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Molecular Interactions (Noncovalent Interactions)
illustrated by biochemical systems
en Español (soon)

revised 9/12/2014

Loren Williams, Georgia Tech


Table of Contents

A Introduction
B Short range repulsion
C Electrostatic interactions
C1 Ion Pairs in Proteins
D Dipolar interactions
D1 Molecular dipoles
D2 Dipole-dipole interactions
D3 Dipole-induced dipole interactions
D4 Dipole-charge interactions
E Fluctuating dipoles (London Dispersion)
F Hydrogen bonding
F1 General Description
F2 Geometry
F3 Water
F4 Ammonia
F5 Cooperativity
F6 Molecular recognition and assembly
F7 Template-directed catalysis
G Cation-π interactions
H Hydrophobic effect
H1 Water and Biology
H2 Molecular structure of water in the crystalline state
H3 Molecular structure of water in the liquid state
H4 Empirical description of the hydrophobic effect
H5 Molecular basis of the hydrophobic effect
H6 Thermodynamic basis of the hydrophobic effect
I Counterion release
J About this document

A. Introduction.
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Covalent interactions (bonds) hold 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 (also called noncovalent interactions or intermolecular interactions), which are interactions between molecules. Molecular interactions are important in diverse fields of protein folding, drug design, separation technologies, etc.

Molecular interactions seem weak. The enthalpy of a given 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 are significant.

Boiling Points. 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). The forces between molecules in H2O(liq) are greater than those in N2(liq). When a molecule transitions from the liquid to the gas phase (as during boiling), all molecular interactions are broken. In an ideal gas there are no adhesive molecular interactions. It is a good general rule that differences in boiling temperatures give good qualitative estimates of strengths of molecular interactions within various liquids.

Pushing and Pulling. In their native states, a protein is generally folded into a globular structure and DNA is double-stranded. The number of molecular interactions within a folded native protein or a long double-stranded DNA is enormous. However if you unfold the protein (denature it) or separate the DNA strands, the interior becomes exposes to the surrounding aqueous media. Intra-molecular interactions in the native state are replaced by molecular interactions with water molecules in the non-native state.

Huge numbers of molecular interactions within a native state are balanced by huge numbers of molecular interactions of the non-native state (with surrounding water molecules). Native states are held in 'delicate balance between powerful countervailing forces' contributed primarily by massive numbers of molecular interactions. Native states are marginally stable: the equilibrium constant for the transition from native to unfolded state is small. A small difference between these large effects, can be contributed by weak interactions, changing the direction of the folding 'reaction'. A small change in pH or temperature can tip the balance.

Have you ever denatured a protein (converted it from the native folded state to a non-native unfolded state also known as a random coil)? Yes. When you heat an egg to around 60° C, the albumin 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.

Molecular interactions 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 adhesive/cohesive force 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 sufficiently predictive models.

There are many different ways of parsing or classifying molecular interactions. The categories in the Table of Contents are used here because they are the clearest and easiest to understand and are broadly used in the literature.

All molecular interactions are fundamentally electrostatic in nature and can described by some variation of Coulombs Law.


B. Short Range Repulsion.
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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.

Atom Name
VDW Radius (r, Å)
H
1.2
C
1.7
N
1.6
O
1.5
P
1.8
S
1.8

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, described by well-defined van der Waal radii (r) and hard van der Waal surfaces. As two atoms approach each other their van der Waals surfaces make contact when the distance between them decreases to the sum of their van der Waals radii. At this point the repulsive energy skyrockets. The smallest distance between two non-bonded atoms is the sum of the van der Waals radii of the two atoms. A sulfur atom and a carbon atom can come no closer together than rS + rC = 1.8 + 1.7 = 3.5 Å. Of course we are assuming here that bonds do not form. When two atoms form a bond, they come close together such that van der Waals radii and surfaces are violated.

Short range repulsion is important to you. It prevents atoms from collapsing into tightly packed states of density of 1014 g/ml, which is the density of condensed atomic nuclei. Very high gravitation forces, as in neutron stars, overwhelm short range repulsion and cause atoms to collapse.

