# Model Binding Systems

Mb (a monomer containing 8 a-helices, A-H) and Hb (a heterotetramer with two a -and two b-subunits, each which also contains 8 a-helices) are both oxygen binding proteins. Dioxygen is transported from the lungs, gills, or skin of an animal to capillaries, where it can be delivered to respiring tissue. It has a low solubility in blood (0.1 mM). Whole blood, which contains 150 g Hb/L, can carry up to 10 mM dioxygen. Invertebrates can have alternative proteins for oxygen binding, including hemocyanin, which contains Cu and hemerythrin, a non-heme protein. On binding dioxygen, solutions of Hb change color to bright red. Solutions of hemocyanin and hemerythrin change to blue and burgundy colored, respectively, on binding dioxygen. Some Antarctic fish do not require Hb since dioxygen is more soluble at low temperature. Mb is found in the muscle, and serves as a storage protein for oxygen transported by Hb.

### Hemoglobin

• 1st protein whose molecular weight was determined
• 1st protein to be assigned a specific function - dioxygen transport
• has a prosthetic group (non-amino acid) heme group (protoporphyrin IX with a ferrous ion) covalently attached to the protein. The heme group binds dioxygen.
• 1st protein in which a point mutation (single base pair charge) causes a single amino acid change in the protein, marking the start of molecular medicine
• 1st protein with high resolution x-ray structure
• theory for dioxygen binding explain control of enzyme activity
• the binding of dioxygen is regulated by binding of H+, CO2, and bisphosphoglcyerate which bind to sites distant (allosteric) from oxygen binding site.
• crystals of deoxy-Hb shatter on binding dioxygen, indicating significant conformational changes on binding.

#### Heme Group

Figure: Heme

The heme group contains protoporphyrin IX, with four tetrapyrrole rings linked by methene bridges. Attached to the tetrapyrrole structure are four methyl, two vinyl, and two proprionate groups. These can be arranged in 15 ways; only one (IX) occurs in biological systems. Ferrous ion bonded to the protoporphyrin IX constitutes the heme group. The heme fits into a hydrophobic crevice in the proteins with the proprionate groups exposed to solvent.

The Fe2+ ion is coordinated to 4 N's on the 4 pyrrole rings, The 5th ligand is a supplied by proximal His (the 8th amino acid on helix F) of the protein. In the absence of dioxygen, the 6 ligand is missing, and the geometry of the complex is square pyramidal with the Fe above the plane of the heme ring. A distal His (E7) is on the opposite side of the heme ring, but too far to coordinate with the Fe. When dioxgen binds, it occupies the 6th coordination site and pulls the Fe into the plane of the ring, leading to octahedral geometry. CO, NO, and H2S also bind to the 6th site, but with higher affinity than dioxygen, which can lead to CO poisoning. The distal His keeps these ligands (including dioxygen) bound in a bent, non-optimal geometry. This minimizes the chances of CO poisoning.

When oxygen binds to heme Fe2+, the geometry of the complex becomes octahedral. The Fe2+ has 6 electrons in d orbitals. (The electronic configuration of Fe is 3d64s2 while the Fe2+ ion is 3d6). From crystal field theory (review a general chemistry text), the ligand electrons pairs (treated as anions) interact with the d orbital Fe2+ electrons. They interact most strongly (in a repulsive fashion) with the dz2 and dx2-y2 Fe2+ electrons, which are oriented at the axial ends and equatorial corners, respectively, of the octahedral complex. This repulsion raises the energy of these two orbitals. The other three d orbitals feel less repulsion by the ligand electrons and are lower in energy. The difference in energy between the three lower energy levels of d electrons (in t orbitals) and the higher energy levels of electrons (in g orbitals) allows photons matching that energy difference to be absorbed as electrons are promoted to the g orbitals. Ligands that interact strongly with the dz2and dx2-y2 electrons raise their energy even more, increasing the energy of the photon required to promote an electron from the t to g orbitals. Dioxygen is one of those ligands, leading to the absorbance of high energy photons, causing the solution to appear bright red (since blue light is absorbed). Because of this strong ligand, the significant energy gap between the t and g orbitals causes the electrons to reside mostly in the lower energy t orbitals where they remained paired, giving the complex a low spin state in which all 6 d electrons are paired. Hence oxyhemoglobin is diagmagnetic. The heme complex can also exist in a high spin state in which the electrons are easily excited to the g orbitals which are closer in energy to the t orbitals when the ligand is weakly interacting with the Fe2+ electrons. In these cases, the heme is paramagnetic since unpaired electrons are possible. (We will discuss paramagnetism later in the course during our exploration of oxygen chemistry.

Figure: Heme-O2 Octahedral Complex

When dioxyen binds, the oxidation state of the Fe2+ ion does not change, even through dioxygen is a great oxidizing agent. Hence the Fe2+ ion is a reversible carrier of dioxygen, not of electrons. Free heme in solution is oxidized by dioxygen, forming a complex with water which occupies the 6th position, with the iron in the Fe3+ state. An intermediate in this process is the formation of a dimer of 2 hemes linked by 1 dioxygen. This can't occur readily when the heme is in Hb or Mb. Other heme proteins (like Cytochrome C) are designed to be carriers of electrons. A small amount of the Fe2+ ion gets oxidized to Fe3+ ion. Mb and Hb in this state are called metHb and metMb. A enzyme is required to reduce the iron back to the Fe2+ state.

