Anslyn pp. 144 – 200

p. 147 — The dielectric constant is measured by how much a substance can alter the capacitance of two plates when placed between them.  If you want to see a variety of ways to actually measure capacitance see http://www.pupman.com/listarchives/1998/April/msg00625.html

p. 149 — Connections — Introduction of 6 different parameters of solvent properties is a real yawner (but necessary).  The connections box on this page makes the reader snap to attention, as they show a real use of two of them(alpha and beta).  Very nice.  Another very nice use of the solvent parameters is the connections box on p. 172. 

The 6 solvent parameters remind me of the 6 blind men and the elephant.  They speak to the same truth — a solvent has many distinct aspects, none of which are the whole story.

p. 152  — last paragraph — “fluxuation” — time for the spellchecker to come out.

p. 156 — DeBye Huckel theory — 50 years ago in grad school we snickered that it only describes slightly contaminated distilled water.  Never forget that the activity coefficient is a fudge factor determined by experiment, not predicted a priori.  Every year my wife and I have dinner with a friend from that era (currently a chemistry department chair), I ask him for the status of DBH and he tells me this is still true (as of Oct ’10).  Remember the concentration of salt in our cells is .3 MOLAR (not a misprint).

In 1962 activity coefficients were used to ‘explain’ why sodium outside cells is 140 milliMolar (roughly) while inside it’s around 10, and why potassium levels are 10 times higher inside cells than outside.   Of course, it’s not an explanation at all.  Coming fresh from grad school, I found this amazingly irritating.  A lot of medicine is like that.  Shut up and remember the way things are, since we don’t know why things are the way we are.  Things have improved presently since we know more about ion channel selectivities, and ion pumps, but there’s still plenty we don’t understand — why we need sleep for one.  

p. 158 — “Energy is not force, but driving force gives a good mental image.”  Anslyn and Dougherty really missed the boat here.  Why call the chemical potential a potential at all?  Because in mechanics the derivative of of the potential energy IS a force.  Why isn’t the Gibbs free energy a force?  Think about it.

Well, as they say, energy isn’t a force.  But there is a deeper reason, moreover the reason is chemical.  When a net force acts on an object there is NOTHING to oppose it.  A difference in Gibbs free energy isn’t the same thing as a force — because of activation energy (italics).  If there were no activation energy a free energy of a chemical change would act exactly like a force.

p. 165 — Excellent discussion of salt bridges in proteins.  Every  paper I’ve read discussing the structure of a particular protein, implicitly assumes that salt bridges are stabilizing.  The excellent discussion shows that (1) it depends on where the salt bridge is (on the outside of a protein, or deep inside) (2) the dielectric constant near the salt bridge — only guessed at in most cases (3) stability is always relative to something else, and compared to hydrophobic side chains of comparable size to asp, glu, lys and arg, the salt bridge deep inside a protein is actually less stable.

p. 166 — An explanation of why the potential energy of ion dipole interactions falls off as 1/r^2 while that of a simple coulombic interaction falls off as 1/r  would be nice. 

p. 168 — A great explanation of the Magic Angle used in NMR spectroscopy.  It’s the angle of offset at which two parallel dipoles (by definition in the same plane) feel no force between them.  

       The potential energy of two parallel dipoles is given by

     E  = -mu1 * mu2 (3 cos^2theta -1)/(4 * pi * r^3 epsilon)

       Where mu1 and mu2 are the dipole moments of the two dipoles, theta is the angle of offset of the two dipoles, r the distance between them, and epsilon is the dielectric coefficient.   E = 0 when theta = arccos {(1/sqrt(3)] which turns out to 54.7 degrees.  So the tube with the NMR sample is inclined by the magic angle to the imposed field, and spun rapidly.  This removes dipole/dipole interactions which would extremely complicate NMR spectra.  It doesn’t affect spin/spin splitting.

      I realize this isn’t a physics textbook, but a pointer to where this and other formulas are derived would be nice.  Otherwise the formulas seem like magic themselves. 

p. 168 “for weak to moderate hydrogen bonds”  — what energy range are we talking about? One of the great strengths of physical organic chemistry (and this book) is its quantitative nature.   The answer is given on p. 171 — you should point to it here, or put the values here.

p/ 172 — Connections — The fact that stronger O – H . . . O bonds have a shorter O – O distance shouldn’t be found here, but where hydrogen bonds are first discussed. 

p. 176  — Going Deeper — very nice discussion.  Anything which helps us understand protein structure more deeply is worthwhile.

p. 179 — The proton sponge and the logical thinking of why para methoxy groups don’t help while ortho methoxy groups do — is exactly why I love organic chemistry.  Have an idea?  Then build a molecule to test it.

p. 184 — re pi stacking.  What about the stacking of the nucleotide bases in DNA and RNA (which we know occurs).  Some mention of this should be made.  In the classic B form of the DNA double helix there are 10.3 bases/turn and they are stacked every 3.4 Angstroms.  Isthe 30 degree shift of each base in this form enough to consider it slip stacking?

Also what about the lady at Cal Tech  (Jacqueline Barton) who calls DNA a pi wire.  [ Proc. Natl. Acad. Sci. vol. 96 pp. 8353 – 8358 ’99 ] I’ve always wondered about this.   The bases stack on top of one another and it seems that charge could easily be transfered through the stack — which she calls a pi-way.   Surely a physical organic chemist should be able to weigh in on this.  I don’t see anything about it in the index.   

p. 189  — “The precise physical origin of the hydrophobic effect has been intensely investigated and is still debated” (as of 2006).  Great statement !   Statements in papers tend to be authoritative.  It’s good to see an honest appraisal of where the field stands.

p. 190 — How are the relative amoungs of linear (anti) and curled up (gauche) n-butane in water actually measured ?  

p. 199 — Fabulous — an explanation of molecular dynamics at last (it uses the derivatives of the molecular mechanics force field equations to get the actual forces involved.  Then clockwork Newtonian universe is set in motion, and stopped after a very short time (Femtoseconds), then the energy of the configuration calculated and the universe set in motion again. 

