My work falls in the category of Biophysics. Biophysics in my view is more than the use of physics to help biologists solve problems they find challenging. Biophysics is an attempt to identify the essential physical principles involved in various biological systems, such as large biological molecules. Although the basic physical laws are well known, their interplay produces new and unexpected behavior, much as high temperature superconductivity represented an unexpected collective phenomenon in solids. While there is enormous complexity in biomolecules, the challenge is to discern the essential features without having to know all the details.
Biophysics is a timely enterprise. With the increasing power of modern genetics, it becomespossible to discover all kinds of biomolecules, and even to modify them. The ultimate goal, of course, is to be able to read a gene, and thereby determine what kind of molecular structure the gene encodes and what that molecule would do. We are quite far from that goal today: given a sequence of amino acids, we are not very good at predicting the resulting molecular geometry, and even given a molecule whose structure we know we still find it quite challenging to discover its behavior without major clues from nature (like finding out where it appears and what it links with.)
Short of this "Holy Grail", one hopes to understand biomolecules at least well enough to deal with their malfunctions, as in the case of various diseases. One of the best studied molecules is the oxygen transporter, hemoglobin. A small mutation turns this simple molecule into a potentially dangerous agent in sickle cell disease. Usually hemoglobin molecules fill the red cell like beans fill a bean bag, leaving it flexible and floppy, but in sickle cell disease the molecules aggregate to stiffen the red cell and block circulation. Our laboratory is actively studying the behavior of sickle hemoglobin molecules to find approaches for the treatment of this disease, and to gain deeper insights into molecular aggregations in biology.
Sickle cell disease holds a special position as the first disease for which an underlying molecular cause was identified--by Linus Pauling in 1945. The consequences of the simple replacement of a charged amino acid (Glu beta 6) with a hydrophobic, neutral Val are far ranging, and understanding their details remains a vital area of current investigation.
Structure
The amino acid replacement leads to the formation of long, multistranded structures. The structures utilize a double stranded motif, which is also seen in crystals of HbS. The double strand involves a variety of intermolecular contacts, but oddly enough only one of the replaced amino acids is involved in an up-down contact along the polymer. Unlike the crystal, the fibrous double strand found in solutions or cells is twisted, and the identification of the contacts between Hb molecules relies on understanding how the twist occurs and affects the crystal contacts.
The predominant structure seen in solutions or cells is composed of seven double strands: six wrapped around a central double strand The interplay of twist and contact energy has been proposed as the limiting feature on the 14 strand polymer. In the diagram below, each molecule of hemoglobin (MW 64,000) is shown as a sphere.
Because only one of the two mutation sites is involved in the polymer, mixtures of HbA and HbS can copolymerize if they are able to reproportionate subunits. In the absence of mixing subunits, or for other hemoglobins such as HbF even with subunits mixed with HbA, copolymerization does not occur.
The polymers form what is called a gel, which itself has structure. The polymers are cross linked to one another, as well as linked in parallel. There is enough flexibility to allow polymers to bend through angles at least as great as 23° in a few microns. Gels allowed to age a short time will show structures called polymer domains in which polymers radiate in all directions. Such domains are readily viewed in thin solutions placed between crossed polarizers, which yield a characteristic Maltese Cross pattern When fibers are placed on a grid for electron microscopy most of the interfiber contacts and even some of the lengthwise contacts are broken.
Thermodynamics of polymer formation
The polymerization can be well described by a solubility, in analogy with crystallization. Polymer formation is favored by elevated temperature; at low temperature hemoglobin is more soluble than at high temperatures.
In understanding the solubility it is important to appreciate the molecular crowding in a Hb solution at concentrations typically found in an erythrocyte. At 34 g/dl, a typical intracellular concentration, Hb molecules are 1.6 molecular diameters apart center to center, but only 1.1 diameters apart edge to edge. (Moreover, their natural motion assures that they will encounter each other every few nanoseconds.) The center to center distance is directly related to the number of particles per unit volume, which is a good measure of activity in dilute solutions. In concentrated solutions particles are much closer and activity must be measured by the product of concentration times an activity coefficient. Activity coefficients are extremely concentration dependent, but fortunately are approximated very well by calculations which only employ the hard sphere radii of the molecules. (Longer range interaction, such as those dominated by electrostatics, involve temperature dependent activity coefficients). Activity coefficients are not only important because polymerization occurs in a crowded milieu, but also because species incompetent to polymerize, such as oxy-hemoglobin will contribute to the crowding.
Relation to Oxygenation
The thermodynamics and kinetics of oxygenation of dilute HbS is no different from HbA. However, in concentrated solutions which exceed the solubility, the interplay between function and assembly becomes apparent.
