神經(jīng)電生理數(shù)學(xué)模型---Hodgkin-Huxley方程課件

1、n 應(yīng)用數(shù)學(xué)方法建立神經(jīng)元膜上動作電位產(chǎn)生和在傳導(dǎo)的模型應(yīng)用數(shù)學(xué)方法建立神經(jīng)元膜上動作電位產(chǎn)生和在傳導(dǎo)的模型。n Hodgkin and Huxley Model was published in 1952 described a series of experiments that allowed the development of a model of the action potential. n This work was awarded a Nobel Prize in 1963.n Partial Differential Equation (PDE): function of

2、time and length Ordinary Differential Equation (ODE): function of timen Neural system is consisted of millions of neurons（1012）, neuron is the basic unit of the neural system. 前言前言BackgroundGiant axon of squid 9.1 9.1 動作電位產(chǎn)生和傳導(dǎo)的神經(jīng)生物學(xué)機(jī)制動作電位產(chǎn)生和傳導(dǎo)的神經(jīng)生物學(xué)機(jī)制9.1.1 神經(jīng)細(xì)胞與神經(jīng)信息傳遞神經(jīng)細(xì)胞與神經(jīng)信息傳遞9.1.2 神經(jīng)細(xì)胞膜的離子通道特性神經(jīng)

3、細(xì)胞膜的離子通道特性9.1.3 動作電位與神經(jīng)細(xì)胞膜離子通道特性動作電位與神經(jīng)細(xì)胞膜離子通道特性9.1.1 神經(jīng)細(xì)胞與神經(jīng)信息傳遞神經(jīng)細(xì)胞與神經(jīng)信息傳遞nsoma 胞體胞體nsynapse 突觸突觸ndendrite 樹突樹突nAxon 軸突軸突Diagram of typical neuron神經(jīng)細(xì)胞神經(jīng)細(xì)胞神經(jīng)細(xì)胞各個(gè)部分在信息傳遞中的作用神經(jīng)細(xì)胞各個(gè)部分在信息傳遞中的作用nThe neurons cell body is connected to a number of branches The neurons cell body is connected to a number of

4、branches called dendritescalled dendrites（樹突）（樹突）and long tube called the axonand long tube called the axon（軸突）軸突）that connects the cell body to the presynapticthat connects the cell body to the presynaptic terminals (synapse terminals (synapse 突觸突觸). ). nDendrites are the receptive surfaces of the

5、neuron that receive Dendrites are the receptive surfaces of the neuron that receive signals from thousands of other neurons; signals from thousands of other neurons; nThe single axon is served as an transmission line to move The single axon is served as an transmission line to move information from

6、one neuron to anothersinformation from one neuron to anothers. . 9.1.2 神經(jīng)細(xì)胞膜的離子通道特性神經(jīng)細(xì)胞膜的離子通道特性 細(xì)胞膜把細(xì)胞內(nèi)外分隔，細(xì)胞膜兩側(cè)的離子成分和濃度不同：細(xì)胞膜把細(xì)胞內(nèi)外分隔，細(xì)胞膜兩側(cè)的離子成分和濃度不同： 細(xì)胞內(nèi)細(xì)胞內(nèi) 正離子：主要是鉀離子正離子：主要是鉀離子 負(fù)離子：有機(jī)小分子負(fù)離子：有機(jī)小分子 細(xì)胞外細(xì)胞外 正離子：主要是鈉離子正離子：主要是鈉離子 負(fù)離子：氯離子負(fù)離子：氯離子 在這兩種方向相反的作用下達(dá)到平衡在這兩種方向相反的作用下達(dá)到平衡時(shí)，沒有離子通過細(xì)胞膜；時(shí)，沒有離子通過細(xì)胞膜； 達(dá)到

7、平衡狀態(tài)時(shí)，細(xì)胞膜內(nèi)外的電位差稱為該類離子的達(dá)到平衡狀態(tài)時(shí)，細(xì)胞膜內(nèi)外的電位差稱為該類離子的Nernst電位電位V*； 不同類離子的不同類離子的Nernst電位不同。電位不同。神經(jīng)細(xì)胞膜電活動神經(jīng)細(xì)胞膜電活動由于細(xì)胞內(nèi)外離子的濃度差，由于細(xì)胞內(nèi)外離子的濃度差，某一種離子要從高濃度側(cè)向低某一種離子要從高濃度側(cè)向低濃度側(cè)擴(kuò)散。濃度側(cè)擴(kuò)散。由于離子帶電，擴(kuò)散到另一側(cè)的由于離子帶電，擴(kuò)散到另一側(cè)的離子積累起來的電荷排斥將擴(kuò)散離子積累起來的電荷排斥將擴(kuò)散過來的帶有同一類電荷的離子。過來的帶有同一類電荷的離子。平衡平衡離子通過離子通道的驅(qū)動力離子通過離子通道的驅(qū)動力設(shè)：細(xì)胞的膜電位為設(shè)：細(xì)胞的膜電位為V，

