By means of an expansive innervation, the serotonin (5-HT) neurons of the dorsal raphe nucleus (DRN) are positioned to enact coordinated modulation of circuits distributed across the entire brain in order to adaptively regulate behavior. Yet the network computations that emerge from the excitability and connectivity features of the DRN are still poorly understood. To gain insight into these computations, we began by carrying out a detailed electrophysiological characterization of genetically identified mouse 5-HT and somatostatin (SOM) neurons. We next developed a single-neuron modeling framework that combines the realism of Hodgkin-Huxley models with the simplicity and predictive power of generalized integrate-and-fire models. We found that feedforward inhibition of 5-HT neurons by heterogeneous SOM neurons implemented divisive inhibition, while endocannabinoid-mediated modulation of excitatory drive to the DRN increased the gain of 5-HT output. Our most striking finding was that the output of the DRN encodes a mixture of the intensity and temporal derivative of its input, and that the temporal derivative component dominates this mixture precisely when the input is increasing rapidly. This network computation primarily emerged from prominent adaptation mechanisms found in 5-HT neurons, including a previously undescribed dynamic threshold. By applying a bottom-up neural network modeling approach, our results suggest that the DRN is particularly apt to encode input changes over short timescales, reflecting one of the salient emerging computations that dominate its output to regulate behavior. The forebrain-projecting serotonin (5-HT) neurons of the dorsal raphe nucleus (DRN) play a key role in regulating behavior in dynamic environments, but the precise nature of this role is still not well understood . DRN serThe spiking statistics of 5-HT neurons necessarily shape and constrain their computational role. For instance, the slow firing rate (~5 Hz) of 5-HT neurons, in large part attributable to a large after-hyperpolarization potential (AHP) , may appComputational modeling is a standard approach to link levels of description and is thus well suited to delineate how network-level function emerges from excitability features identified at the single-cell level. In spite of their conceptual utility, the most detailed single cell models, including those of DRN neurons , do not augmented GIFs). This approach recapitulated and extended past findings on DRN neurons by showing that the best-performing models of 5-HT neurons featured slow membrane time constants, an A-type potassium current, and strong adaptation mechanisms. Network simulations of optimized GIF models of both 5-HT and GABAergic SOM neurons organized in a feed-forward inhibitory circuit revealed that 5-HT neuron populations context-dependently encode a mixture of the intensity and temporal derivative of their inputs. Our overall approach further allowed us to trace back specific features of these population responses (e.g. gain) to defined excitability features of DRN neurons.In this study, we developed and validated for DRN neurons a hybrid modeling approach that lies between reductionist GIF and biophysical Hodgkin-Huxley-type models to capture excitability features of individual neurons for accurate simulations of population dynamics and, by extension, network computation inference. To this end, we carried out cellular electrophysiological recordings from genetically identified DRN 5-HT and SOM neurons to (1) extract and validate, from sets of noisy inputs, parameters for the automatic development of accurate GIF models and (2) experimentally define complementary biophysical mechanisms to be grafted onto the GIF models to iteratively improve their prediction accuracy  characterized in great detail in several other cell types  model that captured the effect of this conductance on single-cell voltage dynamics (see Methods). In keeping with previous studies, AI introduced a kink in the subthreshold voltage leading up to spike threshold . When we set the corresponding parameters in our toy model to experimentally determined values from 5-HT neurons, we observed the same qualitative relationship between spike latency and initial voltage . Whereas subthreshold fluctuations yielded time-locked spikes without AI .Next, we used our experimentally validated toy model to understand how thout IA , they in present . This de latency  since th latency . Taken tWe next sought to develop a model able to capture the essential biophysical features of DRN neurons and accurately predict their responses to naturalistic inputs. GIF models offer a flexible modeling framework well suited to this purpose because they can be trained to accurately reproduce the firing patterns of individual neurons using less than 5 min of electrophysiological data per neuron . In thisAI regulates spike timing in 5-HT neurons because of its nonlinear subthreshold effects. Foreseeing that the presence of this prominent current may limit the accuracy of canonical GIF models—which are not designed to capture nonlinear subthreshold effects—we first augmented the canonical GIF model  spike timing on validation data, To establish comparative GIF model benchmarks across cell types, we carried out whole-cell electrophysiological recordings not only from DRN 5-HT and SOM cells but also from canonical deep-layer pyramidal neurons of the medial prefrontal cortex (mPFC). For each recording, we applied two distinct instantiations of noisy in vivo-like inputs  and achieving AI, the aGIF model not only better predicted the voltage  in 5-HT neurons. As previously intuited, the canonical GIF model performed rather poorly in 5-HT neurons , predictp=0.644; , suggestp=0.644; . Thus, aR2 = 0.600 ± 0.238 and Turning to the other main cell type of the DRN, we next analyzed the performance of each model in SOM cells . In thes neurons . NonetheIA, and particularly prominent adaptation mechanisms.Our model selection approach identified the most salient components required to capture the input-output functions of individual neurons and allowed us to identify functional differences across cell types. 5-HT neurons were distinguishable from SOM and mPFC cells by their long membrane time constants  and by tThe development and validation of accurate single-cell models allowed us to identify the population-level computations operating in the DRN. We took advantage of the one-to-one correspondence between our GIF models and real neurons to construct synthetic populations with realistic neuron-to-neuron heterogeneity by sampling from banks of single-cell models . In respWe next considered the underlying mechanisms giving rise to the distinctive time-dependent gain of 5-HT neurons. We found that the characteristically strong spike-triggered adaptation of 5-HT neurons (spike-triggered hyperpolarizing adaptation current and threshold movement shown in AI in 5-HT neurons and the feedforward inhibition (FFI) enacted by local DRN interneurons . The gain of the transient component of the 5-HT response increased markedly when the conductance of AI was set to zero  and generalized linear models (GLMs), which are trained using only the spike output and external input to each cell and do not consider the subthreshold voltage . DespiteIA on the network-level processing features of the DRN without the aGIF model.Does the aGIF modeling approach represent an unnecessary complication of the GIF model framework or, conversely, an oversimplification of detailed Hodgkin-Huxley models? GIF models that do not explicitly account for the effects of specific ionic conductances produce highly accurate spiketrain predictions in many cell types ; indeed,AI in controlling the sensitivity of the stationary response to sustained inputs  are expected to influence how AI controls the transient and stationary components of the response. Finally, it