Membranes and Transport Topic II-1 Biophysics
Nernst Equation 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 P i = ( i k B T)/d = D i /d, with D – diffusion constant [cm 2 /sec]
Example – simple Neuron Note: Can define Nernst potential for each ion, V k = -80 mV; V Na = +58 mV. Relative permeabilities make membrane potential closer to V k 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 V? with b = P Na /P K Do Soma 1 (Nernst)
Electrical Model g is like conductance (=1/R) and like permeability This equation is equivalent to Godman-Hodgkin- Katz equation. (from Kirchoff’s laws)
Example squid axon Remember electric field points in direction of force on positive test charge E always points from higher potential (for ions) [K] in =125mM [K] out = 5 mM V m = -60 V K = -75 I K = g K (V m – V K ), V m = -60 mV I K = g K (-60 – (-75)) mV = g K (+15 mV). g always positive. V = V in – V out positive current = positive ions flowing out of the cell. V m not sufficient to hold off K flow so ions flow out. When V m = V k then no flow. [K] in =125 mM [K] out = 5 mM E E ds Do Soma 3 (Resting Potential)
Donnan Rule and other considerations Example of two permeable ions and one impermeable one inside K o Cl o = K i Cl i Donnan Rule Electroneutrality Osmolarity Goldman- Hodgkin-Katz Apply electroneutrality inside and out and plug in Donnan rule and get
Animal Cell Model C i (mM)*C o (mM)P>0? K+K+ 1255Y Na N** Cl Y A-A- 1080N H2OH2O55,000 Y * 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 Osmolarity must be same inside and out Concentration of permeable solutes must be same inside and out S i = S o and S i + P i = S o (Osmolarity) Solutions: cell wall, P water = 0, P extra cellular solutes = 0 Cell impermeable to sucrose
Animal Na impermeable model Apply electroneutrality outside, Donnan, and osmolarity Get unknowns and V m = -81 mV
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. student.ccbcmd.edu/.../eustruct/sppump.html with = (n/m)(P Na /P K ),n/m = 2/3 V m V K.
Electrical Model Now include current for pump, I p as well as input current I. Do Soma conductance and Na pump)
Patch Clamping Invented by Sakmann and Neher [Pflugers Arch 375: , 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). I x = g(V h -V x ) where x is for each ion and V x is Nernst potential for that ion. With equal concentration of permeable ion on both sides, get g easily
Voltage Gated Channels When [ions] not limiting, can get nernst potential when current reverses I = g x *(V h – V x ) 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
Multiple Channels Get several channels on a patch –Gives quantized currents Parallel: g eq = g i ; Series: 1/g eq = 1/g i –g = 1/R I t
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)
Facilitated Transport Get Saturation Kinetics Lower activation energy J max = N Y D Y /d 2 N Y = number of carriers D Y = diffusion constant of Carrier d = membrane thickness CoCo J max