Polymer formation is inhibited by the presence of oxygen. This is understood in terms of the well established allosteric model for hemoglobin. Hb can assume two packings of its 16400 MW subunits. Deoxygenated Hb packs in a tense or T conformation, whereas oxygenated Hb packs in a relaxed or R conformation. The change in conformation is close to, but not exactly represented by the fraction of hemoglobin saturated with ligand. The change in structure is responsible for inter-subunit communication and hence cooperative oxygen binding. The registry between polymer-stabilizing molecular contacts present in the T structure is absent when hemoglobin assumes the R structure. Thus it is the structural changes accompanying oxygenation which prevent prevent polymer formation. Effectors, such as 2,3 diphospoglycerate shift the equilibrium between R and T, and accordingly favor polymer formation at partial saturations by biasing the equilibrium toward T (in addition to direct solution effects on the overall solubility.) When hemoglobin polymerizes, it can still bind oxygen, but the binding is noncooperative (since the hemoglobin polymerized cannot change structure). The affinity is also about 3 fold lower than solution T state affinity , most likely as the result of imprisoning of the salt bridges (as is seen in crystals, in which hemoglobin binds oxygen with about 5 fold lower affinity than solution T state molecules ).
Kinetics
The energetic benefit from assembling a monomer into a polymer is not very great. However, there is a significant entropic cost, for the monomer in solution has substantial motional freedom only partially compensated by the motion permitted within a polymer lattice. Each monomer contacts slightly more than four other monomer in a 14 stranded polymer structure, and a substantial fraction of these contacts typically must be made before the energetic gain exceeds entropic cost. Since the entropic losses depend on the initial solution concentration, the energetic turning point will depend on initial concentration as well.
This interplay between entropic loss and bond gain means that small aggregates are less stable than the monomers. Many monomers must coalesce before adding one more monomer (growing the aggregate) is energetically more favorable than evaporating one monomer. Such a phenomenon is familiar in the condensation of droplets in supersaturated vapor, and is referred to as nucleation.
The nucleation process just described differs from biological processes which involve nucleating centers. The nucleus described above represents a thermodynamic bottle-neck, which possesses intrinsically low stability, rather than a preferred structure which may be quite stable. The thermodynamic nature of the nucleus likewise implies that its size can vary as solution conditions are changed, since it represents no special arrangement or structure.
At a microscopic level, the formation of this unfavorable nucleus represents numerous attempts to form a large aggregate, one of which has randomly grown large enough to cross over to a region of increasing stability. This type of process is called homogeneous nucleation. In macroscopic samples, a large number of homogeneous nuclei form; in samples of cellular volume the number may be as low as one.
Once a nucleus forms, a polymer grows simply, i.e. without cooperativity or other complications. The polymer is not absolutely rigid, and its growing end dances about in Brownian motion, allowing the polymer to curve as it grows.
The process of forming a nucleus is somewhat simplified if other polymers are already present. An aggregate that begins growing on a polymer surface has a number of contact sites (and energies) already available, permitting a smaller size aggregate to become a nucleus. This means a second polymer can nucleate and grow along side its "parent". The nucleus formed in this fashion is called heterogeneous, and accounts for the majority of polymers which are formed. The pathway was proposed by Ferrone, Hofrichter and Eaton as the critical ingedient in the mechanism form polymer formation by homogeneous and heterogeneous nucleation pathways called the double nucleation model, shown schematically below. Not until concentrations near 40 g/dl are the equilibrium numbers of polymers formed by heterogeneous and homogeneous nucleation predicted to be equal. At lower concentrations heterogeneous nucleation is dominant.
When a large number of monomers must assemble a nucleus, the reaction will have a large concentration dependence. Activity coefficients further enhance the apparent reaction order. Consequently, due in almost equal part to activity coefficients and nuclear size, the polymerization of sickle hemoglobin has a reaction order that varies from an average of 36 th power in concentration at low concentrations (20 g/dl to 30 g/dl) to an average of 16th power at higher concentrations (30 to 40 g/dl)
The polymers heterogeneously nucleated will commonly splay from the original polymer after a parallel run of some distance. (It is not yet known what governs this.) The pictures below were taken by Dr. Robin Briehl and assoicates using Differential Interference Contrast Microscopy, which produces a diffraction broadened image of the smaller fibers, but still allows their growth to be followed. Note how the new polymers were formed and splay at points marked b.
This means that one homogeneous nucleus forms an initial polymer, which give rise to additional polymers, that in turn form an expanding array. The array, or domain, initially resembles a bow tie, and if allowed to evolve long enough will form a spherulite.