is interesting to note that AI is also highly expressed in the dendrites of cortical neurons, where it may have an analogous function  enhance the DRN ) rather Our heuristic model of the DRN helps to illustrate the unexpectedly multifaceted nature of the computations performed by this evolutionarily ancient region, but, like most heuristics, it remains an oversimplification. Some of the qualitative features of DRN processing emerging from our simulations are not explained by our “input intensity plus temporal derivative” heuristic , presenThe role of 5-HT signaling in modulating behavior is increasingly conceptualized through the lens of reinforcement learning (RL) theory. Indeed, 5-HT output has been proposed to loosely encode or modulate every component of classical RL , includiIf the electrophysiological features of individual 5-HT neurons directly participate in shaping the computations enacted by the DRN, the same is likely true for other neuromodulatory systems, and this work may offer overall guiding principles. For instance, dopamine neurons, well known for their reward prediction error-like coding properties , bear soIf the derivative-like operation identified here does not directly contribute to computing one of the key components of RL, what might its role in the DRN be? One possibility is that strong spike-triggered adaptation may optimize the efficiency of neural coding by filtering out temporally redundant information, a phenomenon referred to as predictive coding and that is ubiquitous in sensory systems . As the Slc6a4-cre::Rosa-TdTomato (SERT-Cre) and Sst-cre::Rosa-TdTomato transgenic lines were used to fluorescently label DRN 5-HT and somatostatin (SOM) GABA neurons, respectively. Animals were group-housed and kept on a 12:12 hr light/dark cycle with access to food and water ad libitum. All experiments were carried out in accordance with procedures approved by the University of Ottawa Animal Care and Veterinary Services .Experiments were performed on male and female C57/Bl6 mice aged 4–8 weeks. 4, 1.0 mM CaCl2, 1.0 mM NaH2PO4, 1.3 mM sodium ascorbate, 11.0 mM glucose, 26.2 mM NaHCO3; saturated with 95% O2/5% CO2. A Leica VT1000S vibratome was used to cut 300-µm coronal sections of midbrain containing the DRN or of the cortex containing the mPFC in the same ice-cold choline dissection buffer. After cutting, slices were placed in a recovery chamber filled with artificial cerebrospinal fluid containing the following: 119.0 mM NaCl, 2.5 mM KCl, 1.3 mM MgSO4, 2.5 mM CaCl2, 1.0 mM NaH2PO4, 11.0 mM glucose, 26.2 mM NaHCO3; ∼298 mOsm, maintained at 37°C, and continuously bubbled with 95% O2/5% CO2. The recovery chamber was allowed to equilibrate to room temperature for 1 h before beginning experiments.Animals were deeply anesthetized using isofluorane (Baxter Corporation) before being euthanized by decapitation. The brain was quickly removed from the skull and submerged into ice-cold dissection buffer containing the following: 119.0 mM choline chloride, 2.5 mM KCl, 4.3 mM MgSO3, 10 mM EGTA, 5 mM TEA Cl, 1 mM CaCl2, 10 mM Na HEPES, 4 mM Mg ATP, 2 mM GTP, 2 mM QX-314, and 10 mM Na phosphocreatine; adjusted to pH 7.25 with CsOH, 280–290 mOsm) and in the presence of bath-applied 100 µM (2 R)-amino-5-phosphonovaleric acid (APV) and 5 µM 2,3-dioxo-6-nitro-1,2,3,4-tetrahydrobenzo[f]quinoxaline-7-sulfonamide (NBQX). For voltage clamp experiments, whole-cell capacitance compensation was applied manually following break-in, and leak current subtraction was performed post hoc using membrane leak conductance estimated based on a –5 mV pulse at the start of each sweep. Experiments were carried out at room temperature except where noted. For current clamp experiments used to fit GIF models, access resistance was compensated using an active electrode compensation method  equipped with differential interference contrast and a ×40, 0.8 NA water-immersion objective. Whole-cell recordings were obtained from fluorescently labeled DRN 5-HT and SOM neurons and unlabeled mPFC L5 pyramidal neurons using glass electrodes . For most experiments, the following potassium gluconate-based internal solution was used: 135 mM potassium gluconate, 6.98 mM KCl, 10 mM HEPES, 4 mM Mg ATP, 0.40 mM GTP, 10 mM Na phosphocreatine; adjusted to pH 7.25 with KOH, 280–290 mOsm. A subset of experiments (GABA synaptic physiology) were carried out using a cesium-based internal solution (120 mM CsMeSOn method . For volThe GIF and Na-inactivation GIF (iGIF) models have been described previously in detail . Brieflywhere where The equilibrium voltage-dependent change in spike threshold as the definition of the subthreshold dynamics of the aGIF model.The procedures for fitting the GIF and iGIF models to electrophysiological data have also been described previously in detail . BrieflyOur toy model of a neuron with an inactivating potassium current is based on an LIF augmented with where where AI and KI , respectively. These were defined as followsThe voltage-gated potassium currents in 5-HT neurons were modeled in terms of an inactivating current and a non-inactivating current, we refer to as K = –101 mV is the reversal potential of potassium in our recording conditions. Note that although this value is not physiological, the effect of varying this parameter is very similar to the effect of varying where – 1), and where To keep the number of parameters in our current model to a minimum, we assumed that the where iability ), correcDRN network models were constructed by connecting a population of 400 SOM neuron models to a population of 600 5-HT neuron models in a feed-forward arrangement. Population models were bootstrapped by sampling with replacement from a bank of experimentally constrained GIF models. SOM neuron models were randomly connected to 5-HT neuron models with a connection probability of 2%, such that the expected number of GABAergic synapses on each 5-HT neuron model was 8. We used a conductance-based model of GABAergic synapses with a fixed reversal potential of –76.7 mV, conductance of 0.3 nS, and biexponential kinetics with AI were generated by setting Simulated 5-HT populations with decreased or increased for 5-HT_model in 5-HT_population; doSOM_model = random_choice(SOM_models)  5-HT_model.eta.coefficients= SOM_model.eta.coefficients  5-HT_model.gamma.coefficients= SOM_model.gamma.coefficients  end for.https://github.com/pozzorin/GIFFittingToolbox; AI .Simulations were implemented in Python and C++ using custom-written extensions of the GIF Fitting Toolbox  feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.Our editorial process produces two outputs: (i) Decision letter after peer review:eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and John Huguenard as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Jochen Roeper (Reviewer #1); Hitoshi Morikawa (Reviewer #2); Paul Miller (Reviewer #3).Thank you for submitting your article "Temporal derivative computation in the dorsal raphe network revealed by an experimentally-driven augmented integrate-and-fire modeling framework" for consideration by The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.Essential revisions:In this study, Harkin and colleagues examined the biophysical properties of dorsal raphe (DR) serotonin neurons using a combination of whole-cell patch clamp recording in brain slices and biophysical computational modeling. The authors adopted the approach called a generalized integrate-and-fire [aGIF] model, which incorporates a relatively small number of salient biophysical properties (ionic currents) of a specific neuron, and whose parameters are optimized based on voltage dynamics obtained experimentally. First, the authors observe two prominent features in serotonin neurons. The first is a prominent spike frequency adaptation, resulting from after-hyperpolarization potentials. The second is a "kink" in the voltage trace leading up to the