The quantum theory applied to biology


Water is a Lewis acid and a Lewis base at the same time. Both its electrostatic properties and its frontier orbitals are important for understanding the chemical reactions of water. Water is important in biology because water acts as a solvent and it participates in important enzymatic reactions (e.g. enzymatic hydrolysis).

We calculated the equilibrium structure of water using GAMESS. The calculation was done using DFT with the B3LYP potential and a 6-31G+(d,p) basis.
Atom X (ångström) Y (ångström) Z (ångström)
Oxygen 0.0586892 0.0586892 0.0000000
Hydrogen 1.0149135 -0.0736028 0.0000000
Hydrogen -0.0736028 1.0149135 0.0000000

The table below shows the Mulliken population analysis of the HOMO and LUMO and the CHelpG charge.
OXYGEN 1 -0.79360 1.07484 0.75375
HYDROGEN 2 0.39680 -0.03742 0.12313
HYDROGEN 3 0.39680 -0.03742 0.12313

  • The electric charge is calculated from the molecular electrostatic potential that depends on the electron density. The electron density can be calculated from the Kohn-Sham orbitals. We used a DFT B3LYP calculation to find the Kohn Sham orbitals.
  • Mulliken population analysis was done with the molecular orbitals obtained from an MP2 calculation. MP2 corrects for the correlation energy, but the orbitals have vary much the same physical meaning as the Hartree Fock orbitals. That allows us the use the mulliken population analysis to understand the HOMO and the LUMO.
  • Oxygen will act as an electron donor because the HOMO has the highest density on oxygen.
  • There will be no covalent charge transfer to the hydrogens.
  • The high partial charges on oxygen an hydrogen indicate that there can be a significant contribution from the coulombic interaction energy when water interacts with other molecule. This is important because water acts as a solvent in biology.
  • The mulliken population analysis also shows that the HOMO and the LUMO have the highest density on the SP hybrid orbitals on the oxygen atom

Charge transfer upon hydrogen bonding in hexagonal ice.

Water molecules in liquid water and in ice interact withone another by forming hydrogen bonds. Hexogonal ice is the form of natural ice and snow.

Amino Acids

Enzymes control most biochemical reactions in living organisms, they do this by means of catalysis and inhibition. The enzymes (and proteïns in general) usually contain one or more polypeptides. Polypeptides are polymers and amino acids are the monomers comprising the polypeptides. As a consequence the chemical properties of these amino acids are very important to understand the properties of enzymes.

A lot of research has been done on enzymes. You can crystalize purified enzymes and then obtain their 3-dimensional molecular structure with x-ray and neutron diffraction experiments. Scientist often deposit the result of their research on the protein databank. You can view and download these structures directly from their website.

Calculations on amino acids :

We calculated equilibruim structures for the aminoacids shown in the table below. These calculation serve as examples of what results can be obtained with electronic structure calculations. These are the equilibrium structures for the neutral aminoacids in vacuum. The results from these calculations cannot be exptrapolated to a biological context.

We used a 6-31G+(d,p) basis set. The charges and the equilibrium geometry were calculated with density functional methods. The HOMO and the LUMO were calculated with HF MP2 methods. We did not use DFT to calculate the HOMO and the LUMO because Hartree Fock orbitals have a phsysical meaning.The Kohn Sham orbitals should be used the calculate the electron density and the properties that can be derived from these ( e.g. molecular structure and molecular electrostatic potential ) .

Then we calculated the charges on the atoms so that they fit to the molecular electrostatic potential. These charges are reactivity indexes that can be used to predict reaction mechanisms of charge controlled reactions. They will provide information about the initial step of a reaction mechnism.When two or more molecule approach later in the reaction, these charges can change due the intermolecular interaction. Note that the charges on atoms "inside" the molecule have little value because other molecule cannot get ot them.

We also calculated the mulliken analysis of the HOMO and the LUMO of these amino acids.
Alanine (Ala) Arginine (Arg) Arginine protonated (Arg) Aspartate (Asp)
Aspartate anion (Asp) Asparagine (Asn) Cysteine (Cys) Glutamate (Glu)
Glutamine (Gln) Histidine (His) Histidine protonated (His) Glycine (Gly)
IsoLeucine (Ile) Leucine (Leu) Lysine (Lys) Lysine protonated (Lys)
Methionine (Met) Phenylalanine (Phe) Proline (Pro) Serine (Ser)
Threonine (Thr) Thyrosine (Tyr) Thryptophan (Trp) Valine (Val)

The biochemical properties of carbohydrates derive from their Lewis acid and Lewis base properties.

Biological organisms use carbohydrates for energy storage and as structural components. Carbohydrates can be linked to serine, asparagine or threonine through glycosidic bonds. Monosaccharides are aldehydes or ketones. Dihydroxyacetone and d-glyceraldehyde are the smallest monosaccharides they have three carbon centers.

We calculated the Lewis acid base reactivity indices for both molecules. These reactivity indices predict that the C-O ketone bond and the C-O aldehyde bond are a Lewis acids and that the ketone and aldehyde oxygen are a Lewis bases. We did a Mulliken population analysis for the atomic orbitals for the HOMO and the LUMO. This analysis gives detailed information about the electronic rearrangement in the molecule at the initial stage of the reaction.

Dihydroxyacetone and d-glyceraldehyde equilibrium structures and reactivity indices

dihydroxyacetone XYZ file Results summary
d-glyceraldehyde XYZ file Results summary

Other monosaccharides like d-ribose and d-glucose have five and six carbon atoms. The carbon atoms of these molecules are asymmetric as a consequence there are many monosaccharides that differ only in the 3 dimensional arrangement of their atoms

α-d-glucopyranose and d-glucose equilibrium structures and reactivity indices

d-glucose XYZ file Results summary
α-d-glucopyranose XYZ file Results summary

Monosaccharides are linked through glycosidic bonds to form disaccharides and more complex polysaccharides.
  • Aside is the structure of sucrose (α-D-glucopyranosyl-(1→2)-β-D-fructofuranose) or sugar.
  • The electrostatic charges on the atoms have been calculated so that they correspond to the molecular electrostatic potential.
  • Sucrose is a highly polar molecule just like water. This explains why water is a good solvent for sucrose.

Sucrose equilibrium structure with charges ( XYZ file )

The lewis acid and base reactions relate molecular genetics to quantum physics.

DNA and RNA, the molecules that carry genetic information are called nucleic acids. Four nucleotides GMP, AMP, CMP, TMP are be linked through phosphoester bonds. This results in long unbranched polymers that interact with other polynucleotids through hydrogen bonding. The phosphodiester bridges acts as a Lewis base and allow for interaction with proteins.

Molecular genetics is the field of biology and genetics that studies the structure and function of genes at a molecular level. Most important biological and chemical molecular properties of nucleic acids are Lewis acid base reactions.

We calculated the equilibrium structures and the charges for these nucleotides. We used a 6-31G+(d,p) basis set. The charges and the equilibrium geometry were calculated with density functional methods.

Results for nucleic acids equilibrium structures :

GMP XYZ file Results summary
AMP XYZ file Results summary
CMP XYZ file Results summary
TMP XYZ file Results summary