Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 291Bi 1 Session 5Tuesday, April 4, 2006“Deriving” ion concentration gradients and fluxes2What is the most abundant molecule in an organism?3H2O MW = 18Density ~ 1 kg/lTherefore the concentration of water in an aqueous solution is ~ (1000 g/liter )/(18 g/mol) = 55 mol/liter or 55 M.All other molecules in the body are at least 100 times less concentrated.A reminder from Chem 1:4Ionic compositions inside and outside a typical mammalian cell5One clue to a cell’s ionic concentrations:Sea Water6Membranes provide a barrier to diffusion around cells,forming compartmentsLittle Alberts 2-20© Garland Little Alberts 12-2© GarlandLittle Alberts 12-1© Garland. . . But specialized proteins (channels and transporters) control the permeation of many molecules7One Benefit of Compartmentalization and Membranes:molecules can be improved by selection8A typical protein has 500 amino acid residues.An average residue has a molecular mass of 110.Therefore the average protein has a molecular mass of 55,000.( 4 x 10-3 mol/liter) x (5.5 x 104 g/mol) = 2.2 x 102 g/l= 220 g/l.The cell is ~22% protein! How much is 4 mM protein?9ExternalMonovalent cations:High Na+Low K+Na+Na+Na+Na+Na+Na+Na+Na+Internal:same asExternalNa+Na+Na+Na+Na+A Cell that Lacks Concentration GradientsK+K+10ExternalMonovalent cations:High Na+Low K+Na+Na+Na+Na+Na+Na+Na+Na+K+Internal:Low Na+High K+K+K+K+K+Storing energy in a concentration gradient without osmotic stress:Simply reverse the ratio of Na+ and K+K+11The “Na+ pump” splits ATP to make a Na+ and K+ concentration gradient A transporter protein moves a few ions for each conformational change32Little Alberts 12-10 © Garland12Na+Na+Na+Na+Na+Na+Na+Na+K+K+K+K+Converting a concentration gradient to an electrical potential: Create permeability to one ionic species (K+)Lost positive charge leads to net negative interior potential K+ channelsHundreds or thousands of ions flow through a channel protein for each openingK+13K+K+K+K+K+The Nernst potential: the energy of discharging the concentration gradient for K+ ionsbalances the energy of moving the K+ ions through the potential difference14Chem 1 textbook (OGN)Figure 12-1015Deriving the Nernst potential (chemical notation)OGN Figure 7-716Deriving the Nernst potential (for physicists and electrical engineers)R = N k, w h e r e N i s A v o g a d r o ’ s n u m b e r a n d k i s B o l t z m a n n ’ s c o n s t a n t ; A n d F = N e, w h e r e e i s t h e c h a r g e o n t h e e l e c t r o n . T h e r e f o r e mV25106.13001038.11923CJekTFRT ( w e a r e f a m i l i a r w i t h t h e s t a t e m e n t t h a t k T = 2 5 m e V ) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - A n d a 1 0 - f o l d c o n c e n t r a t i o n r a t i o l e a d s t o a m e m b r a n e p o t e n t i a l o f mV5810ln FRT17Deriving the Nernst potential (for Biologists)Class votes here: Strategy Vote Comments Don’t derive; Just measure 2 Look in Little Alberts Ch 12 p. 410 Or Nestler p. 37 7 Ask a physicist 35 Measure; then do IPO on NASDAQ 318Na+Na+Na+Na+Na+Na+Na+Na+What is the selective advantage . . .that the membrane is permeable at rest to K+ rather than to Na+? [K+]I = 140 mM; [Na+]I = 10 mM. A leak of 10 mM: [Na+] would increase from ~ 10 mM to 20 mM, doubling [Na+]I and causing a 17 mV change in the Nernst potential.a small inward leak of Na+ would change the internal [Na+] by fractionally more than a small outward leakage of K+ would change internal [K+ ]But a similar outward leak in K+ would decrease [K+]i from 140 mM to 130 mM, causing a < 2 mV change in the Nernst potential for [K+]. Conclusion: cell function is more stable when the resting permeability is to K+ .19Under what circumstances do cells use Cl- fluxes? Apparently it’s not straightforward to make a permeability pathway that distinguishes among anions using protein side chains. Therefore there is no “anion pair” corresponding to K+ / Na+. Few cells use anions to set the resting potential.But some channels do use anion (mainly Cl-) fluxes (Lecture 21, cystic fibrosis).Could cells utilize plasma membrane H+ fluxes? Probably not.There are not enough protons to make a bulk flow, required for robustly maintaining the ion concentration gradients.(but some very small organelles (~ 0.1 m) and bacteria do indeed store energy as H+ gradients).Other monovalent ions20What is the selective advantage that cells maintain Ca2+ at such low levels? Cells made a commitment, more than a billion yr ago, to use high-energy phosphate bonds for energy storage. Therefore cells contain a high internal phosphate concentration. But Ca phosphate is insoluble near neutral pH. Therefore cells cannot have appreciable concentration of Ca2+; they typically maintain Ca2+ at < 10 –8 M.What is the selective advantage that cells don’t use Mg2+ fluxes?The answer derives from considering the atomic-scale structure of a K+ -selective channel (next slide), which received the 2003 Nobel Chemistry Prize:http://www.its.caltech.edu/~lester/Bi-1/kcsa.pdb(Swiss-prot viewer must be installed on your computer)Divalent Cations21K+ ions lose their waters of hydration and are co-ordinated by backbone carbonyl groups when they travel through a channel.H2OK+ ioncarbonyl22Na+ , K+1 ns(~ 109/s)Ca2+5 ns(2 x 108/s)Mg2+10 s(105/s)Time required to exchange waters of hydrationConclusion:Na+ , K+, and Ca2+ can flow through single channels at rates > 1000-fold greater than Mg2+Mg2+ is suitable for transporters, but not for channels.23These gradients can be used in two ways:1. The gradients are used for uphill “exchange” to control the concentrations of other small molecules. 2. Transient, local increases in intracellular Ca2+ and Na+ concentrations can now be used for signaling inside cells!Next imageCells have evolved elaborate processes for pumping out intracellular Na+ and Ca2+24 Na+-coupled cell membrane neurotransmitter transporters:Antidepressants (“SSRIs” = serotonin-selectivereuptake inhibitors):Prozac, Zoloft, Paxil, Celexa, LuvoxDrugs of abuse: MDMAAttention-deficit disorder