first spike, which can be attributed to the effect of A-type potassium currents (I-A). Using the data, the authors constructed aGIF model of serotonin neurons which contains I-A, two Hodgkin-Huxley currents and a stochastic spike generation process. Next, the authors constructed a simple network model using aGIF serotonin and GABA neurons, and show that heterogeneous feedforward inhibition due to heterogeneous electrophysiological properties of local GABA neurons lead to divisive inhibition of serotonin neuron firing . Finally, using a ramp depolarization, the authors found that serotonin neurons encode the temporal derivative of depolarization, i.e., the slope of ramp depolarization. This property can be ascribed to the prominent spike-frequency adaptation observed in serotonin neurons.The reviewers found the conclusions of this study very interesting and functionally relevant. The reviewers also thought that the experiments and modeling are generally sound and rigorous, and the results are presented clearly. However, the reviewers have identified various concerns and points to be clarified.1. The slice experiments were carried out in room temperature, which distorts the kinetics of ion channels and pumps relevant for in vivo electrical activity. Ideally, some of the main conclusions should be confirmed at room temperature. In case this is difficult, please explicitly discuss this caveat and potential impacts on conclusions.2. The series resistance up to 30 Mohm remains uncompensated and in combination with potassium currents in the range of 1 nA generates voltage errors up to 30 mV. In addition, gating properties of A-type currents will be distorted under these recording conditions. Do the main experimental results hold with a more stringent cutoff of the series resistance? Conversely, how robust are the modeling results with respect to the specific gating properties of A-type currents including the inactivation kinetics?3. Some of the model parameters appear to be non-physiological. For example, the reversal potential of potassium is given as at least 20mV lower than that used typically in the literature. Please justify the use of -101mV rather than the range -75mV to -85mV as is more common. Please clarify whether the results depend on this very low reversal potential.4. It is unlikely that the derivative-like computation holds in all of potential input regimes. It is important to clarify in what conditions derivative-like computation is a good approximation of the input-output relationship of serotonin neurons, and when it breaks down.5. The derivative-like computation and its role in reinforcement learning are emphasized in the manuscript (e.g. abstract). However, as discussed above, the derivative-like computation likely occurs only in a limited input regimen, and the relevance to reinforcement learning is very speculative. The reviewers thought that these points need to be a little toned down.Reviewer #1 (Recommendations for the authors):The electrophysiological characterization of 5-HT neurons has a number of shortcomings that should be addressed by additional experiments:1. Experiments are carried out in room temperature. This distorts the kinetics of ion channels and pumps relevant for in vivo electrical activity.2. The series resistance up to 30Mohm remains uncompensated and in combination with potassium currents in the range of 1 nA generates voltage errors up to 30 mV. In addition, gating properties of IA-currents will be distorted under these recording conditions3. An intracellular solution is used without calcium buffering. Given the key role of adaptation and relevant calcium-dependent conductances in 5-HT neurons this is not state-of-the-art4. 4-AP is not a selective Kv4 (IA) channel blocker. There are more-selective, commercially available alternatives like Heteropodatoxin-2 or AmmTx3.5. Author show that augmentation of the GIF-model with IA-currents does not specifically improve the model in comparison to a generic iGIF model . Doesn´t this call in into question the whole strategy of using experimentally validated biophysical enhancements of GIFs? Does the experimentally augmented GIF outperform the standard computational model of 5-HT neurons (see Tuckwell & Penington (2014) Computational modeling of spike generation in serotonergic neurons of the dorsal raphe nucleus. Prog Neurobiol 118:59-101).6. Authors should experimentally study the biophysics of adaptation in 5-HT neurons as this is most related to temporal derivative computation, the key insight of this ms. For experimental conditions see 3.Reviewer #2 (Recommendations for the authors):1) Electrophysiological recordings are conducted at room temperature. It is not clear why the authors did not conduct recordings at more physiological temperature, as temperature should affect properties on many ion channels, and thus the excitability of neurons.2) The authors may want to briefly mention the potential behavioral conditions in which endocannabinoids could be released in the dorsal raphe.3) Dopamine neurons are also known to display low frequency firing, large afterhyperpolarizations, and A-type K currents. It would be helpful to briefly discuss whether similar computations could be applied to these neurons, especially in light of their role in reinforcement learning,4) P. 14: Figure 1C3 is not present in Figure 1. There might be other places where figure panels are not correctly referred to.Reviewer #3 (Recommendations for the authors):The paper is very well written and clear, with a solid approach.p.10 the reversal potential of potassium is given as at least 20mV lower than any I have come across. Please justify the use of -101mV rather than the range -75mV to -85mV as is more common.p.11 "within 8 ms": this seems like an arbitrary time range and a rather large one to predict spike timing given typical membrane time constants and jitter. Also, it is unclear if this is related to the "1.5 ms before to 6.5 ms after" a spike where the dV/dt is constrained – and again, why this 8 ms window? And why the smaller window for SOM neurons for the fitting of dV/dt, though not the validation of spike times?p.21-p.22 The authors state that the aGIF is more parsimonious than the iGIF but it appears that the aGIF has more parameters so the reverse would be true? Perhaps because the aGIF includes a known, well-characterized current, the number of free parameters is smaller even if the total number is greater? Or am I missing something? For sure if the current is shown to be present in the neuron then it is reasonable to use a model with that current rather than the iGIF, but "more parsimonious" would not be the reason.The authors then on p.22 state the aGIF "best accounts" for the data, but again the iGIF appears to fit the data just as well, and no other model currents or neural were tested. I think the valid conclusion is that adding the extra current(s) improves the fit, no more. It would be good to see a criterion like AIC used to justify the improvement to fit is greater than that bound to arise with extra free parameters.Figure 5: Given the 5-HT neuron has a sustained response that depends on step height, its output is not the differential of its input. This is an important proviso in any discussion of the properties of the circuit as a differentiator, since it is not one.p.32, Figure 6 caption. "includes a strong subtractive component (F2)". I think "E2" may be meant as I see a shift between "Het SOM" and "Hom SOM" curves in E2 but not in F2. Also it is important to be clear when discussing the "input-output function" of a neuron whether the transient peak response is being discussed, or the sustained response, or both. Normally sustained firing rate to sustained input would be meant, so if it is the peak of the transient, that should be added in the description.p.33 Figure 7 caption. "output is … linearly related": again, only