A comparison of methods to determine neuronal phase-response curves

The phase-response curve (PRC) is an important tool to determine the excitability type of single neurons which reveals consequences for their synchronizing properties. We review five methods to compute the PRC from both model data and experimental data and compare the numerically obtained results from each method. The main difference between the methods lies in the reliability which is influenced by the fluctuations in the spiking data and the number of spikes available for analysis. We discuss the significance of our results and provide guidelines to choose the best method based on the available data.Comment: PDFLatex, 16 pages, 7 figures

Electrical Compartmentalization in Neurons

The dendritic tree of neurons plays an important role in information processing in the brain. While it is thought that dendrites require independent subunits to perform most of their computations, it is still not understood how they compartmentalize into functional subunits. Here, we show how these subunits can be deduced from the properties of dendrites. We devised a formalism that links the dendritic arborization to an impedance-based tree graph and show how the topology of this graph reveals independent subunits. This analysis reveals that cooperativity between synapses decreases slowly with increasing electrical separation and thus that few independent subunits coexist. We nevertheless find that balanced inputs or shunting inhibition can modify this topology and increase the number and size of the subunits in a context-dependent manner. We also find that this dynamic recompartmentalization can enable branch-specific learning of stimulus features. Analysis of dendritic patch-clamp recording experiments confirmed our theoretical predictions.Peer reviewe

An Inverse Approach for Elucidating Dendritic Function

We outline an inverse approach for investigating dendritic function–structure relationships by optimizing dendritic trees for a priori chosen computational functions. The inverse approach can be applied in two different ways. First, we can use it as a “hypothesis generator” in which we optimize dendrites for a function of general interest. The optimization yields an artificial dendrite that is subsequently compared to real neurons. This comparison potentially allows us to propose hypotheses about the function of real neurons. In this way, we investigated dendrites that optimally perform input-order detection. Second, we can use it as a “function confirmation” by optimizing dendrites for functions hypothesized to be performed by classes of neurons. If the optimized, artificial, dendrites resemble the dendrites of real neurons the artificial dendrites corroborate the hypothesized function of the real neuron. Moreover, properties of the artificial dendrites can lead to predictions about yet unmeasured properties. In this way, we investigated wide-field motion integration performed by the VS cells of the fly visual system. In outlining the inverse approach and two applications, we also elaborate on the nature of dendritic function. We furthermore discuss the role of optimality in assigning functions to dendrites and point out interesting future directions

A Sparse Reformulation of the Green's Function Formalism Allows Efficient Simulations of Morphological Neuron Models

We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green's function (GF) formalism can be rewritten to scale as O (n) with the number n of inputs locations, contrary to the previously reported O (n(2)) scaling. We show that the linear scaling can be combined with an expansion of the remaining kernels as sums of exponentials to allow efficient simulations of equations from the aforementioned class. We furthermore validate this simulation paradigm on models of nerve cells and explore its relation with more traditional finite difference approaches. Situations in which a gain in computational performance is expected are discussed.Peer reviewedFinal Accepted Versio