Covalent interactions (bonds) hold the atoms together within molecules. Covalent bonds are strong, and their enthalpies are on the order of 100 kcal/mole (400 kjoule/mole). Covalent bonds remain intact when ice melts, when water boils, when proteins unfold, when RNA unfolds, when DNA strands separate, and when membranes disassemble.
The processes of melting, boiling, and unfolding involve disruption of molecular interactions (aka noncovalent interactions), which are interactions between molecules. Molecular interactions are important in diverse fields of protein folding, drug design, separation technologies, etc.
Molecular interactions are weak. The enthalpy of a molecular interaction is 1-10 kcal/mol, which in the lower limit is on the order of RT and in the upper limit is significantly less than a covalent bond. Even though they are weak individually, cumulatively the energies of molecular interactions can be significant. Molecular interactions underlie the differences in boiling points of liquids. The boiling point of H2O is hundreds of degrees greater than the boiling point of N2 because of differences in molecular interactions in H2O(liq) versus N2(liq).
Molecular interactions drive proteins to fold and DNA to anneal. The number molecular interactions between the functional groups within a globular protein is enormous. Huge numbers of weak molecular interactions within a folded protein are balanced by the molecular interactions of the unfolded protein with surrounding water molecules. The protein is held in 'delicate balance between powerful countervailing forces' contributed primarily by molecular interactions. It is the small difference between these large effects that determines direction of the folding 'reaction'. The equilibrium constant is generally small. A small change in pH or temperature can tip the balance.
Have you ever denatured (unfolded) a protein? Yes. When you heat an egg to around 60 deg C, the proteins denature and aggregate. The aggregated protein forms large assemblies that scatter light, giving the egg a white appearance. When you add lemon juice to milk, the pH drops and the proteins denature and aggregate. Have you ever melted DNA? Yes, if you have run a PCR reaction.
Noncovalent forces were discovered by the Dutch scientist Johannes Diderik van der Waals. He noticed that molecules are sticky. The phrase 'van der Waals interaction' has come to mean a adhesion/cohesion between molecules that are close together in space. The term 'van der Waals interaction' is not sufficiently informative or descriptive for our purposes here. A van der Waals interaction describes a totality of various types molecular interactions. We avoid the term "van der Waals interaction" because that phrase does not decompose the interactions in a physically meaningful way or provide predictive models.
There are many different ways of parsing or classifying molecular interactions. The categories in the Table of Contents are the clearest and easiest to understand.
All molecular interactions are fundamentally electrostatic in nature and can described by some variation of Coulombs Law.
Atoms take space. When two atoms approach each each other, at some distance the overlap of the occupied orbitals causes electrostatic repulsion between the electrons of the two atoms. This repulsive energy between atoms acts over a very short range, but goes up sharply when that range is violated.
The repulsion goes up as 1/R12. It is important only when atoms are in
very close proximity, but then it becomes very important. Because this
repulsive term rises so sharply as distance decreases it is very often reasonable
to think of atoms as hard spheres, like small pool balls, defined by van der Waal radii and van der Waal surfaces. As two atoms approach each other their van der Waals surfaces make contact as the distance between them decreases to the sum of their van der Waals radii. The smallest distance between two non-bonded atoms is the sum of the van der Waals radii of the two atoms. Of course we are assuming that bonds do not form. When bonds form van der Waals radii and surfaces are violated.
The van der Waals radius of carbon is evident from the spacing between the layers in graphite. Those coordinates are
here [coordinates]. The distance
between atoms in different layers of graphite is never less than twice
the van der Waals radius of carbon (2 x 1.7 = 3.4 Å). The atoms
within a graphite layer are covalently linked and so are in violation of
the van der Waals radius. vdw surfaces are also violated by hydrogen
Figure 2 shows how short range repulsion sets the distance of 3.4 Å between sheets in graphite.
How to sense short range repulsion? Try compressing a liquid.