the peak of the transient response appears to have a linear relationship. This is not the same as the neuron's output in general.It would be nice to see that the output of the neuron responding to some range of fluctuating inputs, I(t), has higher linear correlation with dI/dt than with I or to show the neuron responds more to dI/dt than I(t) via some other statistical test. In particular, if dI/dt is more and more negative, does the rate decrease more and more (or is it only a positive slope detector)?Figure 7F is too opaque for me to understand. It seems like two different manipulations on one plot, but then it is unclear why the different manipulations and color scales correspond to different regions of the x-y plane. I am confused, so I suggest a bit more explanation, or 2 figures if 2 manipulations are carried out.p.39 temporal difference learning for example is not the same as producing the time-derivative of an input. It is the difference between two inputs  – or one can calculate it as the difference across trials from some average reward to the current reward, but that difference between the current input and trial-averaged input is over a far slower timescale than that of the peak responses to a change in input demonstrated here. Essential revisions:In this study, Harkin and colleagues examined the biophysical properties of dorsal raphe (DR) serotonin neurons using a combination of whole-cell patch clamp recording in brain slices and biophysical computational modeling. The authors adopted the approach called a generalized integrate-and-fire [aGIF] model, which incorporates a relatively small number of salient biophysical properties (ionic currents) of a specific neuron, and whose parameters are optimized based on voltage dynamics obtained experimentally. First, the authors observe two prominent features in serotonin neurons. The first is a prominent spike frequency adaptation, resulting from after-hyperpolarization potentials. The second is a "kink" in the voltage trace leading up to the first spike, which can be attributed to the effect of A-type potassium currents (I-A). Using the data, the authors constructed aGIF model of serotonin neurons which contains I-A, two Hodgkin-Huxley currents and a stochastic spike generation process. Next, the authors constructed a simple network model using aGIF serotonin and GABA neurons, and show that heterogeneous feedforward inhibition due to heterogeneous electrophysiological properties of local GABA neurons lead to divisive inhibition of serotonin neuron firing . Finally, using a ramp depolarization, the authors found that serotonin neurons encode the temporal derivative of depolarization, i.e., the slope of ramp depolarization. This property can be ascribed to the prominent spike-frequency adaptation observed in serotonin neurons.The reviewers found the conclusions of this study very interesting and functionally relevant. The reviewers also thought that the experiments and modeling are generally sound and rigorous, and the results are presented clearly. However, the reviewers have identified various concerns and points to be clarified.1. The slice experiments were carried out in room temperature, which distorts the kinetics of ion channels and pumps relevant for in vivo electrical activity. Ideally, some of the main conclusions should be confirmed at room temperature. In case this is difficult, please explicitly discuss this caveat and potential impacts on conclusions.i.e., Figures 1S5, 2S2, 2S3, 3S3, 4S2, 5S5, and 7S1, results reported on pages 7, 15, 18, 20, and 26).This is a valid and admittedly important point. Because this issue was presented as perhaps the chief concern related to our experimental work, we have spent considerable time and effort to experimentally address it. Experiments were initially carried out at room temperature simply because of our difficulty in obtaining high quality and stable recordings at a higher temperature. To address the possibility that some of our results could be an artifact of this experimental limitation, we optimized some slicing procedures and had a more experienced electrophysiologist in our group carry out key recordings closer to physiological temperature. We managed to carry out recordings at 29°C to 30°C measured in the recording bath. In brief, we found that the voltage-dependence and kinetics of IA were indeed slightly altered at increased temperatures, and that the very strong adaptation observed in serotonin neurons was somewhat attenuated due to a reduction in the spike-triggered threshold movement. These quantitative changes prompted us to revisit our simulations seeking to determine the output of the DRN in response to inputs of different derivatives. However, these simulations revealed that increasing temperature was not accompanied by substantive qualitative changes to our main conclusions (the simulations are different though). Since we believe other readers may share this important concern, we have added several supplementary figures to our manuscript that directly illustrate this point . This cutoff was used for early and still expanding datasets and somehow got carried forward. Upon closer inspection prompted by this comment, we realized that the overwhelming majority of the voltage-clamp recordings used to characterize IA in 5-HT neurons had a significantly lower series resistance . A standard series resistance cutoff of 20 MOhm ended up excluding only three of the thirteen original recordings (series resistance of the ten remaining recordings: 12.1 +/- 4.0 MOhm). We have added a note about these values on page 37 of our revised manuscript.Do the main experimental results hold using the more stringent cutoff?Yes. The estimates of IA peak amplitude, time to peak, and decay time constant using this more rigorous inclusion criterion are only marginally different from the original estimates (see table below). We agree with the reviewer that a more stringent cutoff would be preferable. Unfortunately, this would involve rerunning all of our simulations involving the aGIF (which is a significant portion of this study). The absence of a significant change in the kinetics strongly indicates that rerunning the simulations would not produce different results. We have made a note of the series resistance values (above) and their effects on the estimated parameters of IA   in the mConversely, how robust are the modeling results with respect to the specific gating properties of A-type currents including the inactivation kinetics?The modeling results do not depend on our experimental measurements of IA’s inactivation kinetics and are expected to be robust to Ra-related distortion of the equilibrium gating curves. The features of IA most important to our modeling results are that the current both activates and inactivates below spike threshold and that the inactivation time constant is not very small relative to the membrane time constant. If the ‘true’ activation and inactivation gating curves were located further to the left or rise more rapidly than the ones we report due to series resistance-related voltage errors, this current would still activate and inactivate below threshold, leaving unaltered our main conclusions. Moreover, and importantly, because the inactivation time constants of IA used in our simulations are estimated directly from the fluctuating input data as part of the GIF model fitting procedure, these values represent effective quantities that take into account the impact of IA on the subthreshold dynamics of 5-HT neurons and are not sensitive to the same sources of error as our equilibrium gating curves.  