### Myoglobin

• Mb is extremely compact, and consists of 75% α -helical structure.
• 8 α-helices are present, labeled A-H.
• 4 α-helices are terminated by Pro
• The interior amino acids are almost entirely nonpolar. The only polar amino acids found completely buried are the two His (proximal and distal) found at the active site of dioxygen binding.
• Jmol:  Met-Myoglobin

#### Difference Between Hb and Mb

Hb is a tetramer of two a and two b subunits held together by IMF's (an example of quarternary protein structure), and 4 bound hemes, each of which can bind a dioxygen. In a fetus, two other subunits make up Hb (two zeta - z and two epsilion - esubunits -analogous to the two a and two b subunits, respectively). This changes in fetuses to two a and two g subunits. Fetal Hb has higher affinity for dioxygen than adult Hb. Mb is a single polypeptide chains which has higher affinity for dioxygen than Hb.

The a and two b chains are similar to Mb, which is unexpected since only 24 of 141 residues in the a and bchains of Hb are identical to amino acids in Mb. This suggests that different sequences can fold to similar structures. The globin fold of Mb and each chain of Hb is common to vertebrates and must be nature's design for dioxygen carriers. A comparison of the sequence of Hb from 60 species shows much variability of amino acids, with only 9 identical amino found. These must be important for structure/function. All internal changes are conservative (e.g. changing a nonpolar for a nonpolar amino acid). Not even Pro's are conserved, suggesting there are different ways to break helices. The two active site His are conserved, as is Gly B6 (required for a reverse turn).

Plots of Y (fractional saturation) vs. L (pO2) are hyperbolic for Mb, but sigmoidal for Hb, suggesting cooperative binding of oxygen to Hb (binding of the first oxygen facilitates binding of second, etc). (see Preclass Question Below.)

Figure: Plots of Y (fractional saturation) vs. L (pO2) are hyperbolic for Mb, but sigmoidal for Hb

The affinity of Hb, but not of Mb, for dioxygen depends on pH. This is called the Bohr effect, after the father of Neils Bohr, who discovered it.

Figure: Bohr effect

Protons (decreasing pH), carbon dioxide, and bisphosphoglycerate, all allosteric ligands which bind distal to the oxygen binding sites on the heme, shift the binding curves of Hb for oxygen to the right, lowering the apparent affinity of Hb for oxygen. The same effects do not occur for Mb. These ligands regulate the binding of dioxygen to Hb.

From these clues we wish to understand the molecular and mathematical bases for the sigmoidal binding curves, and binding that can be so exquisitely regulated by allosteric ligands. The two obvious features that differ between Mb and Hb are the tetrameric nature of Hb and its multiple (4) binding sites for oxygen. Regulation of dioxygen binding is associated with conformational changes in Hb.

### MWC (Monod, Wyman, and Changeux)- Symmetry Model

In this model, in the absence of ligand (oxygen), Hb exists in two distinct conformations, the T state (equivalent to the crystal structure of deoxyHb) and the R state (equivalent to the crystal structure of oxyHb without the oxygen). In the absence of dioxygen, the T state (T0) is greatly favored over the unliganded R state (R0) at equilibrium. An equilibrium constant (more equivalent to a dissociation constant) can be defined as L = T0/ R0. (Note: L is not the ligand concentration.) In addition, let us assume that Hb can not exist with some of the monomers in a tetramer in the T state while others in the same tetramer are in the R state. Hence this model is often called the symmetry model. Finally let's assume that each oxygen can bind to either the T or R state with the dissociation constants KTand KR respectively. These constants do not depend on the number of oxygens already bound to the tetramer. Hence KR = [R0][O2]/[R1] = [R1][O2]/[R2] = ... etc., where the subscript on R refers to the number of oxygens bound to that form of R.

Now define two new parameters:
a= [pO2]/KR which is really a normalized ligand concentration describing how many times the KR the ligand concentration is.

$c = \dfrac{K_R}{K_T}.$

If oxygen binds preferentially to the R form of Hb, c would be a small fractional number. In the limiting case, when oxygen did not bind to the $$T$$ form, $$K_T$$ would be infinite, and $$c) would equal 0. Using these definitions and equations, the following equation showing \(Y$$, fractional saturation vs. $$a$$ can be derived, with $$n$$, the number of binding sites per molecule, = 4 for Hb.

$Y = \dfrac{ a(1+a)^{n-1} + Lca(1+ca)^{n-1}}{(1+a)^n +L(1+ca)^n}$

Figure: Y Vs alpha with varying L and c - MWC MODEL

When L is set at 9000 and c = 0.014, the Y vs a curve fits the experimental oxygen binding data well. The graph below shows the best experimental dioxygen binding data that I could find (obtained from a graph, not from a table), and the best fit Y vs L using a Hill coefficient of n=2.8 (fitting equation 3 above), and the best fit of Y vs L using the MWC model, with L=9000, c=0.014, and Kr = 2.8 torr.

### Another Way to Think About the MWC Model

The MWC model assumes that oxygen binds to either the T or R form of Hb in a noncooperative fashion. That is KT and KR are constant, independent of the number of oxygens bound to that form. If that is so, what is the basis of the cooperative oxygen binding curves? The answer can be seen below. The red curve might reflect the binding of a ligand to the T form of a macromolecule, with Kd = 50 uM, for example. Notice that the binding curve is hyperbolic. Likewise, the blue curve might reflect the binding of a ligand to the R form of the macromolecule with Kd = 10 μM. If the T and R form are linked through the T ↔ R equilibrium, which will be shifted to the tighter binding R form with increasing ligand concentration, assuming that the ligand binds preferentially to the R form. This shifts the actual binding curve from that resembling the T form at low ligand (red) to that of the R form as ligand increases (blue), imparting sigmoidal characteristics to the actual binding curve (purple).

