Somatodendritic HCN channels in hippocampal OLM cells revealed by a convergence of computational models and experiments

Determining details of spatially extended neurons is a challenge that needs to be overcome. The oriens-lacunosum/moleculare (OLM) interneuron has been implicated as a critical controller of hippocampal memory making it essential to understand how its biophysical properties contribute to function. We previously used computational models to show that OLM cells exhibit theta spiking resonance frequencies that depend on their dendrites having hyperpolarization-activated cation channels (h-channels). However, whether OLM cells have dendritic h-channels is unknown. We performed a set of whole-cell recordings of OLM cells from mouse hippocampus and constructed multi-compartment models using morphological and electrophysiological parameters extracted from the same cell. The models matched experiments only when dendritic h-channels were present. Immunohistochemical localization of the HCN2 subunit confirmed dendritic expression. These models can be used to obtain insight into hippocampal function. Our work shows that a tight integration of model and experiment tackles the challenge of characterizing spatially extended neurons.

Determining details of spatially extended neurons is a challenge that needs to be overcome. The 23 oriens-lacunosum/moleculare (OLM) interneuron has been implicated as a critical controller of 24 hippocampal memory making it essential to understand how its biophysical properties contribute 25 to function. We previously used computational models to show that OLM cells exhibit theta spiking 26 resonance frequencies that depend on their dendrites having hyperpolarization-activated cation 27 channels (h-channels). However, whether OLM cells have dendritic h-channels is unknown. We 28 performed a set of whole-cell recordings of OLM cells from mouse hippocampus and constructed 29 multi-compartment models using morphological and electrophysiological parameters extracted 30 from the same cell. The models matched experiments only when dendritic h-channels were 31 present. Immunohistochemical localization of the HCN2 subunit confirmed dendritic expression. 32 These models can be used to obtain insight into hippocampal function. Our work shows that a tight 33 Introduction 37 The challenge of understanding brain function given its many cell types and circuits is being greatly 38 aided by the development of sophisticated experimental techniques, big data, and interdisciplinary 39 collaborations (Ecker et al., 2017). Furthermore, the use of computational brain models is becoming 40 more established as an important tool that can bridge across scales and levels (Bassett et al., 2018; 41 42 consider the unique contributions of specific cell types and circuits in order to understand brain 43 behaviour (Luo et al., 2018). In particular, we know that different inhibitory cell types can control 44 circuit output and brain function in specific ways (Abbas et Roux and Buzsáki, 2015) and, by extension, disease states (Marín, 2012). 46 The contribution of a specific cell type to network and behavioural function is necessarily 47 grounded in its biophysical properties. While immunohistochemical and single-cell transcriptomic 48 studies provide insight into which ion channels might be present in a particular cell type, how 49 different cell types contribute to function must necessarily include its activity within circuits (Kopell 50 et al., 2014). An individual neuron's activity largely arises from its ion channel kinetics, densities, and 51 localization across its neuronal compartments. In this regard, mathematical multi-scale (channel 52 and cellular), multi-compartment computational models are needed to help provide insights and 53 hypotheses of how specific cell types contribute to brain function and disease processes. However, 54 developing such mathematical models come with their own set of caveats and limitations. Creating 55 such models requires quantitative knowledge of the precise characteristics of the particular cell 56 type, and it is highly challenging, if not impossible, to obtain comprehensive knowledge of all the 57 relevant biophysical parameters of each compartment of each cell type experimentally. Conversely, 58 mathematical models, no matter how detailed, are always a