Simple models of quantitative firing phenotypes in hippocampal neurons: Comprehensive coverage of intrinsic diversity

Patterns of periodic voltage spikes elicited by a neuron help define its dynamical identity. Experimentally recorded spike trains from various neurons show qualitatively distinguishable features such as delayed spiking, spiking with or without frequency adaptation, and intrinsic bursting. Moreover, the input-dependent responses of a neuron not only show different quantitative features, such as higher spike frequency for a stronger input current injection, but can also exhibit qualitatively different responses, such as spiking and bursting under different input conditions, thus forming a complex phenotype of responses. In previous work, the comprehensive knowledge base of hippocampal neuron types Hippocampome.org systematically characterized various spike pattern phenotypes experimentally identified from 120 neuron types/subtypes. In this paper, we present a complete set of simple phenomenological models that quantitatively reproduce the diverse and complex phenotypes of hippocampal neurons. In addition to point-neuron models, we created compact multi-compartment models with up to four compartments, which will allow spatial segregation of synaptic integration in network simulations. Electrotonic compartmentalization observed in our compact multi-compartment models is qualitatively consistent with experimental observations. The models were created using an automated pipeline based on evolutionary algorithms. This work maps 120 neuron types/subtypes in the rodent hippocampus to a low-dimensional model space and adds another dimension to the knowledge accumulated in Hippocampome.org. Computationally efficient representations of intrinsic dynamics, along with other pieces of knowledge available in Hippocampome.org, provide a biologically realistic platform to explore the large-scale interactions of various neuron types at the mesoscopic level.

Patterns of periodic voltage spikes elicited by a neuron help define its dynamical identity.
Experimentally recorded spike trains from various neurons show qualitatively distinguishable features such as delayed spiking, spiking with/without frequency adaptation, and intrinsic bursting. Moreover, the input-dependent responses of a neuron not only show different quantitative features, such as higher spike frequency for a stronger input current injection, but 15 can also exhibit qualitatively different responses, such as spiking and bursting under different input conditions, thus forming a complex phenotype of responses. In a previous work, Hippocampome.org, a comprehensive knowledgebase of hippocampal neuron types, systematically characterized various spike pattern phenotypes experimentally identified from 120 neuron types/subtypes. In this paper, we present a comprehensive set of simple 20 phenomenological models that quantitatively reproduce the diverse and complex phenotypes of hippocampal neurons. In addition to point-neuron models, we created compact multicompartment models with up to four compartments, which will allow spatial segregation of synaptic integration in network simulations. Electrotonic compartmentalization observed in our compact multi-compartment models is qualitatively consistent with experimental observations. 25 Furthermore, we observed that adding dendritic compartments to point-neuron models, in general, allowed soma to reproduce features of bursting patterns and abrupt non-linearities in some frequency adapting patterns slightly more accurately. This work maps 120 neuron types/subtypes in the rodent hippocampus to a low-dimensional model space and adds another dimension to the knowledge accumulated in Hippocampome.org. Computationally efficient 30 representations of intrinsic dynamics, along with other pieces of knowledge available in Hippocampome.org, provide a biologically realistic platform to explore the dynamical interactions of various types at the mesoscopic level.

Introduction 50
Complex interactions among a myriad of neurons make it challenging to study the functions of brain regions. Although each neuron is different, their landmark features such as the dendritic structure and patterns of somatic voltage spikes help define types of neurons, and, such grouping allows for a tractable description and investigation of complex interactions in a network. For instance, large-scale network models of brain regions can include precisely 55 defined neuronal types to create a biologically realistic platform for hypothesis testing. While neurons differ in their morphological, biochemical and electrophysiological features, precisely what features are useful and relevant for neuronal grouping is a topic of great interest [1].
