Hemoglobin S polymerization and sickle cell disease: A retrospective on the occasion of the 70th anniversary of Pauling's Science paper

Abstract 70 years ago, Linus Pauling, the legendary genius of 20th century chemistry, published his famous work on the molecular cause of sickle cell disease, a paper that gave birth to what is now called molecular medicine. In this paper, Pauling left important questions unanswered that have motivated an enormous amount of scientific and clinical research since then. This retrospective discusses the basic science studies that have answered those questions directly related to the kinetics and thermodynamics of hemoglobin S polymerization.


| INTRODUCTION
In this retrospective on the occasion of Pauling's 1949 Science paper, 1 I present the major findings on the thermodynamics, kinetics, and mechanism of hemoglobin S polymerization. And, I describe how these basic science studies have led to a deeper understanding of the molecular pathogenesis of the disease and strategies for inhibiting polymerization, the root cause of the pathology. Because I have worked on normal and sickle hemoglobin for almost 50 years, my presentation will have a historical perspective and I will only consider those aspects of polymerization that have been closest to my own research. Accounts of polymerization and its role in disease pathogenesis can be found in previous articles by others. 2,3 2 | PAULING'S DISCOVERY According to his account, 4,5 Pauling instantly jumped to the conclusion that the disease was caused by an abnormal hemoglobin molecule in 1945 at dinner with a group of noted physicians. This was a committee appointed by President Franklin D. Roosevelt to recommend how the US government could assist in medical research at the conclusion of the second world war. At the dinner, William B. Castle, the famous Harvard hematologist, was telling the group about a disease called sickle cell anemia. He mentioned that the red cells have a characteristic sickle form when the cells are deoxygenated, but are prevented from sickling by oxygen. Pauling immediately pointed out that the "hemoglobin molecules in the red cells are involved and that [sickling] results from an abnormal kind of hemoglobin, which when deoxygenated has the power of combining with itself into long rigid rods that twist the red cell out of shape". 4 It might seem remarkable that a theorist, who showed how the new physics of quantum mechanics could explain chemical bonding, could jump immediately to this unprecedented conclusion about a disease with so little information. It is, however, not all that surprising; Pauling was one of the world's experts on hemoglobin at the time. He became interested in hemoglobin in the 1930's. In an incredibly brilliant paper, he presented a model that quantitatively explained cooperative oxygen binding with just two adjustable parameters. 6 The fundamental thermodynamics of his model were rediscovered 31 years later and have been applied to many proteins. 7 Pauling's sequential model was replaced in 1965 by the the allosteric model of Monod, Wyman, and Changeux (MWC). In the allosteric model cooperative oxygen binding results from a shift of the quaternary structural equilibrium from a low oxygen-affinity T conformation, to a high oxygen-affinity R conformation, as successive molecules of oxygen bind. 8 As discussed below, the MWC model is extremely important for explaining how oxygen controls polymerization.
From 1945 to 1949, Pauling worked very hard with his postdoctoral fellow, Harvey Itano, to find a difference in structure between hemoglobin A and hemoglobin S. The only structural tools available to them at the time were sedimenation and diffusion, from which they could obtain information on the size and shape of the two molecules and could find no difference. In 1948, Pauling visited Arne Tiselius who told him how to build an electrophoresis apparatus. With this apparatus Pauling discovered the difference between the two molecules, which he reported in his famous 1949 paper: "Sickle cell anemia, a molecular disease". 1 In the paper Pauling reported two major results. First, hemoglobin S is more positively charged than hemoglobin A and second, a 50-50 mixture of hemoglobin S and hemoglobin A has a very similar electrophoretic pattern to the hemoglobin from the parents of sickle cell disease patients. From these two experimental facts, genius Pauling drew four grand conclusions. (i) Sickle cell anemia is due to an abnormal hemoglobin molecule-it is a "molecular disease." (ii) From measurements of the acid-base titration curves of the two molecules he determined that hemoglobin S has 2-4 more net positive charges than hemoglobin A, most probably due to a difference in the number of charged amino acids. (iii) The mutation site must be on the molecular surface to cause aggregation and the structures of oxygenated and deoxygenated hemoglobin must be different to account for the fact that oxyhemoglobin S does not aggregate. (iv) The similarity of the electrophoretic patterns of the parent's hemoglobin and a 50-50 mixture of hemoglobins A and S indicated that the disease was not autosomal dominant, as had previously been suggested, but followed an inheritance pattern of Mendelian genetics. Of course all of his conclusions turned out to be correct. [9][10][11] What is not widely known is that Pauling effectively withdrew conclusions (ii) and (iv) in his presentation at the April 1950 meeting of the US National Academy of Sciences 12 because no difference in charged amino acids could be detected using the technology of the time and hemoglobin S levels in sickle trait could be as low as 25%. 13,14 I have previously published a more extensive account of this very interesting part of the story. 15 Pauling left three important questions for scientists ands clinicians to answer. What is the structure of the aggregated hemoglobin? -his "long rigid rods." What are the thermodynamics, kinetics, and mechanism of polymerization? How can the disease be treated?