       (added 30 June ’11 ) Why such a short time?  Because “experience has shown” that allowing the system to follow a trajectory longer that 10^-15 seconds will carry a system into unrealistic geometries, because the forces used in molecular dynamics simulations aren’t true forces (because the potentials they are derived from aren’t true potentials).   Why?  For a great example see problem #27 p. 140.  This is what happens at long bond lengths if a cubic term is added to the quadratic form of the harmonic oscillator to make it more “Morse-like”

  The references at the end of the chapter are pretty skimpy.  Dill’s book “Molecular Driving Forces”, which I’m about to start, doesn’t have a molecular dynamics entry in its index.  Does anyone have any good references for a beginner in moleular dynamics simulations.  If so, post a comment please. 

Molecular dynamics didn’t exist in the 60’s as the computational power for it was nowhere to be found. 

All in all a fabulous chapter.

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Comments

  • MJ  On June 29, 2011 at 10:09 pm

    Re: molecular dynamics references for a beginner – there’s a text by Andrew Leach called “Molecular Modeling” (I have the 2nd edition) that is an overview of the computational chemistry/biochemistry field ranging from computational quantum mechanics to MD to Monte Carlo and a variety of applications. I found useful while in starting out in grad school not quite 10 years ago now, although I am sure there are probably more up-to-date references.

    Re: magic angle spinning in NMR spectroscopy – how detailed of a background are you interested in finding? Malcolm Levitt covers the material briefly in his “Spin Dynamics” textbook (I think there’s two pages dedicated to magic angle spinning, as I recall), and texts on solid state NMR cover it to varying extents.

    Essentially, all NMR-relevant interactions that can be described via a second-rank tensor (which also includes the chemical shift anisotropy and the quadrupolar coupling to an extent) will be averaged out/modulated by spinning at the magic angle to varying extents.

    Re: ion-dipole interaction – I recall that if one tries to solve for the energy of an ion interacting with a dipole via Coulomb’s law (where one basically has two point charges in the place of the dipole separated by a distance that is smaller than the distance from the dipole center to the ion), the r^2 dependence falls right out of the math. I remember doing this years ago for some homework problem for…some class, it’s kind of foggy now. I should do this for myself again, as it’s actually the kind of question I could see someone asking me in the future.

  • luysii  On June 30, 2011 at 9:56 am

    MJ — thanks for all your comments. The molecular biological literature and protein structure literature, is full of molecular dynamics. I never understood how it was done or where it came from until now. It seems to emerge from molecular mechanics (which Anslyn describes VERY critically on pp. 133 – 135 — opening with #1 “There is no theoretical justification for the method” and continuing for #2 – #9) I’ll have a look at Leach, it’s in one of the local college libraries

  • MJ  On June 30, 2011 at 10:36 pm

    My pleasure.

    MD has its origins – at least as I recall them – in the days prior to computers, in fact, where people would do things like get a bunch of ball bearings together in a confined volume and try and understand the structure of liquids. This, I deduce, would have been a suitable companion for any analytical efforts on the structure of liquids under a hard-sphere approximation. But I think it’s fair to say that MD has its origins more in the physics of liquids/condensed matter community than in the computational chemistry realm.

    The authors might mean “there is no *rigorous* theoretical justification for the method” – not only so as to avoid underestimating the ingenuity of theoretical chemists, but to show that connecting it to quantum chemical studies of molecular/electronic structure is, at the very least, non-trivial and requires a fair amount of mental gymnastics.

    Of course, I would be tempted to ask – if using classical mechanics-flavored methods is unjustifiable for small organic/organometallic molecules, wouldn’t it be more acceptable to use analogous classically-inspired methods for macromolecules (biological or otherwise), given that they are larger and therefore a bit further into the regime that can be described by classical mechanics? Heh.

  • luysii  On July 1, 2011 at 7:36 pm

    If chapter II had anything to say, it was how crucial the solvent is for reactions taking place in it. The main problem with applying molecular dynamics to matters biological and the huge molecules and molecular complexes involved is that we don’t understand water very well. The Curious Wavefunction had a great post in the past year or so concerning how poor the force field for water is. Maybe he can provide a link to it.

  • MJ  On July 1, 2011 at 8:34 pm

    Point taken in terms of understanding solvation for understanding (bio)chemical reactions in adequate detail.

    I honestly had something more mechanical in mind, such as correlated domain motions in proteins*, where you have a cleft opening or closing in response to binding of a ligand or cofactor. Certainly, the ligand binding event, and any subsequent chemistry, is going to be dependent on solvation, among other considerations. But I would think that (admittedly rather sophisticated) classical mechanics-based models for simulating how two shapes linked by a spring would open and close is not too ludicrous of a notion, especially if you’re interested in larger-scale dynamics and behavior. But that is almost certainly a reflection of my own interests, where despite working in a chemistry department, I really don’t do that much chemistry. Heh.

    *: The prime example that comes to mind is where a research group examines alcohol dehydrogenase and the cleft opening/closing in response to the presence of a cofactor: http://dx.doi.org/10.1103/PhysRevLett.101.138102

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