Keren, Naomi, Noam Peled, and Alon Korngreen. Constraining compartmental models using multiple voltage recordings and genetic algorithms. J Neurophysiol 94: 3730 -3742, 2005. First published August 10, 2005; doi:10.1152/jn.00408.2005. Compartmental models with many nonlinearly and nonhomogeneous distributions of voltagegated conductances are routinely used to investigate the physiology of complex neurons. However, the number of loosely constrained parameters makes manually constructing the desired model a daunting if not impossible task. Recently, progress has been made using automated parameter search methods, such as genetic algorithms (GAs). However, these methods have been applied to somatically recorded action potentials using relatively simple target functions. Using a genetic minimization algorithm and a reduced compartmental model based on a previously published model of layer 5 neocortical pyramidal neurons we compared the efficacy of five cost functions (based on the waveform of the membrane potential, the interspike interval, trajectory density, and their combinations) to constrain the model. When the model was constrained using somatic recordings only, a combined cost function was found to be the most effective. This combined cost function was then applied to investigate the contribution of dendritic and axonal recordings to the ability of the GA to constrain the model. The more recording locations from the dendrite and the axon that were added to the data set the better was the genetic minimization algorithm able to constrain the compartmental model. Based on these simulations we propose an experimental scheme that, in combination with a genetic minimization algorithm, may be used to constrain compartmental models of neurons. I N T R O D U C T I O NThe majority of synapses in the CNS connect to dendrites. These dendrites transform information received from synapses into a code that is then translated by the axon to action potentials (APs) that are transmitted to other neurons. The properties and functions of dendrites in the CNS have been intensively studied especially over the past decade (for reviews see Johnston 1999;Johnston et al. 2003;Migliore and Shepherd 2002;Stuart et al. 1999), mainly as a result of patch-clamp recordings from visually identified dendrites in brain slices (Stuart et al. 1993) and novel imaging techniques (Antic 2003;Antic et al. 1999;Denk et al. 1994;Lasser-Ross et al. 1991; Tsien 1989). Action potentials initiated at or near the soma actively back-propagate into the dendritic tree (Bischofberger and Jonas 1997;Chen et al. 1997Chen et al. , 2002Häusser et al. 1995;Spruston et al. 1995;Stuart and Sakmann 1994). Furthermore, dendrites generate complex regenerative Ca 2ϩ and Na ϩ spikes (Amitai et al. 1993;Antic 2003;Ariav et al. 2003;Bischofberger and Jonas 1997;Johnston et al. 1996Johnston et al. , 2003Magee et al. 1996Magee et al. , 1998Martina et al. 2000;Migliore and Shepherd 2002;Schiller et al. 1997;Zhu 2000), modulate synaptic potentials (Magee 1999;Magee and Johnsto...
Constructing physiologically relevant compartmental models of neurones is critical for understanding neuronal activity and function. We recently suggested that measurements from multiple locations along the soma, dendrites and axon are necessary as a data set when using a genetic optimization algorithm to constrain the parameters of a compartmental model of an entire neurone. However, recordings from L5 pyramidal neurones can routinely be performed simultaneously from only two locations. Now we show that a data set recorded from the soma and apical dendrite combined with a parameter peeling procedure is sufficient to constrain a compartmental model for the apical dendrite of L5 pyramidal neurones. The peeling procedure was tested on several compartmental models showing that it avoids local minima in parameter space. Based on the requirements of this analysis procedure, we designed and performed simultaneous whole-cell recordings from the soma and apical dendrite of rat L5 pyramidal neurones. The data set obtained from these recordings allowed constraining a simplified compartmental model for the apical dendrite of L5 pyramidal neurones containing four voltage-gated conductances. In agreement with experimental findings, the optimized model predicts that the conductance density gradients of voltage-gated K + conductances taper rapidly proximal to the soma, while the density gradient of the voltage-gated Na + conductance tapers slowly along the apical dendrite. The model reproduced the back-propagation of the action potential and the modulation of the resting membrane potential along the apical dendrite. Furthermore, the optimized model provided a mechanistic explanation for the back-propagation of the action potential into the apical dendrite and the generation of dendritic Na + spikes.
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