datasets. Those datasets often encode biologically meaningful signals along with background noise that is recorded along with the biological data during experiments. Background noise masks the real signal but originates from other sources, for example from the equipment used to perform the measurements or environmental disturbances. When it comes to analyzing the data, distinguishing between the real biological signals and the background noise can be very challenging. Many existing programs designed to help scientists with this problem are either difficult to use, not freely available, or only appropriate to use on very specific types of datasets. The research presented here embodies our goal of helping others to analyze their data by employing a powerful but novice-friendly program that describes multiple features of biological activity in its raw form without abstract transformations. We show the program’s applicability using two different kinds of biological activity measured in our labs. It is our hope that this will help others to analyze complex datasets more easily, thoroughly, and rigorously.


Introduction 74
It can be difficult to identify and characterize biological signals encoded within non-linear, dynamic 75 and stochastic experimental data using analytical methods without introducing bias due to a priori 76 assumptions about the data structure and nature of the signals. This is a challenge faced widely 77 across biological disciplines as many biological datasets are non-ideal (e.g., the frequency 78 resolution is low due to undersampling of the time domain, or the signal-to-noise ratio is low due 79 to limited measurement sensitivity) and the encoded signals are often of irregular shape. The 80 Fourier transform and derivative analytical tools [1], which are widely used to analyze biological 81 time series, have limited capacity to accurately identify and characterize biological signals 82 encoded in such data. A wealth of non-linear methods exist that aim at analyzing these kinds of 83 data series (e.g., using filters and transformations [2,3], multifractals for invariant structures [4]), 84 but most are field-specific and only applicable to a specific type of experimental data (e.g., 85 electroencephalogram and electrocardiogram recordings [5,6]), and would require major 86 optimization prior to application to other types of experimental data with different data structures 87 and signal shapes. Information about a signal of interest is obtained from data that has been 88 subject to differing degrees of pre-and post-hoc processing. We contend that biologically 89 meaningful, easily interpretable information can be readily derived from signals in their raw form, 90 even if they are non-stationary. 91 In this paper, we demonstrate the utility of a novel frequency-independent biological signal 92 identification (FIBSI) program as a first-line tool for isolating biological signals from unprocessed 93 95% CI with all points included. Data in (J) were analyzed using a 1-way ANOVA (F(2, 72) = 169 15.05, P < 0.0001) followed by Dunnett's multiple comparisons test. Data in (K) were analyzed 170 using a Brown-Forsythe 1-way ANOVA (F(2.00, 30.78) = 31.95, P < 0.0001) followed by Dunnett's 171 T3 multiple comparisons test. Data in (L-M) were analyzed using Kruskal-Wallis tests (KW = 172 26.12, P < 0.0001 and KW = 16.37, P = 0.0003, respectively) followed by Dunn's multiple 8 comparisons test. **P < 0.01, ***P < 0.001. ANOVA, analysis of variance; CI, confidence interval; 174 MP, membrane potential. 175 176 Finally, it is assumed that signal analysis techniques like the fast Fourier transform (FFT) 177 capture the dominant frequencies associated with membrane potential oscillations (or fluctuations 178 as we refer to them, to include highly irregular changes in potential) in rodent sensory neurons 179 [20][21][22][23][24][25][26][27]. To test this assumption, a subset of the -45 mV recordings (n = 10 neurons per group) 180 were analyzed using the FFT. The dominant frequencies were highly variable (ranges: rat RA = 181 0.2-50 Hz, rat NA = 0.15-15 Hz, mouse NA = 0.15-10 Hz; FFT results are available online, see 182 Program and Data Availability section in Methods) and did not completely agree with the 183 published FFT results of 15-107 Hz for NA-like small-diameter neurons isolated from rats [20]. 