8、 某個(gè)離子的某個(gè)離子的Nernst電位為電位為V*；那么那么 （VV*）是這種離子通過該離子通道的驅(qū)動力。是這種離子通過該離子通道的驅(qū)動力。e.g. （VVNa）是鈉離子通過細(xì)胞膜鈉離子通道的驅(qū)動力。是鈉離子通過細(xì)胞膜鈉離子通道的驅(qū)動力。（VVk） 是鉀離子通過細(xì)胞膜鉀離子通道的驅(qū)動力。是鉀離子通過細(xì)胞膜鉀離子通道的驅(qū)動力。Neurons, like all living cells, are surrounded（包圍）（包圍） by a plasma membrane that is impermeable （不可滲透（不可滲透 ）to ions. This property allows

9、 a neuron to maintain different concentrations of ions between the inside and outside of the cell.神經(jīng)細(xì)胞膜內(nèi)外不同的離子濃度神經(jīng)細(xì)胞膜內(nèi)外不同的離子濃度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 extracellu

10、lar environments. In addition, the interior of the neuron has a high concentration of large negatively charged proteins.神經(jīng)細(xì)胞膜內(nèi)外不同的鉀離子濃度、鈉離子濃度神經(jīng)細(xì)胞膜內(nèi)外不同的鉀離子濃度、鈉離子濃度The plasma membrane is composed of a lipid bilayer (脂脂類類層層 ). Its hydrophobic （疏水）（疏水）nature prevents the diffusion of ions across the mem

11、brane.神經(jīng)細(xì)胞膜神經(jīng)細(xì)胞膜的構(gòu)成和離子跨膜擴(kuò)散的構(gòu)成和離子跨膜擴(kuò)散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.神經(jīng)細(xì)胞膜上不同類的離子通

12、道神經(jīng)細(xì)胞膜上不同類的離子通道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 membra

13、ne when the neuron is at rest.神經(jīng)細(xì)胞膜靜息：大部分通道關(guān)閉部分鉀離子通道開啟神經(jīng)細(xì)胞膜靜息：大部分通道關(guān)閉部分鉀離子通道開啟In a typical neuron, the internal concentration of potassium is higher than the external concentration. K+ ions are pulled by two opposing forces： First, a DIFFUSION FORCE drives K+ ions along their concentration gradient

14、towards the exterior of the cell.鉀離子濃度細(xì)胞內(nèi)高于細(xì)胞外鉀離子濃度細(xì)胞內(nèi)高于細(xì)胞外, , K K+ + ions ions 受擴(kuò)散力推向細(xì)胞外受擴(kuò)散力推向細(xì)胞外The movement of potassium ions out of the cell increases the internal negative charge. The positively charged potassium ions are attracted to the internal negative charge, and this ELECTRICAL FORCE pull

15、s potassium ions back into the cell.鉀離子鉀離子受受電相斥力推回細(xì)胞內(nèi)電相斥力推回細(xì)胞內(nèi)The diffusion and electrical forces eventually come into balance, and an electrical potential, or voltage, is reached at which the electrical force exactly balances the diffusion force. At this point, there is no NET movement of potassium

16、 ions into or out of the cell.兩類相反的作用力達(dá)到平衡兩類相反的作用力達(dá)到平衡, , 此時(shí)沒有離子通過細(xì)胞膜此時(shí)沒有離子通過細(xì)胞膜The electrical potential across the membrane can be measured by inserting an electrode into the cell. A neuron at rest has a voltage difference of about -70 -60 mv across the membrane.神經(jīng)元的靜息膜電壓神經(jīng)元的靜息膜電壓n 離子通道是分布在細(xì)胞膜上的跨膜蛋