simplification relative to biological 59 reality and limited by the available experimental data. It is therefore important not to lose sight of 60 the limitations of both model and experiment by having an ongoing dialogue between the two. 61 It is now well-known that the characteristics of a given cell type are not fixed ( stood. Therefore, how should one proceed in building cellular, computational models? Averaging 73 of experimental variables such as conductance densities as a way of accounting for variability 74 leads to erroneous conductance-based models (Golowasch et al., 2002). As a consequence, single, 75 "canonical" biophysical models cannot capture inherent variability in the experimental ion channel 76 data. A more desirable approach is to develop multiple models to capture the underlying biological 77 variability (Marder and Taylor, 2011). Indeed, such populations of models representing a given cell 78 type have been developed to examine, for example, co-regulations between different conductances 79 that might exist in a given cell type (Hay et (Stuart and Spruston, 2015). Thus, these aspects must be tackled along with considerations 89 of cellular variability. 90 In this work we focus on the oriens-lacunosum/moleculare (OLM) cell, an identified inhibitory 91 cell type in the hippocampal CA1 area (Maccaferri and  previous computational study where h-channels were found to modulate the spiking preference of 104 OLM cell models -incoming inhibitory inputs recruited either a higher or lower theta frequency 105 (akin to Type 1 or Type 2 theta, respectively -Kramis et al. (1975)) depending on the presence 106 or absence of dendritic h-channels (Sekulić and Skinner, 2017). In that computational study, our 107 OLM cell models were derived from previously built populations of OLM cell multi-compartment 108 models in which appropriate OLM cell models were found with h-channels present either in the 109 soma only or uniformly distributed in the soma and dendrites (Sekulić et al., 2014). We had 110 previously leveraged these models and showed that appropriate OLM cell model output could be 111 maintained, even if h-channel conductance densities and distributions co-vary, so long as total 112 membrane conductance due to h-channels is conserved (Sekulić et 121 Considering all of the above, we aimed to build "next generation" multi-compartment models of 122 OLM cells to achieve a two-pronged goal. First, we wanted to determine whether multi-compartment 123 models built using morphological and electrophysiological data from the same cell would produce 124 consistent results regarding h-channel localization to dendrites or not, and second, to determine 125 the biophysical characteristics of h-channels in OLM cells. We considered our models to be next 126 generation over previous multi-compartment OLM cell modelling efforts because each model was 127 built using experimental data from the same cell, including its morphology, passive properties, and 128 biophysical h-channel characteristics. Using transgenic mice in which yellow fluorescent protein 129 (YFP) was expressed in somatostatin (SOM)-containing neurons, we visually targeted OLM cells 130 from CA1 hippocampus, and fully reconstructed three OLM cells for multi-compartment model 131 development with h-channel characteristics fit to each particular cell. We found that in order to 132 be compatible with the experimental data, all three models needed to have h-channels present 133 in their dendrites. Further, we performed immunohistochemical experiments that supported this 134 prediction of dendritic h-channel expression in OLM cells. Finally, using two of these reconstructed 135 models, we completed their development into full spiking models by including additional ion 136 channel currents whose parameters were optimized based on voltage recordings from the same 137 3 of 40 cell. These resulting models and associated experimental data are publicly available and can be 138 subsequently used to develop further insight into the biophysical specifics of OLM cells and to help 139 understand their contributions to circuit dynamics and behaviour. This work also demonstrates the 140 feasibility of combining experimental and computational studies to address the challenging issue 141 of determining the density and distribution of specific dendritic ion channel types.

