Stochasticity and functionality of neural systems: Mathematical modelling of axon growth in the spinal cord of tadpole
Stochasticity and functionality of neural systems: Mathematical modelling of axon growth in the spinal cord of tadpole
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DOI：
10.1016/j.biosystems.2008.03.012
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发表时间：
2008-07-01
期刊：
影响因子：
1.6
通讯作者：
Roberts, Alan
中科院分区：
文献类型：
--
作者：
Borisyuk, Roman;Cooke, Tom;Roberts, Alan
本文研究了蝌蚪脊髓中轴突生长的一个简单数学模型。轴突的发展是由一个系统的三个差分方程（背腹和纵向坐标的生长锥和生长角）与随机组件。我们找到最佳的参数值，通过拟合模型的轴突实验测量的特性，并使用二次成本函数。拟合的模型在上升和下降方向上生成与实验测量的轴突相似的不同神经元类型的轴突。通过对轴突生长模型的研究，得到了轴突生长过程中背腹坐标变化和生长角度变化的动力学解析解。公式提供了条件的情况下，当增加的方差是有限的和饱和度的解析表达式。值得注意的是，最优参数始终满足方差增加有限的条件。考虑到实验数据的神经元细胞体分布沿着脊髓和背腹侧分布的树突，我们产生一个生物学上的整个蝌蚪脊髓的现实架构。对Morris-Lecar神经元模型的电生理特性的初步研究表明，该模型可以在很宽的参数值范围内产生与实验观察到的蝌蚪游泳模式活动相对应的电活动。(C)2008爱思唯尔爱尔兰有限公司保留所有权利。
In this paper we study a simple mathematical model of axon growth in the spinal cord of tadpole. Axon development is described by a system of three difference equations (the dorso-ventral and longitudinal coordinates of the growth cone and the growth angle) with stochastic components. We find optimal parameter values by fitting the model to experimentally measured characteristics of the axon and using the quadratic cost function. The fitted model generates axons for different neuron types in both ascending and descending directions which are similar to the experimentally measured axons. Studying the model of axon growth we have found the analytical solution for dynamics of the variance of the dorso-ventral coordinate and the variance of the growth angle. Formulas provide conditions for the case when the increase of the variance is limited and the analytical expression for the saturation level. It is remarkable that optimal parameters always satisfy the condition of limited variance increase. Taking into account experimental data on distribution of neuronal cell bodies along the spinal cord and dorso-ventral distribution of dendrites we generate a biologically realistic architecture of the whole tadpole spinal cord. Preliminary study of the electrophysiological properties of the model with Morris-Lecar neurons shows that the model can generate electrical activity corresponding to the experimentally observed swimming pattern activity of the tadpole in a broad range of parameter values. (C) 2008 Elsevier Ireland Ltd. All rights reserved.