17、白。離子通道是分布在細(xì)胞膜上的跨膜蛋白。 Ion channels are membrane protein complexes . They play an essential role in the diffusion of ions across cell membrane.n 具有復(fù)雜的門控（開關(guān)）特性，離子電導(dǎo)性決定神經(jīng)元放電模式具有復(fù)雜的門控（開關(guān)）特性，離子電導(dǎo)性決定神經(jīng)元放電模式 。 Gating: The conformational change between open and closed . open the conformation in which channel

18、 allow ions to pass； closed the conformation in which channel forbid ions to pass.n 離子通道的狀態(tài)（關(guān)閉、開放和失活）與膜電位和時(shí)間有關(guān)，離子通道的狀態(tài)（關(guān)閉、開放和失活）與膜電位和時(shí)間有關(guān)，n 某一個(gè)離子通道的狀態(tài)可以通過測定通道的電導(dǎo)來評估。某一個(gè)離子通道的狀態(tài)可以通過測定通道的電導(dǎo)來評估。Electrical properties of ion channels Ion channels can be classified according to their gating mechanism1. 電壓門

19、控電壓門控2. 配體門控配體門控細(xì)胞外配體細(xì)胞外配體 細(xì)胞內(nèi)配體細(xì)胞內(nèi)配體3. 機(jī)械門控機(jī)械門控根據(jù)門控機(jī)制的不同，離子通道可分為三類：根據(jù)門控機(jī)制的不同，離子通道可分為三類： 9.1.3 細(xì)胞膜離子通道特性與動作電位細(xì)胞膜離子通道特性與動作電位Action potentialn動作電位是神經(jīng)元編碼信息，及與其它神經(jīng)元通訊的手段，動作電位是神經(jīng)元編碼信息，及與其它神經(jīng)元通訊的手段，n動作電位的產(chǎn)生是由于神經(jīng)細(xì)胞膜跨膜電位的變化，動作電位的產(chǎn)生是由于神經(jīng)細(xì)胞膜跨膜電位的變化，n細(xì)胞膜上的鉀離子通道、鈉離子通道等離子通道電導(dǎo)特性，細(xì)胞膜上的鉀離子通道、鈉離子通道等離子通道電導(dǎo)特性， 在動作電位的產(chǎn)

20、生中起關(guān)鍵作用。在動作電位的產(chǎn)生中起關(guān)鍵作用。nH-H模型描述神經(jīng)細(xì)胞膜上的離子通道電導(dǎo)狀態(tài)產(chǎn)生和模型描述神經(jīng)細(xì)胞膜上的離子通道電導(dǎo)狀態(tài)產(chǎn)生和 沿著軸突傳導(dǎo)動作電位。沿著軸突傳導(dǎo)動作電位。nAction Potential: all-or-none: action potential does not decrease in amplitude as it is conducted away from its site of initiation;The action potential is due to voltage and time-dependent changes in condu

21、ctance.nResting potential: -70 -60mVnAction potential: +20 +30mVAction potential動作電位的動作電位的5個(gè)相位個(gè)相位n 靜息電位（靜息電位（ The resting potential ）：極化）：極化（polarization）n 閾值電位（閾值電位（threshold）n 上升（上升（The rising phase）：去極化（）：去極化（depolarization）n 下降（下降（The falling phase)：復(fù)極化（：復(fù)極化（repolarization）n 恢復(fù)期（恢復(fù)期（The recovery

22、 phase）When the neuron is at rest, only a small subset of potassium channels are open, permitting K+ ions to enter and exit the cell based on electrochemical forces. For each K+ ion that leaves the cell, another returns, maintaining the membrane potential at a constant value.openclosedThe resting po

23、tential靜息狀態(tài)（極化）靜息狀態(tài)（極化）處于靜息電位處于靜息電位（-70 -70 60mV60mV）As a depolarizing stimulus arrives at the segment of the membrane, a few Na+ channels open, permitting Na+ ions to enter the neuron. The increase in positive ions inside the cell depolarizes the membrane potential (making it less negative), and br

24、ings it closer to the threshold at which an action potential is generated.Threshold閾值電位閾值電位當(dāng)細(xì)胞膜受到刺激，部分Na+通道打開，允許Na+進(jìn)入膜內(nèi)。由于Na+離子內(nèi)流，細(xì)胞膜內(nèi)電位上升并超過閾值電位。If the depolarization reaches the threshold potential, additional voltage gated sodium channels open. As positive Na+ ions rush into the cell, the voltage

