Fletterick, RJ
Lecture Notes Biophysics 204 Robert Fletterick
February 12, 2016
Part 4 Protein-Protein Interactions- Theory
Compare protein binding to ligands that are small molecules and protein binding to
other proteins. What are the differences?
It’s all the same chemical physics, but the protein-protein system is elaborate
because the interacting molecules themselves may become altered in the
formation of the bonding interactions.
Induced fit, as this is called, may also occur for a small molecule, like a peptide
binding to a protease, but usually the changes in conformation of the ligand are
small. The change in conformation of the protein can be quite large, however, as
when an ATP binding protein binds ATP. Often this event cause partial closure of
the two subdomains that form the ATP binding domain.
For two proteins, one or both of the protein molecules may change their
conformations, tertiary structures and the free energy of interaction is
accounted for in a structural sense only by evaluating the free energy
changes for the entire system.
The system is two proteins and solvent water that makes up about 25 % of the
molecular weights of the proteins. What forces and features of the interface are
expected to apply to protein to protein interfaces?
ForcesElectrostatic
Consider hydrogen bonds to be electrostatic forces with directionality due to the
changes in presentation of the dipoles that interact. Hydrogen bonds and electrostatic
interactions will be made directly from the protein atoms of one partner to the
protein atoms of the other partner. These polar protein atoms will mostly have
been interacting with water before the interfaces come together.
Will there be unsatisfied H bonds in a close packed protein interface?
Not usually when water is excluded, because unsatisfied H bonds are a net
unfavorable free energy when water is excluded.
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Since the surface must be water soluble when the partnership is adjourned, the
solvent to protein H bonds will be partly replaced by the specific interactions of the
protein partner. This exchange complicates the thermodynamic assessment.
The direct interactions are probably necessary for specificity (a term that I use to
mean directing recognition) and discrimination (meaning rejection, like a positive
electrostatic field rejecting positive charges) among partners.
Analogous to the rarity of paired charges to be found buried inside of proteins, few
charged interactions are expected in the interface, but those that appear there may
be critical and strong, e.g. trypsin and its substrate where the substrate presents
an Arg that is removed from solvent and juxtaposed with an Asp from trypsin, deep
within the substrate primary recognition pocket.
Van der Waals
The protein surface that will form the interface is either in contact with water or the
protein partner. So that we expect some compensation in the exchange of water
contacts for protein contacts in that solvent is replaced by protein.
Note that the enthalpy is similar whether a protein atom “sees” water or an atom of
the protein partner. The details of the steric fit however and density of interactions
may be greater for protein-protein interactions. In the case of the protein two
aromatic sidechains may efficiently stack, for example.
Flexibility
Depending on the type of interaction that is whether the partner is shared among a
family of proteins, or whether it is a fixed dimer, or an allosteric interaction,
flexibility is expected to be important to achieve pairing, but not so much as to pay
an extensive entropy debt. The entropy seems to be a major component of
interaction for members of trans scription complexes where the dissociation
constants are weak, and the complex is short lived. For several cases, one or both
components forming the interface are disordered until the interaction forms. This
association mimics protein folding rather than protein associations.
Side chains should be more conformationally adjustable than main chain
rearrangements because most main chain is participating in extended secondary
structure interactions. Again exceptions are well known as we will discuss in a
focus paper.
Solvent
Solvent effects could be considerable as the solvent at the interfaces is exchanged
into bulk water with non specific interactions. The perfection of fit and exclusion of
solvent should be important to make the interface stable. Surface water molecules
are fundamentally different from bulk water which is easy to see if you think about
the number of configurations each type of water may take. To form protein pairs
some disordering of bound water on surfaces would provide favorable entropy.
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What happens to solvent as surfaces explore the fit? The first layer of solvent
covering a protein is not bulk water, it is special. This class of protein bound water
is tenacious; it takes a temperature of 100° and high vacuum to remove the last
traces of water from a protein! Perhaps 20 to 30 % of the protein mass is strongly
associated water. The solvent layer at the surface has different properties from
bulk water, and bulk water probably starts about two or three solvent radii out from
the surface.
Solvent may have another role, that being to facilitate mating and hydrogen bond
matching, and so provide some adaptability. Water molecules may act as polar
bridges to mate polar atoms of complimentary side chains.