#### KNF (Koshland, Nemethy, and Filmer) - Sequential Model

This model was developed to address concerns with the concerted model. One of the major problems with the concerted model is that it seemed unrealistic to expect all the subunits to change conformation together. Why should not there be some difference in subunit conformation? The KNF model also fits the experimental data well.

Figure: EQUILIBRIA IN KNF MODEL

### Conformational Selection: Isomeric Antibodies and Ubiquitin

In our study of hemoglobin structure in the MWC model, we developed the idea that there were two forms of hemoglobin in solution, the taut and relaxed form, which are pre-exisiting and interconvertible even in the absence of dioxygen. Oxygen was presumed to bind preferentially to the relaxed form. In the KNF model we saw that ligand binding can induce conformational changes in adjacent subunits, promoting cooperative binding of ligand. In general these two models distill down to combinations of two simpler models. The first might be called the conformational selection in which ligand binds tightly to a preexisting conformations in a "lock and key manner" without inducing subsequent macromolecular conformational change. Alternatively, the ligand might bind loosely and then alter the macromolecular conformation to produce tighter binding, an example of an induced fit model. For the binding of dioxygen to hemoglobin, thermodynamic cycles could be drawn showing either binding of ligand and subsequent conformational changes in protein structure or conformational changes in protein structure proceeding binding. Is there additional evidence to support the conformational selection model of binding of ligand to a protein that can, in the absence of ligand, exist in two conformations? The answer is yes.

Antibodies are immune system protein molecules than can bind "foreign" molecules and target them for biological neutralization. Many crystal structures have been determined of antibodies in the presence or absence of a "foreign" ligand molecule. In these cases, the conformation of the bound antibody is different from that of the free. Either an induced fit model for ligand binding or a lock and key model of binding of ligand to one of two different pre-existing conformations of the antibody could account for this observation. These different mechanisms could be differentiated experimentally by stop-flow kinetic technique since both display slow and fast phases that are affected differently by ligand concentration. Theoretically, in the induced fit model, only one ligand type could bind to the antibody which would undergo a conformational rearrangement to produce tighter binding. However, in the two preexisting conformational models, a different structural ligand might bind to each of the two main antibody conformations. James et al. have recently shown through stop flow kinetics techniques (to investigate binding) and x-ray crystallography (to investigate final structures) that one antibody molecule can, through existing in two different preexisting conformations, bind two different ligands (antigens). One antibody conformation binds small aromatic molecules with low affinity (including the small molecule 2,4-dinitrophenol, the immunizing molecule or hapten) and then rearranges to produce a high affinity binding complex in which the DNP is bound in a narrow cavity (reducing the effective off rate of the bound ligand). A second antibody conformation binds a protein ligand over a broad, flat binding site of the antibody molecule.

Lange (2008) et al, using a NMR technique, residual dipolar coupling, that allows sampling of structures in the microsecond time scale, have shown that the solution structure of ubiquitin (which we modeled in our first lab), in the absence of ligand, exists in an ensemble of conformational states. More importantly, these different conformational states are identical to those found in the 46 crystal structure of ligand complexed to various protein ligands, strongly supporting the concept of conformational selection. In all likelihood, a combination of both induced fit and conformational selection probably occurs within a 3D energy landscape in which an initial binding encounter by either a lock and key fit to the "optimal fit" conformer or to a higher energy conformer in which the bound state relaxes to a lower energy through the induction of shape changes in the binding protein.

Figure: Conformational Selection vs Induced Fit Binding (after Boehr and Wright, Science 320, 1429 (2008)

### Natively Unfolded Helixless Variant of Rabbit I-BABP

An interesting experimental model to distinguish conformational selection versus induced ligand binding was offered by Rea et al. They studied rabbit ileal bile acid binding protein (I-BABP). The wild type protein has a helix-turn-helix motif at its N terminus. They produced a mutant (Δa-I-BABP) that replaced this motif with a Gly-Gly-Ser-Gly linker, causing the protein to unfold. Next they conducted binding and folding studies on addition of taurochenodeoxycholate (TCDC) using stopped-flow fluorescence to measure the binding behavior. They wished to distinguish between two distinct mechanisms – folding before binding (or conformational selection) and binding before folding (or induced-fit model). The data support a two phase model. One phase did not depend on ligand and one did, suggesting binding followed by a conformational change).

##### Induced Fit

P* in the conformational selection models represents a high affinity, pre-existing conformation of the protein. In this model, high ligand shifts the equilibrium to the right.

One way to differentiate these models is to look at the dependency of the different kinetic phases on ligand. In the conformation selection model, the slow step is the formation of the high affinity form of the protein, P*. The first slow step has a nonlinear dependence in L while the fast second step has a linear dependence. The data did not fit this model well.

In the induced fit, the ligand binds to a low affinity and perhaps unfolded form of the protein, which subsequently collapses to the bound form in a slow step.

$k_{slow}= k_{-2} + \dfrac{k_2[L]}{L+\dfrac{k_{-1}}{k_1}}$

$k_{fast}=k_{-1}+k_1[L]$

Both ligand dependent and independent phases were seen. At high ligand concentration, the slow step in the induced fit would be independent of ligand. The authors state the data is consistent with a variant of induced fit called the "fly casting model." In this model the protein first encounters ligand and forms a hydrophobic collapse intermediate (PL) in a fast step characterized by a linear dependence on ligand concentration. Then the intermediate slowly interconverts into a wild type like complex through conformational re-arrangement.  Wild-type protein binds the ligand 1000x as quickly, suggesting entropic barrier to binding of the ligand to the unfolded state and rearrangement of the protein thereafter.

