Weak interactions

So far we have talked about covalent bonds, reactions that form or break covalent bonds, and how things arrange around atoms. A lot of things happen without any bond being formed or borken. These non-bonded interactions are critical for biological activity. Things to keep in mind:

a) Non-bonded interactions are weak - While a covalent bond can be anywere from 60 to 250 Kcal/mol, non-bonded interactions are in the 1 to 15 Kcal/mol range.

b) They are easily reversible and dynamic. The energy required to break a non-bonded interaction is small, comparable in most cases to the random thermal energy of the system. Therefore they appear and disappear rapidly and spontaneously, a lot faster than a covalnet bond, which means that there is no need to catalize their formation or cleavage.

c) Non-bonded interactions are crucial in molecular recognition, that is, the way two things find that they are right for each other. A substrate will first bind to an enzyme through non-bonded interactions, and if it is the wrong substrate, it will fall off the enzyme before any chemistry takes place.

For example, binding of taxol, an anticancer drug, to tubulin is due exclusivelly to non-bonded interactions. Upon binding there is a sizable conformational change in the microtubule polymer that makes it very stable, inhibiting the proper formation of a mytotic spindle, which screws-up cell division, killing the cell. In this case, the interactions may be weak, but they are deadly...

Another important thing to recall is that all chemistry in cells and biological systems happens in water, and therefore we have to study how the non-bonded interactions occur in this solvent.

Properties of water

Water ammounts to 70% of all substances on Earth. This proportion is maintained in all living organisms, and therefore all biochemistry occurs in aqueous solutions. Although it looks simple, water is a chemically rich molecule:

a) It is formed by an O (eng = 3.5) and two H atoms (eng = 2.1). The bond is therefore higly polar (33% ionic character). It is a dipolar molecule, and will therefore interact strongly with other dipolar molecules (other ionic or polar substances).

b) The water molecule has tetrahedral geometry (<H-O-H> = 104.5^o), where the oxygen atom is in sp³ hybridization. Since it shares only two of the six valence electrons to bond with hydrogens, we have two sp³ orbitals occupied by lone electron pairs. Therefore, there is a large electron density on the oxygen (partial negative charge).

c) This allows for the formation of hydrogen bonds: We have a large electron density on the oxygen (two lone pairs). Additionally, the oxygen is more electronegative than the hydrogen, and it will pull the electrons towards it, leaving the hydrogen with a partial positive charge. The end result is that hydrogen atoms in a water molecule can interact with oxygen atoms in other water molecules.

d) As we saw last time briefly, the oxygen in water can act as a nucleophile in hydrolysis reactions. We will see this over an over in enzyme mechanisms.

e) In the definitions section, remember that something is hydrophobic when it does not disolve in water, and hydrophilic when it disolves well in water.

Ionic interactions and salt bridges

When we talked about what atoms form which type of bond, we described that the further appart the elements are from each other in the periodic table, the more polar the bond. Actually, the largest the difference in electronegativies, the more polar character of the bond. In purely ionic bonds, like NaCl, we have all the negative charge (-1) in the electronegative atom (Cl), and all the positive charge (+1) in the electropositive atom (Na). Now, the pull between the two ions can be described easily by the Coulomb equation:

where q₁ and q₂ are the atomic charges, and r is the distance between the point charges. We can see that the ionic interactions depend both on the magnitude (and sign) of the charges, as well as on the distance that separates them.

Now, we don't need to have purely ionic compounds to see this type of interactions. If we have a very polar bond (formed by elements with very different electronegativities), we have the potential for formation of charged groups. Several of the functional groups we discussed last time can do this. In proteins, the carboxyl (R-COOH) and amine (R-NH₂) are the best examples. One looses a proton easily, while the other one gains one (why?):

The R-COO^- and R-NH₃⁺ ions behave the same way that the Cl^- and Na⁺ ions in NaCl, and the same electrostatic equation applies. We call interactions beyween these groups salt bridges.