Here in earth, with our modest gravity, the van der Waals radius of carbon (rC) 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 rC = 2 x 1.7 = 3.4 Å). The atoms within a graphite layer are covalently linked (bonded), which causes interpenetration of van der Waals surfaces. Carbon atoms within a layer are separated by 1.42 Å, which is much less than twice the van der Waals radius of carbon. As explained in other sections of this document vdw surfaces are also violated when molecules form hydrogen bonds.

vdw radius

Figure 2 shows how short range repulsion sets the distance of 3.4 Å between sheets in graphite. If two non-bonded atoms are separated by a distance of less than the sum of their VDW radii, short range repulsion forces them apart.

In B-DNA, the helical rise per base pair of 3.4 Å is determined by short range repulsion between the stacked bases. Bases stack on each other with spacing of 3.4 Å.

How do you sense short range repulsion? Try compressing a liquid.


C. Electrostatic Interactions.
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Electrostatic interactions are between and among cations and anions, which are species with formal charge of ...-2,-1,+1,+2... Electrostatic interactions can be either attractive or repulsive, depending on the signs of the charges. Favorable electrostatic interactions cause the vapor pressure of sodium chloride and other salts to be very low. If you leave table salt (NaCl) out on a table, how long does it take before it sublimes away? A very very long time. The electrostatic interactions within a sodium chloride crystal are called ionic bonds. But when a single cation and a single anion are close together, within a protein, or within a folded RNA, those interactions are considered to be non-covalent electrostatic interactions. Electrostatic interactions can be very strong, and fall off gradually with distance (1/r). As explained later in this document, electrostatic interactions are highly attenuated (dampened) by water.

electrostatics

Figure 3 shows a cross section of a NaCl crystal. Each sodium cation experiences strong electrostatic interactions with adjacent chloride anions. In reality the ionic radius of a sodium cation is less than that of a chloride anion. The coordinates of sodium chloride are here [coordinates].

Electrostatic interactions are the primary stabilizing interaction between phosphate oxygens of RNA (formal charge -1) and magnesium ions (formal charge +2), as shown in the figure below. There are many magnesium ions associated with RNA and DNA molecules in vivo.

electrostatics

Figure 4 shows RNA (within the ribosome) in which anionic phosphate oxygens (-1 charge) engage in attractive electrostatic interactions with a dicationic magnesium ion (+2 charge). The O to Mg2+ distance is 2.1 Å. Here the dashed lines represent favorable electrostatic interactions (not hydrogen bonds: there are no hydrogen atoms between the phosphate oxygens and the Mg2+ ion.)

C1. Ion Pairs in Proteins.
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Favorable electrostatic interactions between paired anionic and cationic amino acid sidechains are reasonably frequent in proteins. Ion Pairs, sometimes called Salt Bridges, are formed when the charged group of a cationic amino acid (like lysine or arginine) is around 3.5 to 5.0 Å from the charged group of an anionic amino acid (like aspartate or glutamate). The charged groups in an Ion Pair are generally linked by hydrogen bonds, in addition to electrostatic interactions.

The electrostatic force between two point formal charges is given by:

Force = k q1 q2 / ε r2

where k = 9.0 x 109 nt-meter2 / coul2

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).

ε 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 biological systems is complex in part because of non-uniformity of the dielectric environment. The dielectric micro-environments are complex and 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:

ΔE = -(9.0x109nt-m2/coul2)(6.02x1023)(1.6x10-19coul)2 /4( 4x10-10m)

= 87 kjoules/mole = 21 kcal/mole

This rough approximation is around 10-fold greater than the values determined experimentally. An ion pair contributes 1-4 kcal/mol (favorable ΔG) to the stability of a native protein.

A note on nomenclature. The attractive forces between a Mg2+ ion and phosphate groups (above) are called electrostatic interactions. This label is unfortunate because ALL molecular interactions are inherently electrostatic in nature. It might have been better to have called these charge-charge interactions. However, by convention we use the term electrostatic to describe interactions between formally charged species. We use other terms (dipole-dipole, dispersion...) to describe (electrostatic) interactions between partial charges.