These are interactions between cations and anions, which are ions and functional groups with formal charge. Electrostatic interactions can be either attractive or repulsive, depending on the charges of the interacting species. Electrostatic interactions can be very strong, and fall off slowly with distance (1/r). These interactions cause the vapor pressure of sodium chloride, for example, to be very low. If you leave table salt out on the counter, how long before it sublimes away? (a very long time.) The electrostatic interactions in a sodium chloride crystal are called ionic bonds. But if a single cation and anion are close together on the surface of a protein, it is called a non-covalent interaction.
Figure 3 shows a cross section of a NaCl crystal. In reality the ionic radius of the sodium cation is less than that of the chloride anion.
The coordinates of sodium chloride are here [coordinates]. The attractive forces between sodium cations and chloride anions in sodium chloride are called 'electrostatic interactions'. This name is unfortunate because ALL molecular interactions are inherently electrostatic in nature. However, by convention we call them electrostatic. These interactions are observed between phosphate oxygens of RNA (formal charge -1) and magnesium ions (formal charge +2) as shown in the figure below.
Figure 4 shows RNA (within the ribosome) in which anionic phosphate oxygens engage in short-range (2.1 A) electrostatic interactions with a magnesium ion. Here the dashed lines do not represent hydrogen bonds. There are no hydrogen atoms between the phosphate oxygens and the Mg2+ ion.
In another example of electrostatic interactions, the amino acids
aspartic acid (an anion) and lysine (a cation) engage in electrostatic interactions when they are close by.
electrostatic force between two point charges is given by:
Force = k q1 q2 / ε r 2
where k = 9.0 x 10 9 nt-meter 2 /coul 2
q = -1.6 x 10 -19 coulombs for an electron.
r = distance between the point charges (meters)
ε = the dielectric constant of the medium (unitless).
reflects the tendency of the medium to shield one charge from another.
ε is 1 in a vacuum, around 4 in the interior of a protein
and 80 in water. The problem of calculating electrostatic effects in
proteins is complex in part because of non-uniformity of the dielectric
environment. The dielectric micro-environment is variable, with less
shielding of charges in regions of hydrocarbon sidechains and greater
shielding in regions of polar sidechains.
The electrostatic energy is given by:
ΔE= k a q1 q2 / ε r
where a = Avogadro's number.
One can crudely estimate the energetics of a charge-charge interaction in a protein. The energy of an amine (charge +1) and a carboxylic acid (charge -1) separated by 4
Å in the interior of protein is given by:
In a molecule with unlike atoms,
electrons are not shared equally. The tendency of any atom to pull
electrons away from other atoms is characterized by a quantity called
In a molecule composed of atoms of
various electronegativities the atoms with lowest electronegativities
hold partial positive charges and the atoms with the greatest
electronegativities hold partial negative charges. In a water molecule, the electronegative oxygen atom pulls electron density away from the hydrogen atoms. The oxygen atom carries a partial negative charge. The hydrogen atoms carry partial positive charges. This phenomena of charge separation is called polarity. Water is a polar molecule. N2 is a non-polar molecule.
Figure 5 shows the charge distribution of a water molecule. The oxygen atom pulls electron density away from the hydrogen atoms. The oxygen carries a partial negative charge and the hydrogen atoms carry partial positive charges.
The extent of charge separation within
a molecule is characterized by the dipole moment μ. The dipole moment of a molecule is determined by the magnitudes of the partial charges and by the distances between them. To quantitate dipole moments, charges are expressed in esu's and distances in centimeters. The dipole moment of an electron and a proton separated by
1 Å is given by:
(4.8 x 10-10 esu) (10-8cm) =
4.8 x 10-18 esu cm
= 4.8 Debye
The dipole moment of water is 1.85 Debye (HCl = 1.1 D; CH3Cl = 1.9 D; HCN = 2.9 D; NH3 = 1.47.
Figure 6 shows the partial charges within a polypeptide. The symbol size is scaled to the magnitude of the partial charge.
Partial Charges on the Atoms of a Peptide
The orientation of the dipole moment of a peptide is approximately
parallel to the N-H bond and in magnitude is around 3.7 Debye.
Figure 7 shows the orientation of the dipole moment of a peptide.