184 This suggested the FFT may not be suitable for making inferences about the DSFs. 185 Next, we used FIBSI to isolate the basic dimensional properties of all DSFs in the RA and 186 NA neuron datasets to determine whether DSFs differed between neuron types and rodent 187 species (Fig 2A-C). Current-clamp recordings had been performed using the same equipment as 188 reported previously [17,18], so we used published cutoffs (≥1.5 mV and ≥20 ms) to eliminate from 189 analysis low-amplitude signals that are likely noise from equipment. For FIBSI analysis, a running 190 median window of 1 s corresponding to 20,000 samples along the x-axis was used, and no filters 191 or transformations were applied to the raw data prior to signal detection. to y = 0 and calculate residuals, identify peaks of DSFs (blue X) that meet user-defined cutoffs 199 (≥3.0 mV amplitude, ≥20 ms duration in this example), and manually approximate the amplitude 200 of suprathreshold DSFs (red X) that produce an AP (see Methods for amplitude substitutions); 201 (C) visual confirmation of the DSF dimensional characteristics. Descriptive information for the 202 subthreshold DSFs include start, peak, and end times, amplitude, duration, and AUC (blue 203 highlight) to the converted running median at y = 0. Descriptive information for the AP waveform 204 (pink highlight) includes the aforementioned properties. (D) Scatter plot of DSF dimensions and 205 exponential plateau curves (cutoffs: ≥1.5 mV and ≥20 ms; rat RA n = 20 neurons, rat NA n = 27 206 neurons, mouse NA n = 28 neurons). Data were fit using exponential plateau models for each 207 neuron type; a single model did not fit all data (F(6, 5689) = 6.696, P < 0.0001). Refer to S1 Table  208 for model parameters. (E) The AUC of the DSFs ≥3 mV was significantly larger in rat NA neurons 209 compared to rat RA neurons. The DSFs in Mouse NA neurons were also significantly larger than 210 in rat NA neurons. (F) The NA neurons exhibited rightward shifts in DSF frequency (%) per 211 amplitude bin compared to the RA neurons. In NA neurons, DSFs ≥5 mV triggered APs and the 212 AP probability rapidly increased to 1 at 7-9 mV. Raster plots depicting frequencies of DSFs ≥3 213 mV in (G) rat RA neurons, (H) rat NA neurons, and (I) mouse NA neurons. The rat and mouse 214 NA neurons with suprathreshold DSFs and ongoing activity at -45 mV correspond to numbers 22-215 27 and 23-28 on the y-axis of (H-I), respectively. (J) The mean frequencies for DSFs ≥3 mV were 216 significantly higher in the NA neurons. Data in (E) shown as the median ± 95% CI with all points 217 included. The raw AUC data collected for (E) were log transformed for the use of parametric 218 statistics. Transformed results were analyzed using a 1-way ANOVA (F(2, 971) = 38.90, P 219 <0.0001) followed by Sidak's multiple comparisons test. Data in (J) shown as medians (gray line) 220 and analyzed using a Kruskal-Wallis test (KW = 23.85, P < 0.0001) followed by Dunn's multiple 221 comparisons test. *P < 0.05. AUC, area under the curve. 222 223 To our knowledge, no statistical model has been reported that describes the relationship 224 between DSF amplitude and duration. Such a model would provide insight into the channel 225 opening and closing dynamics driving DSF generation in nociceptors. This model would also 226 provide a reference against which the effects of various pharmaceuticals can be compared and 227 future treatments for pain may be developed. In order to approach this is an unbiased manner, 228 we employed the Akaike information criterion to compare the quality of fit of several different 229 nonlinear regression models to the neuron datasets. Overall, the exponential plateau model was 230 a better fit for the RA and NA neurons compared to the Gompertz, Logistic, and Malthusian 231 models (see S1 Table for model parameters). We then asked whether the exponential plateau 232 model could fit all data points using the same set of fitting parameters, but a separate set of 233 parameters was necessary for each neuron type (F(6, 5689) = 6.696, P < 0.0001; Fig 2D). All 234 models tested, including the exponential plateau model for each neuron type, failed to pass for 235 homoscedasticity (P < 0.0001 for each model), and the 95% CI for the RA neuron model could 236 not be calculated by the GraphPad Prism software. These results suggest interpretations based 237 solely on statistical models should be made with caution, but they might provide some insight into 238 the relationship between DSF amplitude and duration. 