Extent
Just as some low molecular weight molecules bind tightly and others weakly, we
expect a range of areas in the interactions. In the case of the tightest protein small
molecule interaction, the small molecule biotin binds very strongly to the protein
avidin, but this binding, driven by van der Waals contacts, probably required
careful evolutionary engineering of the protein to build the interface. Proteins have
large surfaces so can easily expect 10 % to interact, and that is a great extent in
comparison to small molecule protein interfaces. Many studies have shown that
Ab's recognize three dimensional surfaces, called epitopes and not a few
sequential side chains in the sequence of the target protein. It is widely
appreciated that some AB’s bind so tightly that they cannot be dissociated without
denaturing the protein.
Historical background
A simple advance was made by trying to understand the nature of the surface area of
the interaction. This was enabled by the methods to calculate surface areas of proteins,
using atomic coordinates from X-ray diffraction, by FM Richards. The first analysis of
interactions using the methods to calculate the extent of surfaces interacting was by
Chothia and Janin in 1975 using the few entries in the available structure database,
insulin, hemoglobin and trypsin-BPTI.
FM Richards and C Chothia and J Janin thought that solvent accessible surface, SAS, would
be related to binding energy as the SAS measures the regions of the protein interacting and
exchanged from water.
Chothia and Janin showed that solvent excluded or buried amounted to 1100 to 1700 Å
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in the interface of these few protein-protein complexes.
On careful study, Chothia and Janin showed the interface to be close packed, as in
crystals of amino acids.
They argued, but did not prove that hydrophobicity is the major factor in stabilizing while
steric complementarity plays the role of selectivity.
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Method: They calculated the solvent accessible surface using the Lee and Richards’s
algorithm:
Area buried = area monomer 1 + area monomer 2 - area of complex of 1 and 2.
Note that they can also calculate the area lost on M1 and M2, these need not be equal,
but they should be similar.
For scaling, the area of an Ala methyl side chain is about 30 Å2. This number comes
about because roughly, from the area formula for a sphere, 4  d, where d is about 3.6
Å for a van der Waals sphere of methane.
What is the source of the energy debt and payback in taking two solvated proteins from
free in solution to one larger protein free in solution?
Experimental measurements
The dissociation constant measured in the lab by titration calorimetry Kd is related to the
free energy by the well known formula:
 Gd = - RT ln Kd referenced to a standard state of 1M for the solutes.
Entropy has a large contribution to this free energy! And the components of the entropy
contributions are surprising. A heavy penalty in entropy is expected from loss of
freedom when two proteins go to one: each monomer has change in rotational and
translational entropy (Sr and St).
Given similar molecular weights and other factors, the Sr and St of the complex is one
half that of the two components when separated in the system. Estimating this
component is very abstract. The proteins are considered as molecules of ideal gas!
This change in entropy can be estimated from the Sackur-Tetrode and rotational
entropy equations that hold perfectly for helium gas, perfect non interacting spheres.
Assuming helium and proteins are similar, these equations give us an estimate of the
rotational and translational entropy lost on two objects combining to form one.
The Sackur-Tetrode equation for an ideal gas is:
S0tr = 3/2R ln M + 5/2R ln T - 2.311,
where S0tr represents the translational entropy in the standard state, i.e., for 1 mole of
the ideal gas at 1 atm. pressure; M is the ordinary molecular weight. If R is taken as
1.987 cal. deg.-1 mole-1, this equation gives the standard translational entropy in E.U.
per mole.
The rotational entropy is:
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S0rot = R (ln Qrot + 1),
where Qrot. = 82 I k T / h2 and I is the moment of inertia.
This entropy factor is surprisingly large, and positive,  GS = + (20- 30) kcal/mol
So,  Gd (measured) =  Gt -  GS
here  GS and  Gd have opposite signs.
Where does  Gt , total free energy change, come from in a structural sense, we need
25 to 50 kcal/mole?
Great scientists differ on the attribution to the free energy. Pauling argued large surface
and H bonds, vdW, etc., Walter Kauzmann argued in the 1960’s that the hydrophobic
effect is dominant, not hydrogen bonds.
It is a sensible proposition that H bonds are stronger between aligned protein atoms
than to water and that van der Waals interactions are some how better in proteins but it
is difficult to explain more than about 10 to 15 kcal/mole.
The hydrophobic effect
Free energy of transfer measurements
Numerous studies of transferring small organic molecules from a moderately
hydrophobic solvent like octanol to water provides an estimate that burying 1 Å 2 of
surface area from water provides 25 cal /mole of hydrophobic free energy. This number
is crude and ignores important aspects of the nature of the interacting surfaces, such as
curvature. Flat surfaces are different from convex/concave ones.
Table 5 shows the calculations for the three complexes:
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The last row in this table is obtained by multiplying 25 cal/Å times the surface area.