25、 across the membrane rapidly reverses and reaches its most positive value.openThe rising phase膜電位超過閾值電位，導(dǎo)致更多鈉離子通道開放，電導(dǎo)GNa 增加，使鈉離子內(nèi)流；內(nèi)流的鈉離子電流導(dǎo)致進(jìn)一步的去極化，使鈉離子電流進(jìn)一步增加。At the peak of the action potential, two processes occur simultaneously. First many of the voltage-gated sodium channels begin to close. S

26、econd, many more potassium channels open, allowing positive charges to leave the cell. This causes the membrane potential to begin to shift back towards the resting membrane potential.At the peak of the action potential當(dāng)膜電位達(dá)到最大值時(shí)（膜電壓趨近鈉離子的靜息電位VNa）： Na+離子通道閉合，GNa逐漸減小至零； 部分K+離子通道開放，使得K+離子外流。As the mem

27、brane potential approaches the resting potential, voltage-gated potassium channels are maximally activated and open.The falling phase部分K+離子通道開放，使K+離子外流；K+離子通道電導(dǎo)GK增加，使膜電位下降。The membrane actually repolarizes beyond the resting membrane voltage. This undershoot occurs because more potassium channels ar

28、e open at this point than during the membranes resting state, allowing more positively charged K+ ions to leave the cell. The recovery phaseGk 的增加導(dǎo)致的增加導(dǎo)致K+離子外流，外流的離子外流，外流的K+離子離子電流引起進(jìn)一步超極化，進(jìn)而使電流引起進(jìn)一步超極化，進(jìn)而使K+離子電流離子電流進(jìn)一步增加，促使膜電位進(jìn)一步增加，促使膜電位V下降到趨近下降到趨近K+離子的離子的Nernst電位電位Vk，低于靜息電位。，低于靜息電位。The return to st

29、eady state continues as the additional potassium channels that opened during the action potential now close. The membrane potential is now determined by the subset of potassium channels that are normally open during the membranes resting state.The return to steady state膜電位逐漸恢復(fù)到靜息電位膜電位逐漸恢復(fù)到靜息電位細(xì)胞膜的離子

30、通道特性與動作電位細(xì)胞膜的離子通道特性與動作電位n極化（極化（polarization）：）：細(xì)胞處于靜息電位（細(xì)胞處于靜息電位（-70 -60mV）時(shí)稱為極化。）時(shí)稱為極化。n閾值電位（閾值電位（threshold）當(dāng)細(xì)胞膜受到刺激，部分當(dāng)細(xì)胞膜受到刺激，部分Na+離子通道打開，允許離子通道打開，允許Na+進(jìn)入膜內(nèi)。由于進(jìn)入膜內(nèi)。由于Na+離子內(nèi)流，離子內(nèi)流，細(xì)胞膜內(nèi)電位上升并超過閾值電位。細(xì)胞膜內(nèi)電位上升并超過閾值電位。n去極化（去極化（depolarization）：）： 膜電位超過閾值電位，導(dǎo)致更多鈉離子通道開放，膜電位超過閾值電位，導(dǎo)致更多鈉離子通道開放， 電導(dǎo)電導(dǎo)GNa增加，使鈉離

31、子內(nèi)流；增加，使鈉離子內(nèi)流； 內(nèi)流的鈉離子電流導(dǎo)致進(jìn)一步的去極化，使鈉離子電流進(jìn)一步增加。內(nèi)流的鈉離子電流導(dǎo)致進(jìn)一步的去極化，使鈉離子電流進(jìn)一步增加。當(dāng)膜電位達(dá)到最大值時(shí)（膜電壓當(dāng)膜電位達(dá)到最大值時(shí)（膜電壓V趨近鈉離子的趨近鈉離子的Nernst電位電位VNa），）， Na離子通道閉合，離子通道閉合，GNa逐漸減小至零；部分逐漸減小至零；部分K+離子通道開放，使得離子通道開放，使得K+外流。外流。n復(fù)極化（復(fù)極化（repolarization）：）： 部分部分K+ 離子通道開放，使得離子通道開放，使得K+外流；外流；K+ 離子通道電導(dǎo)離子通道電導(dǎo)GK增加，使得膜電位下降。增加，使得膜電位下降。