A few studies have created large-scale network models of brain regions [2][3][4][5]. The major methodological difference among these studies is the level of biological details captured in the 60 individual components of the network and there is often a tradeoff between such biological details and the scale of the network. For example, a microcircuit model of the rat somatosensory cortex [4] simulated ~31,000 neurons with ~37 million synapses, where each neuron was a biophysically detailed description of one of 207 morpho-electrical types identified experimentally. On the other hand, a large-scale description of thalamocortical systems [2], 65 which used simplified phenomenological neuron models [6], simulated a network of much larger scale (one million neurons and half a billion synapses), but it only included 22 abstract types among the neurons. In current work, with a vision of creating a real-scale network model of the rodent hippocampus that nevertheless captures biological details at the mesoscopic level, we have created phenomenological models of 120 hippocampal neuron types and subtypes using 70 their intrinsic dynamics identified experimentally. More recently, a large-scale effort [7] created a database of simple models for hundreds of neurons of various transgenic types in the mouse primary visual cortex with a similar vision. knowledgebase of neuron types in rodent hippocampal formation (dentate gyrus, CA3, CA2, 75 CA1, subiculum, and entorhinal cortex). It provides information on morphology, electrophysiology, and molecular marker profiles of more than 100 neuron types, where the type of a neuron is primarily determined based on its neurite invasion pattern across hippocampal parcels. Latest enhancement to this knowledge base annotated 90 of these morphological types with their spike patterns and identified a total of 120 neuron types/subtypes [9]. Features of 80 experimentally recorded spike patterns were extracted for a neuron type from relevant publications and a systematic characterization of spike pattern features revealed nine unique families of intrinsic dynamics such as delayed spiking, non-adapting spiking, simple adapting spiking, and persistent stuttering among hippocampal neurons. Furthermore, many neuron types exhibit different classes of spike patterns for different input currents resulting in complex 85 spike pattern phenotypes.
In this article, we present a comprehensive set of point neuron models that quantitatively reproduce various spike pattern phenotypes of hippocampal neurons. We also created multicompartment models that are compact extensions of point neurons in order to allow spatial context for synaptic integration in a network. In addition, our compact multi-compartment models 90 exhibit electrotonic properties consistent with experimental observations. We also report interesting relationships between the abstract model parameters and various biological properties. The models were created using an automated modeling framework [10], and they further enhance the existing accumulated knowledge in Hippocampome.org, where they are freely available to download. By identifying several possibilities for a quantitative phenotype in 95 phenomenological space, current work comprehensively maps hippocampal neuron types to low-dimensional model subspaces, which can be used as sampling regions for biologically realistic large-scale network simulations of hippocampal circuits.

Methods
The class of a spike pattern is identified based on various transient and/or steady-state 100 elements present in the pattern. (PSWB) if a slow after-hyperpolarizing potential is present in an otherwise PSTUT pattern.
Thus, the key features are fsl, sfa, pss and the number of ISIs (nISIs) for a spiking pattern, and burst widths (bw), post-burst intervals (pbi), number of bursts (n_bursts) and nISIs within a burst (b-nISIs) for a stuttering/bursting pattern. Refer to [9] for more details on the criteria for various spike pattern classes. These temporal features identify the class of a single spike pattern, and 115 all classes of patterns exhibited by a neuron under different input currents collectively define the spike pattern phenotype of that neuron. Thus, our approach emphasizes the temporal patterns in the periodic voltage spikes rather than the shape of the spike or subthreshold dynamics to define the intrinsic dynamics.
We used a two-dimensional quadratic model (QM) [6,11]  excitability level and magnitude of sfa). Compact multi-compartment models with up to four 130 compartments were modeled using an asymmetric coupling mechanism by calculating coupling currents in somatic ( ) and dendritic ( )compartments as follows: Where is the coupling strength and denotes the degree of coupling asymmetry, which 135 determines the influence of a compartment on the overall model dynamics [12]. As reported before [10], most of our compact multi-compartment models specify a much weaker coupling toward the soma than away from it, making the somatic compartment dominate the overall model intrinsic dynamics. Compact multi-compartment models were also constrained to exhibit appropriate relative excitabilities and input resistances between soma and dendrites, and sub-140 and supra-threshold signal propagation properties.