D. Dipole Interactions.

D1. Molecular dipoles.
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Before we can think very much about dipole-dipole interactions, or understand them, we have to know about dipoles and electronegativities. In a molecule with unlike atoms, electrons are not shared equally. The tendency of any atom to pull electrons towards itself, and away from other atoms, is characterized by a quantity called electronegativity. A greater difference in the electronegativities of two bonded atoms causes the bond between them to become more polar, and the partial charges on the atoms to become larger in magnitude. In biological systems, oxygen is generally the most electronegative atom, carrying the largest partial negative charge.

Atom Name Electronegativity
H 2.2
C 2.6
N 3.0
O 3.5
P 2.2
S 2.5

In a molecule composed of atoms of various electronegativities, the atoms with lowest (smallest) electronegativities hold partial positive charges and the atoms with the greatest electronegativities hold partial negative charges. In a methanol molecule (CH3OH), the electronegative oxygen atom pulls electron density away from the carbon and hydrogen atoms. In a water molecule, the electronegative oxygen atom pulls electron density away from the hydrogen atoms. The oxygen atom of water 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 because the two nitrogen atoms share electrons equally.

bond dipole / molecular dipole

Figure 5 shows the charge distribution and dipole moment of a water molecule. The electronegative 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. Bond dipoles (center) and molecular dipoles (right) can be represented as vectors. The arrows point from positive charge toward negative charge.

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 equals:

(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.

peptide partial charges

Figure 6 shows the partial charges within a polypeptide. The symbol size (δ) is scaled to the magnitude of the partial charge. Oxygen atoms are the most electronegative and have the greatest negative partial charge.


Partial Charges on the Atoms of a Peptide
Atom Name partial charge (e-)
N -0.42
HN +0.27
+0.12
C' +0.60
O -0.57


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.

peptide dipole moment

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.

peptide resonance structures

Figure 8 shows two 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. These interactions are called Charge-Dipole Interactions (or Ion-Dipole Interactions). Dipoles can also interact with other dipoles (called Dipole-Dipole Interactions), and can induce charge distribution (polarization) in surrounding molecules (causing Dipole-Induced Dipole Interactions). We will discuss each of these interactions separately.

D2. Dipole-dipole interactions.
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Two dipoles 'feel' each other through space. The positive end of the first dipole is attracted to the negative end and is repelled by positive end of the second dipole. The strength of a dipole-dipole interaction depends on the size of both dipoles and on their proximity and orientations. The total interaction energy between two dipoles can be either positive or negative. Parallel end to end dipoles attract while antiparallel end to end dipoles repel. Listed below are the energies of interaction for various orientations of two dipoles with moments of 1 Debye at a distance of 5 Å in a medium of ε = 4.

 dipole dipole interactions

Figure 9 shows how dipole-dipole interactions depend on the orientations of the dipoles. Dipole-dipole interactions can be attractive or repulsive.

In liquids the orientations of molecular dipoles change rapidly as molecules tumble about. However, dipole moments tend to orient favorably. Therefore, in liquid acetone for example, favorable dipole-dipole interactions outweigh unfavorable dipole-dipole interactions. Dipole-dipole interactions fall off with 1/r3.

D3. Dipole-induced dipole interactions.
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A molecule with a permanent dipole moment creates a surrounding electrostatic field. This electrostatic field will shift the electrons around a bit (induce a dipole moment) in a second molecule that is located nearby in space. This induction of a dipole moment in one molecule by another is called polarization. The ease with which electrons are shifted by an external electronic field is called polarizability. Molecules with π electrons, such as phenylalanine and tryptophan, are more polarizable than molecules such as isoleucine, which lack π electrons.

dipole induced dipole interactions

Figure 10 shows how a static dipole can induce a dipole in an adjacent molecule. When two isolated molecules (left) are brought together in a liquid or solid (right), the static dipole 'polarizes' the adjacent molecule. π Electrons are more polarizable (more easily perturbed by an adjacent dipole) than σ electrons. The strength of a dipole-induced dipole interaction depends on the size of the dipole moment of the first molecule and on the polarizability of the second molecule.

