Teka Wondimu W, Upadhyay Ranjit Kumar, Mondal Argha
UTSA Neurosciences Institute, The University of Texas at San Antonio, San Antonio, TX, USA.
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, India.
Neural Netw. 2017 Sep;93:110-125. doi: 10.1016/j.neunet.2017.05.007. Epub 2017 May 17.
Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF) model. Models with fractional (non-integer) order differentiation that generalize power law dynamics can be used to describe complex temporal voltage dynamics. The main characteristic of FLIF model is that it depends on all past values of the voltage that causes long-term memory. The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing.
锥体神经元产生不同的放电模式来处理信息、相互通信并转换信息。这些放电模式具有复杂且多时间尺度的动力学特性，已通过分数阶漏电积分发放（FLIF）模型进行了描述。具有分数（非整数）阶微分的模型，可推广幂律动力学，可用于描述复杂的时间电压动力学。FLIF模型的主要特征是它依赖于导致长期记忆的电压的所有过去值。该模型产生具有高脉冲间隔变异性的尖峰，并显示出几种放电特性，如向上的脉冲频率适应性和对恒定刺激的长脉冲潜伏期。我们表明，当分数阶α从1减小到较小值时，分数阶模型的阈下电压和放电率会从指数动力学转变为幂律动力学。放电率显示出由初始值变化引起的不同类型的脉冲时间适应性。我们还表明，电压记忆痕迹和分数系数是这些不同类型放电特性的原因。代表长期记忆的电压记忆痕迹具有反馈调节机制，并影响放电活动。结果表明，分数阶模型可能适用于理解多时间尺度的神经元动力学。总体而言，具有分数动力学的神经元表现出依赖历史的活动，这对于有效的信息处理可能非常有用且强大。