239 Making comparisons based solely on DSF amplitude (like done previously [17,18]) limits 240 interpretation of the results because it omits any influence duration may have on DSF size, as the 241 DSFs do not exhibit regular waveforms. Therefore, we asked whether the total AUC of DSFs 242 differed between neuron types. A cutoff of ≥3 mV was chosen because it is at the lower bound of 243 the range of amplitudes that may be functionally relevant under pain-associated conditions when 244 neurons are depolarized [17,18]. The AUC of DSFs in rat NA neurons was larger than in RA 245 neurons, and the AUC of DSFs in mouse NA neurons was the largest (Fig 2E). We then binned 246 DSFs by amplitude to determine their frequency of occurrence (reported as a percentage of total 247 DSFs generated in each amplitude bin), and the amplitude necessary to generate APs (Fig 2F). 248 The mean frequency of DSFs per amplitude bin was higher in NA neurons than RA neurons for 249 rats. No DSFs triggered APs in the RA neurons, but a fraction of the large amplitude DSFs (≥5 250 mV) in NA neurons did trigger APs (Fig 2F). Mouse NA neurons tended to require larger DSFs to 251 trigger APs before the AP probability plateaued. Finally, we used raster plots to depict the 252 differences in frequencies of DSFs ≥3 mV between RA and NA neurons (Fig 2G-I). Few RA 253 neurons generated DSFs ≥3 mV (Fig 2G). The frequency of DSFs ≥3 mV was significantly higher 254 in NA neurons from mice (Fig 2I) than rats (Fig 2H-J). The frequencies of DSFs ≥3 mV detected 255 in NA neuron recordings by FIBSI were orders of magnitude lower than the oscillation frequencies 256 reported based on similar measurements using the FFT [20]. 257 258

Using fluorescence contrasted visualization and FIBSI to analyze gut motility in the larval 259 zebrafish 260
Direct intestinal injections and oral gavage can be used to deliver dyes into zebrafish larvae 261 [28,29]. However, these methods are invasive, can be deterrents without adequate technical 262 expertise, and may directly influence motility. We first determined whether immersing awake 263 larvae in embryo medium (E3) media supplemented with Nile Red dyewithout using an egg 264 emulsion to promote feeding [30]was a viable non-invasive alternative for staining the intestinal 265 luminal space (Fig 3A-B [32]. A total of 19 ROIs were evenly positioned along the foregut, midgut, and hindgut regions of 271 the intestinal tract (Fig 3B-C). We predicted that the Nile Red fluorescence intensity would change 272 periodically, reflecting contraction waves traveling through the gut (Fig 3D-E); retrograde 273 contractions coincide with a decrease in intensity in the foregut, anterograde contractions coincide 274 with an increase in intensity in the midgut and hindgut, and rapid movement of the cloaca coincide 275 with high-frequency oscillations in intensity in the hindgut. Indeed, contractions were visible in the 276 fluorescence intensity recordings as they propagated rhythmically through the intestinal tract at 277 <0.1 Hz, and the directional changes in intensity matched our predictions (Fig 3F). During our development process, we noticed that some recording periods were primarily 292 high fluorescence, with contractions signaled by a sudden reduction in fluorescence (a trough 293 event), whereas other recordings were primarily low fluorescence, punctuated by sudden 294 increases in fluorescence (a peak event). This is likely related to differing contraction physiology 295 in the foregut, midgut, and hindgut. In order to increase the comparability of these events and 296 standardize the identification of amplitude, we implemented a second normalization procedure 297 that traces a fitted line peak-to-peak (or trough-to-trough) of events identified in the first round of 298 13 normalization (i.e., sliding median). This new line is used as the reference against which the data 299 is compared and events identified again. The peak-to-peak function was applied to the foregut 300 (ROIs 1-7) and hindgut , and the trough-to-trough function was applied to the midgut 301 (ROIs 8-16). The following running median window sizes were used: 50 x-samples for ROIs 1-7 302 and 10 x-samples for  Processed fluorescence intensity data for the foregut (Fig 4A-C), midgut (Fig 4D-F), and 304 hindgut ROIs (Fig 4G-I) revealed several features: foregut contractions were overall larger in 305 amplitude, foregut and midgut contractions had similar durations, and the high-frequency 306 oscillations coinciding with cloaca movement in the hindgut were overall shorter and smaller. 