Our modeling framework [10] uses evolutionary algorithms (EA) and employs a featurebased error function. By incorporating spike pattern features (fsl, sfa etc.) and qualitative class criteria (delay factor, number of piecewise linear fit parameters of ISIs etc.) [9] in the error landscape, our approach enforces a fine level of granularity in the key quantitative features of 145 various spike pattern classes. The operators of the EA (mutation, crossover etc.) were configured by taking into account the features of error landscape created by the QM parameters [13]. In order for a model found by the EA to be accepted, the classes of its spike patterns must match those of experimental traces. There is, however, one exception: Without additional dendritic dynamics, the QM failed to reproduce RASP.ASP. class of patterns, which show a 150 strong and rapid adaptation (in the first 2 or 3 ISIs) followed by a very weak and sustained adaptation. Therefore, single-compartment models of seven neuron types, which experimentally showed this complex transient pattern, were accepted with RASP.NASP patterns instead (see results).
Pairwise correlations were performed to explore the relationships between QM 155 parameters and various pieces of knowledge such as biomarker expression that have been accumulated in Hippocampome.org. Continuous QM parameters were converted into categorical variables appropriately by marking positive and negative or by labelling top-and bottom-one-third ranges respectively as high and low. Correlations between the categorical variables were evaluated using Barnard's exact test for 2x2 contingency tables. This test 160 provides the greatest statistical power when row and column totals are free to vary [14].

Single-compartment models of diverse intrinsic spike pattern phenotypes
The intrinsic dynamics of a neuron is identified in experiments typically by injecting step input   [15]. Digitally reconstructed morphology was reproduced from Neuromorpho.org [16]. (B) Simple phenotype of a CA1 Basket neuron that elicits patterns of class NASP for +0.15nA and +0.31nA [17]. Note that sfa in red trace is not statistically significant to qualify this pattern as ASP. (C) The phenotype of a CA1 Trilaminar neuron shows different classes of patterns for +0.025nA and +0.05nA [17]. In 190 addition, this neuron elicits rebound spikes (RBS) for a hyperpolarizing input of -0.1nA.
(D) The phenotype of a medial-entorhinal cortex (MEC) neuron shows different classes of patterns for +0.2nA and an unknown input (denoted by '*') near its excitability level [18]. and a spiking pattern for +0.6nA (grey) [19]. Digitally reconstructed morphology [20] was reproduced from Neuromorpho.org [16]. (B) The voltage trace recorded from an entorhinal layer-5 neuron shows both bursting and spiking features for +0.4nA [21]. (C) A DG granule neuron transiently bursts for both +0.2nA and +0.4nA with quantitative 200 difference [22]. Digitally reconstructed morphology was reproduced from Neuromorpho.org [16]. (D) A dentate gyrus neuron that transiently bursts near its excitability level (red) elicits a spiking pattern with a strong sfa (grey) for a higher input In the simplest case, a neuron exhibits spike patterns of the same class regardless of the input current strength. For example, the three spike patterns recorded under different input currents from a DG Total Molecular Layer neuron were identified as ASP. (Fig 1A), and the two patterns recorded from a CA1 Basket neuron were identified as NASP. (Fig 1B). Such simple-210 behavior neurons typically show different quantitative features among different patterns of the same class. In the former example, the three ASP. traces were experimentally recorded under +0.075nA (red), +0.100nA (black), and +0.200nA (grey) [15]. The ISI counts (nISIs) are 5, 9, and 19, and sfa magnitudes are 0.142, 0.114, and 0.056 respectively for the red, black and grey traces. The model of this neuron type was constrained to quantitatively reproduce the spike 215 pattern features for similar input currents: nISIs of 5, 9 and 19, and sfa magnitudes of 0.142, 0.082, and 0.032 respectively for +0.073nA, +0.102nA and +0.205nA. Note that a minimum of two spikes are required in order to identify a class, hence, single-spike traces are not assigned a class label. However, such single-spike traces help capture the excitability levels in the models more precisely. 220 Additionally, a neuron can show more complex behaviors by eliciting patterns of different classes under different input currents (Fig 1C-D). Both CA1 Trilaminar, and MEC LV-VI Pyramidal-Polymorphic neurons include ASP. in their phenotypes (grey traces), but they show different dynamics close to their respective excitability levels. Whereas the former quickly fired a few spikes before going into a silence mode (ASP.SLN), the latter showed delayed-spiking 225 (D.NASP). The model quantitatively reproduces the characterizing features of these different classes (see pss for ASP.SLN and fsl for D.NASP). Also, note that the model reproduces the rebound-spiking behavior for a hyperpolarizing input current, a known feature of CA1 Trilaminar neurons [17].