32、Gk 的增加導(dǎo)致的增加導(dǎo)致K+外流，外流的鉀離子電流引起進(jìn)一步超極化，進(jìn)而使鉀離子電流進(jìn)一外流，外流的鉀離子電流引起進(jìn)一步超極化，進(jìn)而使鉀離子電流進(jìn)一步增加，促使膜電位步增加，促使膜電位V下降到趨近鉀離子的下降到趨近鉀離子的Nernst電位電位Vk，低于靜息電位。，低于靜息電位。n恢復(fù)期（恢復(fù)期（recovery）：）：膜電位逐漸恢復(fù)到正常靜息電位。膜電位逐漸恢復(fù)到正常靜息電位。nExcitation transmission When a neuron sends an excitatory signal to another neuron, then this signal will be

33、 added to all of the other inputs of that neuron. If it exceeds a given threshold then it will cause the target neuron to fire an action potential, if it is below the threshold then no action potential occurs.n Transmission velocity can be reach to : 100m/sec神經(jīng)細(xì)胞興奮神經(jīng)細(xì)胞興奮（在軸突上的）（在軸突上的）傳遞傳遞 9.2 H-H 模型

34、的建立模型的建立描述動作電位產(chǎn)生和（在軸突上的）傳遞描述動作電位產(chǎn)生和（在軸突上的）傳遞H-H 方程9.2.1. Equivalent Circuit Model for the Cell MembraneNa-K PumpJVVkVLVNaCmJcJNaJLJkGkGLGNaVL - Leak equilibrium potentialVk- equilibrium potential of K+VNa- equilibrium potential of Na+JL - Leakage currentJk - Na+ currentJNa - Na+ currentJc - Capaciti

35、ve currentCm - Capacitance of the membraneV - Cell membrane potential (about -60 mV)GL - Leak ConductanceGk- Potassium ConductanceGNa- Sodium ConductanceNa-K PumpJVVkVLVNaCmJcJNaJLJkGkGLGNa膜電流密度膜電流密度 J 為為設(shè)設(shè)G 和和C 分別為單位面積的電導(dǎo)和電容，根據(jù)電路知識可得分別為單位面積的電導(dǎo)和電容，根據(jù)電路知識可得將上（將上（9.1）代入（）代入（9.2），可得），可得（9.1）小，可忽略小，可忽略（

36、9.2）（9.3）Not a constant, depends on V9.2.2 動作電位（在軸突上）傳遞動作電位（在軸突上）傳遞設(shè)神經(jīng)纖維為管狀結(jié)構(gòu)，為了表示神經(jīng)纖維上不同位置電位的大小，沿神經(jīng)纖維建設(shè)神經(jīng)纖維為管狀結(jié)構(gòu)，為了表示神經(jīng)纖維上不同位置電位的大小，沿神經(jīng)纖維建立一維坐標(biāo)（立一維坐標(biāo)（O-X）；神經(jīng)纖維直徑為）；神經(jīng)纖維直徑為d（截面積為（截面積為A=D2/4），長度為），長度為l，D l；神經(jīng)纖維內(nèi)部電導(dǎo)均勻分布，單位長度電阻系數(shù)為神經(jīng)纖維內(nèi)部電導(dǎo)均勻分布，單位長度電阻系數(shù)為R。在在 t 時(shí)刻時(shí)刻 x 處，膜電位為處，膜電位為v(x,t)。在在x，電阻為，電阻為在在 t 時(shí)刻

37、，從時(shí)刻，從 x 到到 x x 膜電位變化量為膜電位變化量為 設(shè)電流與設(shè)電流與 X 軸方向一致為正，通過橫截面的電流平均值為軸方向一致為正，通過橫截面的電流平均值為 i ，根據(jù)，根據(jù)Ohm定律可得定律可得取極限取極限 ，得到通過，得到通過 x 點(diǎn)神經(jīng)纖維截面的點(diǎn)神經(jīng)纖維截面的電流為電流為在在x 和和 x+ x 位置上，通過神經(jīng)纖維橫截面的電流分別是位置上，通過神經(jīng)纖維橫截面的電流分別是 i 和和 i+ i （ i 是由于是由于從從x 到到 x+ x 這一段神經(jīng)纖維表面生物膜上有穿過膜表面的電流產(chǎn)生）這一段神經(jīng)纖維表面生物膜上有穿過膜表面的電流產(chǎn)生）Def. 膜電流密度膜電流密度 ( J ) 穿

