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Membranes and Transport

Membranes and Transport. Topic II-1 Biophysics. Nernst Equation. www.kcl.ac.uk/teares/gktvc/vc/lt/nol/Nernst.htm. F = 96,400 Coulomb/mole Simplest equation for membrane potential – one ion. Goldman-Hodgkin-Katz Equation.

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Membranes and Transport

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  1. Membranes and Transport Topic II-1 Biophysics

  2. Nernst Equation www.kcl.ac.uk/teares/gktvc/vc/lt/nol/Nernst.htm • F = 96,400 Coulomb/mole • Simplest equation for membrane potential – one ion

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

  4. Example – simple Neuron • Note: Can define Nernst potential for each ion, DVk = -80 mV; DVNa = +58 mV. Relative permeabilities make membrane potential closer to DVk 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? Do Soma 1 (Nernst)

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

  6. [K]in =125 mM ds E E [K]out = 5 mM [K]in =125mM VK = -75 Vm = -60 [K]out = 5 mM 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. • Remember electric field points in direction of force on positive test charge • E always points from higher potential (for ions) Do Soma 3 (Resting Potential)

  7. 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

  8. Animal Cell Model • * Should really use Molality (moles solute/ kg solvent) instead of per liter – accounts for how molecules displace water (non-ideality). • ** More on this later

  9. Maintenance of Cell Volume • 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 Cell impermeable to sucrose http://www.himalayancrystalsalt.com/html/images/PAGE-osmosis.gif www.lib.mcg.edu/.../section1/1ch2/s1ch2_25.ht

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

  11. Active Transport • 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. with a = (n/m)(PNa/PK),n/m = 2/3  Vm VK. student.ccbcmd.edu/.../eustruct/sppump.html

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

  13. 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

  14. 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 • When [ions] not limiting, can get nernst potential when current reverses I = gx*(Vh – Vx)

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

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

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

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