We conclude that the buried surface area provides the necessary energy to pay for the
entropy loss and provide the energy of association.
Note that the surface is being counted twice, once for the piece of BPTI and once for
trypsin for example.
It is interesting that Chothia and Janin in 1975 suggested that the surface area buried
needs to be at least 600 Å 2 per monomer to form stable complexes. Structures were
determined 15 years later for several Fab protein complexes with protein antigens
attached and the buried surfaces were approximately as predicted.
The conclusion is that hydrophobic energy is abundant and non specific, and that the
interaction is registered by complementary interactions, steric fit and hydrogen bonds.
Complications
Several issues were hidden in the preceding analysis.
These are:
1. no accounting for the nature of buried surface was made
Does burying oxygen that likes water count as much as burying a methyl group that
prefers a nonpolar environment?
2. no account for conformational changes
3. no account of whether all parts of the surface count nearly equally or whether some
special hot spots were important for the interaction.
The analysis also suffered from only three data points.
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Fletterick, RJ
A review by Janin [Janin J. Elusive affinities. Proteins, 1995 Jan, 21(1):30-9.] nicely
summarizes the problems. Quoting Janin- The affinity of two proteins for each other
and its temperature dependence are determined by the change in enthalpy, free energy,
entropy, and heat capacity upon dissociation.
The forces that stabilize protein-protein association can be modeled and the structures
of the complex if known, can in principle be used to derive values for the
thermodynamic parameters. Gas phase calculations by molecular mechanics, followed
by solution calculations using hydration parameters calibrated on small molecules have
been used to estimate enthalpy and entropy changes. But gas phase calculations have
large errors even with the approximation that the proteins associate as rigid bodies.
Except for the dissociation heat capacity, the fit to experimental data (binding and
calorimetric measurements) is poor. The dissociation heat capacity can be attributed
mostly to the hydration step and correlated with the size of the interface.
The nature of interfaces for homodimers and general protein complexes are cataloged
in two technical papers. The papers are: J Mol Biol. 1999 Feb 5; 285(5): 2177-98. The
atomic structure of protein-protein recognition sites. Lo Conte L, Chothia C, Janin J.
analysis of interfaces in 75 protein-protein complexes showed that
52 have "standard-size" and few conformational changes, 1600 (+/-400) Å2
20 with large conformational changes are 2000 to 5000 Å2
the interface has non-polar character like the protein surface as a whole
water molecules contribute to the close-packing providing complementarity
In cataloging homodimers interfaces, Proteins. 2003 Nov 15; 53(3): 708-19, Dissecting
subunit interfaces in homodimeric proteins. Bahadur RP, Chakrabarti P, Rodier F, Janin
J., Janin showed that
An average interface buries 2000 Å2 -each monomer
the range of size and of hydrophobicity is wide among 122 examples
a core, 77% of the interface, made of residues buried in the dimer is surrounded by a
rim of residues with atoms that are accessible to water
the core resembles the protein interior except for the presence of arginine residues
Crystal structures deposited in the Protein Data Bank illustrate the diversity of biological
macromolecular recognition. Acta Crystallogr D Biol Crystallogr. 2007 Jan;63(Pt 1):1-8.
J Janin et al
Janin found that crystal-packing interfaces are usually much smaller; they bury fewer
atoms and are less tightly packed than specific assemblies. Typical protein interfaces
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bury 1200-2000 Å squared of protein surfaces that assemble with no conformation
changes.
Results of the blind prediction experiments show that docking algorithms efficiently and
accurately predict the mode of assembly of proteins that do not change conformation.
Conformational changes in proteins as they associate
Two extreme cases in pairing of proteins can be imagined. One where the two proteins
that form the interaction undergo no significant conformational change on paring, like
trypsin and its inhibitor, as we shall see in the focus paper. The other is where both
proteins are unfolded and fold when the come together to form the interface and protein
complex. There are few examples in this category as it is difficult to prove the case.
One is in the assembly of interaction domains of the two transcriptional coactivators,
p160 type proteins, and CPB. Nuclear hormone receptors are transcription factors that
change their structure, binding partners on binding of their cognate hormones. The
nuclear receptors regulate the expression of genes. The hormone response proceeds
through the recruitment of coactivator proteins; two are p160 and the general
transcriptional coactivator CBP/p300, which function synergistically in the activation
program.
Horton and Lewis analysis. Analysis for the interactions of 30 proteins.
The Horton Lewis paper- an analysis of the energetics and thermodynamics using atomic
solvation parameters.
Horton N; Lewis M. Calculation of the free energy of association for protein complexes. Protein
Science, 1992 Jan, 1(1):169-81.