307 These features mirrored observations made during video playback and predictions about signal 308 shape (Fig 3D-E). A cutoff of ≥0.05 amplitude (F/F0 units) and duration of ≥10 s (duration cutoff 309 inferred from published contraction frequencies and intervals, see [31,[33][34][35]) was used to isolate  We then asked whether the spatiotemporal information extracted from our time-lapse 321 datasets using FIBSI could be used to detect differences in gut motility between unfed and fed 322 larvae. A recent study using image velocimetry and spectral analysis reports differences in motility 323 between unfed and fed zebrafish larvae at 7 dpf [35], but the study is limited to the midgut, and 324 no other comparable datasets have been published. First, we confirmed that muscle contraction 325 frequencies did not differ between unfed AB (0.026 ± 0.001 Hz, n = 8) and unfed transgenic Tg(-326 8.3phox2bb:Kaede) larvae (0.028 ± 0.001 Hz, n = 8; unpaired t test P = 0.158). Contraction 327 frequencies in the cloaca also did not differ between the two lines (0.046 ± 0.004 Hz and 0.051 ± 328 0.003 Hz, respectively; unpaired t test P = 0.407). Therefore, the two lines were pooled to increase 329 statistical power for comparison to fed AB larvae. Muscle contraction frequencies were higher in 330 fed compared to unfed larvae (Fig 4L). from the peak-to-peak or trough-to-trough trend line (red) and the trend line was normalized to y 337 = 0. Event peaks (blue X) were identified only for the waveforms with start/end times that crossed 338 y = 0 (red X). After processing, event durations and amplitudes were plotted for inspection and 339 filtering (1 dot = 1 event, events are color coded by ROI). Cutoffs (dotted red lines, amplitude of 340 ≥0.05 and duration ≥10 s) were applied to isolate low-frequency contractions in Q4 of al 19 ROIs. significantly increased mean contraction frequencies in the foregut (ROIs #1-7), but exhibited no 349 differences from unfed larvae along the midgut (ROIs #8-16) and hindgut .

358
We then asked whether motility in fed larvae was higher along the entire gut, or if the 359 increased motility was limited to a specific functional gut segment. The frequency of retrograde 360 contractions in the foregut was higher in fed compared to unfed larvae (Fig 4M). In contrast to the 361 prior study [35], we observed no differences between unfed and fed groups for anterograde 362 contractions in the midgut or hindgut (Fig 4M). Finally, we observed a significant decrease in the 363 frequency of cloaca movements in fed compared to unfed larvae (Fig 4N). The data collected 364 using our fluorescence contrast-based assay of gut motility, in conjunction with signal detection 365 and data analysis using FIBSI provided novel insights into individual functional gut segments of 366 larval zebrafish. We were able to characterize peristalsis along the whole intestinal tract as well 367 as high-frequency, low-amplitude oscillatory movements of the cloaca. 368 369 3. Discussion 370

Overview 371
In this study we introduce a new signal detection algorithm implemented in the free program FIBSI 372 that can be used to analyze a diverse array of non-linear, dynamic and stochastic experimental 373 datasets by extracting biologically meaningful signals from background noise. As experimental 374 biologists, we wanted to develop FIBSI to be particularly suited to the needs of other 375 experimentalists. As such, strengths of FIBSI include its capability to process non-ideal datasets 376 such as those we included here to demonstrate the utility of the program. These may include 377 datasets with low signal-to-noise ratios, irregular signal shapes, and low-resolution (i.e., under-378 sampled) time series. In contrast to many other signal detection programs, FIBSI requires no 379 modification of the raw data, and minimal ad-hoc assumptions regarding data structure and signal 380 shape are needed prior to processing and signal detection. That is, FIBSI captures quantitative 381 information for all signals contained with the dataset. We validated the performance of FIBSI using 382 two different types of measurements: electrophysiological whole-cell current-clamp recordings

Membrane potential fluctuations differ between nociceptors in two rodent species 390
