神经电生理数学模型-- Hodgkin-Huxley方程

神经细胞各个部分在信息传递中的作用
The neuron’s cell body is connected to a number of branches called dendrites（树突）and long tube called the axon（轴突） that connects the cell body to the presynaptic terminals (synapse 突触).
e.g.
（V－VNa）是钠离子通过细胞膜钠离子通道的驱动力。 （V－Vk） 是钾离子通过细胞膜钾离子通道的驱动力。
神经细胞膜内外不同的离子浓度
Neurons, like all living cells, are surrounded（包围） by a plasma membrane that is impermeable （不可渗透 ）to ions. This property allows a neuron to maintain different concentrations of ions between the inside and outside of the cell.
➢ 在这两种方向相反的作用下达到平衡时，没有离子通过细胞膜； ➢ 达到平衡状态时，细胞膜内外的电位差称为该类离子的Nernst电位V*； ➢ 不同类离子的Nernst电位不同。
离子通过离子通道的驱动力
设：细胞的膜电位为V， 某个离子的Nernst电位为V*；
那么 （V－V*）是这种离子通过该离子通道的驱动力。
神经细胞膜的构成和离子跨膜扩散
The plasma membrane is composed of a lipid bilayer (脂类层 ). Its hydrophobic （疏水）nature prevents the diffusion of ions across the membrane.
Biblioteka Baidu
神经细胞膜静息：大部分通道关闭部分钾离子通道开启
When a neuron is at rest, most ion channels are closed. However, some potassium channels (blue) are open, permitting potassium ions to diffuse out of the cell down their concentration gradient. Note that sodium channels are normally closed, and thus sodium ions cannot cross the membrane when the neuron is at rest.
9.1 动作电位产生和传导的神经生物学机制
9.1.1 神经细胞与神经信息传递 9.1.2 神经细胞膜的离子通道特性 9.1.3 动作电位与神经细胞膜离子通道特性
9.1.1 神经细胞与神经信息传递
神经细胞
soma 胞体 synapse 突触 dendrite 树突 Axon 轴突
Diagram of typical neuron
Background
前言
应用数学方法建立神经元膜上动作电位产生和在传导的模型。
Hodgkin and Huxley Model was published in 1952 described a series of experiments that allowed the development of a model of the action potential. This work was awarded a Nobel Prize in 1963.
Dendrites are the receptive surfaces of the neuron that receive signals from thousands of other neurons;
The single axon is served as an transmission line to move information from one neuron to anothers.
神经细胞膜内外不同的钾离子浓度、钠离子浓度
In a typical mammalian neuron, there is a large difference in the concentration of ions, such as sodium (Na+) and potassium (K+), between the intracellular and the extracellular environments. In addition, the interior of the neuron has a high concentration of large negatively charged proteins.
9.1.2 神经细胞膜的离子通道特性
神经细胞膜电活动
细胞膜把细胞内外分隔，细胞膜两侧的离子成分和浓度不同： 细胞内 — 正离子：主要是钾离子 负离子：有机小分子 细胞外 — 正离子：主要是钠离子 负离子：氯离子
由于细胞内外离子的浓度差， 某一种离子要从高浓度侧向低 浓度侧扩散。
平衡
由于离子带电，扩散到另一侧的 离子积累起来的电荷排斥将扩散 过来的带有同一类电荷的离子。
神经细胞膜上不同类的离子通道
The only way ions can move across the lipid bilayer is by passing through specialized channels. These channels are transmembrane pores that permit the movement of particular ions while excluding others. Such channels can be in an open or closed state.
Giant axon of squid
Partial Differential Equation (PDE): function of time and length Ordinary Differential Equation (ODE): function of time
Neural system is consisted of millions of neurons（1012）, neuron is the basic unit of the neural system.