with an interquartile range of 27 to 77 ms (N=18), consistent with the values obtained using voltage clamp experiments). Lastly, the simulations shown in Figure 2S1 show empirically that reducing the effective inactivation time constant of IA by more than 40% does not qualitatively alter our results. Altogether, the modeling results robustly hold up to variability of gating parameters significantly beyond that expected for series resistance-mediated distortion.3. Some of the model parameters appear to be non-physiological. For example, the reversal potential of potassium is given as at least 20mV lower than that used typically in the literature. Please justify the use of -101mV rather than the range -75mV to -85mV as is more common. Please clarify whether the results depend on this very low reversal potential.Thank you for the opportunity to clarify this aspect of our methodology. The low potassium reversal was initially chosen to match our experimental conditions to ensure accurate model parameter estimates (we have noted this point on page 41 of our revised manuscript). Since the most important results that emerge from our simulations are related to spike timing and firing rate, which occur within the voltage range above the physiological reversal potential of potassium, raising the reversal potential of potassium would have the exact same effect as reducing the maximal conductance associated with IA . We have extensively explored the effects of changing this parameter in Figures 2B, 6A, 7E, and 7G, and therefore changing the reversal potential of potassium would not significantly affect our conclusions. Nonetheless, to empirically support this idea, we adjusted the potassium reversal potential to -89.1 mV  in our aGIF models fitted to the data collected near physiological temperature. As noted in our response to point #1, the results obtained using these models are consistent with our main conclusions.4. It is unlikely that the derivative-like computation holds in all of potential input regimes. It is important to clarify in what conditions derivative-like computation is a good approximation of the input-output relationship of serotonin neurons, and when it breaks down.e.g., Figure 1S1 and 5). Our results suggest that the DRN is best conceptualized as encoding both the intensity and temporal-derivative of its input. We have added a toy rate-based model of the DRN to capture this idea and to clarify its limitations . Reassuringly, we found that the derivative-like computation dominates DRN output precisely when the derivative of the input is large (and positive), but we have amended the results and Discussion sections to clarify when and why this computation breaks down . We have also changed our wording of this result throughout the manuscript to emphasize that the DRN encodes a mixture of the intensity and temporal derivative of its input .This is an important point, especially considering that 5-HT neurons can exhibit sustained firing even when the derivative of the input is zero (5. The derivative-like computation and its role in reinforcement learning are emphasized in the manuscript (e.g. abstract). However, as discussed above, the derivative-like computation likely occurs only in a limited input regimen, and the relevance to reinforcement learning is very speculative. The reviewers thought that these points need to be a little toned down.Thank you for this feedback: we entirely agree that the role of this computation in RL is at this time purely speculative. After deliberation, we removed the explicit link to RL from the abstract and significantly rewrote and toned down the Discussion section on this speculative point .Reviewer #1 (Recommendations for the authors):The electrophysiological characterization of 5-HT neurons has a number of shortcomings that should be addressed by additional experiments:1. Experiments are carried out in room temperature. This distorts the kinetics of ion channels and pumps relevant for in vivo electrical activity.essential point #1 above.We have experimentally addressed this point. Please see our response to 2. The series resistance up to 30Mohm remains uncompensated and in combination with potassium currents in the range of 1 nA generates voltage errors up to 30 mV. In addition, gating properties of IA-currents will be distorted under these recording conditionsPlease see our response to essential revision #2.3. An intracellular solution is used without calcium buffering. Given the key role of adaptation and relevant calcium-dependent conductances in 5-HT neurons this is not state-of-the-arteLife 2016). There are likely other parameters of ionic conductances expressed in 5-HT neurons that can be regulated by intracellular Calcium. As such, it is by design that we chose to omit Calcium chelators from our intracellular solution in order to have recording conditions that are as physiological as possible. In this line, the GIF formalism is designed to extract excitability parameters from spiking in such naturalistic conditions, and is thus aptly applied in conditions without Calcium buffering. Moreover, because Calcium buffering would alter the contribution of a potentially unknown set of  conductances to these spiking behaviors, these experiments would be fundamentally challenging to interpret.This is an important point. 5-HT neurons are indeed endowed with several Calcium-dependent conductances that are bound to regulate their firing behaviors. As a mere example, 5-HT neurons are well known to exhibit a prominent calcium- and SK channel dependent AHP  channel blocker. There are more-selective, commercially available alternatives like Heteropodatoxin-2 or AmmTx3.We were initially primarily concerned with an algorithmic description of this conductance, and not so much with its molecular identification. That said, we followed this reviewer’s suggestion and found that Heteropodatoxin-2 and AmmTx3 block most of the transient component of the outward current readily observed in 5-HT neurons. These results are now in the revised manuscript . It is noteworthy that the delay in obtaining these particular drugs are in large part responsible for delaying the submission of this revised manuscript.5. Author show that augmentation of the GIF-model with IA-currents does not specifically improve the model in comparison to a generic iGIF model . Doesn´t this call in into question the whole strategy of using experimentally validated biophysical enhancements of GIFs? Does the experimentally augmented GIF outperform the standard computational model of 5-HT neurons (see Tuckwell & Penington (2014) Computational modeling of spike generation in serotonergic neurons of the dorsal raphe nucleus. Prog Neurobiol 118:59-101).Thank you for the opportunity to clarify these points. Concerning aGIF vs iGIF, although both models predict the spike trains of 5-HT neurons with comparable accuracy, we would like to emphasize that the aGIF model predicts the subthreshold voltage of these cells significantly more accurately than the iGIF model . Although accurately predicting the subthreshold voltage is certainly not always necessary , we contend that this represents an important feature in cases where the primary interest lies in exploring the causal relationships between mechanisms operating in subtreshold regimes and spiking behaviors. We have briefly noted this point on page 31 of our revised manuscript.Beyond this point, the fact that aGIF and iGIF models achieve similar spike timing prediction using squarely different mechanisms has two possible interpretations: either both models capture the same variance (they explain the same phenomenon using different mechanisms) or the models complement one another (they capture different phenomena). Although we believe that the flexibility of the iGIF model makes the former more likely, if it were the latter, this would suggest that GIF models should be gradually augmented with various mechanisms, in a manner indeed reminiscent of Hodgkin-Huxely-type modelling.There remains, however, an important drawback to biophysically-detailed Hodgkin-Huxley-style models, such as the model of Tuckwell and Penington (2014). Off-the-shelf