Junker et al. used atomic force microscopy (AFM) to observe the effects of ligand binding on the folding/unfolding fluctuations of a single molecule of calmodulin (CaM), a calcium-binding protein that binds amphiphilic helical peptides which leads to a large conformation change in the protein. To do this, they sandwiched a single CaM molecule between filamins that serve as attachment points for the AFM tip and a surface. A slow pulling force was then applied to the molecule, and the length gain was measured as the protein unfolded. The rapid fluctuations between folded and unfolded states were quantified and used to derive a complete energy landscape for the folding of CaM. They conducted these experiments in the presence of two ligands, Ca2+ and mastoparan (Mas), a wasp venom peptide. They found that Mas does not affect the folding rate of CaM, although it does stabilize the already folded form. This suggests that Mas does not bind to the transition state or the unfolded protein, but rather selects a particular conformation from an ensemble of possible choices. Ca2+ however, increases the folding rate, which suggests that it stabilizes both the transition state and the folded state. FM offers a considerable degree of precision in drawing energy landscapes of protein folding and unfolding, and it has several applications that are yet to be explored.

### Binding, Intrinsically Disordered Proteins, and MoRFs

As described above, binding of a protein to a ligand (including another protein) could occur by a lock and key mechanism, possibly through a conformational selection process, or through an induced fit when an initial binding event is followed by a conformation rearrangement to form a more tightly bound complex. But how does binding to completely intrinsically disorder protein (which has been documented) occur? These cases are quite removed from those envisioned in simple induced fit mechanisms. To accommodate binding to IDPs, a new idea has emerged, that of Molecular Recognition Features (MoRFs)

MoRFs are typically contiguous and continuous amino acid linear but disordered sections of a disordered protein that first encounter a binding partner (a protein for example). Mohan et al. conducted a structural study of MoRFs by selecting short regions (less than 70 amino acids) from mostly disordered proteins that were bound to protein greater than 100 amino acids from protein complexes found in the Protein Data Bank. They chose sequences of 70 amino acids and smaller since they would be most likely to display conformational flexibility before binding to a target. 2512 proteins fit their criteria. For comparison, they created a similar database of ordered monomeric proteins. The analysis showed that after they encounter a binding surface on another protein, the MoRF would adopt or "morp" into several types of new conformations, including alpha-helice (α-MoRFs), beta-strands (β-MoRFs), irregular strands (i-MoRFs) and combined secondary structure (complex-MoRFs), as shown in the figure below.

Figure: Types of Molecular Recognition Features in Intrinsically Disordered Proteins. (A) α-MoRF, Proteinase Inhibitor IA3, bound to Proteinase A (PDB entry 1DP5). (B) A β-MoRF, viral protein pVIc, bound to Human Adenovirus 2 Proteinase (PDB entry 1AVP). (C) An ι-MoRF, Amphiphysin, bound to α-adaptin C (PDB entry 1KY7). (D) A complex-MoRF, β-amyloid precursor protein (βAPP), bound to the PTB domain of the neuron specific protein X11 (PDB entry 1X11). Partner interfaces (gray surface) are also indicated. Vacic, V. et al. Journal of Proteome Research 6, 2351 (2007). Permission from Copyright Clearance Center's Rightslink /American Chemical Society

Vacic et al. have further characterized the binding surfaces between MoRFs and their binding partners using structural data from PDB files. Interfaces were studied by determining the differences in accessible surface area between MoRF and their binding partners, and the protein in unbound states. These were compared to ordered protein complexes, including homodimers and antibody-prantigenotein interactions that were not characterized by disordered interactions. Their findings are summarized below.

• MoRF interfaces have more hydrophobic groups and fewer polar groups compared to the surface of monomers. This is true even as the overall amino acid composition of intrinsically disordered protein shows them to be enriched in polar amino acids, which leads them to adopt a variety of unfixed solution conformations.

• α-MoRFs have few prolines, which is expected as prolines are helix breakers.

• Methionine is enriched in both MoRFs and in their binding partner interface. Methionine is unbranched, flexible, and contains sulfur, which is large and polarizable, making it an ideal side chain to be involved in London forces in a hydrophobic environment.

• Even though MoRFs have few residues, their binding interfaces were of similar or larger size than other protein binding interfaces, a result which also applies to IDPs as a whole. MoRFs interfaces also have a larger solvent-exposed surface area, similar to IDPs. This is consistent with the notion MoRFs are disordered before binding and that a defined structure is not possible with little buried surface area.

• As MoRFs have significant nonpolar character within a IDP that is highly enriched in polar amino acids, MoRFs should be highly predictable by search algorithms.

Hemoglobin is an amazing molecule. Unlike myoglobin, it displays cooperative binding of dioxygen. In addition, not only does it bind dioxygen (at the heme Fe), it also binds protons and carbon dioxide at other, or allosteric sites. Binding of these ligands influences the binding of dioxygen, as seen from the rightward shift of the oxygen binding curves at lower pH's, such as would be encountered in respiring tissues. The linkage of the binding of dioxygen, and protons or carbon dioxide can be visualized easily with simple thermodynamics which you learned in general chemistry. Consider the equilibria shown below.