One thing that we haven't mentioned here yet is how these ions (or ions in general) behave in water. Since water is polar, it will interact with the charged species. The negativelly charged oxygen in water will position itself close to cations, while the positivelly charged hydrogen will arrange so that it maximizes its interactions with the anions. Although we have a local organization of the water molecules, and therefore a loss in entropy (bad), we have very strong electrostatic interactions and a gain in enthalpy (good) that favour the global process. We call these compounds or groups hydrophilic (they love water).

The water molecules that surround the positive and negative ions are called the hydration shell, which has the apparent effect of enlarging the ions. Another effect of the hydration shell is that it will shield the charges from each other: Since we have several water molecules around the ions, the charges that they see across the solvent are effectively smaller. Althoug hthis is a microscopic phenomenon, we see the macroscopic effect as the dielectric constant of the solvent (D). It is a dimenssionless constant that needs to be included in the Coulomb equation to account for solvation and charge shielding. Thus, in solution, the Coulomb force is:

D is the dielectric constant. In water, it is ~ 80. In vacuum, electrostatic interactions can be several hundred Kcal/mol. In aqueous solution, however, they are only in the order of 10 to 15 Kcal/mol due to charge shielding. The optimum distance between two charged groups is approximately 2.8 Å. Below that, we start having steric clashes between the electron coluds of the atoms that increase the energy of the system.

Interaction range: long, but damped by solvent.

Hydrogen bonding

We briefly talked about this when discussing water. To form a hydrogen bond (or h-bond) we need two atoms in addition to the hydrogen atom: A donor atom, which will contribute the hydrogen, and an acceptor, which has high electron density (usually lone electron pairs) and will capture the proton. In water, one oxygen atom act as the donor, and another one from another water molecule as the acceptor. H-bonds are not limited to oxygen as donor and acceptor atoms. We just need an atom that is willing to loose a proton, i.e., a labile proton, and one that can capture it. Thus, the following groups can participate in h-bonds:
 

Donors	Acceptors
H-O-H	H-O-H
R-NH2	R-P(=O)-(OH)2
R-NH-C(=O)-R	R-NH-C(=O)-R
R-OH	R-OHR-O-R
R-COOH	R-COOH

These are not in order: Any donor can use any acceptor. Also, only a brief list is presented here. On the other hand, protons attached carbon (C-H) don't participate in h-bonds, because the C-H bond is non-polar.

H-bonds are also electrostatic in nature, so, as a rough approximation, the Coulomb laws apply. However, h-bonds do not form between charged species, but from partially charged species. Therefore, the electrons are still around the atom, but arranged asymetrically around it. These menas that there is a direction in which the interactions are greater: hydrogen bonds are directional, with the largest interactions occuring when the three atoms involved are aligned (D-H^...A). As for charged interactions, the optimal distance between the donor and acceptor is approximatelly 2.8 Å. The energies involved in h-bonds are in the 2 to 5 Kcal/mol range.

H-bonds are very important, because proteins are stuffed with groups can that participate in h-bonding: The amide bond that forms when two amino acids condense has both a donor and an acceptor. Usually, protein chains fold to a defined three-dimensional (3D) structure that is stabilized by hundreds of h-bonds between groups in the amide bonds. They hold the protein in place, and define the way in which the protein folds into its final 3D structure. In enzymes, there can also be h-bonds that will stabilize the enzyme-substrate complex.

Furthermore, we can make drugs that have well placed donor and acceptor groups so that they interact with a particular region of a particular protein - These can either prevent the proper folding of the protein, or could prevent the protein to bind to a particular substrate, with all the implications that this will bring about.

We can 'see' h-bonds experimentally. If you take the infra-red (IR) spectrum of a molecule containing h-bonds, an absorption band for the D-H^...A bond will appear (the position depends on the nature of the donor and acceptor). Additionally, nuclear magnetic resonance (NMR) can be used to detect h-bonds. The chemical shift of labile protons changes a lot with temperature, because they can exchange with the solvent (water). If they are involved in strong h-bonding, the exchange with water is not that big, and the change of chemical shift with temperature is a lot smaller.

