Using Multi-Compartment Ensemble Modeling As an Investigative Tool of Spatially Distributed Biophysical Balances: Application to Hippocampal Oriens-Lacunosum/Moleculare (O-LM) Cells

Abstract

Multi-compartmental models of neurons provide insight into the complex, integrative properties of dendrites. Because it is not feasible to experimentally determine the exact density and kinetics of each channel type in every neuronal compartment, an essential goal in developing models is to help characterize these properties. To address biological variability inherent in a given neuronal type, there has been a shift away from using hand-tuned models towards using ensembles or populations of models. In collectively capturing a neuron's output, ensemble modeling approaches uncover important conductance balances that control neuronal dynamics. However, conductances are never entirely known for a given neuron class in terms of its types, densities, kinetics and distributions. Thus, any multi-compartment model will always be incomplete. In this work, our main goal is to use ensemble modeling as an investigative tool of a neuron's biophysical balances, where the cycling between experiment and model is a design criterion from the start. We consider oriens-lacunosum/moleculare (O-LM) interneurons, a prominent interneuron subtype that plays an essential gating role of information flow in hippocampus. O-LM cells express the hyperpolarization-activated current (I h). Although dendritic I h could have a major influence on the integrative properties of O-LM cells, the compartmental distribution of I h on O-LM dendrites is not known. Using a high-performance computing cluster, we generated a database of models that included those with or without dendritic I h. A range of conductance values for nine different conductance types were used, and different morphologies explored. Models were quantified and ranked based on minimal error compared to a dataset of O-LM cell electrophysiological properties. Co-regulatory balances between conductances were revealed, two of which were dependent on the presence of dendritic I h. These findings inform future experiments that differentiate between somatic and dendritic I h, thereby continuing a cycle between model and experiment.

Computational models of O-LM cells are recruited by low or high theta frequency inputs depending on h-channel distributions

“…One curve shown per model, with different colours for H distributions. ( B ) Sample output traces of one of each morphology and dendritic H distribution, using the time constant of activation of I h , specific membrane resistivity ( R m ), and specific membrane capacitance ( C m ) from the original database from Sekulić et al (2014) (black) as well as optimized values for these parameters used in the current work (orange). DOI: http://dx.doi.org/10.7554/eLife.22962.006

10.7554/eLife.22962.007Figure 1—figure supplement 2.Synaptic parameters for models.( A ) Sample range of varied values for inhibitory and excitatory synaptic conductances (x,y-axes) for an example model with somatic H and morphology 1 (left) and somatodendritic H and morphology 2 (right), resulting in differences in firing rates (z-axis). Heat map corresponds to firing frequency (Hz).

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

“…In doing this, we were able to show that our OLM cell models best matched the experimental data if h-channels are present in the dendrites. Interestingly, while the total h-channel conductance ranged from 2.2-4.2 nS in the three cells that were fully analyzed ( Table 4 ), the conductance density in each of the three cells is about 0.1 pS/ μ m 2 , which is the value found in highly ranked OLM cell models from our previously developed model databases ( Sekulić et al, 2014 ; Sekulić and Skinner, 2017 ). Zemankovics et al (2010) obtained total conductance values averaging approximately 4 nS, which are near the upper limit of our measurements.…”

“…This conceptualization states from the outset that the goal of modelling is not to find optimal or realistic models per se, but rather to develop models in such a way that a specific physiological question is raised and can lead to experimental examinations. In our initial studies, we asked the question of whether OLM cells expressed h-channels in their dendrites and thus built OLM cell model databases that either did or did not have h-channels in their dendrites ( Sekulić et al, 2014 ). The most relevant aspect of this approach in terms of answering the question of whether models are realistic or not is the recognition that the process is cyclical.…”

“…A more desirable approach is to develop multiple models to capture the underlying biological variability ( Marder and Taylor, 2011 ). Indeed, such populations of models representing a given cell type have been developed to examine, for example, co-regulations between different conductances that might exist in a given cell type ( Hay et al, 2011 ; Sekulić et al, 2014 ; Soofi et al, 2012 ). In this way, populations of models could help suggest what balance of conductances are important for cellular dynamics and their function in circuits.…”

“…From a functional perspective, the consequences of dendritic h-channel expression in OLM cells was explored in our previous computational study where h-channels were found to modulate the spiking preference of OLM cell models – incoming inhibitory inputs recruited either a higher or lower theta frequency (akin to Type 1 or Type 2 theta, respectively - Kramis et al (1975) ) depending on the presence or absence of dendritic h-channels ( Sekulić and Skinner, 2017 ). In that computational study, our OLM cell models were derived from previously built populations of OLM cell multi-compartment models in which appropriate OLM cell models were found with h-channels present either in the soma only or uniformly distributed in the soma and dendrites ( Sekulić et al, 2014 ). We had previously leveraged these models and showed that appropriate OLM cell model output could be maintained, even if h-channel conductance densities and distributions co-vary, so long as total membrane conductance due to h-channels is conserved ( Sekulić et al, 2015 ) – a finding that was also demonstrated in cerebellar Purkinje neurons ( Angelo et al, 2007 ).…”