38、過膜表面穿過膜表面單位面積元單位面積元上的電流，設(shè)電流流入為負(fù)，流上的電流，設(shè)電流流入為負(fù)，流出為正。圓柱形膜表面面積為出為正。圓柱形膜表面面積為 ，電流的關(guān)系應(yīng)該有，電流的關(guān)系應(yīng)該有取極限取極限 ，并將（，并將（9.6）代入得）代入得（9.6）（9.8）9.2.3 H-H 方程方程npartial differential H-H equation （9.9）nordinary differential H-H equation（9.12） If C0 = 18.74 m/sec， H-H PDE ODE9.2.3 H-H 方程方程npartial differential H-H equa

39、tion （9.9）nordinary differential H-H equation（9.12） If C0 = 18.74 m/sec， H-H PDE ODE 9.3 H-HH-H方程中的離子通道電導(dǎo)方程中的離子通道電導(dǎo) nG GNaNa, , G Gk k and and G G0 0 are not constants, there values are functions of membrane are not constants, there values are functions of membrane potential potential V Vm me.g. e.g

40、. At resting potential: At resting potential: V Vm m = -70 = -70 - 60mV high - 60mV high G Gk k , , low low G GNaNa 在動作電位的頂峰在動作電位的頂峰: : V Vm m = 20 30mV low = 20 30mV low G Gk k , , high high G GNaNanTechniquesTechniques（鉗制膜電壓，測量膜電流電流，獲得電導(dǎo)）鉗制膜電壓，測量膜電流電流，獲得電導(dǎo)）Voltage clamp Voltage clamp 電壓鉗（電壓鉗（測量局部膜

41、總電流測量局部膜總電流 膜片上總電導(dǎo)）膜片上總電導(dǎo)）Patch clamp Patch clamp 膜片鉗（膜片鉗（測量離子通道電流測量離子通道電流 離子通道電導(dǎo)）離子通道電導(dǎo)）nConductance estimationConductance estimationEstimation of Conductance in H H ModelVoltage Clamp 電壓鉗技術(shù)電壓鉗技術(shù)n Breakthroughs in scientific research often rely on the development of Breakthroughs in scientific rese

42、arch often rely on the development of new technologies. In the case of the action potential, detailed new technologies. In the case of the action potential, detailed understanding came only after of the invention of the voltage clamp understanding came only after of the invention of the voltage clam

43、p technique by Kenneth Cole in the 1940s. technique by Kenneth Cole in the 1940s. n This device is called a voltage clamp because it controls, or clamps, This device is called a voltage clamp because it controls, or clamps, membrane potential (or voltage) at any level desired by the experimenter.mem

44、brane potential (or voltage) at any level desired by the experimenter.Voltage ClampPatch Clamp 膜片鉗技術(shù)膜片鉗技術(shù)n 一種記錄通過離子通道微小電流的技術(shù)。用微電極一種記錄通過離子通道微小電流的技術(shù)。用微電極接觸接觸細(xì)胞膜，使細(xì)胞膜，使電極的尖開口處和細(xì)胞膜片電極的尖開口處和細(xì)胞膜片“封接封接”（與周圍絕緣），產(chǎn)生（與周圍絕緣），產(chǎn)生1010 以以上大阻抗，在固定膜電位時(shí)，測量該膜片上離子通道的離子電流上大阻抗，在固定膜電位時(shí)，測量該膜片上離子通道的離子電流(pA級級) 。n 膜片鉗技術(shù)的建立，是生物

45、醫(yī)學(xué)，特別是神經(jīng)科學(xué)的一項(xiàng)重大技術(shù)膜片鉗技術(shù)的建立，是生物醫(yī)學(xué)，特別是神經(jīng)科學(xué)的一項(xiàng)重大技術(shù)革命。記錄單離子（或多個(gè)）通道的離子電流來研究細(xì)胞膜上單個(gè)革命。記錄單離子（或多個(gè)）通道的離子電流來研究細(xì)胞膜上單個(gè)（或多個(gè)）離子通道的分子水平電活動，將電生理技術(shù)從細(xì)胞水平提（或多個(gè)）離子通道的分子水平電活動，將電生理技術(shù)從細(xì)胞水平提高到分子水平高到分子水平。Patch Clamp 操作過程：找細(xì)胞、形成封接、破膜等操作過程：找細(xì)胞、形成封接、破膜等Patch Clamp 膜片鉗技術(shù)膜片鉗技術(shù)n Patch Clamp is a technique capable of measuring the c