| THE POLYMER STRUCTURE
Structural studies began with a study by the Nobel Laureate Max Perutz in collaboration with his colleague John Finch at the MRC Laboratory of Molecular Biology in Cambridge. I received a preprint of the structure they published based on transmission electron microscopy. Their polymer was a hollow fiber consisting of a helical stack of rings of six hemoglobin S molecules with the 2-fold symmetry axis of the hemoglobin molecule pointing radially. 16 After making polarized optical absorption measurements on sickled cells, which gave information on the orientation of the hemoglobin molecules in the fiber, 17 James Hofrichter and I went to Richard Feldmann at NIH, one of the pioneers in molecular graphics, to observe a three-dimenional picture of hemoglobin and see how our results would add information to the fiber structure. To our surprise, the 2-fold symmetry axis pointing radially required the site of the sickle mutation to face the solvent, far from any intermolecular contact. Consequently, there was no structural explanation on how the mutation could cause aggregation. I wrote a letter to Perutz, telling him that he made a mistake in his orientation of the molecule in the fiber, but that we could tilt the molecule sufficiently to allow a beta 6 intermolecular contact and still be consistent with his fiber structure and our optical data. Perutz replied with an invitation, with all expenses paid, to The hollow structure was never seen again and was probably the fiber from some bacterial contaminant. The correct structure was discovered using transmission electron microscopy and sophisticated image reconstruction methods by Stuart Edelstein. Warner Love had solved the X-ray structure of deoxyhemoglobin S a few years earlier, but it was not clear at the time whether his structure, which showed the details of a beta 6 intermolecular contact, had any relationship to the fibers that form in sickle cells. 18 Edelstein recognized that he could construct a 14-stranded fiber structure that is consistent with both fiber-diffraction data of Magdoff-Fairchild and our optically-determined molecular orientation from seven helically twisted double strands of the X-ray structure. 19,20 Subsequent polymerization studies by Ronald Nagel, Ruth Benesch, Rheinhold Benesch and their colleagues on mixtures of hemoglobin S with non-S hemoglobin variants (site directed mutagenenis did not exist in those days) were critically important for additional structural studies (for key references see ref 21,22). This information allowed Edelstein and Robert Josephs to build molecular models at amino acid residue resolution, which remain the currently operative models today. 21,22