We were the first to automate the quantification of DSFs and demonstrate their functional 391 importance for AP generation in putative C-type nociceptors using the prototype algorithm upon 392 which FIBSI is based [17]. We showed that DSFs bridge the gap between the resting membrane 393 potential and AP threshold of a neuron and presumably play a role in driving ongoing pain-related 394 information from nociceptors [41,42]. We have also begun to identify associated cellular 395 mechanisms (e.g., dependence upon cell signals such as cyclic AMP-dependent protein kinase 396 and exchange protein activated by cyclic AMP-associated pathways) [17,18,43] [45]. Given the limited research on DSFs, our current study is the first to make direct 400 comparisons between similar nociceptors in two rodent species commonly used in pain-related 401 studies. This was done to 1) confirm whether nociceptors in rats and mice function similarly, and 402 2) to validate FIBSI in its new, generalized form using the same data type as in our original studies 403 [17,18]. 404 The NA neurons isolated from rats and mice recapitulated several of the specializations 405 we have described that promote ongoing activity and ongoing pain [17,18,[41][42][43]. Under naïve 406 conditions (i.e., no injury), rat NA neurons are clearly more excitable than RA neurons. A novel 407 finding presented here is that mouse NA neurons are more excitable than rat NA neurons with 408 enhanced rheobase values and depolarized resting membrane potentials. A plausible explanation 409 for the species-specific differences in NA neuron excitability is that the neurons in mice may be 410 smaller in size, as suggested by the smaller membrane capacitance measures. This raises the 411 interesting question of whether the membrane densities and compositions of the channels 412 underlying the DSFs differ between species; this is of ongoing interest in the Walters lab and 413 under investigation. These specializations are expected to prime the NA neurons to activate more 414 readily in response to intra-and extracellular signals associated with nociceptive and potentially 415 painful stimuli. This hypothesis is further supported by our analysis of DSFs using FIBSI. The 416 mouse NA neurons generate larger, more frequent DSFs than rat NA neurons. However, the 417 greater DSF size and frequency, and necessity for larger-amplitude DSFs to generate APs in 418 mice compared to rats is unexpected because naïve rats and mice have similar AP voltage 419 thresholds while the mice have a more depolarized RMP compared to rats. We also compared 420 exponential growth models to describe the dimensional properties of the DSFs and found different 421 models were necessary for each neuron type. These models need to be compared further under 422 other pharmacological and pain-related conditions in order to better understand the differences 423 between species. Finally, the frequency results we obtained in our FFT analysis did not 424 recapitulate the results for the same type of neuron [20], and other studies do not fully report their 425 results for comparison [21][22][23][24][25][26][27]. One possible explanation for the discrepancy is that the longer (see [46,47]). The use of FIBSI and similar analytical approaches used to study DSFs will improve 445 our understanding of basic nociceptor physiology in multiple species and help to identify 446 fundamental mechanisms for driving pain that may be shared by rodents and humans. 447 448

Validation of a simple, fast, and cost-effective assay of gut motility in larval zebrafish 449
The current approach for assessing gut motility in vertebrates in vivo and ex vivo is to generate 450 spatiotemporal maps of the intestinal tract and measure changes in pixel opaqueness as indices 451 of movement [31,32,34,[36][37][38][39][40]. Inspection of these maps can be done manually but the process 452 is laborious and possibly subject to human unconscious bias. More recent studies have improved 453 the analysis of gut motility in that the process has been semi-automated, which also enables 454 assessment of a wider range of parameters (e.g., contraction amplitude in µm). However, these 455 methods require custom microscopy equipment [48], complex image velocimetry and spectral 456 analysis [35], and/or use of customized "in-house" [49] or proprietary software [33,40]. Here, we 457 developed a simpler, faster, and more cost-effective assay using fluorescence contrast-based 458 imaging to visualize gut motility in vivo. The resulting time series datasets can be processed using 459 FIBSI to analyze muscle contractions. While 8-and 16-bit grayscale bright field images can also 460 be analyzed using FIBSI, fluorescence intensity measurements have a larger dynamic range, and 461 the resulting time series have a higher signal-to-noise ratio (i.e., contractions are more visible) 462 The advantage of FIBSI over existing programs used to analyze gut motility is its user-friendliness 463 and free availability. 