Dipole-induced dipole interactions are important even between two molecules that both have permanent dipoles. A permanent dipole is changed by the dipole of an adjacent molecule. For example, in liquid water (where molecules are close together), all water molecules are polarized. The permanent dipole of each water molecule polarizes all adjacent water molecules. The dipole of a water molecule induces a change in the dipole of a nearby water molecule, compared to the permanent dipole of an isolated water molecule (in the gas phase).

water polarization

Figure 11 shows how water molecules polarize each other. Each water molecule polarizes neighboring water molecules and increases neighboring dipole moments. 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 is increased in magnitude, and the partial positive charge on the proton of the bottom water molecule is also increased. Here the symbol size is scaled to the magnitude of the partial charge.

Dipole-induced dipole interactions are always attractive and can contribute as much as 0.5 kcal/mole to stabilization of molecular associations. Dipole-induced dipole interactions fall off with 1/r4. Formally charged species (Na+, Mg2+, -COO-, etc.) also polarize nearby molecules and induce favorable dipoles. The resulting interactions, called charge-induced dipole interactions (or ion-induced dipole interactions). These interactions are important, for example in protein structure, but are not broken out into a separate section in this document.

D4. Dipole-charge interactions.
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A molecule with a permanent dipole can interact favorably with cations and anions. This type of interaction is called a dipole-charge or ion-dipole interaction. Dipole-charge interactions are why sodium chloride, composed cationic sodium ions and anionic chloride ions, and other salts tend to interact well with water, and are very soluble in water, which has a strong dipole.

charge-dipole interactions, ion-dipole interactions

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. If the ion is an anion, such as chloride, the water molecules switch direction and direct the positive ends of their dipoles toward the anion. Here the dashed lines do not represent hydrogen bonds. There are no hydrogen atoms between the Mg2+ cation and the water oxygen atoms.


E. Fluctuating dipoles (Dispersive interactions, London Forces).
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We can see resonance all around us. A child on a swing, the tides in the Bay of Fundy and the strings on a violin all illustrate natural resonant frequencies of physical systems. The Tacoma Narrows Bridge is one of the most famous examples of resonance.

Molecules resonate too. Electrons, even in a spherical atom like Helium or Xenon, fluctuate over time according to the natural resonant frequency of that atom. Even though chemists describe atoms like Helium and Xenon as spherical, if you could take a truly instantaneous snapshot of one of these atoms, you would always catch it in a transient non-spherical state. Xenon is spherical on average, but not at any instantaneous timepoint.

Fluctuating electrons cause fluctuating dipoles. When the instantaneous electron density of a molecule or atom fluctuates, the dipole moment also fluctuates. Therefore, molecules and atoms behave like oscillating dipoles. In molecules that are located nearby to each other the oscillating dipoles sense each other and couple. They oscillate in synch. The movements of the electrons in adjacent molecules are correlated. Electrons in one atom tend to run away from those in the next, 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).

London dispersion

Figure 13 shows how fluctuating dipoles of liquid Xenon (or Helium or Neon, etc) are coupled. Darker blue indicates higher electron density. 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 Nobles. 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.

F1. General Description of Hydrogen Bonds.
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The idea that a single hydrogen atom could bond simultaneously to two other 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.

hydrogen bond

Figure 14 illustrates the elements of a hydrogen bond, including the HB acceptor and HB donor, the lone pair and the acidic proton. N, O, S are the predominant hydrogen bonding atoms (A & D) in biological systems.

