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Automatic Construction of Predictive Neuron Models through Large Scale Assimilation of Electrophysiological Data

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ABSTRACT

We report on the construction of neuron models by assimilating electrophysiological data with large-scale constrained nonlinear optimization. The method implements interior point line parameter search to determine parameters from the responses to intracellular current injections of zebra finch HVC neurons. We incorporated these parameters into a nine ionic channel conductance model to obtain completed models which we then use to predict the state of the neuron under arbitrary current stimulation. Each model was validated by successfully predicting the dynamics of the membrane potential induced by 20–50 different current protocols. The dispersion of parameters extracted from different assimilation windows was studied. Differences in constraints from current protocols, stochastic variability in neuron output, and noise behave as a residual temperature which broadens the global minimum of the objective function to an ellipsoid domain whose principal axes follow an exponentially decaying distribution. The maximum likelihood expectation of extracted parameters was found to provide an excellent approximation of the global minimum and yields highly consistent kinetics for both neurons studied. Large scale assimilation absorbs the intrinsic variability of electrophysiological data over wide assimilation windows. It builds models in an automatic manner treating all data as equal quantities and requiring minimal additional insight.

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Experimental and theoretical voltage output by Neuron 1 under stimulation by longer current steps.A depolarizing current step is applied between 100 ms and 300 ms. Its amplitude increases from 50 pA (Epoch 5) to 130 pA (Epoch 9) in steps of 20 pA. A constant hyperpolarizing current of −80 pA is applied between 500 ms and 700 ms in all epochs. The predicted voltage (right column) is obtained by integrating the 5 current protocols with the completed model of N1.
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f4: Experimental and theoretical voltage output by Neuron 1 under stimulation by longer current steps.A depolarizing current step is applied between 100 ms and 300 ms. Its amplitude increases from 50 pA (Epoch 5) to 130 pA (Epoch 9) in steps of 20 pA. A constant hyperpolarizing current of −80 pA is applied between 500 ms and 700 ms in all epochs. The predicted voltage (right column) is obtained by integrating the 5 current protocols with the completed model of N1.

Mentions: We then tested the model ability to predict the excitatory response hence the current threshold of a neuron. The experiment was performed by applying a depolarizing current step of 200 ms duration followed by a hyperpolarizing step (Fig. 4). The amplitude of the depolarizing current was increased through the threshold of the neuron in steps of 20 pA (Panels (a)–(e)). Predictions were made by forward integrating the experimental current protocols of panels (a)–(e) with the completed model of N1. The predicted output in each case is plotted in panels (f)–(j). The model describes the main features of the excitatory response namely, the increase in firing frequency with increasing current stimulation, the correct number spikes per burst (±1 spike), the decay in spike amplitude and widening of inter-spike intervals. The model exaggerates the rebound of the membrane voltage after the release of hyperpolarization. These results show that a single assimilation protocol (Fig. 2) is sufficient to evaluate the firing threshold to a good degree of accuracy: 50 ± 5 pA. Spike bursts evoked by long current steps are difficult to validate through direct comparison with experiment in the manner of Figs 2 and 3 because of the poor reproducibility of real neurons under tonic stimulation3940.


Automatic Construction of Predictive Neuron Models through Large Scale Assimilation of Electrophysiological Data
Experimental and theoretical voltage output by Neuron 1 under stimulation by longer current steps.A depolarizing current step is applied between 100 ms and 300 ms. Its amplitude increases from 50 pA (Epoch 5) to 130 pA (Epoch 9) in steps of 20 pA. A constant hyperpolarizing current of −80 pA is applied between 500 ms and 700 ms in all epochs. The predicted voltage (right column) is obtained by integrating the 5 current protocols with the completed model of N1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5015021&req=5

f4: Experimental and theoretical voltage output by Neuron 1 under stimulation by longer current steps.A depolarizing current step is applied between 100 ms and 300 ms. Its amplitude increases from 50 pA (Epoch 5) to 130 pA (Epoch 9) in steps of 20 pA. A constant hyperpolarizing current of −80 pA is applied between 500 ms and 700 ms in all epochs. The predicted voltage (right column) is obtained by integrating the 5 current protocols with the completed model of N1.
Mentions: We then tested the model ability to predict the excitatory response hence the current threshold of a neuron. The experiment was performed by applying a depolarizing current step of 200 ms duration followed by a hyperpolarizing step (Fig. 4). The amplitude of the depolarizing current was increased through the threshold of the neuron in steps of 20 pA (Panels (a)–(e)). Predictions were made by forward integrating the experimental current protocols of panels (a)–(e) with the completed model of N1. The predicted output in each case is plotted in panels (f)–(j). The model describes the main features of the excitatory response namely, the increase in firing frequency with increasing current stimulation, the correct number spikes per burst (±1 spike), the decay in spike amplitude and widening of inter-spike intervals. The model exaggerates the rebound of the membrane voltage after the release of hyperpolarization. These results show that a single assimilation protocol (Fig. 2) is sufficient to evaluate the firing threshold to a good degree of accuracy: 50 ± 5 pA. Spike bursts evoked by long current steps are difficult to validate through direct comparison with experiment in the manner of Figs 2 and 3 because of the poor reproducibility of real neurons under tonic stimulation3940.

View Article: PubMed Central - PubMed

ABSTRACT

We report on the construction of neuron models by assimilating electrophysiological data with large-scale constrained nonlinear optimization. The method implements interior point line parameter search to determine parameters from the responses to intracellular current injections of zebra finch HVC neurons. We incorporated these parameters into a nine ionic channel conductance model to obtain completed models which we then use to predict the state of the neuron under arbitrary current stimulation. Each model was validated by successfully predicting the dynamics of the membrane potential induced by 20–50 different current protocols. The dispersion of parameters extracted from different assimilation windows was studied. Differences in constraints from current protocols, stochastic variability in neuron output, and noise behave as a residual temperature which broadens the global minimum of the objective function to an ellipsoid domain whose principal axes follow an exponentially decaying distribution. The maximum likelihood expectation of extracted parameters was found to provide an excellent approximation of the global minimum and yields highly consistent kinetics for both neurons studied. Large scale assimilation absorbs the intrinsic variability of electrophysiological data over wide assimilation windows. It builds models in an automatic manner treating all data as equal quantities and requiring minimal additional insight.

No MeSH data available.