Fast and accurate low-dimensional reduction of biophysically detailed neuron models

Abstract

Realistic modeling of neurons are quite successful in complementing traditional experimental techniques. However, their networks require a computational power beyond the capabilities of current supercomputers, and the methods used so far to reduce their complexity do not take into account the key features of the cells nor critical physiological properties. Here we introduce a new, automatic and fast method to map realistic neurons into equivalent reduced models running up to > 40 times faster while maintaining a very high accuracy of the membrane potential dynamics during synaptic inputs, and a direct link with experimental observables. The mapping of arbitrary sets of synaptic inputs, without additional fine tuning, would also allow the convenient and efficient implementation of a new generation of large-scale simulations of brain regions reproducing the biological variability observed in real neurons, with unprecedented advances to understand higher brain functions.

Figure 1. A method to reduce the computational complexity of realistic models of neurons.

(a) (left) typical 3D reconstruction of a realistic hippocampal CA1 pyramidal neuron (cell c70863 from the neuromorpho.org public archive), composed by 843 membrane segments; red circles indicate synapses location; different colors for dendrites highlight the different clusters used for this kind of cell population; (middle) Flow-chart illustrating the main steps to reduce a morphologically and biophysically detailed neuron model into a reduced, but functionally equivalent, version; (right) schematic representation of the equivalent model (27 membrane segments) obtained after application of the reduction method. (b) Somatic membrane potential of the full (black traces) and the reduced (red traces) model during a simulation activating 140 (left) or 420 (right) synapses. (c) (left) Average (n = 10, ±sd) number of APs elicited in 500 ms long simulations as a function of the number of synaptic inputs activated in the original (black) or in the reduced (red) model; the two curves are statistically indistinguishable (Wilcoxon Signed Rank test, p = 0.879); (right) normalized InterSpike Interval (ISI) distribution, from 10 simulations of the original (black) or the reduced (red) model during a simulation activating 140 synapses; the two curves are statistically indistinguishable (Wilcoxon Signed Rank Sum test, p = 0.626).

Figure 2. The method is accurate and robust to fluctuations of model parameters.

(a) Schematic representation of accuracy calculation in a typical case (cell cd1152); somatic traces obtained from simulations of the full (black) and reduced (red) model were scanned to test for mismatch of spikes or silent periods occurring within a variable time window (see Methods); light green: True Positive; dark green: True Negative; light pink: False Positive; dark pink: False Negative; Accuracy = 0.9; (b) accuracy of the reduced model for cell c70863 as a function of the number of active synaptic inputs using the original set of the full model parameters (black), and average accuracy (n = 10) for ±25% or ±20% random fluctuations in peak channels conductance (red) or in the critical input max Stim (blue), respectively.

Figure 3. The method is accurate for different morphologies.

(a) Average accuracy (n = 17, ±sd) obtained for the reduced models of all morphologies as a function of the number of active synaptic inputs; (b) average accuracy for the reduced model of each morphology, from 260 simulations using a different number of synaptic inputs with random spatial redistribution, activation times, and peak conductance; (c) average accuracy for 10, 140, and 340 synaptic inputs as a function of the simulation length; in all cases, α = 0.35 and τ = 10 ms; (d) average accuracy (n = 170) obtained for the reduced models of all morphologies from 500 ms long simulations with 10, 140, and 340 synaptic inputs as a function of τ (black plots, α = 0.35), and as a function of α (gray plots, τ = 10 ms).

Figure 4. The method greatly reduces the run time.

(black) Average runtime for a 500 ms simulation, as a function of the number of active synaptic inputs (α = 0.35, τ = 10 ms), for the original models (circles) and their reduced version (triangles). (gray) Average run time reduction (error bars represent 95% confidence interval).