An atom (A) containing a basic lone pair of electrons (i.e., a Lewis Base) can interact favorably with a hydrogen atom (H) that is covalently bound to a donor atom (D). A hydrogen bond requires that atoms A and D are both electronegative. H-D must have acidic properties. In a hydrogen bond, the Lewis Base (A) is called hydrogen bond acceptor and the acidic group (H-D) is called the hydrogen bond donor. Hydrogen is the only atom that (i) forms covalent bonds with electronegative atoms like N and O, and (ii) uses the inner shell (1S) electron(s) for bonding. When its bonding partner pulls electrons away from hydrogen, the nucleus (a proton) is exposed on the back side (distal from the bonding partner). An unshielded proton is thus available for electrostatic interactions with electron lone pairs. Hydrogen is the only atom that exposes its nucleus this way. Other atoms have inner shell non-bonding electrons that shield the nucleus. The salient features of a generic hydrogen bond are illustrated in the figure above.

A hydrogen bond is not an acid-base reaction, where the proton (H+) is fully transferred from H-D to A to form D- and HA+. However, the strength of a hydrogen bond correlates well with the acidity of donor H-D and the basicity of acceptor A. In a hydrogen bond, the H+ is partially transfered from H-D to A, but H+ remains covalently attached to D. The H-D bond remains intact.

hydrogen bond

Figure 15a 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.

The most common hydrogen bonds in biological systems involve oxygen and nitrogen atoms as A and D. Keto groups (=O), amines (R3N), imines (R=N-R) and hydroxyl groups (-OH) are the most common hydrogen bond acceptors in DNA, RNA, proteins and complex carbohydrates. Hydroxyl groups and amines/imines are the most common hydrogen bond donors. Hydroxyls and amines/imines can both donate and accept hydrogen bonds.

hydrogen bond

Figure 15b shows the most common hydrogen bond acceptors and donors in biological macromolecules.

In traversing the Period Table, increasing the electronegativity of atom D strips electron density from the proton (in H-D), increasing its partial positive charge, and increasing the strength of any hydrogen bond. Thiols (-SH) can can both donate and accept hydrogen bonds but these are generally weak, because sulfur is not sufficiently electronegative. Hydrogen bonds involving carbon, where H-D equals H-C, are observed, although these are weak and infrequent. C is insufficiently electronegative to form good hydrogen bonds. Hydrogen bonds are essentially electrostatic in nature, although the energy can be decomposed into additional contributions from polarization, exchange repulsion, charge transfer, and mixing.

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.

F2. Geometry of Hydrogen Bonds.
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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. The distances depend on the atom types of A and D. If both A and D are oxygen atoms, then optimally, H to A = 1.8 Å and D to H = 1.0 Å. The most stable hydrogen bonds are close to linear (D to H to A angle of 180°). The hydrogen bonds in antiparallel β-sheets are linear, while the hydrogen bonds in parallel β-sheets are non-linear.

parallel and antiparallel beta-sheet

Figure 16 illustrates the non-linearity of parallel β-sheet hydrogen bonds and the linearity of antiparallel β-sheet hydrogen bonds.

Hydrogen bonds can be two-center (as in a β-sheets and ideal ice), three-center, or four-center. Two-center hydrogen bonds are generally shorter, more linear, and stronger than three- or four-center hydrogen bonds. Three-center bonds are sometimes called bifurcated while four centered hydrogen bonds are sometimes called trifurcated.

non linear hydrogen bonds

Figure 17 illustrates two-, three- and four-center hydrogen bonds. The two-center hydrogen bond is closest to an 'ideal' hydrogen bond, and is stronger than the other types. The left hand four-center hydrogen bonding scheme is observed in crystalline ammonium, where one acceptor lone pair has to accomodate three donors (see section on ammonia, below.

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.

F3. Hydrogen Bonding in Water.
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An isolated molecule of water (H2O) can form strong hydrogen bonds, with either hydrogen bond donors or acceptors. One water molecule can accept two hydrogen bonds and donate two hydrogen bonds (or more if the hydrogen bonds are bifurcated or trifurcated).

H bond

Figure 18 Illustrates hydrogen bonding between two water molecules as observed in crystalline water (ice). The hydrogen bonds are short, linear and strong. These are two-center hydrogen bonds. Although each water molecule in ice forms four hydrogen bonds, only one hydrogen bond is shown here.

