# MathSciDoc: An Archive for Mathematician ∫

#### Data Analysis, Bio-Statistics, Bio-Mathematicsmathscidoc:2104.42004

Proceedings of the National Academy of Sciences of the United States of America, 116, (30), 15244-15252, 2019.7
Complex dendrites in general present formidable challenges to understanding neuronal information processing. To circumvent the difficulty, a prevalent viewpoint simplifies the neuronal morphology as a point representing the soma, and the excitatory and inhibitory synaptic currents originated from the dendrites are treated as linearly summed at the soma. Despite its extensive applications, the validity of the synaptic current description remains unclear, and the existing point neuron framework fails to characterize the spatiotemporal aspects of dendritic integration supporting specific computations. Using electrophysiological experiments, realistic neuronal simulations, and theoretical analyses, we demonstrate that the traditional assumption of linear summation of synaptic currents is oversimplified and underestimates the inhibition effect. We then derive a form of synaptic integration current within the point neuron framework to capture dendritic effects. In the derived form, the interaction between each pair of synaptic inputs on the dendrites can be reliably parameterized by a single coefficient, suggesting the inherent low-dimensional structure of dendritic integration. We further generalize the form of synaptic integration current to capture the spatiotemporal interactions among multiple synaptic inputs and show that a point neuron model with the synaptic integration current incorporated possesses the computational ability of a spatial neuron with dendrites, including direction selectivity, coincidence detection, logical operation, and a bilinear dendritic integration rule discovered in experiment. Our work amends the modeling of synaptic inputs and improves the computational power of a modeling neuron within the point neuron framework.
mathematical neuroscience, model reduction, effective model, dendritic computation
• Using applied math approaches including mathematical analysis and scientific computing, our work first demonstrates that the modeling of synaptic input currents in traditional point neuron models is incorrect, despite that these models have been widely used in the mathematical neuroscience field for decades. We then mathematically derived a novel form of point neuron model that is able to characterize synaptic inputs thereby nonlinear dendritic computations performed by a neuron. Importantly, our derived model based on math analysis has been successfully verified in electrophysiological experiments. Therefore, our work provides a nice illustration of the type of role that applied math can play in modern neuroscience. Our work has been reported as important research progress by national natural science fondation of China.
```@inproceedings{songting2019dendritic,
title={Dendritic computations captured by an effective point neuron model},
author={Songting Li, Nan Liu, Xiaohui Zhang, David McLaughlin, Douglas Zhou, and David Cai},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210407172744400801780},
booktitle={Proceedings of the National Academy of Sciences of the United States of America},
volume={116},
number={30},
pages={15244-15252},
year={2019},
}
```
Songting Li, Nan Liu, Xiaohui Zhang, David McLaughlin, Douglas Zhou, and David Cai. Dendritic computations captured by an effective point neuron model. 2019. Vol. 116. In Proceedings of the National Academy of Sciences of the United States of America. pp.15244-15252. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210407172744400801780.