versions of these models typically predict about half of the variance predicted by GIF models . Fitting the maximal conductances to data improves the prediction, typically reaching a performance on par with GIF models. Importantly, however, the fitting of biophysical models is exceedingly difficult and may be impossible on limited amounts of data. The fitting process for biophysically-detailed models also uses about 1000 times more computer time. As a result, even if GIF-model-based approaches appear more and more complex, they remain fundamentally tractable such that they can be calibrated on typical datasets (as we have done in this paper).6. Authors should experimentally study the biophysics of adaptation in 5-HT neurons as this is most related to temporal derivative computation, the key insight of this ms. For experimental conditions see 3.e.g., Mensi, Naud, et al., 2012, Pozzorini, Naud, et al., 2013) and does not require independent characterization of the underlying biophysical mechanisms. This is entirely different from the situation that arose with IA, where augmenting the GIF with this current required separate experiments to characterize its voltage-dependence (as briefly noted in our discussion on page 30). In an independent study, we have carried out voltage-clamp recordings that characterize IAHP in some depth , but similar experiments have previously been reported and it is unclear to us how these results would be integrated into our approach . Furthermore, it is not immediately apparent what type of experiments would be required to fully parameterize the dynamic change in threshold that also contributes to adaptation in these cells. Altogether, we respectfully submit that while the proposed experiments are certainly interesting, it is not clear how they would be incorporated into our model-based approach and they are therefore not required to support the main message of our work.One of the main contributions of our GIF approach was to estimate the functional amplitude and kinetics of adaptation in 5-HT neurons directly from their spiking and subthreshold responses to in vivo-like fluctuating input . Somewhat surprisingly, this approach demonstrated that an increase in threshold contributed to adaptation in these neurons, in addition to the AHP that has previously been well described in these neurons. The procedure used by GIF-type models to estimate adaptation is well-established (Reviewer #2 (Recommendations for the authors):1) Electrophysiological recordings are conducted at room temperature. It is not clear why the authors did not conduct recordings at more physiological temperature, as temperature should affect properties on many ion channels, and thus the excitability of neurons.essential point #1.We have experimentally addressed this point; please see our response to 2) The authors may want to briefly mention the potential behavioral conditions in which endocannabinoids could be released in the dorsal raphe.e.g., Haj-Dahmane, PNAS 2018) to affect synaptic transmission . We have participated in this research effort by showing that glutamatergic synapses onto DRN GABAergic neurons are far more sensitive to cannabinoid-mediated inhibition than their counterpart onto 5-HT neuron . Despite these advances, the conditions that lead to endocannabinoids release in the DRN during behavior are far less understood. For instance, while it has been shown that 5-HT neuronal activity per se regulates tonic release of endocannabinoid in the DRN, it is unknown whether this is also true for GABAergic neurons. Thus, beyond these broad strokes of guiding principles governing endocannabinoid release in the DRN, our knowledge is very superficial and remains mainly speculative. That said, the homogeneous rise of cannabinoid receptor activation induced by recreational cannabis use is likely to be broadly recapitulated by our modeling. We made a mention on page 34 of the revised manuscript.There is an expanding literature that is outlining with increasing mechanistic and molecular detail how endocannabinoids are release and retrogradely transmitted in the DRN (3) Dopamine neurons are also known to display low frequency firing, large afterhyperpolarizations, and A-type K currents. It would be helpful to briefly discuss whether similar computations could be applied to these neurons, especially in light of their role in reinforcement learning,We thank the reviewer for this point, this is indeed the case and increases the scope of our work. We have added a remark to that effect in the Discussion section on reinforcement learning (page 35).4) P. 14: Figure 1C3 is not present in Figure 1. There might be other places where figure panels are not correctly referred to.Thank you for pointing this out! We have corrected this error and reviewed the manuscript for similar issues.Reviewer #3 (Recommendations for the authors):The paper is very well written and clear, with a solid approach.p.10 the reversal potential of potassium is given as at least 20mV lower than any I have come across. Please justify the use of -101mV rather than the range -75mV to -85mV as is more common.Please see our response to essential revision #3.p.11 "within 8 ms": this seems like an arbitrary time range and a rather large one to predict spike timing given typical membrane time constants and jitter. Also, it is unclear if this is related to the "1.5 ms before to 6.5 ms after" a spike where the dV/dt is constrained – and again, why this 8 ms window? And why the smaller window for SOM neurons for the fitting of dV/dt, though not the validation of spike times?The 8ms precision used to calculate the Md* spiketrain similarity metric is admittedly somewhat arbitrary. Previous work carried out in cortical neurons used a precision of 4ms. This number was based on a systematic comparison of the spike timing precision and the intrinsic reliability (the consistency of spike timing across repetitions for a given spike timing precision) . We have chosen Δ according to a similar assay in DRN neurons and added a note to this effect on page 42 of our revised manuscript.The precision used in the Md* metric is unrelated to the “1.5 ms before to 6.5 ms after” window around each spike during which the voltage is ignored. Because integrate-and-fire models including GIF-class models do not explicitly model the membrane voltage during a spike, it was necessary to remove spikes from our data before attempting to fit the subthreshold components of our models. We define the timing of a spike as the instant that the membrane voltage rises past 0 mV, and creating a window of several milliseconds around this point ensures that the entire action potential is removed. The duration of this window varies slightly across cell types due to differences in action potential shape.p.21-p.22 The authors state that the aGIF is more parsimonious than the iGIF but it appears that the aGIF has more parameters so the reverse would be true? Perhaps because the aGIF includes a known, well-characterized current, the number of free parameters is smaller even if the total number is greater? Or am I missing something? For sure if the current is shown to be present in the neuron then it is reasonable to use a model with that current rather than the iGIF, but "more parsimonious" would not be the reason.Thank you for the opportunity for clarification. The “non-linear coupling term” that differentiates the GIF and iGIF models mentioned in our results text actually consists of a non-parametric function of past voltage. The non-parametric definition of this term introduces roughly ten additional free parameters compared with the GIF and aGIF models , and, as with non-parametric models in general, the fitted values of these parameters can be difficult to interpret. We believe that this makes the aGIF model more parsimonious and have added clarification to the methods and Results sections to