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P63: Morphological determinants of neuronal dynamics and function
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**Christoph Kirch**, **Leonardo Gollo**

Neurons use their complex dendritic tree to integrate complex spatio-temporal patterns of incoming signals. The nonlinear interactions of spikes along the bifurcating branches allows the neuron to perform dendritic computations [1]. While models often aim to realistically simulate the complicated chemical properties of these signals, they often do this at the cost of simplifying the spatial structure to one (e.g., Hodgkin Huxley, integrate-and-fire) [2] or few compartments [3]. These simplified structures do not accurately represent the morphology, and thus it is not possible to infer how the dendritic structure can shape a neuron’s output.

Here, we used detailed neuron reconstructions from the online database NeuroMorpho.Org [4]. Each neuron is made up of one somatic compartment and up to 10,000 dendritic compartments. By treating these compartments as an excitable network [5, 6], we could apply a simple discrete model of dendritic spike propagation to investigate how the morphology affects the firing behavior of a neuron.

Our approach allows for a detailed analysis of the neuron’s dendritic activity pattern. For example, we can generate spatial heatmaps of firing rate, revealing a significant spatial dependence of dynamics. By comparing the compartmental activity for different strengths of external stimulus, we can investigate the dynamic range – over what range of input strength a compartment’s firing rate is varied the most. We find that dendritic bifurcations boost the local dynamic range. Thus, a soma located in densely bifurcated regions tends to have large dynamic ranges.

Identifying how effectively a neuron utilizes its dendritic tree to amplify stimuli can be achieved by comparing the average dendritic compartment activity against how often the soma fires. Since it takes energy to control the ion channels responsible for dendritic spikes, we call this ratio the relative energy consumption of the neuron. If it is 1, the neuron is inefficient. We identified two morphological features – the number of somatic branches, and the centrality of the soma – that can be used to categorize the energy behavior of neurons (Fig. 1).

The classification scheme we have proposed provides an important testable basis in explaining structural differences across neurons. For example, depending on the required computational function, certain features of the dendritic tree would be more favorable. Our model can be applied to any of the 100,000+ reconstructions available at NeuroMorpho.Org, and can be extended to investigate the effect of changes in dendritic structure.

**References**

1\. London, M. and M. Häusser, Dendritic computation. Annu. Rev. Neurosci., 2005. 28: p. 503-532.

2\. Izhikevich, E.M., Simple model of spiking neurons. IEEE Transactions on neural networks, 2003. 14(6): p. 1569-1572.

3\. Izhikevich, E.M., Dynamical systems in neuroscience. 2007: MIT press.

4\. Kirch, C. and L.L. Gollo, Spatially resolved dendritic integration: Towards a functional classification of neurons. bioRxiv, 2019: p. 657403.

5\. Gollo, L.L., O. Kinouchi, and M. Copelli, Active dendrites enhance neuronal dynamic range. PLoS computational biology, 2009. 5(6): p. e1000402.

6\. Gollo, L.L., O. Kinouchi, and M. Copelli, Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation. Physical Review E, 2012. 85(1): p. 011911.

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Neurons use their complex dendritic tree to integrate complex spatio-temporal patterns of incoming signals. The nonlinear interactions of spikes along the bifurcating branches allows the neuron to perform dendritic computations [1]. While models often aim to realistically simulate the complicated chemical properties of these signals, they often do this at the cost of simplifying the spatial structure to one (e.g., Hodgkin Huxley, integrate-and-fire) [2] or few compartments [3]. These simplified structures do not accurately represent the morphology, and thus it is not possible to infer how the dendritic structure can shape a neuron’s output.

Here, we used detailed neuron reconstructions from the online database NeuroMorpho.Org [4]. Each neuron is made up of one somatic compartment and up to 10,000 dendritic compartments. By treating these compartments as an excitable network [5, 6], we could apply a simple discrete model of dendritic spike propagation to investigate how the morphology affects the firing behavior of a neuron.

Our approach allows for a detailed analysis of the neuron’s dendritic activity pattern. For example, we can generate spatial heatmaps of firing rate, revealing a significant spatial dependence of dynamics. By comparing the compartmental activity for different strengths of external stimulus, we can investigate the dynamic range – over what range of input strength a compartment’s firing rate is varied the most. We find that dendritic bifurcations boost the local dynamic range. Thus, a soma located in densely bifurcated regions tends to have large dynamic ranges.

Identifying how effectively a neuron utilizes its dendritic tree to amplify stimuli can be achieved by comparing the average dendritic compartment activity against how often the soma fires. Since it takes energy to control the ion channels responsible for dendritic spikes, we call this ratio the relative energy consumption of the neuron. If it is 1, the neuron is inefficient. We identified two morphological features – the number of somatic branches, and the centrality of the soma – that can be used to categorize the energy behavior of neurons (Fig. 1).

The classification scheme we have proposed provides an important testable basis in explaining structural differences across neurons. For example, depending on the required computational function, certain features of the dendritic tree would be more favorable. Our model can be applied to any of the 100,000+ reconstructions available at NeuroMorpho.Org, and can be extended to investigate the effect of changes in dendritic structure.

1\. London, M. and M. Häusser, Dendritic computation. Annu. Rev. Neurosci., 2005. 28: p. 503-532.

2\. Izhikevich, E.M., Simple model of spiking neurons. IEEE Transactions on neural networks, 2003. 14(6): p. 1569-1572.

3\. Izhikevich, E.M., Dynamical systems in neuroscience. 2007: MIT press.

4\. Kirch, C. and L.L. Gollo, Spatially resolved dendritic integration: Towards a functional classification of neurons. bioRxiv, 2019: p. 657403.

5\. Gollo, L.L., O. Kinouchi, and M. Copelli, Active dendrites enhance neuronal dynamic range. PLoS computational biology, 2009. 5(6): p. e1000402.

6\. Gollo, L.L., O. Kinouchi, and M. Copelli, Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation. Physical Review E, 2012. 85(1): p. 011911.

Monday July 20, 2020 7:00pm - 8:00pm CEST

Slot 05

Slot 05