It should be obvious from these equations than K1 K4 = K2 K3 , where Ki are the dissociation constants for the various equilibrium. Remember than DG is a state function and independent of path. Hence DGo1 + DGo4 = DGo2 + DGo3 , where DGoi = -RTln(1/Kdi). From the oxygen binding graphs, it is also clear that K1 < K3. Therefore, it is clear that K2 < K4. This shows that protons bind to deoxyHb more tightly than to oxyHb. Hence, the presence of higher [H+] drives the dissociation of O2 from oxyHb. As described in the book, H+ bind to side chains which have an increased affinities for H+ in the deoxyHb state. The conformation change in Hb alters the effective environment of some side chains (specifically His b146, His a122, and the aamino group of the achain), increasing their pKa values The protonated HisH+ then makes a salt bridge to Asp b94 in the FG corner of the same bchain, forming a salt link which stabilizes the deoxyHb or taut state.

Figure: A review of thermodynamic cycles - linked equilibria - other examples

### When Does a Protein Monomer Form a Dimer, Trimer, Tetramer?[1]

OLIGOMER FORMATION (under construction)

Many proteins are found in aggregated states biologically. Hemoglobin consists of two alpha and two beta monomers (or protomers) which assemble to produce the biologically relevant heterotetrameric protein. As we discussed in Chapter 5A - Reversible Binding I, a given monomer can self aggregate to form homooligomers (dimers, trimers, tetramers, or Mn). The polymers display symmetry with respect to the geometric arrangement of the subunits. Symmetry, as we have just seen, is an important component of the MWC model. Most oligomeric proteins contain protomers symmetrically arranged. What mechanism determines whether a monomeric protein forms a homooligomer? Why do they stop at a certain n value? Can proteins be engineered to do so? If mutation can induce oligomer formation, then fewer mutations would be required to produce a symmetric oligomer from subunits since fewer mutations would be required as a single mutation in a single monomer would be represented n times in a single oligomer of n monomers. This fact probably underlies the reason that oligomers display exquisite symmetry. Hence a basic knowledge of symmetry of protein oligomers is necessary.

In the study of small molecules, chemists describe symmetry through the use of mathematical symmetry operations and elements, which find great use in analysis of structure and in molecular spectroscopy. These concepts are usually first encountered in physical and inorganic chemistry classes. A symmetry operation is a movement of an object like a molecule that leads to an identical, superimposable molecule. Each operation has a symmetry element (point, line, or plane) about which the motion occurs. Some examples are shown below:

Table: Symmetry Elements and Operations

 Element (with Jmol link) Operation inversion center (i) projection through center (point) of symmetry of point x,y,z to point -x,-y,-z proper rotation axis (Cn) rotation around a Cn axis by 360o/n where C denotes Cyclic horizontal (sh) and vertical (sv) symmetry plane reflection across a horizontal or vertical plane improper rotation axis (Sn) rotation around a Sn axis by 360o/n followed by reflection in plane perpendicular to the axis.

Luckily for students trying to apply these rules to protein oligomers, biomolecules made up of chiral monomers (such as the L-amino acids of proteins) can not be converted to identical structures using inversion or reflection since the chirality of the monomer would change - for proteins this would entail and L to D amino acid change. That excludes all but proper rotation axes (Cn) from the list above.

A point group is a collection of symmetry operations that define the symmetry about a point. The 4 types of symmetries around a point are those described above: rotational symmetry, inversion symmetry, mirror symmetry, and improper rotation. The types of point groups around a point include:

• cyclic (Cn) - contain one single Cn rotation axis. A biological example is the tobacco mosaic virus double disk (34 monomers, C17). In this point group note that the n in Cn is equal to the number of monomers and the angle of rotation is 360o/n.

Figure: C2 Symmetry

• dihedral (Dn) - These have mutually perpendicular rotation axes. Specifically they contain at least 1 C2 axis perpendicular to a Cn axis (Canter and Schimmel. Biophysical Chemistry - Part 1). The minimal number of subunits is n. Most protein oligomers fall into this category. The packing (or asymmetric) unit does not have to be a single monomer but could be a heteodimer.

1. A D2 point group has 1 C2 axis and 2 perpendicular C2 axes, and 4 monomers (like Hb). These proteins can dissociate into two dimers (such as two a/b dimers for Hb). Note that a different arrangement of 4 monomers could produce a oligomer with C4 symmetry instead of D2.

2. A D4 point group has 1 C4 axis and 4 C2 axes, along with 2n=8 subunits. An example of a D4 point group is ribulose bisphosphate carboxylase/oxygenase (RuBisCO) which has 8 subunits (where a subunit, or more technically the asymmetric subunit, is a dimer of a small and large molecular weight protein). This point group could arise from quaternary structure of two C4 tetramers or four C2 dimers.

Figure: D2 Symmetry

• cubic - contain four C3 axes connecting opposite corners of a cube (so the lines are effectively diagonals) arranged as the four body diagonals (lines connecting opposite corners) of a cube. The tetrahedron (4 sides), cube (6), octahedron (8), and icosohedron (20), perfect Platonic solids (in which all faces, edges and angles are congruent) all have related 3 C3 axes (diagonals connecting opposite corners for cubes, diagonals from a vertex to the opposite face for tetrahedrons, line connecting two opposite faces for octahedron, etc ) so they all can be considered to be part of the cubic point group.

Cubes have a total of 13 symmetry axes comprising 3 types (three C4 axes passing through the centers of opposite faces, four C3 axes passing through opposite vertices, and six C2 axes passing through the centers of opposite edges). An octahedron can be aligned with a cube and be shown to have the same symmetry axes.

Tetrahedrons have a total of 7 symmetry axes comprising two types (four C3 axes of the cube and three C2 axes which are the same as the C4 axes of the cube. First note the relationship between a cube and an inscribed tetrahedron.