From the foregoing description it is no surprise that the number of monomers taken up in polymers grows almost exponentially. (It is exactly exponential if polymers are assumed to be infinitely thin; with a finite width and surface nucleation, the form is not quite exponential.) Observing the polymerized monomer content of a sample then shows an abrupt exponential growth. Since the initial polymers are difficult to detect, the exponential is seen in its growing phase at a time which appears to "lag" the initiating event. This apparent delay is a useful way to characterize the kinetics of sickle hemoglobin polymerization, and is also physically instructive, for it implies that the sample characteristics are virtually unchanged during the delay period (due to the extremely small polymer mass). However, this is an instrumental effect, and a fine enough probe will detect polymers even at the start. If we take as a measure of this apparent delay a time to form 10% of the final monomer concentration, it is found that, at 35 °C, the tenth time varies from 10 ms to 10 ks as the concentration is varied from 20 to 40 g/dl .
A different type of delay arises in the wait for the first successful nucleation event. The unsuccessful attempts to form a nucleus leave no trace, and in that case, observation during the delay time can in principle give no clue as to the time elapsed (just as a radioactively decaying nucleus has no signature for its time of formation.) This type of delay is intrinsically random and the distribution of these random delays allows the homogeneous nucleation process to be studied in a unique and sensitive way. The nucleation event can be recorded because an entire polymer domain forms from each stochastic homogeneous nucleation event, and thus amplifies the original random process.
The double nucleation process also endows the reaction with a spatial dependence, since the rate of heterogeneous nucleation in a given volume depends on the number of polymers in that volume. In a given domain growth and heterogeneous nucleation may be occuring in the outer part while saturation has occurred in the inner part. At the same time, regions far from the domain may possess no polymers at all. Thus, even at early times in the reaction--during the apparent delay period--some saturation processes are likely to be operative as well as nucleation and growth.
Spatially dependent reactions allow for diffusion effects to play a role. The polymers are much less mobile than the monomers, which retain essentially their free diffusion coefficients. As molecules are removed from the monomer pool to form polymers, new monomers will thereafter diffuse in to take their place. The makes the total hemoglobin concentration spontaneously rise at the center of polymer domains.
Why is this a disease?
The central reason that sickle cell polymerization causes problems is that the polymer mass behaves like a solid--not even like a viscous fluid! Hence circulation of the oxygen-transporting cells becomes inhibited, and downstream tissues can be deprived of their oxygen supply. But the story is not that simple, for otherwise patients would immediately succumb to the disease. The factor that permits survival is that oxygen delivery is required to begin the process of polymerization, as described above. Clearly this has a major kinetic component: occlusion will depend on the rates involved.
The transition through the circulatory system takes only a few seconds in the movement from arteries to veins, and 15 sec to reach the lungs. From the range of delay times it is evident that not all cells will have even reached a tenth of the reaction in their passage through the smaller vessels, nor even in the overall transit between oxygenation. This argument can be made more quantitative. Morphological examination of arterial blood indicates about 10% of the circulating cells are sickled, and this is in reasonable agreement with equilibrium analysis that estimates about 5% sickle cells. On the other side of the capillaries, the mixed venous return shows about 20% sickled cells, in dramatic contrast to the expected equilibrium values of over 90% sickled cells at such pressures. Polymer formation kinetics clearly have a pivotal role in determining which cells are eligible for potentially occlusive sickling. However, small though the percentage of cells which sickle in the circulation may be , a smaller fraction still must be responsible for occlusion, for otherwise the microcirculation would rapidly become permanently blocked.
Most kinetic laboratory experiments have been carried out on fully deoxygenated solutions. The few that have been done in the presence of ligands have predominantly been done in the presence of a fixed ligand concentration. Polymerization in vivo occurs in a dramatically different setting. Oxygen saturation is reduced from 95 to 50% in a few seconds, during which time the probability is greatest for becoming stuck inside a capillary or at its entrance.
There are several consequences to this fact. First of all, cells whose exponential growth is slow enough that they do not accumulate significant polymers until times longer than seconds have little direct risk of occlusion (though other damage, e.g, membrane transport, etc., may still occur). Secondly, highly concentrated cells which could sickle in times much less than a second in the laboratory encounter an obstacle to this rapid growth in the rate of oxygen removal. Such rapid polymerization will consume the available deoxyhemoglobin in forming polymers, and must then proceed at a rate limited by the rate of oxygen removal. This has the effect of softly clamping the rate of polymer formation to be near the rate of oxygen delivery.