The large dipole moment of a peptide bond should lead one to expect that dipolar interactions are important in protein conformation and interactions. They are. The large dipole of a peptide bond can be attributed in part to resonance. However, these simple resonance structures present an oversimplified view of the electronic structure of a peptide.
Figure 8 shows two of the resonance structures of a peptide. The real structure is a hybrid of the resonance structures. The peptide bond is a partial double bond, and cannot rotate freely.
A dipole can interact with point
charges (called Charge-Dipole Interaction), other dipoles (called Dipole-Dipole
Interaction), and can induce charge distribution in surrounding
molecules (called Dipole-Induced Dipole Interaction). We will discuss each of
these interactions separately.
interaction energy between two dipoles can be either positive or negative and can be calculated with Coulomb's Law. Listed below are the energies of interaction for two dipoles with moments of 1 Debye at a distance of 5 Å in a medium of ε = 4.Dipole-dipole interactions fall off with 1/r3.
Figure 9 shows how dipole-dipole interactions depend on the orientations of the dipoles. Dipole-dipole interactions can be attractive or repulsive. In solution the orientations of molecular dipoles change rapidly as molecules tumble about. The time-average force is attractive.
D3. Dipole-induced dipole interactions.
| Table of Contents |
Structure Tool |
Williams Home |
A molecule with a permanent dipole can induce a dipole in a second molecule that is located nearby in space. The strength of the interaction depends on the dipole moment of the first molecule and the polarizability of the second. Molecules with Π electrons, such as benzene and phenylalanine are more polarizable that molecules without Π electrons. Dipole-induced dipole interactions are always attractive and can contribute as much as 0.5 kcal/mole to stabilization. Dipole-induced dipole interactions fall off with 1/r4.
Figure 10 shows how a static dipole can induce a dipole in an adjacent molecule. The static dipole 'polarizes' the adjacent molecule. Π electrons are more polarizable (more easily shifted) than σ electrons.
Dipole-induced dipole interactions are important even between molecules with permanent dipoles. For example, the dipole of one water molecule will influence the electron distribution in an adjacent water molecule.
Figure 11 shows how water molecules polarize each other. When the two water molecules approach each other and form a hydrogen bond as shown here, the partial negative charge on the oxygen of the top water molecule increases, and the partial positive charge on the proton of the bottom water molecule also increases. The symbol size is scaled to the magnitude of the partial charge.
Figure 12 shows four water molecules interacting favorably with a magnesium dication. The negative ends of the water dipoles are directed toward the positively charged magnesium ion. Here the dashed lines do not represent hydrogen bonds. There are no hydrogen atoms between the Mg2+ cation and the water oxygen atoms.
Molecules behave like oscillating
dipoles. In molecules that are located nearby to each other the oscillators are coupled. The movements of the electrons in molecules are correlated. Electrons tend to run away from each because of electrostatic repulsion. Coupled fluctuating dipoles experience favorable electrostatic interaction known as dispersive interactions. The strength of the interaction is related to the polarizabilities of the two molecules (or atoms).
Figure 13 shows how fluctuating dipoles of liquid Xenon (or Helium or Neon, etc) are coupled. The fluctuations are correlated and are very fast, on the femtosecond (10-15 second) timescale. Adjacent Xenon atoms experience electrostatic attraction from the transient dipoles. Two different representations of fluctuating dipoles are shown.
Dispersive interactions are always attractive and occur between any pair of molecules, polar or non-polar, that are nearby to each other. Dispersive interactions are the only attractive forces between atoms in liquid He (bp 4.5 K), Ne (27K), Ar (87K) and between molecules of N2 (77K). Without dispersive interactions there would be no liquid state for the Nobels. About a 25% of the attractive forces between water molecules are dispersive in nature. The total number of pairwise atom-atom dispersive interactions within a folded protein is enormous, so that dispersive interactions can make a large contribute to stability.
Fluctuating dipole interactions fall
off with 1/r6.
F. Hydrogen bonding.
| Table of Contents |
Structure Tool |
Williams Home |
The idea that a single hydrogen atom could bond simultaneously to other two atoms was proposed in 1920 by Latimer and Rodebush and their advisor, G. N. Lewis. Maurice Huggins, who was also a student in Lewis' lab, describes the hydrogen bond in his 1919 dissertation.