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 (rO=1.5 Å; rH=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 (rO=1.5 Å).

H bond water

Figure 19 shows how hydrogen bonds link two water molecules. This figure illustrates the difference between a covalent bond, linking an oxygen atom to a hydrogen atom, and a hydrogen bond, also linking an oxygen to a hydrogen. A hydrogen bond is a non-covalent molecular interaction. Oxygen atoms are red and hydrogen atoms are white. The space filling representation on the right shows how hydrogen bonding causes violations 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 hydrogen bonds. 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].

H bond water

Figure 20 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.

The coordinates of a very small ice cube are here [coordinates]. For additional information on water, see the section on water and the hydrophobic effect.

F4. Hydrogen Bonding in Ammonia.
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A comparison of ammonia to water shows part of the significance of the self-complementarity of water. A single ammonia molecule (NH3), like a single water molecule, can form strong hydrogen bonds, with either hydrogen bond donors or acceptors. However unlike water, ammonia does not have a balanced number of hydrogen bond donors and acceptors. Water is self-complementary, while ammonia is not. A water molecule has equivalent numbers of acceptor and donor sites.

An ammonia molecule has more hydrogen bond donor sites than acceptor sites. Yet, in the crystalline state, each ammonia molecule donates three and accepts three hydrogen bonds. How does this happen? To achieve six hydrogen bonds per ammonia molecule, the single lone pair orbital on each nitrogen is shared by three hydrogen bond donors (N-H's) of three adjacent ammonia molecules. This hydrogen bond is trifucated, as described above (see figure). All of these hydrogen bonds are sub-optimal. Each hydrogen bond in crystalline ammonia is long, bent and weak.

NH<sub>3</sub> Hbond

Figure 21 Illustrates the hydrogen bonding as observed in crystalline ammonia. The hydrogen bonds are longer than those in ice and are non-linear. Although each ammonia molecule forms hydrogen bonds with six neighbors in the crystal, only two ammonia molecules are shown here.

The boiling point of ammonia is −33 °C, much lower than that of water (100 °C), indicating that molecular interactions in NH3 (liq) are significantly weaker than in H2O (liq). Although the number of hydrogen bonds per molecule is greater in solid/liquid ammonia than in water, the hydrogen bonds in water are much stronger. The coordinates of an ammonia molecule are here [coordinates].

F5. Cooperativity of Hydrogen Bonds.
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In biological systems, hydrogen bonds are frequently cooperative. In systems with multiple hydrogen bonds, the strength of one hydrogen bond is increased by a adjacent hydrogen bond. For example in the hydrogen-bonded systems below (the acetic acid dimer), the top hydrogen bond increases both the acidity of the hydrogen, and the basicity of the oxygen in the bottom hydrogen bond. Each hydrogen bond makes the other stronger than it would be in isolation. Cooperativity of hydrogen bonding is observed in base pairing and in folded proteins.

CG base pair

Figure 22 shows cooperativity via resonance of the hydrogen bonds of an acetic acid dimer (top) and of a G-C base pair (bottom). Formation of one hydrogen bond increases the stability of an adjacent hydrogen bond (and vice versa).

β-sheet H-bond

Figure 23 shows cooperativity via resonance of the hydrogen bonds of an anti-parallel β-sheet.

F6. Hydrogen Bonding in Molecular Recognition and Assembly.
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Because of their directionality, tunability, and ubiquity in simple organic molecules and biological polymers, hydrogen bonding interactions are one of nature's most powerful devices of molecular recognition. Hydrogen bonding donors and acceptors, in complementary 2D and 3D arrays, are observed in many biological assemblies. The locations and directions of the donors and the acceptors are matched, sometimes over vast surfaces. However, not all complementary surfaces in biology involve hydrogen bonds. Leucine zippers, between α-helices, are examples of complementary interactions that involve molecular interactions other than hydrogen bonds.

Figure 24. 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.