emphasize this point (pages 39 and 14 in the revised manuscript).The authors then on p.22 state the aGIF "best accounts" for the data, but again the iGIF appears to fit the data just as well, and no other model currents or neural were tested. I think the valid conclusion is that adding the extra current(s) improves the fit, no more. It would be good to see a criterion like AIC used to justify the improvement to fit is greater than that bound to arise with extra free parameters.biophysical mechanisms responsible for shaping the spiking behaviour of 5-HT neurons rather than the data (see page 15). Regarding the AIC, however, we respectfully disagree as this methodology was invented for cases where data that was not used for model fitting is not available . Our data collection approach was designed to collect a separate validation dataset and obviate the need for statistical tools such as AIC . Cross-validation remains a more accurate approach to model selection that takes into account overfitting.Please see point no. 5 from reviewer 1 for changes related to this point. In writing the manuscript, we were conscious of the equal predictive performance of the aGIF and iGIF , which led us to attempt to make the more limited claim that the aGIF model best accounts for the Figure 5: Given the 5-HT neuron has a sustained response that depends on step height, its output is not the differential of its input. This is an important proviso in any discussion of the properties of the circuit as a differentiator, since it is not one.We believe that DRN is indeed best conceptualized as encoding a mixture of the intensity and temporal derivative of its input. We have added a toy model to formalize this intuition  and have adjusted the manuscript text accordingly. (See our responses to other points.)p.32, Figure 6 caption. "includes a strong subtractive component (F2)". I think "E2" may be meant as I see a shift between "Het SOM" and "Hom SOM" curves in E2 but not in F2. Also it is important to be clear when discussing the "input-output function" of a neuron whether the transient peak response is being discussed, or the sustained response, or both. Normally sustained firing rate to sustained input would be meant, so if it is the peak of the transient, that should be added in the description.Thank you for pointing this out, we have corrected the issue.p.33 Figure 7 caption. "output is … linearly related": again, only the peak of the transient response appears to have a linear relationship. This is not the same as the neuron's output in general.Agreed. We have adjusted the wording of the caption to specify the peak firing rate and added Figure 7S2 to support our broader point.It would be nice to see that the output of the neuron responding to some range of fluctuating inputs, I(t), has higher linear correlation with dI/dt than with I or to show the neuron responds more to dI/dt than I(t) via some other statistical test. In particular, if dI/dt is more and more negative, does the rate decrease more and more (or is it only a positive slope detector)?Thank you for the suggestion. We had initially considered taking a similar approach, but were concerned that quantifying the correlation between the output and dI/dt across multiple timescales and levels of background input would introduce sufficient analytical complexity to alienate part of our target readership (and perhaps ourselves). To add clearer support for our derivative-encoding argument, we have fitted a toy rate model of DRN output as a function of the input and its derivative to the data presented in Figure 7 and compared it with a restricted model that does not take the derivative of the input into account . We hope that the stark differences between the predictions made by the two toy models will be an adequate compromise to address this point.Figure 7F is too opaque for me to understand. It seems like two different manipulations on one plot, but then it is unclear why the different manipulations and color scales correspond to different regions of the x-y plane. I am confused, so I suggest a bit more explanation, or 2 figures if 2 manipulations are carried out.The goal of this figure was to show that two of the biophysical features of 5-HT neurons contribute to shaping the input-output function of the DRN under distinct input regimes. We have updated the caption to emphasize this point and hope that it is now clearer.p.39 temporal difference learning for example is not the same as producing the time-derivative of an input. It is the difference between two inputs  – or one can calculate it as the difference across trials from some average reward to the current reward, but that difference between the current input and trial-averaged input is over a far slower timescale than that of the peak responses to a change in input demonstrated here.essential point 5.Thank you for raising this point. We have made changes to that effect, see


PhysiThe following is a pre-processing pipeline that has been created to remove irrelevant and non-osseous structures  or noise  in a CT scan. It offers the possibility of processing large numbers of CT scans to create large datasets that have relevance for the assessment of human remains in the context of modern populations. The pipeline presents three distinct outputs, 2D images thresholded for the tissue(s) of interest, stereolithography (STL) files for quantitative mesh analysis and 3D printing, and 3D image files readily available for machine learning applications.2The increase in the application of medical imaging and digital data on the analysis of human remains and anatomy in forensic anthropology (FA) is well-documented . This grThe growth of virtual anthropology has resulted in an increasing demand for CT data ,40 that The recent increase in the availability of data from medical imaging and interest in virtual anthropology has resulted in studies which conduct estimation methods based on morphological feature analysis on digital models . This isThe limitation to study sample sizes can be seen as a two-fold problem. Lack of data availability, and the feasibility of manually processing high quantities medical images to acceptable file formats and standards. While the former is being addressed by the emergence of databases such as the NMDID, TCIA, and the usage of diagnostic clinical CT scans from hospitals and medical facilities, the latter is often overlooked in research literature. Forensic science and virtual anthropology studies involving CT scans often overlook or underemphasize the time taken to process medical images for machine learning. As medical images used in virtual anthropology tend to be from post-mortem and/or clinical settings, the scanned specimen may include irrelevant and unnecessary biological and non-biological structures such as the sliding table (as part of the CT scanning apparatus), medical tubing, clothing, fat, skin, or lymph nodes. While noisy structures can be removed in medical imaging programs such as 3D Slicer  using guGiven the current interest to utilise ML in Forensic Anthropology and Virtual Anthropology, large-scale CT databases are being turned to as a viable source of data. However, the manual steps involved in removing noise and unnecessary structures from great quantities of CT images remain a challenge for researchers and the tight timings of research project cycles. The purpose of this technical note is therefore, to introduce a pre-processing pipeline based in Python 3. Allowing users to adapt the Python scripts provided to handle and automatically process CT images to remove noise, and to generate three discrete file outputs relevant to 3D modelling, machine learning, and image analysis in forensic and virtual anthropology.3https://github.com/preprocessing_pipeline.A pre-processing pipeline was designed for application with Python 3.8 programming language to remove noise, generate