46、urrents flowing through single channels was devised in 1976 by Neher and Sakmann.nA glass pipette with a very small opening is used to make tight contact with a tiny area, or patch, of neuronal membrane. After the application of a small amount of suction to the back of the pipette,n The seal（封接）（封接）

47、 between pipette and membrane becomes so tight (1010 ） that no ions can flow between the pipette and the membrane. Thus, all the ions that flow when a single ion channel opens must flow into the pipette. The resulting electrical current, though small (pA) , can be measured with an ultrasensitive ele

48、ctronic amplifier connected to the pipette. Based on the geometry involved, this arrangement usually is called the cell-attached patch clamp recording method. 應(yīng)用膜片鉗技術(shù)獲取電導(dǎo)膜電壓關(guān)系曲線應(yīng)用膜片鉗技術(shù)獲取電導(dǎo)膜電壓關(guān)系曲線nHH方程中電導(dǎo)方程中電導(dǎo)G是膜電壓的函數(shù)是膜電壓的函數(shù)G(v)n應(yīng)用膜片鉗技術(shù)測取電導(dǎo)膜電壓離散點(diǎn)應(yīng)用膜片鉗技術(shù)測取電導(dǎo)膜電壓離散點(diǎn)n fitting（擬合）電導(dǎo)膜電壓關(guān)系曲線（擬合）電導(dǎo)膜電壓關(guān)系曲線Con

49、ductance EstimationConductance Estimation The conductance was estimated by ways of curve fittingPotassium Conductance（鉀電導(dǎo)）（鉀電導(dǎo)）式中，式中，n 服從微分方程服從微分方程 上兩式中，上兩式中，GK0是一常數(shù)，其量綱與單位面積的電導(dǎo)的量綱相同；是一常數(shù)，其量綱與單位面積的電導(dǎo)的量綱相同；n 和和n 是與電位有關(guān)而與時(shí)間無關(guān)的速率常數(shù)（是與電位有關(guān)而與時(shí)間無關(guān)的速率常數(shù)（9.15-9.16)，量綱，量綱時(shí)間時(shí)間-1；n 是一個(gè)無量綱變量，取值在是一個(gè)無量綱變量，取值在0到到1

50、之間。之間。 (9.13)(9.14)Conductance EstimationSodium Conductance （鈉電導(dǎo)）（鈉電導(dǎo)） m 和和 h 服從微分方程服從微分方程 式中，式中，GNa0是一常數(shù)，其量綱為是一常數(shù)，其量綱為電導(dǎo)電導(dǎo)長度長度-2；m ,m ,h ,h 是與電位有關(guān)而與時(shí)間無關(guān)的速率常數(shù)是與電位有關(guān)而與時(shí)間無關(guān)的速率常數(shù) (9.20)-(9.23)，量綱量綱為為時(shí)間時(shí)間-1；m 和和h 是一個(gè)無量綱變量，取值在是一個(gè)無量綱變量，取值在0到到1之間。之間。 (9.17)(9.18)(9.19) 估計(jì)參數(shù)關(guān)系式：在不同鉗位電壓下，測量實(shí)驗(yàn)數(shù)據(jù)（各離子通道跨膜電流密度）估

51、計(jì)參數(shù)關(guān)系式：在不同鉗位電壓下，測量實(shí)驗(yàn)數(shù)據(jù)（各離子通道跨膜電流密度），根據(jù)數(shù)據(jù)擬合根據(jù)數(shù)據(jù)擬合n n n n m m m m h h h h 曲線。各個(gè)參數(shù)與膜電壓的經(jīng)驗(yàn)關(guān)系式如下：曲線。各個(gè)參數(shù)與膜電壓的經(jīng)驗(yàn)關(guān)系式如下：由以上電導(dǎo)的表達(dá)式，可得由以上電導(dǎo)的表達(dá)式，可得以上式子共同組成了以上式子共同組成了HodgkinHuxley方程，其中電壓單位是方程，其中電壓單位是mV，電流密度單位為，電流密度單位為mA/cm2，電導(dǎo)單位為，電導(dǎo)單位為mS/cm2，單位面積電容單位為，單位面積電容單位為F/cm2，時(shí)間單位為，時(shí)間單位為ms。 (9.24) Nobel Prize in 1963n對不同鉗位電壓的作用