| THE THERMODYNAMICS
The thermodynamics of polymerization of completely deoxygenated, purified hemoglobin S turned out to be quite simple, but become considerably more complex when considering the control of polymerization by oxygen and mixtures of hemoglobin S with non-S hemoglobins such as hemoglobins A and F. For sufficiently high concentrations, a solution of deoxyhemoglobin S becomes a viscous gel at equilibrium, that is, when no more polymer forms. As predicted by Allen Minton 23 and confirmed experimentally by Ross et al., 24,25 it is therefore very much like a crystal solution equilibrium, that is, a mixture of two phases, one solid and one liquid. In the case of hemoglobin S, the solid phase consists of aligned fibers, while the liquid phase contains only single hemoglobin molecules with no higher aggregates such as dimers or trimers. 26 The two phase property was demonstrated from the observation that the concentration of hemoglobin S in the supernatant after sedimenting the fibers in an ultracentrifuge is independent of the total concentration of the sample. 24,25 As the total concentration increases, the amount of polymer increases, but the concentration in the liquid (supernatant) phase, the solubility of the fiber, remains unhanged. As the temperature increases the hydrophobic effect becomes stronger, so the solubility decreases because of the hydrophobic nature of the beta 6 contact in the fiber. The solubility has turned out to be a very accurate measure of the fiber stability.
Understanding how oxygen controls polymerization is the result of careful solubility studies, the direct measurement of binding of oxygen to the polymers, and the application of the MWC model. The solubility studies were first performed by Hofrichter using carbon monoxide as a surrogate for oxygen 27  includes activity coeffcients. 28,30 The activity coefficients, which multiply the measured concentration to give the thermodynamically effective concentration, are very large due to the geometric effect of excluded volume in the concentrated protein solutions. At 36 g/dL, for example, the activity coefficient is 100, so the solution behaves as if the concentration were 3,600 g/dL. Allen Minton and Philip Ross were primarily responsible for first recognizing the importance of activity coefficients. 25,31,32 The solubility results are also almost quantitatively explained by postulating that only the T quaternary structure can enter the fiber There remain quite significant differences in copolymerization of hemoglobin F from different laboratories, 30 which, given the importance of the role hemoglobin F today, should be repeated. Moreover, there is only one semi-quantitative study on the solubility of S/F, S/A and S/A2 mixtures as a function of ligand saturation with carbon monoxide on hemolysates, 36 so solubility data using purified hemoglobins and oxygen is needed to obtain more convincing data. The problem is that obtaining accurate solubility data for mixtures is technically demanding and requires a skilled experimentalist trained in physical chemistry or analytical biochemistry.