A dodecahedron with 12 regular pentagon faces (green) and an icosohedron with 20 equilateral triangle sides (red) can be aligned with each other (as can cubes and octahedrons) and have 31 symmetry axes, as shown below. Note also the relations between a cube inside a dodecahedron and a octahedron inside of a dodecahedron that makes sharing of symmetry axes between these pairs more obvious.

vrml files for movies from http://www.georgehart.com/virtual-polyhedra/symmetry_axes.html

Examples of protein complexes with these point groups are:

• aspartate-ß-decarboxylase, tetrahedral, 12 asymmetric units
• dihydrolipoyl transsuccinylase, octahedral, 24 asymmetric subunits
• many spherical viruses, icosahedral, 60 asymmetric units

Proteins, especially those involved in cytoskeletal filaments, can form fibers which contain helical symmetry which differs from those described above since the monomers at the ends of helical fibers, although they have the same tertiary structures as those in the middle of the helical fibers, do not contact the same number of monomers and hence have different microenvironments.

A recent article by Grueninger et al. addresses the question of whether the process of oligomerization can be programmed into the genome. Can simple amino acid substitutions lead to oligomerization? Remember that oligomerization can be beneficial (formation of cytoskeleton filaments) or detrimental (formation of fibers in sickle cell anemia and mad cow disease). Oligomers with long half-lifes (for example cytoskeletal filament such as actin and tubulin) and short half-lives (for proteins causes transient activities are regulated by oligomer formation) are both necessary.

It has long been noted that if a protein chain forms oligomers, then a single amino acid change in the chain would be found n times in an oligomer of n chains. Mutations could either promote chain contact and oligomer formation or dissocation into monomeric or other assymmetric subunit composition if the mutation were in a region involved in subunit association (a contact region). Experimental work in this field of study is hampered by the fact that mutants made by site-specific mutagenesis to prefer the monomeric state often fail to fold (due to hydrophobic exposure and aggregation). Studies have shown that most contact areas between monomers or other asymmetric units are hydrophobic in nature and the contact regions must be complementary in shape. Obviously mutations that replace hydrophobic side chains involved in subunit contact with polar, polar charged, or bulkier hydrophobic side chains would inhibit oligomer formation.

Grueninger et al. were able to successfully engineer dimer formation and oligomer formation as well. First consider the simplest case of a mutation in a monomer that can produce a dimer with C2 symmetry. This is illustrated below, which also shows how a mutation that produces a weak interaction in a monomer could also produce a long helical aggregate (which can't be crystallized) without symmetry (as described above). A mutation at 2 could convert a monomer promote either oligomer helix formation or dimerization.

(adapted from Grueninger et al. Science, 319, 206-209 (2008)

It should be noted that mutation could lead to dimer or oligomer formation by producing a more global conformational change in the monomer (not indicated in the example above) which leads to aggregate formation, as we have seen previously in the formation of dimers and aggregates of proteins associated with neurodegenerative diseases (like mad cow disease).

Grueninger produces mutants of two different proteins that showed dimer formation as analyzed by gel filtration chromatography (but did not crystallize so now 3D structures were determined). In addition the group modified urocanase, a C2 dimer, at 3 side chains to form a tetramer with D2 symmetry. Also, they modified L-rhamnulose-1-phosphae, a C4 tetramer, at a single position to form an octamer with D4 symmetry. The latter two were analyzed through x-ray crystallography. Their work suggests ways that complex symmetric protein structures arose in nature from simple mutation and evolutionary selection.

Other Examples of Conformational Changes in Biological Macromolecules

Conformational changes in macromolecule structure upon ligand binding are common features of such interactions. Interesting examples of conformational effects on binding are described below. Protein activities can often be modeled using the assumption of two major, different conformational forms. The first example, however, describes time-resolved structural changes in a protein on ligand release.

### Unbinding of a Ligand from a Protein

As a complete understanding of an organic reaction requires a knowledge of the structures of reactants, transition states, intermediates and products along the reaction coordinates, so is the knowledge of different structural states along the dissociative pathway necessary for a complete understanding of the dissociative (and by inference the associative) mechanisms of ligand binding. Such a time-resolved pathway can be studied through molecular dynamics simulations. Schotte et al. have recently studied the dissociation of CO from carboxy-L29F-myoglobin to deoxy-L29F-Mb using time-resolved x-ray crystallography. (L29F is a mutant form of the wild type in which Leu 29 has been changed to Phe.) They chose this mutant since evidence of a short-lived (140 ps lifetime) intermediate in the flash-photolyzed dissociation of CO from the mutant was found using time-resolved mid-infrared spectroscopy of CO-L29F-myoglobin. In this technique, the CO-L29F-Mb is pulsed with an orange laser to photolyse the CO-Mb complex. After a brief delay, an IR pulse tuned to the CO stretch was added. The spectra of the mutant Mb showed two bands which converted to one broad band with time. The two bands represent two different orientations of the CO at the heme Fe, while the broad band arises when the CO dissociates from the primary site to other sites. The intermediate represented a structure in which CO was trapped in a binding site adjacent to the heme Fe which presumably is also a binding site for the initial association of the ligand. This site found in molecular dynamics simulations consisted of the heme and Val68, Ile 107, and Leu29 side chains, all of which are conserved in mammalian myoglobins. Time-resolved x-ray structures were obtained after orange laser-induced photolysis, followed by time-delayed x-ray pulses. These structures showed much larger changes in structure than the differences in structure between the deoxy-and oxy-Mb x-ray structures would suggest. The side changes exhibits coordinated motions that "sweeps" the CO away, accounting for the fast dissociation of the bound CO.