These authors added the correction to buried surface by considering the types of atoms
according to Eisenberg and McLachlan model of atomic solvation. They claimed that it
matters that O, N and C are chemically different when buried in protein associations.
In the Horton Lewis empirical approach, G solv =    i (Ai - Ar i), referred to
standard state, summed over all atoms, where A is the area for each atom in the folded
and reference states.
  i is a change in the atomic solvation parameter,I and is negative for polar atoms
and positive ( favorable) for nonpolar atoms.
Note that the atomic contributions should account for the type of interaction that the
atom is engaged in.
It costs energy to remove a N or O atom from water. A buried unpaired O atom is
different from one in a hydrogen bond.
Also, we need to account for conformational changes energetically, isomerizations:
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a + b a' b' (ab)'  ab
The modification to the interaction energy equation is:
 Gd (measured) =  Gt interaction -  Gisomerization -  GS , the - signs indicate that
the free energy is of opposite sign from the interaction energy.
 Gt interaction has components that are enthalpic and entropic, H bonds, van der
Waals and electrostatic, and the hydrophobic effect is the entropic component.
Horton and Lewis carefully apply the atomic solvation parameter equation to provide
favorable energy for the buried polar atoms in H bonds.
For simple cases with no isomerization and diffusion limited association rates
a + b  ab
and the Chothia/ Janin free energy equation holds. To calculate the interaction energy
from static structures is an approximation. The association can be considered to be two
steps, a hydrophobic driven association and a settled registered complex:
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Both steps are claimed to be favorable. The interaction energy is written as two
components, the hydrophobic and the registration step:
 Gt interaction =   G nonpolar +   G polar
The difference in the solvent accessible surface area, per atom, on complex formation,
A0i, is from subtracting the area when the two are separated from the area exposed to
solvent in the complex, (A0i - As i) . The sums are formed with attention to the state of
the atoms:
 G nonpolar =    i (A0i - As i) [first part of equation above]
The term exists for polar atoms, N and O, and is added into the summation only if atom i
is not paired in a H bond!
 G polar =    i (A0i - As i)
[second part of equation above]
if atom i is paired!
An unpaired O atom is counted more like a C atom, but its   is unfavorable.
Using published values for the solvation parameters (- Horton and Lewis show that the
ASP's fit the calculated free energy of transfer independent of how the ASP are
counted- as molecular surfaces, volumes, solvent accessible surfaces, etc.), observed
KD’s
and coordinates for 24 complexes,  and  are determined from the fit as is the
rotational and translational entropy term.
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For these 15, where experimentally no change in structure occurs, the fit is remarkable.
is found to be 1.4 ± 0.2 and  is found to be -1.2 ± 0.2. Relative to octanol, proteins
are more hydrophobic.
Note that multiplied by the  for carbon gives an energy and the product is as
reported by Chothia of 25 cal/Å 2.
The polar terms are from  and the -1.2 indicates that the polar atoms contribute favorably.
The values of the hydrogen bonds can be estimated from the table and number of
hydrogen bonds, a total of 131.
The average is -0.24 kcal/mole. Range is 0 to -.71, depending on area change and atom
type. 44 of the bonds are charged and contribute -0.8 to -1.5.
Horton and Lewis have 30 data points, how well does the surface area buried correlate
to the free energies of association? Ten percent considering all 30 but 79% if only rigid
objects are considered. Chothia and Janin were accurate.
What is the relative role of hydrophobic versus H bonds? Figure 5 shows that
hydrophobic atoms alone correlate poorly with the free energy of association.
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Counting the polar and nonpolar buried surface, and the weighting factors, the
correlation is 96%.
The analysis argues that the hydrophobic effect gives about two thirds of the interaction
energy of the polar contributions give one third.
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Fletterick, RJ
The analysis suggests that buried polar atoms contribute favorably if paired, unfavorably in
unpaired and that hydrophobic atoms contribute favorably.
The entropy lost on complex formation is not well explained- it was made an adjustable
parameter in these studies (one of a total of 3 for 15 observables).
The estimate of 15 kcal/mole seems high compared to the observed 6.2 ± 2.2 from this
work. Experimental measurements are difficult but have been estimated to be in the
range of 7 to 11 kcal/mole.
Finally, what about conformational changes?
Trypsin BPTI a rigid complex can be compared with trypsinogen BPTI where X-ray
structures for both complexes, and all individuals, show that only trypsinogen
isomerizes or changes its conformation on forming the complex. The equation gives 17
kcal/mole for the trypsinogen BPTI complex. This deviates 10 kcal/mole from the
observed 17 and is the estimate of the free energy of isomerization. Note that 17
kcal/mole is as expected for trypsin which does not change conformation.