Another level of complexity in spike pattern phenotypes is when the intrinsic dynamics 230 show sharply distinguishable spike pattern classes under different input conditions. For example, a CA1 bistratified neuron stutters (PSTUT) for +0.4nA, and spikes for +0.6nA (ASP.) (Fig 2A). A few neuron types and subtypes in the hippocampus exhibit such a complex phenotype, where PSTUT is typically observed near the excitability level of a neuron. (e.g. CA1 neurogliaform [24], DG Total Molecular Layer subtype [15] etc.). Our simple models capture the 235 characterizing features of both PSTUT and ASP. (Fig 2A) under the right input conditions. It is worth mentioning that all PSTUT neurons are inhibitory neurons and CA1 region has a proportionately larger number of these phenotypes [9,25]. In many cases, however, the characteristic features of interrupted spiking can be only transiently present (Fig 2B). Here, a single pattern presents features of both bursting and spiking, where a relatively longer interval 240 separates a few high frequency spikes (burst) from a train of regular spikes. In another set of examples, Granule cells and Hilar Ectopic Granule in the dentate gyrus (DG) show only transient bursting near excitability (Fig 2C and 2D). However, for an increased input current, Granule cells still showed the same class of TSWB.SLN with quantitative differences such as increased number of spikes, whereas Hilar Ectopic Granule transitioned to ASP. These 245 constrained representations of two different DG neurons fall under the same family of nonpersistent bursting, but they reflect finer quantitative differences in the input-dependent responses between these two neuron types. Thus, our simple models do not only qualitatively capture the rich diversity of dynamical classes defined systematically, but they are also quantitatively constrained representations of experimentally recorded patterns from the 250 hippocampal neuron types.

Multi-compartment models as compact extensions of point-neuron models
The point-neurons presented in the last section would tremendously reduce the computational cost of simulating large-scale networks of hippocampal circuits. However, since they lack spatial dimension, they do not differentiate synaptic inputs from different layers, unlike their biological 255 counterparts. For example, the hippocampal pyramidal neurons receive entorhinal projections on the apical dendrites in stratum lacunosum moleculare (SLM), and intra-hippocampal connections in stratum radiatum (SR), thereby compartmentalizing synaptic integration of distinct laminar inputs. While it is not possible to spatially segregate synaptic integration in a network of point-neurons, it is of interest to see the effects of such segregated synaptic 260 integration mechanisms in a network. Hippocampome.org (ver 1.4) identifies 87 neuron types with their dendrites invading at least two layers. Therefore, for these neuron types, in addition to point neuron models, we created compact multi-compartment models with up to four compartments. Here, each compartment corresponds to a hippocampal layer, and this allows layer-level connectivity specifications for a neuron type. 265 One example for each of the four out of five possible multi-compartment layouts are illustrated here, and the fifth layout is discussed in detail in Section 3.3. The somatic compartment of a compact multi-compartment model quantitatively reproduces the spike patterns experimentally recorded from the soma of the respective neuron type for similar input currents (Fig 3 and Fig 4A).   Furthermore, forward-coupling (from dendrite to soma) between compartments is just strong enough to evoke a somatic excitatory postsynaptic potential (EPSP) with an amplitude in 300 the range [0.1, 0.9] mV for a single synaptic stimulation at a dendritic compartment and to achieve a forward-spike propagation (from dendrite to soma) ratio in the range [0.5, 1.0].
( Supplementary Fig S1C-D). As mentioned in methods, the backward-coupling (from soma to dendrite) is much stronger than the forward-coupling in most of our compact multi-compartment models, consistent with the electrotonic profiles reported for various neuron types [30][31][32]. Such 305 an asymmetric design for coupling enables the somatic compartment to dominantly define the model's overall intrinsic dynamics, while still preserving forward propagation properties for suband supra-threshold signals from dendrites. Thus, our multi-compartment models are compact extensions of point neuron models, which allow spatial contexts for synaptic integration (Fig S2).
