Comparison of alternative designs for reducing complex neurons to equivalent cables

Automated evolutionary optimization of ion channel conductances and kinetics in models of young and aged rhesus monkey pyramidal neurons

Conductance-based compartment modeling requires tuning of many parameters to fit the neuron model to target electrophysiological data. Automated parameter optimization via evolutionary algorithms (EAs) is a common approach to accomplish this task, using error functions to quantify differences between model and target. We present a three-stage EA optimization protocol for tuning ion channel conductances and kinetics in a generic neuron model with minimal manual intervention. We use the technique of Latin hypercube sampling in a new way, to choose weights for error functions automatically so that each function influences the parameter search to a similar degree. This protocol requires no specialized physiological data collection and is applicable to commonly-collected current clamp data and either single- or multi-objective optimization. We applied the protocol to two representative pyramidal neurons from layer 3 of the prefrontal cortex of rhesus monkeys, in which action potential firing rates are significantly higher in aged compared to young animals. Using an idealized dendritic topology and models with either 4 or 8 ion channels (10 or 23 free parameters respectively), we produced populations of parameter combinations fitting the target datasets in less than 80 hours of optimization each. Passive parameter differences between young and aged models were consistent with our prior results using simpler models and hand tuning. We analyzed parameter values among fits to a single neuron to facilitate refinement of the underlying model, and across fits to multiple neurons to show how our protocol will lead to predictions of parameter differences with aging in these neurons.

Influence of asymmetric attenuation of single and paired dendritic inputs on summation of synaptic potentials and initiation of action potentials

Previous studies revealed mechanisms of dendritic inputs leading to action potential initiation at the axon initial segment and backpropagation into the dendritic tree. This interest has recently expanded toward the communication between different parts of the dendritic tree which could preprocess information before reaching the soma. This study tested for effects of asymmetric voltage attenuation between different sites in the dendritic tree on summation of synaptic inputs and action potential initiation using the NEURON simulation environment. Passive responses due to the electrical equivalent circuit of the three-dimensional neuron architecture with leak channels were examined first, followed by the responses after adding voltage-gated channels and finally synaptic noise. Asymmetric attenuation of voltage, which is a function of asymmetric input resistance, was seen between all pairs of dendritic sites but the transfer voltages (voltage recorded at the opposite site from stimulation among a pair of dendritic sites) were equal and also summed linearly with local voltage responses during simultaneous stimulation of both sites. In neurons with voltage-gated channels, we reproduced the observations where a brief stimulus to the proximal ascending dendritic branch of a pyramidal cell triggers a local action potential but a long stimulus triggers a somal action potential. Combined stimulation of a pair of sites in this proximal dendrite did not alter this pattern. The attraction of the action potential onset toward the soma with a long stimulus in the absence of noise was due to the higher density of voltage-gated sodium channels at the axon initial segment. This attraction was, however, negligible at the most remote distal dendritic sites and was replaced by an effect due to high input resistance. Action potential onset occurred at the dendritic site of higher input resistance among a pair of remote dendritic sites, irrespective of which of these two sites received the synaptic input. Exploration of the parameter space showed how the gradient of voltage-gated channel densities and input resistances along a dendrite could draw the action potential onset away from the stimulation site. The attraction of action potential onset toward the higher density of voltage-gated channels in the soma during stimulation of the proximal dendrite was, however, reduced after the addition of synaptic noise.

The sodium-potassium pump controls the intrinsic firing of the cerebellar Purkinje neuron

In vitro, cerebellar Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting, and quiescence. The bimodal pattern consists of tonic spiking and quiescence. It is unclear how these firing patterns are generated and what determines which firing pattern is selected. We have constructed a realistic biophysical Purkinje cell model that can replicate these patterns. In this model, Na(+)/K(+) pump activity sets the Purkinje cell's operating mode. From rat cerebellar slices we present Purkinje whole cell recordings in the presence of ouabain, which irreversibly blocks the Na(+)/K(+) pump. The model can replicate these recordings. We propose that Na(+)/K(+) pump activity controls the intrinsic firing mode of cerbellar Purkinje cells.