2001)
to develop our multi-compartment models. Figure 1A,B shows imaging of the three chosen 163 cells, with the reconstructed cell morphologies shown in Figure 1C, and typical electrophysiological 164 OLM cell profiles with sag characteristics shown in Figure 1D. Details of the model reconstructions 165 are given in the Methods. 166 To capture the passive response of the three cells we used long -120 pA current clamp traces in 167 which all synaptic and voltage-gated channels were blocked. This choice was made because we 168 found that the -30 pA traces were noisier in general (see Figure 2, top panels), and the -120 pA 169 traces best captured the passive response of the cells. This can be seen from a comparison of the Methods. The resulting fitted passive parameters of axial resistivity ( ), specific capacitance ( ), 173 leak conductance ( ) and leak reversal potential ( ) (see Table 6 in Methods, top of Table 2 174 and as summarized in Table 4 later) in conjunction with the respective cell morphologies form the 175 "backbone" of the OLM cell models.

176
Low specific capacitances are a robust feature of OLM cells 177 From our model fits we found that the 's obtained were much lower than the ≈ 0.9-1 F/cm 2 178 that have been previously reported as a "standard" value in mammalian neurons (Gentet et al.,  of the models (Cell 1 and Cell 2) using these four scaling values (0.5, 1.5, 0.9, 1.1). We used our 197 unchanged passive properties previously obtained and examined the responses to a -120pA current 198 clamp step. This served to assess the resulting changes in the responses attributable to errors in 199 electrotonic properties solely due to changing the diameters. We found that changes in diameters    (Figure 3). 231 We demonstrated in our previous work that OLM cell models exhibited a tradeoff between total 232 membrane ℎ and the dendritic distribution of h-channels so that if the total ℎ was conserved, 233 the resulting model output would be appropriate (Sekulić et al., 2015). Now, for the first time, we 234 have a measure of total ℎ . Thus, a key prediction for the resulting multi-compartment models is 235 that the total ℎ will constrain the distribution of h-channels to allow the models to appropriately 236 capture the OLM cell electrophysiological characteristics. To consider this, we added an additional 237 parameter to our models termed , which is defined as the centripetal extent for which h-238 channels are inserted in the dendrites. It is defined by a real-valued number in the range of [0, 1] 239 and represents the fraction of maximum dendritic path length from the soma on a per-cell basis. 240 Compartments with a path length from the soma that was smaller than any given value were 241 included when subsequently inserting h-channels, whereas those compartments whose distance        A staggered re-fitting procedure yields consistent and generalized model fits for 259 260 Given the suboptimal match of our models with the experimental data, even with model parameters 261 determined from experiment on a per-cell basis, we considered the possibility that one or more 262 of the parameters were mismatched between the experimental cells and the parameter values 263 derived from the recordings. We considered re-fitting the various parameters in the model to 264 ensure that ℎ and passive parameters resulted in correct output for each cell. However, due to the 265 sheer number of parameters present in the model, care needed to be taken in how the parameters 266 were adjusted as there are many interdependencies between the fitted parameters. For instance, 267 when ℎ is present, the trajectory of the response upon a step of hyperpolarizing current in a 268 cell depends not just on and , but also on the time constants of activation and deactivation 269 of h-channels ( ℎ ) and, to a degree, the h-channel steady-state activation curve ( ∞ ). Therefore, if 270 there is error in the model response compared to the experimental trace in this portion of the 271 trace ( Figure 4A), the mismatch between model and experiment may have been either due to the 272 passive parameters, or due to ℎ or ℎ , which gated by the activation, determines the amount of ℎ . 273 The problem, then, is how to attribute errors in any particular portion of a trace to any given 274 parameter in the model. 275 We noted that the initial mismatch in the case of =1 and for Cell 1 and Cell 2 seem primarily 276 to be located in the initial hyperpolarizing phase and the sag portion. Because the ℎ functions 277 were constructed using a limited set of data, it was reasonable to suppose that a large source of 278 mismatch in this portion of could be due to errors in the ℎ function itself. We thus re-fitted the 279 parameters for ℎ , namely 1 , 2 , 3 , 4 , 5 for all three cells, against each respective -120pA trace and 280 then compared the models' responses to the other current clamp steps to see how much of the 281 error could be accounted for by re-fitting ℎ alone ( Figure 4B). This re-fitting of ℎ alone could not 282 address the mismatch in between model and experiment although it may have played some 283 role, as evidenced by improving the match in in some cases. Thus other parameter re-fitting 284 needed to be considered. Detailed considerations including "overfitting" are given in the Methods. 285 We adopted the following approach and rationale. Since the passive properties were not as 286 tightly constrained as the ℎ properties, and could account for some of the mismatch in both the 287 transient and steady state portions of the traces, we re-fitted them first. That is, , , , .