Although the major motivation for creating compact multi-compartment models is to 310 allow synaptic segregation in a network model, we also investigated if additional dendritic mechanisms implemented in our compact multi-compartment models could help achieve a better fitting of somatic spike patterns than their point-neuron counterparts. Therefore, we performed pairwise comparisons between the somatic spike pattern features of singlecompartment and compact multi-compartment models. In general, implementing additional dendritic mechanisms in the models only improved the accuracy of bursting features (Fig 4B).
Interestingly, fsl and pss errors were higher in the models due to the addition of dendritic compartments. However, it should be noted that each additional compartment not only adds two state variables, which require more computations for numerical simulation, but also adds ten open parameters (including coupling parameters) making it a more-challenging optimization 320 task. It has been shown that adequate dendritic influence is necessary for bursting to exist in a 2-compartment model [12]. Although our single-compartment models were able to reproduce quantitatively comparable experimental bursting/stuttering patterns (Fig 2) (see [10] for two exceptions), compact multi-compartment models significantly improved the accuracy of bw, a key feature of bursting/stuttering patterns (Fig 4B). 325 Furthermore, while the single-compartment models quantitatively captured various classes of adapting spike pattern phenotype such as ASP., ASP.SLN, ASP.NASP and RASP.NASP, they failed to reproduce RASP.ASP. patterns. These patterns exhibit a strong and rapid adaptation in the first few ISIs, which is then followed by a very weak and sustained adaptation. Interestingly, we found that such a combination was not possible in the QM (red 330 circles in Fig 4B), unless additional dendritic compartments were included. Two different time constants (parameter ' ') for the adaptation variable (state variable ) were required for the somatic-and dendritic-compartments respectively in order to capture such complex transients in the soma. In our single-compartment models, RASP.ASP. is represented by RASP.NASP, since the adaptation followed by RASP. is usually very weak. See Supplementary Fig S2 for an  335 example.

Electrotonic compartmentalization in a 4-compartment model of CA1 pyramidal neurons
In addition to the features discussed in the last section, our compact multi-compartment models show electrotonic structures and interplay between different compartments that are similar to 340 those experimentally observed in the pyramidal neurons of CA1. To illustrate this, here we present a 4-compartment model of CA1 pyramidal neurons and discuss the voltage attenuation and spike propagation properties of apical compartments. First of all, the somatic compartment captures the frequency adaptation (Fig 5B), the characterizing feature of the experimentally recorded spike pattern from a CA1 pyramidal neuron (Fig 5A), quantitatively (Fig 5C -left). 345 Secondly, the dendritic compartments (SR, SLM and SO) are less excitable and have higher input resistances than the somatic compartment (Fig 5C -right). In real neurons, integration of an EPSP is influenced by the location of the synapse, because the voltage attenuates more from a distal dendritic location to the soma, than from a proximal location. This is due to the higher input resistances of more distal dendrites with smaller diameters. However, it has been shown in some CA1 pyramidal neurons that the 365 synapses might be able to compensate for their distance by scaling their conductances in order to sufficiently influence somatic voltage [35,36]. In our model, compared to a synapse stimulated at SR to evoke a somatic (SP) EPSP with an amplitude of 0.2mV, a 12-fold increase in synaptic weight was required at SLM in order to evoke an EPSP with the same amplitude at SP (Fig 5D).
Furthermore, the distal compartments in our 3-and 4-compartment models rarely 370 initiated a spike that successfully propagated to the soma. While the spike initiated at SR successfully triggered a somatic spike (Fig 5E1), the spike initiated at SLM failed to do so ( Fig   5E2 -bottom in left). The same scenario, however, triggered a somatic spike, when SR was slightly depolarized further by a step current of small magnitude and duration (Fig 5E2 -right. Also see top in left). This is consistent with the experimental observation that the activation of 375 CA1 neurons by the perforant path, which projects to SLM, is limited, and, modest activation of Schaffer-collateral synapses at SR facilitates forward propagation of distal spikes [37]. It has been suggested that Schaffer-collateral evoked EPSPs "gate" perforant path spikes in CA1 pyramidal neurons, and pyramidal neurons, in general, have functionally different dendritic domains [26]. To what extent these differences influence the emergent network properties, 380 however, remains to be answered, and our models allow one to explore such questions.