The same effect militates against what is otherwise a dramatic consequence of unmelted polymer. Since reoxygenation may not be complete in the lungs, at high intracellular concentrations it is possible from some small amount of polymer to remain unmelted. When small amounts of polymer are present in solution experiments, it takes extremely little polymer to obliterate the apparent delay. However, in cells in which deoxygenation is not instantaneous, this leftover polymer will only recruit deoxygenated molecules which are provided by the slower deoxygenation process of the cell.
1.F. A. Ferrone, Transient Circular Dichroism Studies of Hemoglobin (1974), (Princeton University) thesis
2.F. A. Ferrone , J.J. Hopfield, & S. E. Schnatterly, "The Measurement of Transient Circular Dichroism: A New Kinetic Technique", Rev. Sci. Instrum., 45, 1392-1396 (1974)
3.F. A. Ferrone & W. C. Topp, "Circular Dichroism and Raman Studies of the Allosteric Transition in Methemoglobin," Biochem. Biophys. Res. Comm., 66, 444- 450 (1975)
4.F. A. Ferrone & J. J. Hopfield, "Rate of Quaternary Structure Change in Hemoglobin," Proc. Nat. Acad. Sci. (USA), 73, 4497-4502 (1976)
5.F. A. Ferrone, J. Hofrichter & W.A.Eaton, "Hemoglobin S Polymerization in the Photostationary State," in Frontiers of Biological Energetics, Vol. II (P.L. Dutton, J. Leigh & A. Scarpa, eds.) Academic Press, New York, pp. 1085-1092 (1978)
6.H.R.Sunshine, F. A. Ferrone, J. Hofrichter & W. A. Eaton, "Gelation Assays and the Evaluation of Therapeutic Inhibitors," in Development of Therapeutic Agents for Sickle Cell Disease, INSERM Symposium No. 9 (J. Rosa, Y., Beuzard & J. Hercules, eds.), Elsevier/North Holland, pp. 31-46 (1979)
7.F. A. Ferrone, J. Hofrichter, H. R. Sunshine, & W. A. Eaton, "Kinetic Studies on Photolysis Induced Gelation of Sickle Hemoglobin Suggest a New Mechanism," Biophys. J., 32, 361-380 (1980)
8.J. Hofrichter, H. R. Sunshine, F. A. Ferrone & W. A. Eaton, "Oxygen Binding and the Gelation of Sickle Cell Hemoglobin," in Proceedings of the Symposium on the Molecular Basis of Mutant Hemoglobin Dysfunction (P. B. Sigler, ed.), Elsevier, North Holland, pp. 225-237 (1981).
9.H. R. Sunshine, J. Hofrichter, F. A. Ferrone & W. A. Eaton, "Sickle Cell Hemoglobin Polymers Bind Oxygen Non-cooperatively," in Proceedings of the Symposium on the Interaction between Iron and Proteins in Oxygen and Electron Transport, (C. Ho, ed.), Academic Press, pp. 291-295 (1982)
10.H. R. Sunshine, J. Hofrichter, F. A. Ferrone & W. A. Eaton,"Oxygen Binding by Sickle Hemoglobin Polymers", J. Mol. Biol., 158, 251-273 (1982)
11.M. Coletta, J. Hofrichter, F. A. Ferrone & W. A. Eaton, "Kinetics of Sickle Haemoglobin Polymerization in Single Red Cells," Nature, 300, 194-197 (1982)
12.M. F. Bishop & F. A. Ferrone, "Kinetics of Nucleation Controlled Polymerization: A Perturbation Treatment for Use with a Secondary Pathway", Biophys. J., 46, 631-644, (1984)
13.F. A. Ferrone, J. Hofrichter & W. A. Eaton, "Kinetics of Sickle Hemoglobin Polymerization I. Studies Using Temperature Jump and Laser Photolysis Techniques", J. Mol. Biol. 183, 591-610 (1985)
14.F. A. Ferrone, J. Hofrichter & W. A. Eaton, "Kinetics of Sickle Hemoglobin Polymerization II. A Double Nucleation Mechanism," J. Mol. Biol.183, 611-631 (1985)
15.F. A. Ferrone, A.J. Martino, & S. Basak "Conformational Kinetics of Triligated Hemoglobin," Biophys. J.48 269-282 (1985)
16.F. A. Ferrone, M. Cho, & M. F. Bishop, "Can a Successful Mechanism for HbS Gelation Predict Sickle Cell Crises?" in Beuzard, Y., Charache, S. & Galacteros, F. (ed) Approaches to the Therapy of Sickle Cell Disease, INSERM, 1986, pp 53-66.