F7. Hydrogen Bonding in Template-Directed Catalysis.
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Biological systems have unique abilities to link complex molecular interactions to catalytic functions. Sophisticated non-covalent interactions control formation of covalent bonds. Some of the most advanced forms of these phenomena are observed in DNA and RNA polymerases, and in the ribosome. In these systems hydrogen bonding and other molecular interactions direct catalytic function. In an RNA polymerase, if 'correct' hydrogen bonding (i.e., C-G or A-U/T Watson-Crick hydrogen bonding) occurs between the template strand and the incoming nucleotide, then the enzyme catalyzes formation of a covalent bond. When 'wrong' interactions (e.g., a G-U pair) are detected, the enzyme kicks out the incoming nucleotide without forming the covalent bond. Therefore one molecule acts as a template that directs synthesis of another molecule, in close analogy with the way that a pastry template directs the shape of the pastry.

Figure 25 shows a pastry template (top left) that directs and controls the shape of a pastry. This figure also shows a molecular template (a DNA molecule), that directs synthesis of a molecule of RNA. The DNA template strand is green, the nascent (growing) RNA strand is blue and the incoming nucleotide is red.


G. Cation-π Interactions.
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A π-system such as benzene, tryptophan, phenylalanine or tyrosine focuses partial negative charge above and below the plane of the ring. A cation can interact favorably with this negative charge when the cation is near the face of the π-system. In the most stable complexes of this type, the cation is centered directly over the π-system and is in direct van der Waals contact with it. The table on the left shows gas phase interaction enthalpies, which are on the same order as the hydration enthalpies for these cations. Therefore, cation-π interactions are roughly similar in strength to cation-dipole interactions formed between water and cations. Small ions with high charge density form stonger cation-π complexes than larger ions. Electron withdrawing groups on the ring system weaken cation interactions while electron donating groups strengthen them.

Cation-π interactions with benzene
Ion ΔH (kcal/mol)
Li+ -38
Na+ -28
K+ -19
NH4+ -19
(gas phase)

Cation-π interactions are important in protein structure. The guanidinium group of arginine and the ε-NH3+ of lysine engage in cation-π interactions with aromatic protein sidechains. A favorable cation-π pair contributes as much to protein stability as a good hydrogen bond or an electrostatic (charge-charge) interaction. Tryptophan is the most frequent π system in protein cation-π pairs while arginine is the most frequent cation. Tryptophan and arginine can form extended coplaner assemblies.

Figure 26. (Left) Optimal geometry for a cation-π interaction between a Na+ cation and a benzene molecule. The distance from the Na+ to the center of the ring is 2.4 Å (ionic radius of Na+ = 0.9 Å, vdw radius of C (rC) = 1.7 Å). (Right) The ε-NH3+ of a lysine engages in cation-π interactions with two tryptophan sidechains and two tyrosine sidechains (glucoamylase, PDB ID 1GAI).


H. The Hydrophobic Effect.

H1. Water and Biology.
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Biology and biochemistry take place in complex aqueous environments. Living organisms are around 80% water by weight. Life as we know it on earth is fully dependent on and intertwined with water. Water is a crucial determinant of structures and properties of cellular assemblies and organelles and of biochemical reactions. Water is a reactive chemical and is a direct and critical participant in some of the most central and universal reactions of biology (hydrolysis and dehydration/condensation). All of life's polymers are synthesized by dehydration/condensation and all are broken down by hydrolysis.

water and biology

Figure 27 shows water as a direct chemical participant in the biosynthesis of the polymers of life.

Water is a powerful solvent for ions and polar substances and is a poor solvent for non-polar substances. Water causes certain amphipathic molecules (with both polar and non-polar functionalities) to spontaneously form compartments. In water, membranes assemble and proteins fold.

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).

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 are minimized by water.

The hydrophobic effect can be understood only after thinking carefully about water. The hydrophobic effect is a consequence of strong directional interactions between water molecules and the complementarity of those interactions.