464 Our attempts to validate the fluorescence contrast-based gut motility assay and the 465 performance of FIBSI against prior studies was challenging due to the fact that many reports do 466 not include sufficient experimental details (e.g., feeding regimen, gut region imaged, and 467 methodology used to calculate contraction frequencies). It is important that future studies are of frequencies for unfed and fed larvae [33,34,50]. The only published study to directly compare 479 gut motility in unfed and fed zebrafish larvae used measurements from the midgut, and it reports 480 feeding at 5-6 dpf increases motility at 7 dpf from 0.035 Hz to 0.041 Hz [35]. We observed similar 481 rates (~0.03 Hz) in the midgut, but feeding zebrafish live paramecia 1 day before testing did not 482 increase the rate of anterograde contractions in the midgut. Instead, we found that feeding 483 increased retrograde contractions in the foregut. Another novel observation was that feeding 484 decreased the rate of oscillatory movements of the cloaca. Adult shorthorn sculpinanother 485 teleost speciesrespond to feeding in a similar manner; orally-directed (retrograde) standing [51], but to our knowledge there are no published reports of sphincter-like function in the hindgut 494 of larval zebrafish. It is possible that a reduction in the oscillations (i.e., relaxation) may facilitate 495 more frequent removal of waste products, but this has yet to be confirmed using transit 496 experiments. Our findings suggest that larval zebrafish are capable of generating functionally 497 complex gut motility patterns in response to feeding, possibly similar to other adult teleost species. 498 This adds to their tractability as a powerful model organism for in vivo imaging. The significance 499 of these gut region-specific phenomena is becoming increasingly apparent (for review [52]), but 500 these complex motility patterns require further attention using methods that yield functional 501 information of the whole gut. Future improvements to our motility assay and FIBSI could link 502 changes in contraction amplitudes to changes in the luminal dimensions of the intestinal tract, 503 similar to using image velocimetry to track movement [35]. 504 There is a pressing need for improved imaging and analysis techniques that can be used 505 to address gut motility in altered physiological states and disease [53]. Analysis with FIBSI yields 506 experimentally valid and reproducible results, and it should be useful to researchers measuring 507 gut motility in zebrafish as a functional output of the enteric nervous system (ENS). The ENS 508 regulates multiple gastrointestinal functions (e.g., gut motility, hormone secretion). Deficiencies in 509 the development and function of the ENS can lead to debilitating neurological disorders (e.g., 510 Hirschsprung's disease) [54][55][56][57][58]. Other factors of interest associated with ENS function (e.g., 511 stress, microbiome, inflammation, visceral pain) [59-61] have traditionally been tested using 512 rodent models. Recent reviews have highlighted the validity of using zebrafish as an analogous 513 model to address some of the above questions [53,[62][63][64][65], and the application of our motility 514 assay and FIBSI to this system will facilitate such research. 515 516

Current and future applications of FIBSI 517
We originally designed the prototype version of FIBSI (first report [17]) for the singular purpose of 518 quantifying DSFs and APs in nociceptors and incorporating the methodologies of others (e.g., 519 estimating AP threshold [66]) within the field. However, collaborative efforts led us to realize the 520 broader applicability of the program to other researchers and types of datasets. Additional 521 features (e.g., filtering methods, down-sampling, trimming) are included for those interested, and 522 we encourage others to make modifications to the existing code (see availability section in 523 Methods) and/or insert their own functions. The signal detection algorithm was tested solely on 524 datasets with fixed sampling rates. Although the minimum requirement for identifying an event is 525 two consecutive x values with the same sign, it is possible some assumptions we have made in 526 other aspects of the algorithm may lead to inaccurate identification of events in datasets with 527 variable sampling rates. Testing and implementing different methods of data interpolation could 528 alleviate this limitation but has not been done by our research group. 