An acceptor atom (A) with a basic lone pair of electrons (i.e., a Lewis Base) can interact favorably with an acidic proton bound to an electronegative atom (D). A strong hydrogen bond requires that both atoms A and D are electronegative atoms. The most common hydrogen bonds in biological systems involve oxygen and nitrogen atoms. Sulfur can also engage in hydrogen bonds. Hydrogen bonds where atom D is a carbon atom are observed although these are relatively weak interactions. Hydrogen bonds are essentially electrostatic in nature, although the energy can be decomposed into additional contributions from polarization, exchange repulsion, charge transfer, and mixing. In traversing the Period Table, increasing the electronegativity of atom D strips electron density from the proton, increasing its partial positive
charge, and increasing the strength of the hydrogen bond.
Figure 14 illustrates three different styles for representing a hydrogen
bond. Atom A is the Lewis base (for example the N in NH3 or the O in H2O) and the atom D is electronegative (for example O, N or S). The conventional nomenclature is confusing: a hydrogen bond is not a covalent bond.
Hydrogen bond strengths form a continuum.
Strong hydrogen bonds of 20-40 kcal/moll, generally formed between
charged donors and acceptors, are nearly as strong as covalent bonds,
Weak hydrogen bonds of 1-5 kcal/mol, sometimes formed with carbon as the
proton donor, are no stronger than conventional dipole-dipole interactions. Moderate hydrogen bonds, which are the most common, are formed between neutral donors and acceptors are from 3-12 kcal/mol.
A hydrogen bond is not an acid-base reaction, where the proton is
transferred from D to A. But the acidity of the proton bound to D
and the basicity of the lone pair of A both correlate roughly with the strength of the hydrogen
Water. Water is an excellent hydrogen bonding solvent. The coordinates of a water molecule linked by hydrogen bonds to two other water molecules are here [coordinates]. Hydrogen bonds cause violations of van der Walls surfaces. The hydrogen-bonding distance from H to O is around 1.8 Å, which is less than the sum of the O and H van der Waals radii (O, 1.5 Å;
H, 1.0 Å). Also notice that the hydrogen-bonding distance from O to O is around 2.8 Å, which is less than twice the van der Waals radius of oxygen (1.5 Å).
Figure 15 illustrates the geometry of hydrogen bonding between two water molecules. The hydrogen bond causes a violation of van der Waals surfaces.
Oxygen is highly electronegative, and gains partial negative charge by withdrawing
electron density from the two hydrogen atoms to which it is covalently
bonded, leaving them with partial positive charges. Water has a balanced
number of hydrogen bond donors and acceptors. In ice, every water
molecule acts as a donor in two hydrogen bonds and an acceptor in two
Figure 16 illustrates that a water molecule can donate two hydrogen bonds and accept two hydrogen bonds. The central water molecule here is donating two and accepting two hydrogen bonds. In bulk liquid water the total number of hydrogen bond donors equals the total number of hydrogen bond acceptors. All hydrogen bonding donors and acceptors are satisfied. Water is self-complementary.
Ammonia (NH3). Ammonia, like water
is an excellent hydrogen bonding solvent. Unlike water, ammonia does not have a balanced number of hydrogen bond donors and acceptors. Ammonia has more hydrogen bond donor sites than acceptor sites. Because of this imbalance, liquid ammonia contains fewer hydrogen bonds than liquid water. Nitrogen is less electronegative than oxygen, and so the hydrogen bonds of ammonia are weaker than those of water. The coordinates of an ammonia molecule are here [coordinates].
Geometry.The geometry of a hydrogen bond can be described by three quantities, the D to H distance, the H to A distance, and the D to H to A angle. Hydrogen bonds are not necessary, or even generally, linear. In fact hydrogen bonds can be two-centered (as shown above) and three-centered and four-centered as shown below.
Figure 17 illustrates three- and four-centered hydrogen bonds
Hydrogen atoms are not observable by
x-ray crystallography as applied to proteins and nucleic acids. So a
geometric description of hydrogen bonding that is dependent on the proton
position is not practical in protein and nucleic acid structures. In
these cases one is usually limited to analysis of the D to A distance.