The capabilities and limitations of conductance-based compartmental neuron models with reduced branched or unbranched morphologies and active dendrites

Conductance-based neuron models are frequently employed to study the dynamics of biological neural networks. For speed and ease of use, these models are often reduced in morphological complexity. Simplified dendritic branching structures may process inputs differently than full branching structures, however, and could thereby fail to reproduce important aspects of biological neural processing. It is not yet well understood which processing capabilities require detailed branching structures. Therefore, we analyzed the processing capabilities of full or partially branched reduced models. These models were created by collapsing the dendritic tree of a full morphological model of a globus pallidus (GP) neuron while preserving its total surface area and electrotonic length, as well as its passive and active parameters. Dendritic trees were either collapsed into single cables (unbranched models) or the full complement of branch points was preserved (branched models). Both reduction strategies allowed us to compare dynamics between all models using the same channel density settings. Full model responses to somatic inputs were generally preserved by both types of reduced model while dendritic input responses could be more closely preserved by branched than unbranched reduced models. However, features strongly influenced by local dendritic input resistance, such as active dendritic sodium spike generation and propagation, could not be accurately reproduced by any reduced model. Based on our analyses, we suggest that there are intrinsic differences in processing capabilities between unbranched and branched models. We also indicate suitable applications for different levels of reduction, including fast searches of full model parameter space.

Quantitative morphometry of electrophysiologically identified CA3b interneurons reveals robust local geometry and distinct cell classes

The morphological and electrophysiological diversity of inhibitory cells in hippocampal area CA3 may underlie specific computational roles and is not yet fully elucidated. In particular, interneurons with somata in strata radiatum (R) and lacunosum-moleculare (L-M) receive converging stimulation from the dentate gyrus and entorhinal cortex as well as within CA3. Although these cells express different forms of synaptic plasticity, their axonal trees and connectivity are still largely unknown. We investigated the branching and spatial patterns, plus the membrane and synaptic properties, of rat CA3b R and L-M interneurons digitally reconstructed after intracellular labeling. We found considerable variability within but no difference between the two layers, and no correlation between morphological and biophysical properties. Nevertheless, two cell types were identified based on the number of dendritic bifurcations, with significantly different anatomical and electrophysiological features. Axons generally branched an order of magnitude more than dendrites. However, interneurons on both sides of the R/L-M boundary revealed surprisingly modular axodendritic arborizations with consistently uniform local branch geometry. Both axons and dendrites followed a lamellar organization, and axons displayed a spatial preference toward the fissure. Moreover, only a small fraction of the axonal arbor extended to the outer portion of the invaded volume, and tended to return toward the proximal region. In contrast, dendritic trees demonstrated more limited but isotropic volume occupancy. These results suggest a role of predominantly local feedforward and lateral inhibitory control for both R and L-M interneurons. Such a role may be essential to balance the extensive recurrent excitation of area CA3 underlying hippocampal autoassociative memory function.

The electrotonic structure of pyramidal neurons contributing to prefrontal cortical circuits in macaque monkeys is significantly altered in aging

Whereas neuronal numbers are largely preserved in normal aging, subtle morphological changes occur in dendrites and spines, whose electrotonic consequences remain unexplored. We examined age-related morphological alterations in 2 types of pyramidal neurons contributing to working memory circuits in the macaque prefrontal cortex (PFC): neurons in the superior temporal cortex forming "long" projections to the PFC and "local" projection neurons within the PFC. Global dendritic mass homeostasis, measured by 3-dimensional scaling analysis, was conserved with aging in both neuron types. Spine densities, dendrite diameters, lengths, and branching complexity were all significantly reduced in apical dendrites of long projection neurons with aging, but only spine parameters were altered in local projection neurons. Despite these differences, voltage attenuation due to passive electrotonic structure, assuming equivalent cable parameters, was significantly reduced with aging in the apical dendrites of both neuron classes. Confirming the electrotonic analysis, simulated passive backpropagating action potential efficacy was significantly higher in apical but not basal dendrites of old neurons. Unless compensated by changes in passive cable parameters, active membrane properties, or altered synaptic properties, these effects will increase the excitability of pyramidal neurons, compromising the precisely tuned activity required for working memory, ultimately resulting in age-related PFC dysfunction.

