Quantum Chemical calculations can be done at a variety of levels of accuracy. You will set up calculations through the Spartan interface at a "Semi-Empirical" level. We will also show you results (that have been performed with a variety of software) at an ab initio level. The ab initio calculations take much much longer than semi-empirical and are capable of giving more reliable answers for a much broader range of compounds. We will discuss the differences in these two methods in this excercise. The semi-empirical approach that you will use, (AM1), is capable of giving reasonable results for amides in a variety of results, and can run very quickly on these workstations. Using the semi-empirical approach you will look at trends in the relative energies stabilities and reactivities of propsed intermediates of the hydrolysis raeaction: for example you will study the effects of solvation, hydrogen bonding, side chain, and conformation on the partial charges.
Create
a directory for the files you will make in this exercise. Spartan also creates a subdirectory
for each molecule you build.
Start Spartan
from
the subdirectory where the results of your calculations will reside
by typing the following command in a Unix window) at the command
prompt: spartan
.
See the Tutorial
on Spartan to help familiarize yourself with this program and learn how to
build molecules, perform molecular orbital (MO) calculations, compute and
display properties of molecules.
Now study these intermediates with a solvent (water and hydrocarbon) model, and with explicit hydrogen bonding partners to mimic the partners seen in the proteases. Do these interactions change your
central conclusion about which species has a dissociative potential for the C-N bond?
It is a good idea
to start a table at this point to keep track of your calculations as you
go.
Stabilities of the Hydrolysis Intermediates
We will consider all possible ionization states of the intermediates of water attack on NMA, under the assumption that protons may be supplied or absorbed freely by the surrounding enzyme active site.
For example, consider the possibility that the nitrogen is protonated first, or that the
carbonyl is attacked first with hydroxide or with water. There are therefore at least five
intermediate species to consider: two cations, an anion, a zwitterion and a neutral species. Draw all of these species and then build them in Spartan. For comparison, build also the products of the reaction (amine and acid, or ammonium and carboxylate) and the reactants (amide and water).
Evaluate their stabilites by making a single point energy calculation and then trying to minimize the energy by asking for a ground state minimized structure. One of these hydrates
will dissociate along the C-N bond: which is it, and why?
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Comparing the Relative Stabilites of the Intermediates
Using appropriate biologal acids and bases, make a valid thermodynamic comparison of the
enthalpies of each intermediate. In order to give meaningful comparisons of heats
of formation, the same numbers/types of atoms must be in the structures of course,
but also the ionization equilibria should involve reasonable acids or bases that
have small molecular weights so that the calculations do not get too slow
(e.g. formic acid/ formate or ammonia/ammonium). Try to locate the energy of the reactive species identified in the last section, relative to the reactants and the products.
Using the Arrhenius equation, assuming that this is the higherst point on the reaction surface, estimate an overall rate for the reaction. How could the enzyme lower this barrier? Using appropriate
hydrogen bonding partners and geometries, estimate the energy of this species in the context of
the enzyme active site.
Studying the Reaction Coordinate with the "Drive" Command
In fact the species identified and studied above, the zwitterionic hydrate of
the amide, is only one species along the reaction coordinate. Build a complex of water and
a simple amide and one general acid or base in the vicinity (e.g. a carboxylate or carboxylic acid) that can serve to activate the water molecule to produce hydroxide for attack on the carbonyl,
and/or could provide the proton to protonate the nitrogen. Design coordinate drive "experiments"
to watch the formation of the reactive zwitterionic species and its decay into products.
Your placement of the general acid or base will influence your results significantly, so you might try experiments w/ and w/o the base or experiments in which you think it is correctly and incorrectly placed. Since you need to deliver a hydroxide and a proton to reach the reactive species, you probably will need to perform two successive drive experiments. Be careful that you have a consxistent model (meaning numbers of atoms, geometry etc. so that the eenergy scales on these two
"drive" calculations will be comarable.
Your Report
In your homework, write the various hydration and dissociation mechanisms you considered. Indicate how you selected the most reasonable among them. Discuss the energy and the structure of the highest point on the pathway and describe how an enzyme active site might lower this energy. Support your statements with a table of
energies calculated with and without solvent models. Using examples from the pdb discuss whether there is any evidence that welll characterized proteases stabilize the critical intermedaite in the way that you described.
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