It is common to ascribe a hydrogen bond if a distance between A and D is
less than the sum of their van der Waal radii. However this limit is
probably too conservative. The best criteria for an H-bond is a distance of less than 3.4 Å between D and A.
Hydrogen Bonding in Biological Systems. In biological systems, hydrogen bonds
are frequently cooperative. For example in the hydrogen-bonded system
below (the acetic acid dimer), hydrogen bond 1 increases both the acidity of the hydrogen, and
the basicity of the oxygen, in hydrogen bond 2.
Figure 18 shows resonance stabilization of the
hydrogen bonds of an acetic acid dimer.
Because of their directionality, tunability, and ubiquity in simple organic molecules, hydrogen bonding interactions are one of nature's most powerful mechanisms of molecular recognition.
Figure 19. Self assembly of biological macromolecules is driven by complementary hydrogen-bonding interactions. (Left) Base pairing between complementary hydrogen bond donors and acceptors on the sidechains of nucleic acids. (Center) Backbone assembly between self-complementary hydrogen bond donors and acceptors of the protein backbone to form anti-parallel β-strands in a β-sheet, and (Right) Self-complementary hydrogen bond donors and acceptors in carbohydrate, between glucose moieties within cellulose.
The hydrophobic effect can be understood only after thinking carefully about water. The hydrophobic effect is a consequence of strong directional and complementary interactions between water molecules.
The unusual cohesion of water molecules can be inferred from water's high melting point, boiling point, heat of vaporization, heat of fusion and surface tension and by water's increase in volume upon freezing. Each of these parameters indicates that water is a special liquid. For example the heat of vaporization of water (540 cal/g) is over twice that of methanol (263 cal/g) and nearly ten times that of chloroform (59 cal/g).
Living organisms are around 80% water by weight. Water is a crucial determinant of the structure and properties of cellular assemblies and organelles and of biochemical reactions. Water is a uniquely powerful solvent for ions and polar substances and is a poor solvent for non-polar substances. Water causes membranes to assemble and proteins to fold. Water is also a reactive chemical and is a direct participant in some of the most central and universal reactions in biological systems (hydrolysis and dehydration/condensations).
Water has a unique ability to shield charged species from each other. Electrostatic interactions between ions are highly attenuated in water. The electrostatic force between two ions in solution is inversely proportional to the dielectric constant of the solvent. The dielectric constant of water (80.0) is huge. It is over twice that of methanol (33.1) and over five times that of ammonia (15.5). Water is a good solvent for salts because the attractive forces between cations and anions minimized by water.
The four valence orbitals of a water molecule (sp3) form a slightly distorted tetrahedron. It is useful to imagine that either a hydrogen atom or a lone pair of electrons is sitting at each apex of the tetrahedron. Oxygen, which is highly electronegative, withdraws electron density from the hydrogen atoms to the extent that they are essentially bare protons on their exposed sides (distal to the oxygen). The charge distribution of a water molecule (partial negative charge on oxygen and partial positive charge on hydrogen) is shown below.
Figure 20 illustrates the two lone electron pairs and the two bonding electron pairs of a water molecule. A four valence orbitals of a water molecule form a slightly distorted tetrahedron. The non-bonding electron pairs take up a little more space than the bonding electron pairs.
X-ray and neutron diffraction of crystalline ice shows that each water molecule is engaged in four hydrogen bonds with intermolecular oxygen-oxygen distances of 2.76 Å. Each oxygen atom is located at the center of a tetrahedron formed by four other oxygen atoms. Each hydrogen atom lies on a line between two oxygen atoms and forms a covalent bond to one oxygen (bond length: 1.00 Å) and
a hydrogen bond to the other (hydrogen bond length: 1.76 Å). The tetrahedral shape of an individual water molecule is projected out linearly into the surrounding crystal lattice. The hydrogen atoms are not located midway between oxygen atoms. For additional information see the section on hydrogen bonding interactions
Figure 21 shows the hydrogen-bonding interactions of one water molecule with four others. A water molecule can donate two hydrogen bonds and accept two hydrogen bonds.