thresholded CT images, 3D models in STL format, and 3D image files in NIfTI format. This pipeline has been developed to run on all operating systems compatible with Python 3.8.0 and the packages required in the pipeline. The packages utilised to construct this pipeline include pydicom, dicom2nifti, scipy, skimage, ITK, and VTK among others. The code and additional detail regarding dependencies is available for review and use at (1)(a)Dataset sorting and extraction scriptData source/input(2)(a)Noise removal and segmentation scriptRestructuring data(3)(a)Thresholding for tissues of interest script(b)Conversion to NIfTI format(c)Conversion to stereolithography format.Useable output3.1Series Number tag of a DICOM file. While the DICOM files are generally extracted and provided in sequential order, each folder for a CT study for each patient could have multiple uncollated series of CT scans (The first set of scripts (S1) takes DICOM images as input and checks for corrupted and non-DICOM files, if found the identified files are deleted. It then sorts them into folders according to the series numbers. This enables the user to automatically sort and extract relevant DICOM files into folders created according to the series of each scan. Each CT study consists of multiple series of DICOM files; each DICOM file is an image consisting of an X-Ray slice of the body and the image metadata, while each series of DICOM files is the collection of the images of the scanned body. Each series may differ depending on the presence or absence of contrast agents or the scanned regions of interest. The metadata contain information such as slice thickness, series number, series date, patient sex, patient age etc. These fields or tags are defined by a pair of four alphanumeric characters , for exaCT scans . This fiCT scans . Finally3.2The second script (S2) removes undesired structures such as the sliding table, which has been highlighted in First, the DICOM file is loaded as an array of pixels and labelled as ‘Original Image’. This array of pixels undergoes a series of thresholding functions to only display the structures which has the radiodensity of bone and surrounding tissue. The thresholding values in S2 can be used as a fixed threshold if the tissue of interest is of bone tissue only. The selected area or area of interest is returned as a ‘Mask’, which denotes the parts of the pixel array that should be kept, returning an area of interest labelled as ‘Mask’. Using the area identified by the ‘Mask’, the ‘Original Image’ is segmented to produce the ‘Final Image’, the ‘Final Image’ array overwrites the original DICOM file while maintaining relevant metadata and the appropriate image matrix size (512 by 512) for future processing. The noise removal function of this script can be visualised in 3.3With the noise removed, the third script, S3, enables users to pass DICOM files through thresholding functions from Pydicom and coded to produce 2D general-purpose image formats. General-purpose image formats such as PNG (portable network graphics) and JPEG (joint photographic experts group) are regarded as standards and widely used as image storage formats and thus, commonly used in image-based machine learning . As bothThe fourth set of script (S4), enables users to compile and convert the processed DICOM files to the NIfTI file format using dicom2nifti package . This paThe fifth script (S5), enables users to pass the processed DICOM files through the visualization toolkit (VTK) package, which is an open-source, Python compatible toolkit for 3D visualization and image processing , and con410.13039/100005622Health Research Authority and 10.13039/100012068Health and Care Research Wales under protocol number 130244. The age of the patients ranged from 19 to 97 for females and 18–99 for males. All scans in the UCLH database were acquired using 120 kVp at 0.50 mm slice thickness on a single scanner – Aquillion ONE ViSION 320-detector row detector scanner . Additionally, the pipeline was tested on single scans obtained from open-source public repositories NMDID and TCIA. The NMDID scans were acquired using 120 kVp at 0.50 mm slice thickness on the Philips Big Bore CT Scanner , while the TCIA scans were acquired using 120 kVp at 0.625 mm slice thickness on an unknown CT scanner. The pipeline described above was tested and implemented on a large-scale database of 3575 CT scans retrieved from the Picture Archiving and Communication System (PACS) office at University College London Hospital (UCLH). The scans were anonymised by removing all patient identifiers identified by NHS Patient Identification Policy and official documentation on Patient Safety Alert ,97, leav5This pre-processing pipeline is an effective tool available to researchers that seeks to process large amounts of DICOM data from hospitals, forensic science institutes, scanned historical collections, or post-mortem databases to create any of the outputs offered for ML, 2D and 3D image analysis. This pipeline is flexible: the DICOM file standardisation allows the processing of any CT scans with little to no changes to the code provided. The processing thresholds and the noise removal (S2) have been tested and demonstrated against three different sets of scans from different data sources and regions of body anatomy. Consequently, the outputs provided at the end of the pipeline present high reliability outputs which can be used for multiple research purposes.The capabilities shown by this preliminary pre-processing pipeline address both growing demands and problems faced by modern forensic and virtual anthropology. Firstly, the demand for modern population data is fully addressed by the pipeline as it has shown the capacity to transform clinical CT data and post-mortem CT data straightforwardly. Second, the pipeline addresses the limitations due to manual segmentations. While it has been noted by previously published studies that noise can be manually deleted through the use of visualization software programs , the tasThe pipeline scripts are publicly available on GitHub for any interested stakeholders or researchers to download, use and validate to produce impactful work in relevant fields. This commitment to Open Science contributes to the transparency of the databases produced, and increases their value as tools in the evaluative interpretations made to assist the court ,114. Mor610.13039/100004811CT datasets from virtually any source and of any size. Finally, the three distinct outputs provided by the pipeline enables the potentially large scale and automated production of 2D and 3D image files for machine learning purposes and 3D models for printing and virtual manipulation at a minimum. In the forensic anthropology context where funding, time, and access to modern population data may be restricted, this pipeline creates a process to transform 10.13039/100004811CT data from a variety of contexts such as post-mortem, living, or virtual preservations of historical collections into ad-hoc datasets with useable and relevant outputs.The pipeline presented here is a set of novel procedures to prepare CT image data, specifically but not limited to clinical data, for forensic and virtual anthropology. The processes automated by the scripts found in the pipeline also allows a greater quantity of CT studies and scans to be processed, thus, removing the manual constraints such as manual segmentations and labelling that have limited the sample sizes of current research. With the automated processes in place, the pipeline grants the user with the flexibility to access and transform The authors declare no conflicts of interest were present in this research.There was no external funding for this research.This research was be presented at ANZFSS 2022 Brisbane, Forensics: Designing the Future. 11–15 Sept 2022 as a keynote presentation.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.