529 We speculate that FIBSI could theoretically work with almost any type of x,y dataset where 530 the measured parameter exhibits deviations from baseline, as FIBSI is adapted to account for 531 changes in the baseline level of activity via the running fit function. This is an improvement over 532 arbitrary decisions for baseline or rudimentary measures (e.g., simple average) that assume the 533 system being studied is fixed. Although we have only fully tested FIBSI for processing of voltage 534 fluctuation time series and fluorescence intensity time series, ongoing projects are currently 535 adapting FIBSI to process other types of datasets (e.g., in vivo nerve recordings and calcium 536 imaging in rodent and zebrafish neurons), and to investigate physiological states and disease 537 models pertinent to our research groups. Other examples of biological datasets that may be 538 processed and analyzed using FIBSI include animal vibrations (e.g., honeybee waggle dance 539 [67]) and sounds (e.g., ultrasonic vocalizations [68,69]). In summary, there exists broad potential 540 for FIBSI to facilitate signal analysis of diverse types of raw data by biologists having quite different 541 backgrounds in quantitative analysis. 542 543 4. Methods 544

Description of frequency-independent biological signal identification (FIBSI) program 545
The signal detection algorithm used by FIBSI was generalized from our initial study where we 546 identified DSFs in nociceptors [17]. It is an extension of the Ramer-Douglas-Peucker algorithm 547 for identifying significant shapes that ought to be retained in an image while reducing the total 548 number of points needed to represent said image [15,16]. The FIBSI program was developed and 549 tested on Ubuntu Linux and Windows 10 operating systems. The data processing is as follows: 550  A vector in which = time points and = independent measured variable in an x, y 551 series is received as input 552 = ( 1 , 2 , … ) 554 (1) 553  The vector can be normalized to an external reference if selected 555 Components of the rising phase: = { ∈ | 0 < < } 581 Components of the falling phase: = { ∈ | < < } 582 R must not contain numbers that cross zero: (∀ ∈ ) ( ) > 0 583 F must not contain numbers that cross zero: (∀ ∈ ) ( ) > 0 584 An 'above' event, , is the union of components in and : = ∪ 585 (∀ ∈ )∄ where ( ) > ( ) ⇒ is the time of the local maximum, is the start time, and 586 is the end time 587 ∴ is the set of numbers contained within a single 'above' event 588 d. The local minima for a 'below' event is therefore defined as ( ) < 0 and a similar 589 set of rules: 590 (∀ ∈ )∄ where ( ) < ( ) 591  Events can be excluded via user-defined duration and amplitude cutoffs, and replaced with 592 the line of best fit connecting the start and end points of the excluded event; this is a 593 generalization of the AP exclusion method described previously [17] 594  Refitting can be applied; this allows additional use of a trend line calculated by tracing the 595 peak-to-peak pathway of identified 'above' or 'below' events; steps (3-4) are repeated to 596 generate a new ( ) and ∆ ( ) ; troughs can also be used to generate ( ℎ) and 597 ∆ ( ℎ)

598
 If exclusions and/or refitting methods are applied, then event detection can be performed 599 again 600  Event directionality (above or below), dimensions (duration, amplitude, AUC), and indices 601 (start, peak, end) are tabulated; graphs and comma-separated x, y series can be generated 602 as optional outputs 603 604

Data analysis 605
Analysis of raw electrophysiological and fluorescence time series data was performed with FIBSI 606 written using the Anaconda v2019.7.0.0 (Anaconda, Inc, Austin, TX) distribution of Python v3.5.2, 607 and the NumPy and matplotlib.pyplot libraries. Custom scripts were also written to analyze the 608 electrophysiological data using the FFT. Statistical analyses of the DSF and gut motility data 609 generated by FIBSI were performed using Prism v8.2.1 (GraphPad Software, Inc, La Jolla, CA). 610 Decisions to compare the DSFs in NA neurons between rats and mice, and to compare the DSFs 611 between the NA and RA neurons in rats were made a priori. Amplitude substitutions for 612 suprathreshold DSFs were calculated manually as described previously [17,18] (see also the 613 FIBSI tutorial included online). One zebrafish (fed) was omitted from analysis due to a lack of 614 muscle movements within the gut, but blood flow was still observed. This was confirmed during 615 video playback and inspection of the raw fluorescence intensity time series. Statistical significance 616 was set at P < 0.05 and all reported P values are two-tailed.