Water molecules in the crystalline state are not closely packed, resulting in tiny cavities of empty space within the crystal. The cavities are formed because the directionality of water-water interactions dominates water-water packing considerations. Small cavities in the solid lattice but not in the liquid are the reason that water increases in volume upon freezing (i.e., ice floats). There are many degrees of freedom in hydrogen bond donor/acceptor relationships that are interconverted by cooperative rotations. Ice is rather disordered in that respect.
In the liquid state, water is not as ordered as in the crystalline state. In the liquid state at O degrees C a time-averaged water molecule is involved in around 3.5 intermolecular hydrogen bonds. Some of them are three- and four-centered. Liquid water is more dense than solid water. Never-the-less, the macroscopic properties of liquid water are dominated by the directional and complementary cohesive interactions between water molecules.
G4. Empirical description of the hydrophobic effect.
| Table of Contents |
Structure Tool |
Williams Home |
Water and oil do not mix. Non-polar substances are not soluble in water. That is the empirical description of hydrophobic effect.
Hydrophobic substances are those that are soluble in non-polar solvents (such as CCl4 or cyclohexane) but are only slightly soluble in water. Hydrophobic substances are non-polar. The definition excludes substances like cellulose which are generally insoluble because of strong intermolecular cohesion. Hydrophobic substances are structurally incapable of forming hydrogen bonds. Hydrocarbons (CH3CH2CH2 .... CH2CH3) are hydrophobic.
Understanding the molecular and thermodynamic nature of the hydrophobic effect is not easy. Many textbooks contain superficial or incorrect explanations. The most important thing to remember is that the hydrophobic effect is fully a function of water, it a consequence of the distinctive molecular structure and self-assembly properties of water. Hydrophobic substances are essentially passive participants in hydrophobic processes such as the separation of oil from water. The molecular interactions of a hydrocarbon with neighboring water molecules in aqueous solution are just as favorable as with neighboring hydrocarbon molecules in pure liquid hydrocarbon. A hydrocarbon molecule is just as happy (forms equally favorable molecular interactions) in aqueous solution as in neat (pure) hydrocarbon.
The molecular interactions of a water molecule adjacent to a hydrocarbon (or other non-polar molecule) are just as strong and favorable (in terms of enthalpy) as the interactions of a water molecule in bulk water, surrounded by water only. There is no net change in favorable molecular interactions when oil and water mix or separate.
If it is not because of changes in molecular interactions, why don't oil and water mix? Why do they spontaneously separate? The reason is that water molecules adjacent a hydrocarbon sacrifice rotational and translational freedom to maintain molecular interactions. Water adjacent to a hydrocarbon pays the price of low entropy to maintain good molecular interactions. The strong directional cohesive interactions between water molecules are maintained, but at a high entropic cost. The low entropy of the water in the interfacial region (ie directly adjacent to a hydrocarbon molecule) arises from the strong directional forces between water molecules. In bulk water, these forces are essentially isotropic (extending in all directions). At the interface these forces are anisotropic because the cyclohexane molecule does not form hydrogen bonds. So an entropic effect leads to an unfavorable free energy of mixing oil and water (ΔG=ΔH-TΔS > 0)
The term 'hydrophobic bond' is a misnomer and should be avoided.
The molecular descriptions of the hydrophobic effect above can be understood by the thermodynamic parameters enthalpy (ΔH, indicates changes in molecular interactions) and entropy (ΔS, indicates changes in available rotational, translational, vibrational states, etc). A hydrocarbon engages in favorable molecule interactions with water in aqueous solution. We know this because the transfer of a mole of hydrocarbon from pure hydrocarbon to dilute aqueous solution has an enthalpy of around zero. So why don't oil and water mix? It is the water. Water drives non-polar substances out of the aqueous phase.