Demarest et al show that the isolated domains are intrinsically disordered yet combine
with high affinity. They become structured to form a cooperatively folded heterodimer.
The reference is:
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Mutual synergistic folding in recruitment of CBP/p300 by p160 nuclear receptor
coactivators. Demarest SJ, Martinez-Yamout M, Chung J, Chen H, Xu W, Dyson HJ,
Evans RM, Wright PE.
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Figure 1 Structural and thermodynamic characterization of free and complexed ACTR
and CBP.
a, 15N-HSQC (heteronuclear single quantum coherence) spectra of [15N]ACTR(1018–
1088) free (black) and in the presence of excess unlabelled CBP(2059–2117) (red).
b, [15N]CBP(2059–2152) free (black) and in the presence of excess unlabelled
ACTR(1018–1088) (red).
c, Urea denaturation of free ACTR(1018–1088) (filled diamonds), free CBP(2059–2152)
(filled circles), ACTR(1018–1088)–CBP(2059–2152) (filled triangles) and ACTR(1018–
1088)–CBP(2059–2117) (filled squares). Denaturation curves for both complexes were
measured in duplicate and each curve was fit separately to a two-state unfolding
model30, giving G°U = 3.7 0.1 kcal mol-1 and m = 1,005 87 cal mol-1 M-1; where
G°U is the standard free energy charge for the unfolding reaction, and M is the
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dependence of the free energy of unfolding on the concentration of denaturant.
Removal of the glutamine-proline-glycine repeat region of CBP (2,118–2,152) did not
perturb the stability of the complex; NMR experiments were therefore performed with
the CBP(2059–2117) construct. All circular dichroism experiments were carried out with
1–20 µM protein in 2 mM phosphate buffer (pH 6.6), 10 mM NaCl.
d, Isothermal titration calorimetry (ITC- In ITC, a syringe with protein number 1 in
solution is titrated into a cell containing a solution with protein number 2. The addition is
done at constant temperature. When protein 1 is injected into the cell a complex forms
and heat is released or absorbed in direct proportion to binding. As protein 2 in the cell
becomes saturated, the heat change falls to the background heat of dilution) data for
titration of 10 µM ACTR(1018–1088) with 120 µM CBP(2059–2117) in 10 mM Tris
buffer (pH 6.9), 50 mM NaCl at 31 °C. The reverse titration gave identical results within
experimental error. The stoichiometric constant (n) varied from 0.97 to 1.03 between the
two experiments, confirming 1:1 binding.
Figure 2 Solution structure of the ACTR–CBP complex. ACTR is pink and CBP blue in
all fig
ures.
a, Stereo view showing best-fit superposition of backbone heavy atoms within the
structured region. Residues at the boundaries of the structured region are numbered.
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b, Ribbon representation, in the same orientation as a. Helices A 1–3 and C 1–3, and
the polyglutamine (polyQ) stretch in CBP are labeled.
c, Surface representation of CBP domain, showing the hydrophobic groove formed by
C 1 and C 3 that accommodates helix A 1 of ACTR. The orientation is the same as in a
and b. Bulky hydrophobic residues from A 1 embedded within the groove are labeled.
d, Surface representation of CBP domain, rotated to show the hydrophobic cleft that
binds helix A 2 of ACTR. The interactions between A 3 and C 3 are also shown. Bulky
hydrophobic residues of ACTR that form the molecular interface are labelled, as is
Asp 1068, which participates in the buried salt bridge.
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Figure 3 Conserved interactions in the ACTR–CBP complex.
a, Sequence alignment of the CBP binding domain of human ACTR(1018–1088) and a
representative set of p160 coactivators.
b, Sequence alignment of the ACTR binding domain of murine CBP with other members
of the CBP/p300 family. Conserved hydrophobic residues (green), conserved acidic
residues (red), conserved basic residues (blue), and other conserved residues (orange)
are indicated (h, human; m, murine, x, Xenopus laevis; d, Drosophila; dr, Danio rerio; c,
Caenorhabditis elegans).
c, XX and XX hydrophobic contact map defining the interface between ACTR
and CBP (denotes hydrophobic residue). The four XX motifs that comprise the
hydrophobic core are enclosed by a green box. The buried intermolecular salt bridge is
indicated.
d, Close-up of the salt bridge between Arg 2105 and Asp 1068 salt bridge. The solventaccessible surface of ACTR is shown.
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