Interaction range: intermediate.

van der Waals interactions

So far we have talked about interactions in charged or partially charged groups. Are there any interactions between neutral atoms? As with all of these 'smart' questions, the answer is 'yes'. When we bring two neutral atoms together in space, the electron clouds of each other will start to interact. The effect on one atom is a deformation of the electron cloud of the other due to electron repulsion. This deformation (dispersion) brings about asymmetry to the electron cloud; an uneven distribution of charge results in a small transient dipole appearing on the atom (on both atoms). The movement of these two dipoles id correlated, so we have have weak attractive interactions between them, called the van der Waals interactions. However, if we go to far, we have the normal steric non-bonded repulsion due to electron cloud overlap. So we have an attractive (dispersion) and a repulsive force (electron cloud overlap) acting. The energy profiles of van der Waals interactions look like bonding profiles, but much lower in energy.

van der Waals interactions are very weak, in the order of 0.5 to 1 Kcal/mol. However, It is through the van der Waals interactions (both the attractive dispersion force and the repulsion of electron cloud overlap) that geometric specificity is achieved in biological systems.

Interaction range: short.

Hydrophobic effects

What happens when you add oil to a glass of water? The oil droplets tend to come together and form a larger blob. Macroscopically, this has the effect of minimizing the contact area between water and oil (remember that if you cut something in two you get a larger surface area). The principle that regulates this at the atomic level has more or less the same origin.

When a very non-polar molecule interacts with water, there is no good place for the water molecules to go to: There are no positivelly or negavelly charged atoms. What happens is that water will try to maximize interactions with other water molecules around the solute. This is very unfavourable entropically, because the shell of water molecules around the non-polar solute is highly ordered and lowers the entropy (bad), but opposed to the case of ionic groups, which have large enthalpic contributions to the stabilization, we have no electrostatic interactions for non-polar groups.

Now, the only way that we have to minimize the energy of a system like this is to minimize the number of ordered water clusters ('cluster' is a fancy word for 'group'). This can be accomplished by packing all the hydrophobic groups together. In this way, the surface area of the hydrophobic molecules exposed to water will be smaller, and we have less unfavourable ordering of water molecules.

These collection of effects are called hydrophobic interactions, or the hydrophobic effect. It is not due to the hydrophobic groups themselves, but more a phenomenon arising from the solvent trying to get rid of the oily stuff. The energetics of this are difficult to compute accurately - we generally assume a fixed 'penalty' for solvating the hydrophobic surface. The energies involved are circa 1 Kcal/mol.

Interaction range: short

Consequences of weak interactions

As we discussed before, non-bonded interactions are crucial in all biological processes. Although that individually they are a lot weaker than the forces acting in covalent bonds, we usually have thousands of non-bonded interactions in a biomolecule, which all work collectively. An atom may have only three covalent bonds, but it can have numerous non-bonded interactions of different types that all pull towards lowering the energy of the final system. This brings about the concept of complementarity of interactions between biological molecules. If two molecules interact, the shape, charges, and h-bond donors and acceptors of one molecule will have to complement as much as possible the shape, charges, and h-bond acceptors and donors of the other.

One thing to keep in mind: If we consider a soution of a certain molecule, the presence or absence of any of the interactions described here will have almost no net effect on the total energy of the system: For example, a hydrogen involved in a h-bond with a particular group in a protein can be just as happy in forming a hydrogen bond with water molecules. The same goes for other non-bonded interactions:There are no empty holes.

You can also picture it in another way: After all the covalent bonds have been formed in a macromolecule, the energy adopts certain value. The only way that the energy can be minimized is by maximizing favourable non-bonded interactions, because we cannot form new bonds.

Finally, from all the stuff we have seen here, we can conclude that molecules that are amphiphilic (i.e., they have both hydrophobic and hydrophilic groups) will tend to expose the polar (hydrophilic) groups towards water, and hide the non-polar, greasy groups and in their innards. micelles, lipid bylayers, globular proteins.

Prepared by Guillermo Moyna, 1999.