1Fig. 1-8 B&L2BATTERYCATHODE ANODECations (K+, Na+, Ca++)Anions (Cl-, HCO3-)3= difference (gradient) across the membrane= electrochemical potential measured in mVx= electrochemical potential difference across the membrane for ion XR = Ideal gas constantT = absolute temperatureln = natural logarithm[X]i/[X]o= concentration difference across the membrane for ion “X”C = chemicalpotential difference across the membrane for ion “X”Z = charge on ion: Na+=+1, K+= +1, Cl-= -1, Ca2+= +2F = Faraday’s constantVm= electrical difference across the membrane in mVE = electrical potential difference across the membrane for ion ‘X”(Nernst Equation)x= RTln + ZxFVm[X]i[X]oCEEquation 1-4p13 B&L4glucose2 mM++++++++++++++++++------------------60 mVglucose5 mMChemical Potential Differencex=C=RTln[X]i[X]oUncharged, No E5Na+12 mM++++++++++++++++++-----------------60 mVNa+145 mMChemical Potential DifferenceElectrical Potential Differencex= RTln + ZxFVm[X]i[X]oCE6K+120 mM++++++++++++++++++-----------------60 mVK+4 mMChemical Potential DifferenceElectrical Potential Differencex= RTln + ZxFVm[X]i[X]oCE7Cl-30 mM++++++++++++++++++-----------------60 mVCl-105 mMChemical Potential DifferenceElectrical Potential Differencex= RTln + ZxFVm[X]i[X]oCE8Nernst Equilibrium Potential (Ex)x= RTln + ZxFVm= 0, [X]i[X]oWhen the electrochemical potential of ion X, there is no movement of ion X.At this condition, the membrane potential Vmis the Nernst Equilibrium Potential (Ex) of ion X.At 37C, it simplifies to:9EX= log 61.5 mVZx[X]o[X]iNernst Equation for Calculation of the Equilibrium Potential EX (Vm) for ion XFig. 2-4 B&L10Extracellular [K+]oand its impact on excitable cellsThe normal range for [K+]ois: 3.6 - 5.0 mM and is controlled largely by kidneys.Normal: [K+]o= 4 mM, EK= -91 mVHyperkalemia: [K+]o= 7 mM, EK= -80 mVHypokalemia: [K+]o= 2 mM, EK= -109 mV• Kidney failure causes hyperkalemia, which depolarizes the membrane and makes it easier for heart cells to initiate action potential. This causes cardiac arrhythmias and even cardiac arrest. • Lethal Injection: rapid infusion of high concentration KCl. • Diurectics (drugs that increase urine output) may cause hypokalemia, which hyperpolarizes the membrane and makes it more difficult for heart cells to initiate action potential. This also causes cardiac arrhythmias and cardiac arrest. EK= log 61.5 mV1[K+]o12011RESTING MEMBRANE POTENTIAL (RMP)1. RMP’s are developed across the cell membranes and are measured from the inside relative to the outside of the cell.2. All cells have RMP’s: (RMP for a neuron is -70 mv and -90 mv for a skeletal muscle cell)3. RMP’s depend on: A) concentrations of ions inside and outside of cellsB) relative permeability (conductance) of the cell membrane to the different ionsC) the RMP is primarily determined by K+ because the membrane ismost permeable to it.4. Only a very small number of ions need to cross a cell membrane to develop a RMP.12Resting Membrane Potential: the Vmat which net current is 0(because I = V/R = V x g)Where G=GNa++ GK++ GCl-13RMP is the weighted sum of ENa+, EK+, ECl-based on the contribution of a conductance in the total conductances.In the model neuron in Fig. 2-4, G=100pS, GNa=15pS (GNa/G=15%) GK=80pS (GK/G=80%)GCl=5pS, (GCl/G=5%) Thus, Vm= 0.15 x 66.6mV + 0.8 x (-90.8mV) + 0.05 x (-33.5mV) = -64.325mVChord Conductance EquationFig. 2-4 B&L14For most cells at rest, the membrane has highest conductance to K+. Thus, the share of Gkin G is the greatestThus, at rest, Vmis closest to EK+,and is largely determined by K+channels.Because Cl-conductance is very small and thus negligible, Vmcannot be bigger than ENa(when GNa/G=1, GK=0),Vmcannot be smaller than EK(when GK/G=1, GNa=0),Thus, EK+< Vm< ENa+G=100pS, GNa=15pS (GNa/G=15%), GK=80pS (GK/G=80%), GCl=5pS, (GCl/G=5%) Vm= 0.15 x 66.6mV + 0.8 x (-90.8mV) + 0.05 x (-33.5mV) = -64.325mV15Time (msec)Memb. pot. (mv)0-90+100+65ENaEKRMP -70RESTING MEMBRANE POTENTIAL (RMP)Why is the RMP not equal to EK?16Time (msec)Memb. pot. (mv)0-90+100+65ENaEKRMP -70RESTING MEMBRANE POTENTIALdepolarization repolarizationhyperpolarization17B&L Pg. 26Only 0.002% of the total number of K+ ions inside the cell need to diffuse out of the cell to establish a membrane potential of -80 mV[K+] inside the cell# of K+ ions that diffuse out of the cell Only a tiny percentage of K+needs to diffuse out to maintain RMPFor details, see p.26 B&L18+0-voltmetermv[K+][K+]+++++70+++++CE1. Na+, K+ pump maintains the ion concentrations by pumping 3 Na+ out for every 2K+ into the cell.2. It is electrogenic and contributes about 5 mV to the RMP.3. It is an active pump that requires ATP to generate energy.ATP-dependent Na+, K+pump3 Na+2 K+ATP[Na+][Na+]CERMP = axon19SUMMARY• Equilibrium potentials for various ions• Nernst equation• Membrane permeabilities (conductances) differ for various ions• Ion channels, concentration gradients and membrane conductances for the generation of the RMP• The high K+ conductance is primarily responsible for the RMP • Ion concentrations are maintained by the ATP-dependent Na+, K+pump in the cell membrane• RMP’s vary among cells: RBC’s = -10 mV; neurons = -70 mV; skeletal and cardiac muscle = -90