288
Turning to the ℎ properties, we first re-fitted the total ℎ , which determines the per-compartment 289 conductance density, as well as the steady-state activation curve ∞ since it determines the voltage 290 dependency of how many channels are open. We could not fit ℎ and ∞ in the reverse order 291 because any error in ℎ -that is, how ℎ scales with voltage when all channels are opened -could 292 be accounted for by refitting ∞ by "flattening" it, thus lowering the total number of channels that 293 are open at any given voltage. This would not be physiologically correct since the model would then 294 imply that ℎ is never fully activated, i.e., ∞ does not reach 1. Thus, by re-fitting ℎ first, followed by 295 ∞ , we increased the likelihood that ∞ did not diverge too much from the experimental data points 296 obtained from the protocol for ℎ activation. Finally, we re-fitted ℎ . If the passive properties and 297 steady-state ℎ due to ℎ and ∞ accounted for much of the mismatch in , then the last step of 298 re-fitting ℎ should allow for any mismatch due to ℎ to be corrected for. 299 Using this approach, which we termed a "staggered" re-fitting, we show the model outputs in 300 Figure 4C where only the -120 pA TTX traces were used for fitting the parameters, with the -90pA TTX 301 traces provided test data to validate the fits. We note that the results with this approach were more 302 successful than the previous approaches. By fitting the parameters in such a way that the ones most  for Cell 3. As shown in Figure 4B and  Table 4, =1 column. 311 All the models in the staggered re-fit were done with =1, because that value was the one that 312 provided the closest fit to the experimental traces ( Figure 4A) when only passive properties were 313 fit to the traces and ℎ parameter values were obtained from the voltage clamp protocols. We 314 examined whether using =0 and applying our staggered re-fitting approach could also produce 315 good, generalizable fits to the experimental data. The models with =0 fitted the experimental 316 traces well in all four current clamp steps as it did for =1, and we show the comparison to 317 the -90pA TTX trace for values of both 0 and 1 in Figure 5A, noting that the -120 pA TTX trace 318 was used for the fitting. The staggered re-fitted values for =0 are also shown in Table 4. From a 319 comparison across Table 4 of parameter values for = 0, 1 and original ℎ parameter values fit to 320 the experimental data, it is clear that the re-fitted parameter values using =0 are inappropriate. 321 Specifically, the total ℎ (shown in bold in Table 4) for the case of =1 was reasonably close to 322 what was measured directly from the I-V plot of the reversal potential experimental protocol, unlike 323 =0, which exhibited ℎ values that were much less than half of the experimentally-derived 324 values. Given that this parameter was taken from the slope of the I-V plot, the values from =0, 325 if correct, would imply that the recorded current values were double the "true" values in the cell. 326 This is graphically depicted in Figure 5B. We deemed this unlikely, and concluded that the relatively 327 small divergence in the re-fitted ℎ with =1 compared to the experimental case indicated a 328 much more reasonable error. Hence, the fact that it was possible to match the experimental 329 traces using both =0 and =1 did not mean that they were equally valid. The benefit of 330 having directly measured experimental values representing ℎ , ℎ , ∞ from the same cell meant 331 that we could confidently state that models with =0, though they fitted the traces, were not 332 appropriate models because they did not match the experimentally-derived values. Thus, only when 333 h-channels were spread into the dendrites did we find models whose responses matched the 334 experimental traces and whose total ℎ and other parameter values were in reasonable agreement 335 with the experimentally measured values. We thus predict that the experimental cells in the dataset 336 used here have h-channels expressed in their dendrites, with biophysical characteristics as given in 337 A. Using a staggered re-fitting, both =0 or 1 are good fits to the experimental data. Note that the -90pA TTX traces are "test" traces and were not used for fitting (-120pA TTX used for fitting), = 0 or 1. B. =1 is clearly more appropriate than =0 relative to the experimental data as shown in plotting I-V curves. cell voltage output at +30 pA, +60 pA and +90 pA depolarizing steps (protocol #2 in Table 5 in the   396 Methods), and we did our fitting using holding currents in line with the experimental data (4 pA 397 for Cell 1 and -5 pA for Cell 2). We note that our fits were done using the specific experimental The most highly ranked optimized models for Cell 1 and Cell 2 are plotted in red, and the experimental data is plotted in blue. Model parameters were optimized using depolarizing +30 pA, +60 pA, and +90 pA current step recordings from protocol #2 in Table 5 specific for Cell 1 and Cell 2.    