Membranes and Transport Topic II1 Biophysics Nernst Equation

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 • There is one membrane potential that counters all concentration gradients for permeable ions • Pi = (mik. BT)/d = Di/d, with D – diffusion constant [cm 2/sec]

Example – simple Neuron with b = PNa/PK b = 0. 02 for many neurons (at rest). [K]i = 125 m. M [K]o = 5 m. M [Na]i = 12 m. M [Na]o = 120 m. M What is DV? • Note: Can define Nernst potential for each ion, DVk = -80 m. V; DVNa = +58 m. V. Relative permeabilities make membrane potential closer to DVk Do Soma 1 (Nernst)

Electrical Model (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 = g. K (Vm – VK), Vm = -60 m. V IK = g. K (-60 – (-75)) m. V = g. K(+15 m. V). [K]in =125 m. M g always positive. Vm = -60 [K]out = 5 m. M VK = -75 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) [K]in =125 m. M E ds [K]out = 5 m. M E Do Soma 3 (Resting Potential)

Donnan Rule and other considerations Example of two permeable ions and one impermeable one inside • • • Ko. Clo = Ki. Cli Donnan Rule Electroneutrality Osmolarity Goldman- Hodgkin-Katz Apply electroneutrality inside and out and plug in Donnan rule and get

Animal Cell Model Ci (m. M)* Co (m. M) P>0? K+ 125 5 Y Na+ 12 120 N** Cl- 5 125 Y A- 108 0 N H 2 O 55, 000 Y * Should really use Molality (moles solute/ kg solvent) instead of per liter – accounts for how molecules displace water (nonideality). ** 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/. . . /section 1/1 ch 2/s 1 ch 2_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 m. V

Active Transport with a = (n/m)(PNa/PK), n/m = 2/3 Vm VK. student. ccbcmd. edu/. . . /eustruct/sppump. 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 Now include current for pump, Ip as well as input current I. Do Soma conductance and Na pump)

Patch Clamping www. essen-instruments. com/Images/figure 2. 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 = g. V). 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 • When [ions] not limiting, can get nernst potential when current reverses I = gx*(Vh – Vx)

Multiple Channels I t • 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)

Facilitated Transport Jmax = NYDY/d 2 NY = number of carriers DY = diffusion constant of Carrier d = membrane thickness • Get Saturation Kinetics • Lower activation energy Jmax Co