Using multi-compartment ensemble modeling as an investigative tool of spatially distributed biophysical balances: application to hippocampal oriens-lacunosum/moleculare (O-LM) cells.
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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 Ih.These findings inform future experiments that differentiate between somatic and dendritic Ih, thereby continuing a cycle between model and experiment.
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Affiliation: Toronto Western Research Institute, University Health Network, Toronto, Ontario, Canada; Department of Physiology, University of Toronto, Toronto, Ontario, Canada.
ABSTRACT
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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 (Ih). Although dendritic Ih could have a major influence on the integrative properties of O-LM cells, the compartmental distribution of Ih 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 Ih. 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 Ih. These findings inform future experiments that differentiate between somatic and dendritic Ih, thereby continuing a cycle between model and experiment. |
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Mentions: Once the general and restricted subsets of appropriate O-LM models were determined, we examined the conductance density space of the models in each subset (Fig. 1, Step 3). For this, we constructed conductance histogram plots (Figs. 4, 5). These plots consist of histograms of the number of models contained in each subset of appropriate O-LM models that possessed any combination of conductance density values for the two ion channel conductances being considered. In order to avoid having to consider a very large set of conductance histogram plots, we used clutter-based dimension reordering (CBDR), an algorithm for the visualization of high-dimensional data in two dimensions, as a way to constrain which conductances we considered [31]–[33]. We considered the conductance density values for all the ion channel conductances of our models as the dimensions of the space, and the distance as the value of any given point in the space. The CBDR algorithm then determined an ordering of the conductances where the resulting structure of the distance space was most sensitive to the high-order conductances, and least sensitive to the low-order conductances. That is, changes in high-order conductance density values would result in large changes in the distance value for models, whereas changes in low-order conductance density values would not result in appreciable changes in the distance values. We could thus eliminate the low-order conductances from further consideration, as they did not seem to affect the behaviour of the models as exercised by the particular depolarizing and hyperpolarizing current injection step protocols used. The high-order conductances were gNad, gKA, gh, gKdrf, and gKdrs, whereas the low-order conductances were gNas, gM, gAHP, gCaL, and gCaT. We proceeded to compute the conductance histogram plots for all pairwise combinations of the high-order conductances as determined by CBDR analysis, in addition to one conductance that straddled the boundary between high- and low-order conductances, gAHP, that provided a check. The gAHP conductance did not interact with any of the higher-order conductances, which served as confirmation that it, and all lower-order conductances, could be discounted from further analysis. We found three resulting categories of relationships between high-order conductances, similar to that found in previous work in an ensemble of model neurons of the crustacean stomatogastric ganglion network [34]. Using similar terminology, we found that conductances showed (1) no clear interaction, (2) a local peak or preference of conductance density values, or (3) a co-regulation. The first two cases were not deemed to be of interest in terms of uncovering putative conductance density balances. In the case of no clear interaction, any change in the maximum conductance density of one or the other conductance had no effect on the resulting models' goodness-of-fit as measured by the number of models contained within the general or restricted subsets of appropriate O-LM models and that possessed those conductance density values (Fig. 4A). For the second case of local preference, more models in the general or restricted subsets of appropriate O-LM models exhibited one particular combination of conductance density values, with tapering-off numbers of models exhibiting nearby combinations of conductance density values (Fig. 4B). In this case, although there was a clear preference for a particular value of one or both conductances, the two conductances did not interact in a meaningful way. The third category of relationships, that of co-ordinated regulation or co-regulatory balance, was demonstrated by the highly-ranked models exhibiting a distribution of pairwise conductances such that models with higher values of one conductance also had higher values of the other conductance. This is visually shown by a characteristic “ridge” in the conductance histogram plots of the two conductances in question (Fig. 5B,D,F). We elected not to do any formal statistical analysis of the co-regulations due to the sparseness of the data (3–5 maximal conductance considered) and also because the “ridge” can be clearly seen. Of all the examined pairwise combination of conductances, we only found three co-regulatory balances. Intriguingly, these three co-regulations were equally present in both the general as well as the restricted subsets of appropriate O-LM models. This indicated that the general subset, as determined by the general cut-off criterion using the difference of distance metric, was not too liberal in producing a set of models that best conformed to electrophysiological O-LM cell recordings. An example can be seen in Fig. 5A–B of two conductance histogram plots for the same two conductances, with one plot obtained from the general subset and the other from the restricted subset, and showing similar co-regulatory “ridges”. |
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Affiliation: Toronto Western Research Institute, University Health Network, Toronto, Ontario, Canada; Department of Physiology, University of Toronto, Toronto, Ontario, Canada.