Online repository of models: An enhancement to hippocampome.org
A comprehensive list of models of 68 types and 52 subtypes of neurons is freely available at Hippocampome.org. Mapping the intrinsic dynamics of each neuron type in a low-dimensional model space enhances the existing knowledge accumulated in this comprehensive knowledge 385 base of hippocampal neuron types.
All the single-compartment and compact multi-compartment model parameters are presented in a matrix on the main page to enable easy browsing (Fig 6A). Within a neuron page, models for all subtypes (if any) for the given morphological type are available for download. This page includes both the experimentally recorded voltage traces and simulated 390 ones for all subtypes (Fig 6B). Simulated spike patterns are also annotated with their class labels. Each type/subtype presents three downloadable files for the user (Fig 6C). A Fit-file includes both the experimental and simulated values for spike pattern features such as fsl and sfa for each available pattern in a JSON format. In addition, an XPP [38] script for single compartment models, and a csv input file that includes both single-compartment and compact 395 multi-compartment models to be simulated using CARLsim [39], a high performance GPUbased simulator, are provided for each type. Links to help pages are provided under section "Simulation of Firing patterns" on http://hippocampome.org for model and feature description and instructions to run the scripts.

Relationship between model parameters and biological features
covers the diversity among neuron types, is that it allows one to explore relationships between the mathematical parameters of the QM and various known biological features. Our analysis revealed some interesting trends and correlations between the QM parameters and biological features, which are presented below. 415 In general, the parameters of the QM collectively determine its spike pattern phenotype.
However, the parameter 'b', which determines if the model is an integrator (b<0) or a resonator (b>0), sufficiently distinguishes two families of phenotypes. Most of the models that show delayed spiking near their depolarizing excitability levels were found in the negative regions of 'b', whereas models that show rebound spiking for hyperpolarized input currents were strictly 420 restricted to the positive regions (Fig 7A). Our results confirm the fact that all rebound spikers are resonators [11], and find that most delayed spikers are integrators with the exception of the ones found in the narrow range 0<b<20. Thus, rebound ( Fig 1C) and delayed ( Fig 1D) spiking are, in general, instances of two qualitatively very different types of intrinsic dynamics. Finally, our modeling framework represents each neuron type as a cloud of possibilities in the model parameter space (Fig 7D). Spike patterns produced by all the models in a cloud strictly adhere to the criteria for the respective target qualitative class, but small errors in the 455 quantitative features were accepted to allow variabilities in the spike pattern features (not shown here). See [10] for more details on the optimization framework design that allows such variabilities and some examples of ranges of quantitative features. At present, these clouds are only identified for single-compartment models due to the computational cost of exploring higher dimensional parameter spaces of multi-compartment models. 460

Discussion
The simple models presented in this work are aimed at creating large-scale network models of hippocampal circuits that are biologically realistic, yet computationally efficient. We first discuss biological realism in the context of variability in the intrinsic dynamics and then discuss how one can take advantage of the computational efficiency of these models in creating network models. However, it is worth discussing their accuracy in a broader context. The intrinsic property of a neuron revealed in its spike patterns is determined by the types and precise distribution of the underlying ion channel conductances such as sodium, potassium, and calcium. However, it has 475 been shown that similar dynamics can arise from a broad range of combinations of these conductances [40][41][42]. Consistent with this notion, our modeling framework represents a spike pattern phenotype as a cloud of possibilities in the parameter space (Fig 7D). Two closely related issues motivate such representation.