to the full spiking models as done experimentally, and found that they were in full agreement with to the first spike. 439 We note that our goal was to obtain spiking models that could adequately recapitulate the 440 data for the particular cell, that is, starting idealized "base" models of OLM cells. These base  , 2015), as was also found in Purkinje cells (Angelo et al., 2007). Thus  and of -9.99 mV ( Table 4). The voltage-dependence of the time constant yielded fits that were 507 different but with overlapping values for the three cells ( Figure 3B). ventral CA1 region (see Figure 3). 539 It has been proposed that OLM cells play a gating role (Leão et al., 2012) Figure 4A). To explain why this may be the case, some general issues in building multi-582 compartment models directly from limited experimental data need to be considered. 583 The experimental data obtained from the OLM cells here, used to extract both passive and 584 h-channel characteristics, were not perfectly optimal. In an attempt to constrain as many distinct 585 parameters within the same cell as possible, we deliberately sacrificed depth for breadth so that 586 practical choices were inevitable in the distribution of efforts. There are inherent limitations to cell 587 stability that require rapid succession through a sequence of experimental protocols ( Table 5). In our 588 hands, the limit of stability was approximately thirty minutes. In this time, we were able to obtain 589 recordings, bath changes, and biocytin fills that allowed us to do reconstructions, and obtain passive specific capacitance values would still be ≈0.5 F/cm 2 (see Table 2). It is interesting to note that in cellular neurophysiology as well as generate hypotheses, refine protocols, and consider additional 645 measurable parameters that can then be incorporated into future model revisions. 646 A particular conceptualization of the role of computational modelling in neuroscience is to 647 help resolve, or at least reframe, these basic concerns of how "realistic" detailed models can be. 648 Rather than the idea of obtaining a detailed model as a crystallized end point of any given study, 649 we consider the role of the detailed modelling as an integral component of a cyclical process 650 of knowledge generation in neuroscience. We have expressed this as the experiment-modelling 651 cycling approach (Sekulić and Skinner, 2018). Although the approach was initially formulated in 652 the context of population or database modelling, it can be generalized for any computational 653 model whose goal is to explain experimental data, develop hypotheses and make predictions. 654 This conceptualization states from the outset that the goal of modelling is not to find optimal or 655 realistic models per se, but rather to develop models in such a way that a specific physiological 656 question is raised and can lead to experimental examinations. In our initial studies, we asked Although doing more than three full reconstructions, analysis and multi-compartment model 667 building may be desirable, we felt that consistently obtaining best matches with dendritic h-channels 668 in all three of our models when fit with data from the same cell was enough to allow for conclusions 669 as to dendritic expression of h-channels in OLM cells. Also, we focused on uniform h-channel 670 distribution in the dendrites since our starting models using either no h-channels or h-channels 671 fully and uniformly distributed in the dendrites did not match the experimental data ( Figure 4A). 672 Considering distributions that were not uniformly distributed (e.g., distributed only in proximal 673 dendrites) would be unlikely to capture the data given that the total h-channel conductance would 674 remain the same.