The schematic diagram above illustrates what happens when a hydrophobic substance (cyclohexane in this case) is converted from vapor to neat liquid to aqueous phase. In the first step, going from vapor phase to neat liquid, there is an increase in intramolecular interactions and a decrease in rotational and translational degrees of freedom. Therefore one expects, and sees, a favorable enthalpy contribution (negative ΔH) and an unfavorable entropy contribution (negative TΔS) for the condensation. In the second step, going from neat liquid to dilute aqueous solution, the change in stability contributed from intramolecular interactions is a wash, no gain or loss. The enthalpy of transfer is zero. But the water loses entropy. Water is more highly ordered in the vicinity of a cyclohexane molecule. Therefore, for this step, ΔH is zero, TΔS is negative and ΔG is positive (ΔG=ΔH-TΔS).
As illustrated below, in the aqueous phase
a region of relatively low entropy (high
order) water forms at the interface between the aqueous solvent and a
Figure 23 shows how aggregation of hydrocarbon molecules causes the release of interfacial water molecules. Therefore the system gains entropy (positive TΔS) upon hydrocarbon aggregation. Release of low entropy interfacial water molecules into the bulk solution drives hydrocarbon aggregation. The bottom panel illustrates that there is more interfacial water on the left hand side of the equation than on the right hand side.
When isolated hydrocarbon molecules aggregate in aqueous solution, the total volume of interfacial water decreases. Thus the driving force for aggregation of hydrophobic substances arises from an increase in entropy of the water. The driving force for aggregation does not arise from intrinsic attraction between hydrophobic solute molecules.
If one considers the entropy of the hydrocarbon molecules alone, a dispersed solution has greater entropy, and is more stable, than an aggregated state. Similarly, a protein may appear to have greater entropy in a random coil than in a native state. Only when the entropy of the aqueous phase is factored into the equation can one understand the separation of water and oil into two phases, and the folding of a protein into a native state.
For many purposes it is useful to think of DNA as a rod that is coated with anionic charge. In aqueous solution the negative rod is surrounded by cations such as Na+, K+ and Mg2+ and/or by polyamines. The high density of negative charge on the rod causes strong radial electric fields. These electric fields lead to steep radial gradients of the cation concentrations. Theoretical considerations (counterion condensation) predict that the local concentration of a monovalent cation such as K+ near the surface of DNA is around 2 Molar. It is counter intuitive, but the concentration of K+ surrounding DNA is largely independent of the K+ concentration in bulk solution. The electrostatic environment surrounding DNA does not depend on the bulk concentration of salt.
Figure 24 shows (left) the radial cation distribution surrounding DNA. (right) The figure shows that ions associated with DNA and protein are released to the bulk aqueous environment when a protein (cationic) binds to DNA (anionic).
Counterions are released when a cationic protein binds to DNA. This release explains the dramatic salt dependencies of DNA-protein complexes. High salt destabilizes DNA-protein complexes. If the bulk salt concentration is low, there is a large entropic gain from counterion release, and the protein binds tightly to the DNA. If the bulk salt concentration is high, the entropic gain from counterion release is small, and the protein binds weakly. Counter ion release explains much of the salt dependencies of DNA melting, RNA folding and DNA condensation.
DNA condensation. Genomic DNAs are
very long molecules. The 160,000 base pairs of T4 phage DNA extend to 54
microns. The 4.2 million base pairs of the E. coli chromosome
extend to 1.4 millimeters. In biological systems, long DNA molecules
must be compacted to fit into very small spaces inside a cell, nucleus or virus
particle. The energetic barriers to tight packaging of DNA arise from decreased
configurational entropy, bending the stiff double helix, and
intermolecular (or inter-segment) electrostatic repulsion of the
negatively charged DNA phosphate groups. Yet extended DNA chains
condense spontaneously by collapse into very compact, very orderly
particles. In the condensed state, DNA helixes are separated by one or
two layers of water. Condensed DNA particles are commonly compact
toroids. DNA condensation in aqueous solution requires highly charged
cations such as spermine (+4) or spermidine (+3). Divalent cations will
condense DNA in water-alcohol mixtures. The role of the cations is to
decrease electrostatic repulsion of adjacent negatively charged DNA
segments. The source of the attraction between nearby DNA segments is
not so easy to understand. One possible source of attraction are
fluctuations of ion atmospheres in analogy with fluctuating dipoles
between molecules (London Forces).