Creation and reduction of a morphologically detailed model of a leech heart interneuron

Conductance-based neuron models aid in understanding the role intrinsic and synaptic currents play in producing neuronal activity. Incorporating morphological detail into a model allows for additional analysis of nonhomogeneous distributions of active and synaptic conductances, as well as spatial segregation of electrical events. We developed a morphologically detailed "Full Model" of a leech heart interneuron that replicates reasonably well intracellular recordings from these interneurons. However, it constitutes hundreds of compartments, each increasing parameter space and simulation time. To reduce the number of compartments of the Full Model, while preserving conductance densities and distributions, its compartments were grouped into functional groups that each share identical conductance densities. Each functional group was sequentially reduced to one or two compartments, preserving surface area, conductance densities, and its contribution to input resistance. As a result, the input resistance and membrane time constant were preserved. The axial resistances of several compartments were rescaled to match the amplitude of synaptic currents and low-threshold calcium currents and the shape of action potentials to those in the Full Model. This reduced model, with intrinsic conductances, matched the activity of the Full Model for a variety of simulated current-clamp and voltage-clamp data. Because surface area and conductance distribution of the functional groups of the Full Model were maintained, parameter changes introduced into the reduced model can be directly translated to the Full Model. Thus our computationally efficient reduced morphology model can be used as a tool for exploring the parameter space of the Full Model and in network simulations.

Rallian "equivalent" cylinders reconsidered: comparisons with literal compartments

In Rall's "equivalent" cylinder morphological-to-electrical transformation, neuronal arborizations are reduced to single unbranched core-conductors. The conventional assumption that such an "equivalent" reconstructs the electrical properties of the fibers it represents was tested directly; electrical properties and responses of "equivalent" cylinders were compared with those of their literal branch constituents for fibers with a single symmetrical bifurcation. The numerical solution methods were validated independently by their accurate reconstruction of the responses of an analog circuit configured with compartmental architecture to solve the cable equation for passive fibers with a symmetrical bifurcation. In passive fibers, "equivalent" cylinders misestimated the spatial distribution of voltage amplitudes and steady-state input resistance, partly due to the lack of axial current bifurcation. In active fibers with a single propagating action potential, the spatial distributions of point-to-point conduction velocity values (measured in meters/second) for a literal branch point differed significantly from those of their "equivalent" cylinders. "Equivalent" cylinders also underestimated the diameter-dependent delay in propagation through the branch point and branches, due to the larger "equivalent" diameter. Corrections to the "equivalent" cylinder did not reconcile differences between "equivalent" and literal models. However, "equivalent" and literal branch fibers had the same (a) steady-state resistance "looking into" an isolated symmetrical branch point and (b) geometry-independent point-to-point propagation velocity when measured in space constants per millisecond except within +/-1 space constant from the geometrical inhomogeneity. In summary, Rall's "equivalent" cylinders did not accurately reconstruct all passive or active electrophysiological properties and responses of their literal compartments. For the modeling of individual neurons, the requirement of single-branch resolution is discussed.

Developmental changes in spinal motoneuron dendrites in neonatal mice

We examined the age-dependent morphological changes of lumbar spinal motoneurons (MNs) in neonatal Swiss-Webster mice during the first 2 weeks of postnatal life. Neurons labeled by intracellular injection of biocytin in hemisected lumbosacral spinal cords in vitro were reconstructed from serial sections. Digitized data were compared for young (P3; postnatal days 2-4; n = 9) and older animals (P11; postnatal days 10-13; n = 8). As expected, measures of dendritic size (e.g., stem branch diameter, total surface area, maximum distance to tips, and lateral tree spread) were all significantly greater for P11 than for P3 mice. In contrast, the number of dendrites per MN and parameters related to tree topology (e.g., terminations per tree and maximum branch order), although slightly greater for P11 animals, were not significantly different between the two ages. Dendrite growth appeared to be proportional throughout the tree because the ratios between average terminal and internal branch lengths were similar for the two groups. Furthermore, this elongation was proportional to enlargement of overall spinal cord dimensions. A variety of other morphometric measures showed no significant difference between age groups. The relative constancy of MN dendritic topology up to P13 was surprising, given the striking maturation in motor function during this time period.