H2. Molecular structure of water in the crystalline state.
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A water molecule has four filled valence orbitals (sp3 hybridized) that form a modestly distorted tetrahedron. Two of the electron pairs form covalent bonds with hydrogen atoms and two are non-bonding. The non-bonding lone pairs take more space than the bonding lone pairs, causing the distortion from a perfect tetrahedron. It is useful to imagine that a water molecule is a tetrahedron with negative charge on two apexes and positive charge on two apexes. Ideally, every water molecule can interact with exactly four other water molecules.

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.

Water Orbitals

Figure 28 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 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

Water H-bond

Figure 29 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.

H3. Molecular structure of water in the liquid state.
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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.

H4. Empirical description of the hydrophobic effect.
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The hydrophobic effect is the insolubility of oil and other non-polar substances in water. If you mix oil and water or CCl4 and water by vigorous shaking, you will observe unmixing. Mixtures of oil and water will spontaneously unmix. This unmixing is very strange and unusual, because mixing entropy is supposed to be positive (mixing is spontaneous because the number accessible states increases upon mixing). If you mix red marbles and blue marbles, or water and ethanol, or N2(g) and O2(g), you will not observe unmixing. For these substances, mixing is spontaneous. But we know non-polar substances are insoluble in water. That is the hydrophobic effect in action. Hydrophobic substances are those that are soluble in non-polar solvents (such as CCl4 or cyclohexane). 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.

H5. Molecular basis of the hydrophobic effect.
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Understanding the molecular and thermodynamic nature of the hydrophobic effect is not easy. Many textbooks contain superficial or incorrect explanations. A very important thing to remember is that the hydrophobic effect is fully a function of water; it a consequence of the distinctive molecular structure of water and the unique self-assembly properties of water. Hydrophobic substances are passive participants in the hydrophobic phenomenon. 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 between water molecules are not disrupted by interaction with hydrocarbon (or other non-polar molecule). Interactions between water molecules at the hydrocarbon interface are just as strong and favorable (in terms of enthalpy) as interactions between water molecules 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, even though Walter Kauzmann, the discoverer of the hydrophobic effect, did often use that phrase.

H6. Thermodynamic basis of the hydrophobic effect.
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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.

enthalpy, entropy and the hydrophobic effect

Figure 30 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 hydrophobic solute.

the hydrophobic effect

Figure 31 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.


I. Counterion Release
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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.

counterion condensation

Figure 32 (left) shows an axial view of DNA, represented as a anionic cyclinder. Cationic counterions (orange shading) surround the cyclinder. The concentration of cations decreases with distance from the surface of the cyclinder. The deeper orange shading indicates more concentrated cations. The panel on the right illustrates how both anionic counterions (blue) associated with a cationic protein, and cationic counterions (orange) associated with anionic DNA, are released to bulk solution when the protein binds to DNA. This release of counterions drives the association (by contributing +TΔS).

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).


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This document on molecular interactions is written in memory of Professor Charles Lochmuller (photo on the left) of Duke University. Dr. Lochmuller was a good guy, a natural comic, and an eminent scientist. I was fortunate that I was able to learn about molecular interactions from Dr. Lochmuller, in his separations class. I follow the basic interaction parsing scheme that Dr. Lochmuller used. Some of the source material for this document is my 1984 Ph.D. thesis.

I wrote this document, starting around 1992, because treatments of molecular interactions in textbooks and on the web are incomplete or incorrect or incoherent. I continuously extend and improve the document, which was originally intended for my own students only. This document is used nearly every year in my graduate level macromolecular structure class and/or my undergraduate biochemistry class.

In around 2013 I began to understand that this document is used by students all over the world. This page was downloaded around 102,000 times from 9/2013 through 11/2014. If you have suggestions for improvements, are confused by something, or see an error, please contact me.

The developement of this document has been supported by the NASA Astrobiology Institute, the National Science Foundation, and the School of Chemistry and Biochemistry at Georgia Tech, all of whom have supported my research laboratory and my public outreach efforts. Sincerely, Loren Williams, Professor, Georgia Tech.