First issue is the existence of intrinsic variabilities in the spike pattern features among 480 different neurons of the same type. For example, all the models representing CA1 Trilaminar type ( Fig 7D) were obtained using the features of voltage traces recorded from a single neuron ( Fig 1C). While this particular neuron elicited 22 spikes with an sfa magnitude of 0.038 for 0.05nA, a different CA1 Trilaminar neuron might show slightly different values for these features under the same input conditions due to intrinsic variability. Furthermore, the recorded intrinsic 485 spike pattern features might be influenced by the conditions such as the type of recording electrode and difference in the species. However, current knowledge about the intrinsic dynamics of these neuron types is limited to the representative traces that the researchers who studied these neuron types chose to publish. Therefore, we allowed a small range in the spike pattern features of a model as long as these features strictly adhere to the definitions of the 490 respective target qualitative class. While the cloud boundaries defining such ranges are currently arbitrary, one could easily enhance our modeling framework to include more realistic ranges, when such ranges are experimentally obtained for all neuron types.
Secondly, neurons have intrinsic plasticity and undergo homeostatic regulations to maintain some constancy in the network activity [42][43][44][45][46]. In cell cultures, intrinsic homeostasis 495 has been shown to modify pharmacologically isolated neurons' non-synaptic ion channel conductances. Such modifications shift the input-dependency of a neuron's responses based on the history of activity. For example, activity deprived neurons showed higher firing rates than control group for the same magnitude current injections [46]. In another study, chronic isolation from normal inputs switched a neuron's response from tonic spiking to intrinsic bursting and this 500 transition was reversed by applying a rhythmic inhibitory drive [43]. While these results suggest that each neuron has a working range that flexibly defines its input-dependent responses, such ranges likely preserve the overall qualitative spike pattern phenotypes [45]. Our EA search for a cloud of models not only included the space of intrinsic QM parameters that define a phenotype, but also included a small range for input current (a 20pA range symmetrically encompassing 505 experimental input current magnitude), allowing a little flexibility for its input-dependency.
Considering the issues discussed above, an approach to modeling biological circuits should assume a flexible range for its components. While Hebbian plasticity rules can enable flexible ranges in synaptic conductances, the rules governing a neuron's intrinsic plasticity remain largely unknown. Although cell-autonomous regulatory rules have been proposed [47], 510 from a network perspective, intrinsic homeostasis have been shown to synergistically result from multiple interacting components in a circuit [48,49]. Exhaustively reductionist approaches to modeling brain regions specify precise descriptions at the level of ion channel conductances.
While data gathered from different experimental conditions or inevitably from different animals drive such intrinsic descriptions, there is no guarantee that they specify dynamically compatible 515 critical ranges necessary for a higher-level integrative property [50].
A large-scale approach to modeling a brain region, rather than being purely reductionist, should attempt to complement the descriptions of individual components with syntactically relevant descriptions at integrative level. For example, temporal sequences of activity in ensembles of hippocampal neurons are correlated with the locations of an animal during spatial 520 navigation [51][52][53]. Such self-organizing ensembles of neurons, in general, have been suggested to form neural syntax [54]. Complex periodic structures in these ensembles such as theta-modulated gamma activity patterns should be enforced in a network model as sparse higher-level descriptions.
Future studies should aim to identify a family of models for an experimentally known 525 network-level property within the anatomical constraints of connectivity among hippocampal neuron types [55] using the sampling regions for those types created in this study. Then, the identified family of models should be evaluated for their predictive power, or one could investigate how the predictive abilities increase by scaling up the network, or by adding more mechanisms such as synaptic plasticity and spatial context for synaptic integration. This 530 approach emphasizes the goal of creating the simplest model with the most predictive power iteratively.
Finally, it is important to identify recurring patterns of self-organization in biological complex systems and translate such patterns into mathematical descriptions that could be enforced on a meta-level using self-adaptive techniques such as an evolutionary algorithm that 535 heuristically explores the given parameter space. If a biological complex system can indeed allow a little flexibility and compensation among multi-level components, then it suggests that a certain property could emerge from multiple, similar configurations in a network parameter space, which a metaheuristic approach can take advantage of. While this might be a computationally expensive task, our simple models with only two state variables per neuron as 540 opposed to hundreds in a biophysically detailed multi-compartment model allow one to approach this problem much more efficiently. Future releases of Hippocampome.org are aimed at approximating the counts of different neuron types and mapping synaptic properties to potential connections. These enhancements will further narrow down the space of biological possibilities to create realistic large-scale models of hippocampal circuits. 545