Order Description of procedure
#1 Voltage clamp seal test. #2 Wash-in of synaptic blockers (DNQX/APV/Gabazine). Current clamp 2s-long steps from -120pA to +90pA in 30pA steps. #3 Voltage clamp protocol for activating ℎ : Holding potential at -40mV, with a 1.2s-long step at progressively hyperpolarized potentials to -120mV, in -10mV increments. #4 Wash-in of TEA, 4-AP and TTX, then current clamp protocol as in step #2. #5 Same protocol for ℎ activation as step #3, but now in the presence of TTX/4-AP/TEA. #6 ℎ reversal potential protocol in voltage clamp mode: Holding potential at -40mV, followed by a prepulse to -120mV for 1.2sec to fully activate h-channels. Then, a depolarized relaxation step at -110mV was performed for 1s before returning to the holding potential. Repeated multiple times, with the relaxation steps becoming successively more depolarized at 10mV intervals across each repeated sweep. #7 Wash-in of ZD7288, then current clamp protocol performed as in step #2. #8 Same protocol for ℎ activation as steps #3 and #5, but now also in the presence of the h-channel blocker ZD7288.
The "order" column displays the sequential order in which the protocols were performed, with a description of each procedure provided in the following column. of displacement with no local maxima close to the peak (Emmenlauer et al., 2009). Accordingly, 812 the algorithm is supposed to be robust to noise and is invariant to linear changes in gray values. 813 In terms of practical application, however, we found that the success of the XuvTools algorithm function, leading to less certainty in how much displacement is needed to find the optimal overlap 822 between image pairs. We next performed volumetric reconstruction of the soma, dendrites, and 823 axons. This was done using the freely-available Neuromantic software package that implements 824 semi-automated tracing (Myatt et al., 2012). The semi-automated tracing procedure resulted in 825 successful tracing of several cells in the experimental dataset used here, but with a fundamental 826 limitation being that 1 m was the minimum possible diameter hard-coded in Neuromantic. The 827 resulting surface areas of the traced cells were too large, and distal dendritic diameters were clearly 828 overestimated. Inhibitory interneurons may possess dendrites with thickness less than a micron, 829 e.g., 0.4 m in cerebellar interneurons (Abrahamsson et al., 2012). Accordingly, we performed full 830 manual reconstructions using Neuromantic.  Table 1 in which the experimental data analysis was performed as in (Yi 866 et al., 2014)). 867 Of these 11 OLM cells, three (Cell 1, Cell 2, Cell 3)  Fitting passive properties in multi-compartment models 875 Simulations of multi-compartment models of neurons were performed using the NEURON sim-876 ulation environment (Hines and Carnevale, 2001). We selected long current clamp steps for the 877 fitting of passive membrane properties rather than shorter voltage clamp "seal test" protocols 878 due to the incomplete clamping of the membrane by short voltage clamp steps (Holmes, 2010). 879 Furthermore, these voltage traces minimize the contribution of active conductances. Recordings 880 were performed with synaptic-and voltage-gated channels blocked, and was initially preferable 881 for passive membrane property fitting in the models. Recordings obtained in the presence of 882 h-channel blocker ZD7288 are referred to as "ZD traces" and are given by #7 in Table 5 as an "undershoot" of the -30pA ZD traces after normalization of the traces was done, so that the 889 -30pA ZD traces showed a marked slowing of compared to both the -120pA ZD as well as -30pA 890 "TTX traces" (i.e., #4 in Table 5, referred to as such due to TTX application, in addition to potassium 891 and synaptic blockers), the latter two being largely overlapping (Figure 2-Figure Supplement 1A). 892 The noisier charging portion of the -30pA ZD traces could be seen more clearly if the time point     session using a nonlinear least squares regression (Figure 2). The amplitude of the traces were 933 normalized at the time point at which depolarizing responses in the "TTX traces" (i.e., #4 in Table 5 934 when TTX/4-AP/TEA applied), due to the h-channel current ( ℎ ) cause the membrane potential to 935 deviate from the (putatively) passive response under the "ZD traces" (i.e., #7 in Table 5 when ZD7288 936 27 of 40 also applied). For each cell, both the -30pA and -120pA ZD traces were used to compare to the 937 TTX traces, as these should both reflect largely passive membrane responses. We note that for 938 most cells, the -30pA TTX trace followed the -30pA ZD trace (left) as well as the -120pA ZD trace 939 (right), Figure 2. Cell 1 in particular exhibited a very good match between the -30pA TTX and -120pA 940 ZD traces. The fitted values for the -120pA ZD trace and -30pA TTX trace are given in Table 7. 941 We also fitted the membrane time constant for the models, using a -120pA current clamp step 942 in the models without ℎ included (see Table 7). Resulting traces were fit in the same way as 943 the experimental traces, except that the data points were weighted by the relative time step of 944 integration in the NEURON simulations such that data points in the vector closely spaced in time 945 would be weighed less. This ensured that the fit was not disproportionately weighed by the early, 946 rapidly changing charging portion with many more data points. 947 Compartmentalization of the models was done in NEURON using the rule where compartment 948 lengths are set to a fraction of the length constant , where =100Hz. We set the fraction of 949 to be 0.1 for all models. Table 7 gives the resulting number of compartments in each of the cells, 950 along with their surface areas in the finalized models, that is, after staggered re-fitting.

