Membranes and Transport Topic II-1 Biophysics

Nernst Equation Simplest equation for membrane potential – one ion www.kcl.ac.uk/teares/gktvc/vc/lt/nol/Nernst.htm RT/F = 0.025861 volts; ln(x) = 2.3log(x) 6.022E23; 1.6E-19 Faraday constant F = 96,500 Coulomb/mole Simplest equation for membrane potential – one ion

Goldman-Hodgkin-Katz Equation P for organic ions = 0 There is one membrane potential that counters all concentration gradients for permeable ions Pi = (mikBT)/d = Di/d, with D – diffusion constant [cm2/sec]

Example – simple Neuron with b = PNa/PK b = 0.02 for many neurons (at rest). [K]i = 125 mM [K]o = 5 mM [Na]i = 12 mM [Na]o = 120 mM What is DV? 298 K Note: Can define Nernst potential for each ion, DVk = -80 mV; DVNa = +58 mV. Relative permeabilities make membrane potential closer to DVk Do Soma 1 (Nernst)

Soma 1 Nernst Potential Alt enter gives full screen Use left and right mouse clicks to change Ckout (concentration of potassium outside cell)

Electrical Model g is like conductance (=1/R) and like permeability (from Kirchoff’s laws) g is like conductance (=1/R) and like permeability This equation is equivalent to Godman-Hodgkin-Katz equation.

Example squid axon IK = gK (Vm – VK), Vm = -60 mV IK = gK (-60 – (-75)) mV = gK(+15 mV). g always positive. DV = Vin – Vout positive current = positive ions flowing out of the cell. Vm not sufficient to hold off K flow so ions flow out. When Vm = Vk then no flow. [K]in =125mM [K]out = 5 mM Vm = -60 VK = -75 Arrows next to V in top diagram just indicating counterforce against concentration gradient. Going from high to low potential. DeltaV = Vfinal-vinitial Remember electric field points in direction of force on positive test charge E always points from higher potential (for ions) [K]in =125 mM [K]out = 5 mM E ds Do Soma 3 (Resting Potential)

Soma 3 Resting Potential Soma 3 – Soma – resting   Three ions: Na, K, Cl. Top graph is VK, VNa, VCl, Vm (E used instead of V) vs time. Bottom graph is IK, INa, ICl, Im vs time Run (play). Why is ICl so low? What is total current? Set gNa=gCl=0. [These are written as QNa etc] You can keep the simulation going as you do this. What happens to Vm? Set gCl = 5, leave gK as 16, Set gNa really high = 100 etc. What happens to Vm?. This is like action potential.

Donnan Rule and other considerations Example of two permeable ions and one impermeable one inside KoClo = KiCli Donnan Rule Electroneutrality Osmolarity Goldman- Hodgkin-Katz Apply electroneutrality inside and out and plug in Donnan rule and get

Animal Cell Model Ci (mM)* Co (mM) P>0? K+ 125 5 Y Na+ 12 120 N** Cl- A- 108 N H2O 55,000 * Should really use Molality (moles solute/ kg solvent) instead of per liter – accounts for how molecules displace water (non-ideality). ** More on this later

Maintenance of Cell Volume Cell impermeable to sucrose http://www.himalayancrystalsalt.com/html/images/PAGE-osmosis.gif www.lib.mcg.edu/.../section1/1ch2/s1ch2_25.ht Osmolarity must be same inside and out Concentration of permeable solutes must be same inside and out Si = So and Si + Pi = So (Osmolarity) Solutions: cell wall, Pwater = 0, Pextra cellular solutes = 0

Animal Na impermeable model Apply electroneutrality outside, Donnan, and osmolarity Get unknowns and Vm = -81 mV

Active Transport with a = (n/m)(PNa/PK),n/m = 2/3  Vm  VK. Na-K Pump http://faculty.ccbcmd.edu/~gkaiser/biotutorials/eustruct/sp1.html Na-K Pump Two sets of two membrane spanning subunits Phosphorylation by ATP induces a conformational change in the protein allowing pumping Each conformation has different ion affinities. Binding of ion triggers phosphorylation. Shift of a couple of angstroms shifts affinity. Exhibits enzymatic behavior such as saturation.

Electrical Model Do soma 4 and 5 Now include current for pump, Ip as well as input current I. Do Soma conductance and Na pump)

Soma 4 Conductance

Soma 5 Na Pump Look at contribution of Na pump contribution to Vm and role of intracellular Na ions is setting the pump rate. Have Vm vs time and INa, [Na]in, and INapump vs time. Note that in equilibrium, current of Na pump and Na equal and opposite. 1. Run. Pump off (Na NaPumpmax =0) Get Vm = -67 mV. [Na]in = 10 mM. 2. Set NaPumpmax to 60 (fM/s). Run for a bit. [Na]in still about 10 mM but Vm now about -74 mV. Increase max pump rate 145, 245 . [Na]in decreases and hyperpolarization is reversed. Why? Put NaPumpmax back to 60. InjectNaStimon is on and have amplitude at nA. Fire. Now depolarization is great and [Na] inside goes up (ofcourse ) and then down.

Patch Clamping www.essen-instruments.com/Images/figure2.gif Invented by Sakmann and Neher [Pflugers Arch 375: 219-228, 1978] Can be used for whole cell clamp (measure currents in whole cell, placing electrode in cell) like on left or pulled patch as on right (potentially measure single channel). Can control [ions]. Usually voltage clamp (command voltage or holding voltage) and observe current (I = gV). Ix = g(Vh-Vx) where x is for each ion and Vx is Nernst potential for that ion. With equal concentration of permeable ion on both sides, get g easily

Voltage Gated Channels There is a degree of randomness in opening and closing of channels Proportion of time open is proportional to Voltage for some channels Average of many channels is predictable PATCH EXERCISES When [ions] not limiting, can get nernst potential when current reverses I = gx*(Vh – Vx)

Multiple Channels Get several channels on a patch Gives quantized currents Parallel: geq = S gi; Series: 1/geq = S 1/gi g = 1/R

Ligand gated channels Nicotine also binds to Ach receptor – called nicotinic receptor When Ach binds, gate opens and lets in Na+ and K+. I is proportional to [Ach]2 (binds 2 Ach) Do Patch Cl, K, Multiple K, ligated)

Patch 1 Cl Single Cl channel. Plot is chloride current in pA vs time. Will have VCl =0 since concentrations of ions on both sides set to zero.   We want to have VCl =0, so scroll down in the parameter window and set ECL = 0. Run. Calculate g. (Note Vhold is 50 mV). I = gV; Change Vh. 75, 99, -50 etc. Is the current proportional to the holding voltage? Is this channel voltage gated?

Patch 2 K HW – calculate g. Show work and screen shot. Same as Cl one, but now have K. HW – calculate g. Show work and screen shot. 1. Run. 2. Change Vh. -60, -70,-40, -30. Is the current proportional to the holding voltage? Is this channel voltage gated?

Patch 4 Multiple K channels

Patch 5 Ligand gated channels

Facilitated Transport Jmax = NYDY/d2 NY = number of carriers DY = diffusion constant of Carrier d = membrane thickness Get Saturation Kinetics Lower activation energy Co Jmax