Anslyn && Dougherty is even more fun than Clayden et. al. It’s far more advanced, and I’m certainly glad I read Clayden first. On p. 24 they talk about the polarizability of molecules, sonething distinct from the dipole moment of the molecule. Polarizability is the ability of the molecule’s electron distribution to distort in the presence of an electric field. I was suprised to find that the usual suspects (e.g. water) aren’t that polarizable and that the champs are hydrocarbons. They don’t say how polarizability is measured, but I’ll take them at face value.
We wouldn’t exist without the membranes enclosing our cells which are largely hydrocarbon. Chemists know that fatty acids have one end (the carboxyl group) which dissolves in water while the rest is pure hydrocarbon. The classic is stearic acid — 18 carbons in a straight chain with a carboxyl group at one end. 3 molecules of stearic acid are esterified to glycerol in beef tallow (forming a triglyceride). The pioneers hydrolyzed it to make soap. Saturated fatty acids of 18 carbons or more are solid at body temperature (soap certainly is), but cellular membranes are fairly fluid, and proteins embedded in them move around pretty quickly. Why? Because most fatty acids found in biologic membranes over 16 carbons have double bonds in them. Guess whether they are cis or trans. Hint: the isomer used packs less well into crystals — you’ve got it, all the double bonds found in oleic (18 carbons 1 double bond), arachidonic (20 carbons, 4 double bonds) are trans – this keeps membranes fluids as well. No, they are cis — thanks to PostDoc for pointing this out. The cis double bond essentially puts a 60 degree kink in the hydrocarbon chain, making it much more difficult to pack in a liquid crystal type structure with all the hydrocarbon chains stretched out. Then there’s cholesterol which makes up 1/5 or so of membranes by weight — it also breaks up the tendency of fatty acid hydrocarbon chains to align with each other because it doesn’t pack with them very well. So cholesterol is another fluidizer of membranes.
How thick is the cellular membrane? If you figure the hydrocarbon chains of a saturated fatty acid stretched out as far as they can go, you get 1.54 Angstroms * cosine (30 degrees) = 1.33 Angstroms/carbon — times 16 = 21 Angstroms. Now double that because cellular membranes are lipid bilayers meaning that they are made of two layers of hydrocarbons facing each other, with the hydrophilic ends (carboxyls, phosphate groups) pointing outward. So we’re up to 42 Angstroms of thickness for the hydrocarbon part of the membrane. Add another 10 Angstroms or so for the hydrophilic ends (which include things like serine, choline etc. etc.) and you’re up to about 60 Angstroms thickness for the membrane (which is usually cited as 70 Angstroms — I don’t know why).
Neurologists and neurophysiologists spent a lot of time thinking about membranes, particularly those of neurons. In all these years, I’ve never hear anyone talk about hydrocarbon polarizability. It ought to be a huge factor in membrane function. Why? Because of the enormous electric field across the membranes enclosing all our cells (not just our neurons). The potential across the membranes is usually given as 70 milliVolts (inside negatively charged, outside positively charged). Why is this a big deal?
Because the electric field across our membranes is huge. 70 x 10^-3 volts is 70 milliVolts. 70 Angstroms is 7 nanoMeters (7 x 10^-9) meters. Divide 7 x 10^-3 volts by 7 x 10^-9 and you get a field of 10,000,000 Volts/meter. If hydrocarbons are ever going to polarize they should in this environment. The college physics book I bought for the Quantum Mechanics course a while ago — “Physics for Scientists and Engineers” 4th edition p. 662 talks about lightning. The potential difference leading to the discharge is the same; 10,000,000 Volts. This results in a much smaller electric field (probably by a factor of 1,000) because clouds aren’t 1 meter off the ground.
So why don’t our cells collapse and we die? I don’t know.
Here are a few Physics 102 questions for the cognoscenti out there.
l. Potential difference is due to charge separation. Assume a flat membrane 1 micron square and 70 Angstroms thick. How much charge must be separated to account for a potential of 70 milliVolts. Answer in number of charges rather than Coulombs.
2. Now let’s get real. We’re talking about neuronal processes here. So lets talk about a cylindrical membrane 1 micron long (remember that some neuronal processes — such as those going from your spinal cord to your big toe are a million times longer than this). Diameters of our nerve fiber range from 1 micron to 25 microns. Ignoring the complication of the myelin sheath, how much charge must be separated to produce a potential across the membrane of the neuronal process of 70 milliVolts.
The more you think about life, the more remarkable it becomes.