951
Mathematical equations for h-channels 952 The specification of the current for h-channels, ℎ , was taken from our previous work (Lawrence The conductance-based mathematical formulation used to represent current flow through h-958 channels is given by: where ℎ is the maximal synaptic conductance for the h-channels, is the activation variable, ℎ is 960 the h-channel reversal potential, ∞ is the steady-state activation, is the slope of activation and 961 1∕2 is the potential of half-maximal activation of ℎ , ℎ is the time constant of activation, is the 962 membrane potential, and is time. The voltage dependence of ℎ is given by a double exponential 963 expression with parameters 1 , 2 , 3 , 4 , 5 as follows:

965
Given our experimental protocol (see Table 5), we were able to obtain h-channel current ( ℎ ) reversal 966 potentials, activation kinetics, and steady-state activation for each of the three chosen cells.

967
Reversal potential: To obtain the reversal potential for ℎ , we first removed the leak components 968 and capacitive transients from the voltage clamp recordings in order to isolate the ℎ components. 969 This was done by taking the traces obtained by the reversal potential protocol (#6 in Table 5) and 970 subtracting from them the capacitive response generated by an equivalent magnitude voltage 971 clamp deflection from the ℎ activation protocol with ZD7288 application (#7 in Table 5 where, for somatic compartments,  Table 10. 1115 32 of 40

AP_amplitude (mV)
The relative height of the AP between the peak voltage and the voltage where the first derivative is higher than 12 V/s, for at least 5 points.

AHP_time_from_peak (ms)
Time between AP peaks and AHP depths.

time_to_first_spike (ms)
Time from the start of the stimulus to the maximum of the first peak. 6. voltage_base (mV) The resting membrane potential before the current step.

AP_amplitude_change
Difference of the amplitudes of the second and the first AP divided by the amplitude of the first AP.

AP_duration_half_width (ms)
Full width at half maximum of each action potential. 9. AHP_depth (mV) Relative voltage difference between the minimum AHP voltage and the voltage base.

mean_frequency (Hz)
The mean frequency of the firing rate.

AHP_slow_time
Time difference between absolute voltage values at the first after-hyperpolarization starting 5 ms after the peak and the peak, divided by interspike interval.

adaptation_index
Normalized average difference of two consecutive ISIs.
2. Fine-tuned the parameter ranges and objectives to avoid areas of the parameter space that 1116 generate undesirable results and keep re-doing the optimizations using this approach until 1117 the top models consistently generate appropriate electrophysiologies. The parameter ranges 1118 used that produced the final models are shown in Table 9. 1119 The top five optimized models for Cell 1 and Cell 2 are presented in Figure 7 and  All of the objective features that were used in the optimization are listed in Table 10, and the 1134 parameter ranges are given in  Traces for all hyperpolarizing current injection steps with synaptic and voltage-gated channel blockers, except ZD7288 ("TTX") and the -30pA trace with ZD7288 application ("ZD") for Cell 1, 2, and Cell 3 (respectively left, middle, right -ordering of cells are the same for remainder of figure). Small circles represent the time point at which all traces were normalized and were determined by eye as the point at which depolarization due to activted h-channels caused TTX traces to deviate from the "passive" ZD condition. This value is unique per cell and relative to the time of step current injection (1000ms) as follows: 44 ms (Cell 1), 60 ms (Cell 2), 60 ms (Cell 3). B. As in A., except the -120pA ZD trace is shown instead of the -30pA ZD trace.      Model traces compared to experiment for Cell 1 with staggered re-fitting procedure, where first passive properties are fitted, followed by total ℎ , ∞ and ℎ . Only the -120pA TTX trace was used for fitting; the other traces show validation of the model's parameters using different current clamp steps.

TEST TEST
=1. Holding current injections: -28 pA for all four steps of -120, -90, -60, -30 pA.  Model traces compared to experiment for Cell 3 with staggered re-fitting procedure, where first passive properties are fitted, followed by total ℎ , ∞ and ℎ . Only the -120pA TTX trace was used for fitting; the other traces show validation of the model's parameters using different current clamp steps.
=1. Holding current injections: 2.7 pA for -120pA step; 3.1 pA for -90 and -60pA steps; 3.4 pA for -30pA step.  When injecting -90 pA and -120 pA current injections to the top spiking models, we accounted for differences in holding currents during experiment with TTX traces or traces from protocol #2 in  Note that the recordings shown here are from the first dendritic compartment adjacent to the soma since calcium channels are not present in the somatic compartment. During hyperpolarizing steps, it is evident from these plots that I ℎ (IH) and the leak current (IL) are the primary contributors to the electrophysiological output. For depolarizing steps, we see the largest contributions are from A-type potassium current (IKa), fast delayed-rectifier current (IKdrf), sodium current (INa), and calcium-dependent potassium current (IKCa), with increasing contributions from M-type current (IM) as the current step magnitude gets larger. Slow delayed-rectifier current (IKdrs) contributes minimally.  Figure 7, we show the +30 pA, +60 pA, and +90 pA current injection steps for models (red) plotted against the corresponding experimental data (blue). Spiking models for Cell 1 and Cell 2 that were ranked second, third, fourth, and fifth are shown from top to bottom.