麻省理工学院：《电气工程与计算机科学》学习资料_Week8

Week 8 Review What was covered pace clamp Current clamp Voltage clamp Hodgkin-Huxley Model Review of last week lectrically small cell vS electrically small cell Graded potential vs. Action potential Decrement conduction vs. Decrement-free conduction pace clam S How to transform an electrically large cell into an electrically small cell? Remember the core conductor model? is the same as saying that the conduction velocity is infinite In an electrically small cell, the potential is everywhere(in space) the same. In a way this Conduction velocity is inversely proportional to the internal and external resistance, ri and ro. In most experiments, ro is very small(sea water). Therefore, if you make ri very small (by inserting a highly conducting wire into the cell), you can make the conduction velocity very very large (i.e. basically infinite on the length scale of the cell and the time scale of the experiment Current Clamp lin We can control the current across the membrane Therefore, we can stimulate with a current pulse and determine if the cell generates an ACTION POTENTIAL What did we learn from current clamp 1. threshold 3. accommodation 4. all the other properties of AP

Week 8 Review What was covered: - Space clamp - Current clamp - Voltage clamp - Hodgkin-Huxley Model Review of last week: Electrically small cell vs. electrically small cell Graded potential vs. Action potential Decrement conduction vs. Decrement-free conduction Space Clamp: How to transform an electrically large cell into an electrically small cell? Remember the core conductor model? In an electrically small cell, the potential is everywhere (in space) the same. In a way this is the same as saying that the conduction velocity is infinite. Conduction velocity is inversely proportional to the internal and external resistance, ri and ro. In most experiments, ro is very small (sea water). Therefore, if you make ri very small (by inserting a highly conducting wire into the cell), you can make the conduction velocity very very large (i.e. basically infinite on the length scale of the cell and the time scale of the experiment) Current Clamp: Iin We can control the current across the membrane. Therefore, we can stimulate with a current pulse and determine if the cell generates an ACTION POTENTIAL. What did we learn from current clamp: 1. threshold 2. refractory 3. accommodation 4. all the other properties of AP

Voltage Clamp ry to understand how cell generates an action potential by control potential across the membrane However, since you are controlling the membrane potential there are NO ACTION POTENTIALS generated in voltage clamp But useful because we can study the current flow through membrane m=Jc +Jion=Jc Jna+Jk+JL): So what did we learn from voltage clamp 1. Assume Gl is -constant 2. initial current transient to Vm step is Jna(m has the fastest time constant) 3. direction of current flow depends on the"drive"(Vm-Vna) 4. after sometime inactivation()starts and Gna goes down Jna goes down 5. at rest, Jk has the biggest effect( Gk is much bigger than others) Hodgkin-Huxley Model Using what was learned from the voltage clamp, we get the Hh model J Potassium and Sodium conductance depend on the membrane voltage. Vk and Vna do not change with an aP since very little ions are actually transported Jm=Cm m+G(m, I( -Vx)+GN,OOm-VNa)+G(m-V) And now we can fill in the black box in the Core Conductor with Hodgkin-huxley models

Voltage Clamp: Try to understand how cell generates an action potential by control potential across the membrane. + _ However, since you are controlling the membrane potential: there are NO ACTION POTENTIALS generated in voltage clamp. But useful because we can study the current flow through membrane (Jm = Jc +Jion = Jc + Jna+Jk+JL): So what did we learn from voltage clamp: 1. Assume GL is ~constant. 2. initial current transient to Vm step is Jna (m has the fastest time constant) 3. direction of current flow depends on the “drive” (Vm-Vna) 4. after sometime inactivation (h) starts and Gna goes down � Jna goes down 5. at rest, Jk has the biggest effect (Gk is much bigger than others) Hodgkin-Huxley Model: Using what was learned from the voltage clamp, we get the HH model: GK GNa GL + VK � + VNa � + VL � Jm CM + Vm � Potassium and Sodium conductance depend on the membrane voltage. Vk and Vna do not change with an AP since very little ions are actually transported… m Jm = Cm ¶V +GK (Vm , t)(Vm -VK ) + GNa (Vm , t)(Vm -VNa ) + GL (Vm -VL ) ¶t And now we can fill in the black box in the Core Conductor with Hodgkin-Huxley models:

2na(r +o)v2 arc avm+Gx(m,I)(m-Vk)+GNa(m DOm-VNa)+GL(m-V) a-p So how do the conductances(Gna and Gk), depend on Vm? GK m, n=Grn(n, 1) where Gk is a constant and only n depends on time and vm (n,1)=Gm(n,1)h(Vn,) where GNa is a constant and m and h depends on time and vm If Vm is kept constant(like in voltage clamp), n, m, and h are just exponential functions of time. Their final value and their time constants depend only on vm n and m go up with Vm and h goes down with Vm n has a much faster time constant 3(ms) 100-75-50-25255075-100-75-50-2 0.2 100-75-50-25 255075 (m2,1)+n(Vn) =n2(m) m(m )+Im(m)at=m

2 2pa(ri 1 + ro )v 2 ¶ V 2 m = Cm ¶ ¶ V t m +GK (Vm , t)(Vm -VK ) + GNa (Vm , t)(Vm -VNa ) + GL (Vm -VL ) ¶t So how do the conductances (Gna and Gk), depend on Vm? GK (Vm , t) = GK n4 (Vm , t) where GK is a constant and only n depends on time and Vm. GNa (Vm , t) = GNam3 (Vm , t)h(Vm , t) where GNa is a constant and m and h depends on time and Vm. If Vm is kept constant (like in voltage clamp), n, m, and h are just exponential functions of time. Their final value and their time constants depend only on Vm. n and m go up with Vm and h goes down with Vm. n has a much faster time constant. t t t t ¥ ¥ ¥ n(Vm , t) + t n (Vm ) ¶n(Vm , t) = n¥ (Vm ) ¶t m(Vm , t) + t m (Vm ) ¶m(Vm , t) = m¥ (Vm ) ¶t h(Vm , t) + t h (Vm ) ¶h(Vm , t) = h¥ (Vm ) ¶t