### An Engineered Allosteric Enzyme

Do you ever wonder if your respiratory infection is viral, bacterial, or fungal in origin? Most patients would probably like an antibiotic but with the rise of resistant bacteria, unwarranted use of antibiotics is not wise. Wouldn't it be great if a quick test could be done to distinguish among these possibilities? A new sensitive and rapid method to analyze for specific DNA sequences (which could provide the needed distinction) has been developed by Saghatelian et. al. They have made an enzyme with a covalently attached single-stranded DNA sequence - an inhibitor-DNA-enzyme (IDE) complex.

Figure: inhibitor-DNA-enzyme (IDE) complex

To the other end of the DNA is covalently attached an inhibitor of the enzyme. The inhibitor, tethered to the ssDNA, can bind to and inhibit the enzyme. Now if a complementary strand of DNA (derived from the bacterial, virus, etc) is added, it can bind to the ssDNA tether through complementary H-bond interactions to form a dsDNA in which the inhibitor is removed from the active site of the enzyme. The complementary DNA is, in effect, an allosteric activator, or more accurately a deinhibitor, of the enzyme. If a substrate is now added which can bind to the enzyme active site and form a fluorescent product, a very sensitive and quick assay is available. Saghatelian used a protease from B. cereus (CNP) and the substrate DABCYL-peptide-EDANS. The DABCYL group on this substrate is a quencher or the EDANS fluorophore. When cleaved by the enzyme, EDANS fluoresces intensely. The assay detected 10 fmol of DNA in less than three minutes.

Controlling the activity of a protein may be achieved through the binding of an allosteric effector at specific binding sites on a given protein. Another technique for allosteric control is to bind two monomeric proteins to form a two-domain complex in which one monomer allosterically activates the other. Lee et al. recently engineered such a binding interaction using a light-sensing protein, phototropin LOV2 (LOV2), as the allosteric effector domain and E. coli dihydrofolate reductase (EcDHFR) as the catalytical domain. The reaction is monitored by the reduction of dihydofolate to tetrahydrafolate. Investigators made chimeras in which the LOV2 domain was connected through its N and C terminal helices to EcDHFR at two sites on its surface: Site A, which noticeably affected the activity of the EcDHFR active site, and Site B, which had little influence on the rate of hydride transfer, khyd (EcDHFR activity). The khyd of the chimeric LOV2-EcDHFR protein bound at Site B was not affected by the conformational shifts of the allosteric effector, which were induced by light. On the other hand, the khyd of the Site A protein was significantly enhanced when light modified the LOV2 structure. This successfully demonstrated substrate activity modification by adjusting the effector.

### HIV Binding to T Helper Immune Cells

It has been notoriously difficult to develop a vaccine against the HIV virus. One type of vaccine results in the formation of protective proteins called antibodies, which bind to an immunogen in the vaccine and ultimately to a "foreign" molecule such as a protein on the surface of an actual virus or bacterial cell. The HIV has a surface protein, gp120, which binds to a receptor protein, CD4, on the surface of certain immune cells like the T helper cell. If this interaction could be prevented, then HIV could not enter cells. Many attempts have been made to develop neutralizing antibodies to gp120 by using gp120 and variants as an immunogen. These have all failed. Further work has shown that when gp120 binds to the receptor protein CD4, the gp120 undergoes a conformational change which allows a newly exposed loop on gp120 to bind to yet another coreceptor, CCR5, on the immune cell, facilitating virus uptake into the cell. The exposed loop conformation of the gp120 seems to resemble the structure of a normal protein ligand (the chemokine RANTES) for the CCR5 receptor. Such examples of molecular mimicry are becoming more common. Recently, the crystal structure of an unliganded simian virus gp120 protein has been determined (Chen et al.). Comparison of this to the bound form (to CD4) shows clear conformational changes. Small inhibitors could be designed to the unbound form, locking it in that conformation which would prevent viral entry into cells.

First consider the cell bound state. There appears to be a very large structural change in gp120 on binding CD4. When this happens, another part of the gp120 protein is exposed, which then binds to another protein "coreceptor" on the cell. This dual binding to the CD4 and the coreceptor "hides" the gp120 from potential neutralizing antibodies, perhaps by steric exclusion.

What about the fee state? Why can't it interact with neutralizing antibodies? Chen et al. have recently determined the structure of the free gp120 protein. On binding to CD4, half of the gp120 refolds, bringing distal residues together to allow binding to co-receptor. Before binding, three copies of gp120 are found on surface viral spikes. Critical residues on gp120 for possible immune recognition appear to be inhibited from antibody binding since they point towards each other which sequesters them. In addition, carbohydrates covalently attached to the gp120 also shield amino acid side chains from immune recognition. Such large changes in protein structure are also seen with part of the influenza virus surface proteins that allow fusion of viral and target cell membranes, and subsequent viral uptake into the cell. They may be a hallmark of viral-target cell interactions.

To a first approximation, the protein may be considered to have two formations, the free and bound forms. Any small molecule which would preferentially bind to the free form could shift the equibrium to that from, and hence prevent viral infectivity. Antibodies that have those properties (i.e. neutralizing) appear to be difficult for the immune system to make. However, small ligand which bind in cavities present in the free form would have such properties. New viral-entry inhibitors have been found that appear to bind in such cavities. Lin et al. PNAS 100, 11013 (2003)

### Parainfluenza Virus Protein

The parainfluenza 5F protein catalyzes the viral and cellular membranes allowing for the entry of the viral genome into the cell. The F protein undergoes refolding during this process, which leads to differing conformations when it is in the pre- and post- transitional states. The parainfluenza virus is similar to other paramyxovirides, (enveloped viruses) which include: mumps, measles, sendai, Newcastle, and the human respiratory sincytial virus. The parainfluenza 5F protein consists of a globular head attached to a trimeric coiled-coil stalk formed by the C-terminal of the HRB region. This exact form of the virus shown in this tutorial is that of the pre-conformational state in which the stalk sits above the viral membrane.