| THE KINETICS AND MECHANISM
The observation in slow temperature-jump experiments of a delay prior to the appearance of polymers was almost simultaneously reported from three different laboratories in 1974 A delay period was observed by Hofrichter et al using birefringence and calorimetry, 37 by Malfa and Steinhardt using viscosity, 38 and by Moffat and Gibson using turbidity. 39 A delay is also characteristic of the aggregation of peptides and proteins to form amyloid that is responsible for neurodegenerative diseases. The difference between amyloid formation and hemoglobin S polymerization is that there is a small concentration dependence to amyloid formation (about second -fourth power), while there is an enormous concentration dependence (~30th power) F I G U R E 1 Schematic structure of Hb S gel partially saturated with oxygen showing that only the T quaternary structure enters the fiber. The total concentration of free HbS tetramers (left) is the solubility, which is an accurate measure of the thermodynamic stability of the fiber (right) to hemoglobin S polymerization. 37 A double nucleation mechanism that could explain both the existence of a delay and a high concentration dependence was not developed until the work of Ferrone et al. in 1980 (Figure 2). This work used photodissociation of the carbon monoxide complex of hemoglobin S to create deoxyhemoglobin S at any temperature in milliseconds, instead of the tens of seconds to a minute in the earlier slow temperature jump experiments. 40 This method also permitted the observation of sub-second polymer formation on cells from patients with homozygous SS disease, which showed that there is little or no difference between deoxyhemoglobin S in purified solutions, and in red cells from patients with the disease. 43 The double nucleation mechanism also accounts for the observation of large fluctuations in the delay time in small volumes as a result of the stochastic formation of the first homogenously-nucleated fiber. 40,41,44,45 The experiment is similar in spirit to the first observation of single membrane channel opening and closings in patch clamp experiments, performed just a few years earlier, in which single protein channel kinetics is observed because of zillions of ions that flow when the channel is open to give rise to a measurable electrical current. 46 In the sickle hemoglobin experiment, the zillions of fibers formed by the heterogeneous nucleation pathway that follow the formation of the first homogenously nucleated fiber in the volume could be detected by light scattering. The mechanism has stood the test of time. 47 Interestingly, the double nucleation hemoglobin S polymerization mechanism is now being used to explain the aggregation kinetics of the Alzheimer's peptide. [48][49][50][51][52] One of the most remarkable predictions of the double nucleation mechanism, confirmed by experiment, is that the concentration dependence of the rate of fiber formation by the homogeneous nucleation pathway should be approximately twice the concentration dependence of the delay time. Cao and Ferrone found a 50th power for the former and a 25th power for the latter, 45 while Christoph et al.
found 40th and 80th powers. 53 Even though I would argue that an 80th power concentration dependence is one of the most amazing results in the history of chemical kinetics, the paper got the "grand slam." That is, it was rejected without review by Nature, Science, PNAS, and Cell.
The most recent important discovery concerning hemoglobin S polymerization kinetics, is that the delay time can be obtained if the supersaturation is known, that is, the ratio of total hemoglobin concentration and the solubility, each multiplied by an activity coefficient, no matter what the composition of the solution -partial oxygenation, mixtures of any kind, pH changes, etc. 54 Since there is much more solubility data than than delay time data, this universal relation between delay time and supersaturation has become a valuable tool for theoretical calculations of sickling on any time scale 55 The double nucleation mechanism for sickle fiber formation. 47 The basic idea of the mechanism is that there are two nucleated polymerization processes to sickle fiber formation, hence the name double nucleation mechanism. 40,41 The first fiber in any given volume forms by the classical Oosawa nucleation growth mechanism, 42 in which there is a competition between the loss of translational and rotational entropy upon aggregation and the stability gained from intermolecular contacts, which is uphill in free energy until a critical nucleus is reached. Addition of molecules to the critical nucleus and all subsequent fiber growth is downhill in free energy. Formation of this first fiber is said to take place by homogeneous nucleation because it occurs in the bulk of the solution. Homogeneously nucleated fiber formation is quickly superceded by a secondary process, called heterogeneous nucleation, because fibers are nucleated on the surface of existing ones from which the growing nucleus gains additional stability from contacts with a fiber surface. As more fibers form there is increasing surface area for heterogeneous nucleation with the result that polymers grow exponentialy, which causes an apparent delay or what is often called a lag phase would contain fibers at partial pressures of oxygen in the tissues. The

| Targeting polymerization for drug therapy
There are dramatic advances in curing sickle cell disease by hematopoetic stem cell transplantation, 64 with gene therapy cures in the near future. 65,66 However, these treatments are expensive and require advanced medical facilities and are therefore not available to the vast majority of patients in the world suffering from sickle cell disease and may not be for decades. Consequently, what is urgently needed now is an inexpensive anti-sickling pill. Therapy will not require a drug that completely inhibits sickling, but one that just increases the delay time to allow more cells to escape the microcirculation before fibers form. There is thus cause for optimism, as there are several mechanisms for increasing delay times other then by increasing fetal hemoglobin synthesis. [67][68][69] These are described in detail in a recent Blood perspective, 70 so they will only be mentioned here. They include increasing cell volume to decrease HbS concentration, binding a drug to the R conformation, thereby shifting the T-R equilibrium toward the non-polymerizing R conformation, decreasing intracellular 2,3-diphosphoglycerate (2,3-DPG) to destabilize the fiber and shifting the quaternary equilibrium toward R, increasing intracellular pH (2,3-DPG also increases intracellular pH), and destabilizing the fiber by binding a drug to block intermolecular contacts.
Fortunately, there are now large libraries available for drug screening and sensitive high throughput screening methods that use intact cells. 71 The most precious is the ReFrame library of the California Institute of Biomedical Research of the Scripps Institute that contains almost 12,000 compounds that have been tested in humans. 72 I am therefore very optimistic that there will shortly be new anti-sickling drugs in addition to hydroxyurea for treating sickle cell disease.

ACKNOWLEDGMENTS
The author is indebted to James Hofrichter and Eric Henry for