### Free Energy and Cooperativity

This is optional material. It is a great example of the use of thermodynamic cycles in modern biochemical analysis.

To change the conformation of deoxyHb to oxyHb requires energy (about 6 kcal/mol, or the equivalent of about 2 H-bonds). Remember from our discussion of protein stability, proteins are not inherently all that stable. They denature at modest temperatures, and are stabilized over the native state only about 10 kcal/mol for a typical protein of 100 amino acids. Energy changes in proteins can arise from ligand binding, or tertiary/quaternary structural changes in the protein. Consider the following important points about O2 binding:

• the beta chain of Hb binds O2 noncooperatively, with a Kd similar to Mb.
• the hemoglobin tetramer (T) readily dissociates into alpha-beta dimers (D), which also bind O2 with high affinity, and noncooperatively.

Hence, when 2D ----> T, there is an energy penalty in the form of a greatly reduced O2 affinity, but what is acquired is the property of cooperativity for O2 binding, which facilitates maximal unloading of O2 under physiological conditions. This cooperativity can be measure as ΔGcoop = ΔGc, where
ΔGc = ΔGO2 bind to tetramer - ΔGO2 bind to same site on dimer, or
ΔGc = ΔGT - ΔGD. The ΔGT and the ΔGD can be determined from the binding isotherms (Y vs [O2] at various dilutions of the tetramer). Then ΔGc can be calculated. The results are shown below.

Table 1: Free Energy of Oxygen Binding to Hb T and D.

The tables above show the ΔGc for oxygen binding to various states of Hb. Notice that ΔGc is positive for the first 3 bindings, and negative for the last.

The cooperativity models for oxygen-Hb binding (the MWC -concerted model and the KNF- sequential model) are based on the two end states (fully ligated and fully unligated) and the stepwise states (1, 2, or 3 O2 bound). They do not describe binding to specific sites on the Hb tetramer. That is, they do not reflect the different possible microstates. For example, there are 4 different microstates possible in which 2 O2 are bound to the tetramer (see Table 1). There are 8 different possible partially liganded microstates (Table 1). It has been difficult to study each of these microstates directly since it is impossible to isolate them in pure form, or to resolve their different properties in a mixture. Three reasons account for this:

• each state is labile and O2 exchanges among the states
• the tetramer (T) dissociates to 2D which reassociates to give hybrids.
• the lower relative abundance of intermediates in a cooperative system.

This problem was solved by using CO, NO, and CN as ligands, since they bind more tightly. Also the Fe can be replaced with Co(II) or Mn (III). We have studied linked equilibria before:

• 2 N-methylacetamide monomers (aq)  → N-methylacetamide H-bonded dimer (nonpolar)
• deoxyHb ↔ oxyHb in the presence of H+ and CO2 (see above)

We have seen, especially in the former case, how thermodynamic cycles or linked equilibria can be used to calculate ΔG and K's for reactions which would be difficult to carry out. Let us now apply these concepts to Hb binding to ligands. Specifically, we wish to calculate ΔGc from the ΔGs for binding of a ligand to a specific site on a dimer and on the tetramer, as shown below.

It should be obvious that:

ΔGo1 + ΔGo2 = ΔGo3 + ΔGo4 , or ΔGo3 - ΔGo1 = ΔGo2 - ΔGo4 = ΔGoc . It is not difficult to determine ΔGo3 - ΔGo1 which can be determined using gel filtration chromatography since dimers can readily be separated from tetramers. Methods can be developed to prepare individual microstates and then the assembly free energy can be determined. From this, using thermodynamic cycles, the ΔGoc can be calculated. The results for a Cyanomet Hb's microstates are shown in Table 2. The 10 microstates are distributed into 3 distinct cooperative free energies. This suggests that there may be a problem with the MWC model which proposes 2 quaternary states, the T and the R. Is there a third quaternary state, or is there a change in the tertiary structure of the R or T states which generate 3 kcal/mol of cooperative free energy? If the unligated "deoxy"state is the T state, and if the microstates 11,12, and 21 are also assigned to the T state, then the T -->R transition occurs when binding creates a tetramer with one or more ligated subunits on each side of the dimer/dimer interface.

The overall ΔGc is generated by two different conformational changes. On binding the first ligand, global conformational changes occur in the ligated dimeric state. The D/D interface acts as a structural constraint against which tertiary structure changes. When oxygen binds to the dissociated dimer, it does not produce a tertiary structural change since there is no interface to oppose the ligand. This strained tertiary conformation raises the energy by +3 kcal/mol. The second conformational change produces a global quaternary change, as the salt bridges break and the T state changes to the R state.

The formation and release of the tertiary constraint is the driving force of cooperative ligand binding. The strength of the T interface is overcome only when unfavorable ligand induced conformational changes occur in both dimers. The T interface can withstand 1 dimer with the changed tertiary conformation, not 2. The movement of Fe into the plane of the heme ring triggers the tertiary change. The trigger for the quaternary change is the tertiary changes in the dimers.

Now that you understand dioxygen binding, explain the following picture.

### References

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### Contributors

17:38, 17 Dec 2013