17.F. A. Ferrone, "Allosteric Interpretation of the Measurement of Cooperative Free Energy in Cyanomethemoglobin", Proc. Nat. Acad. Sci. USA, 83 6412-6414 (1986)
18.F. A. Ferrone, S. Basak, A. J. Martino & H. X. Zhou, "Polymer Domains, Gelation Models and Sickle Cell Crises", in Nagel, R. (ed.) Pathophysiological Aspects of Sickle Cell Vasoocclusion, Alan R. Liss (1987) 47-58.
19.A. Weber, J. Northrup, M. F. Bishop, F. A. Ferrone & M. M. Mooseker, "Nucleation of Actin Polymerization by Villin & Elongation at Subcritical Monomer Concentration," Biochemistry, 26 2528-2536 (1987)
20.A. Weber, J. Northrup, M. F. Bishop, F. A. Ferrone & M. M. Mooseker, "Kinetics of Actin Elongation and Depolymerization at the Pointed End," Biochemistry, 26 2537-2544. (1987)
21.S. Basak, & F. A. Ferrone, "A Simple, Externally-Triggered Filter Changer" Rev. Sci. Instrum. 59 505-506 (1988)
22.S. Basak, F.A. Ferrone, & J. T. Wang, "Kinetics of Domain Formation by Sickle Hemoglobin Polymers", Biophys. J. 54 829-843. (1988)
23. S. Basak & F. A. Ferrone, "Numerical Linearization of a SIT vidicon Response", Rev. Sci. Instrum. 59 1423-1425 (1988)
24.F. A. Ferrone, "Kinetic Models and the Pathophysiology of Sickle Cell Disease," Ann. N. Y. Acad. Sci. 565 63-74. (1989)
25.A. J. Martino & F. A. Ferrone "The Rate of Allosteric Change in Hemoglobin Measured by Modulated Excitation Using Fluorescence Detection" Biophys. J. 56 781-794 (1989)
26. N. Zhang, F. A. Ferrone, & A. J. Martino "Allosteric Kinetics and Equilibria Differ for Carbon Monoxide and Oxygen Binding to Hemoglobin". Biophys. J. 58 333-340 (1990)
27. H. X. Zhou & F. A. Ferrone, "Theory of the Spatial Dependence of the Polymerization of Sickle Hemoglobin," Biophys. J. 58 695-703 (1990)
28. M. R. Cho & F. A. Ferrone, "Monomer Diffusion into Polymer Domains in Sickle Hemoglobin", Biophys. J. 58 1067-1073 (1990)
29. F. A. Ferrone, "Modulated excitation and conformational change in hemoglobin", Comments in Biophysics (1991) 7 309-332.
30. F. A. Ferrone, "Sickle hemoglobin polymerization: the relationship between kinetics and pathophysiology:" Clin. Hemorheology 12 163-175 (1992)
31. M. R. Cho & F. A. Ferrone, "Monomer Diffusion and Polymer Alignment in Domains of Sickle Hemoglobin" Biophys. J. 62 205-214 (1992)
32. M. Zhao, J. Jiang, M. Greene, F. A. Ferrone, M. Andracki, S. Fowler & J. A. Walder," Allosteric Kinetics and Equilibrium of CrossLinked Hemoglobin." Biophys. J. 64 1520-1532 (1993)
33. F. A. Ferrone, "Polymerization of Sickle Hemoglobin in Solutions and in Cells", Experientia, 49 99-185 (1993)
34.Q. Dou & F. A. Ferrone, "Simulated Formation of Polymer Domains in Sickle Hemoglobin (1993) Biophys. J. 65 2068-2077 (1993)
35. D. Liao, J. Jiang, M. Zhao & F. A. Ferrone, "Modulated Excitation of Singly Ligated Carboxyhemoglobin," Biophys. J. 65 2059-2067 (1993)
36. F. A. Ferrone, "Modulated Excitation Spectroscopy in Hemoglobin," Methods Enzymol 232 292-321 (1994)
37. F. A. Ferrone, "Oxygen Transits and Transports," in Sickle Cell Disease: Basic Principles and Clinical Practice , Hebbel, Mohandas and Steinberg, Raven Press, New York, 89-98 (1994)
38. Z. Cao & F. A. Ferrone, "A 50th order reaction predicted and observed for sickle hemoglobin nucleation" J. Mol. Biol. (1996) 256 219-222.
39. D. Liao, J. J. Martin de Llano, J-P Himanen, J. M. Manning & F. A. Ferrone "Solubility of Sickle Hemoglobin Measured by a Kinetic Micromethod" Biophys. J. (1996) 70 2442-2447
40. Z. Cao & F. A. Ferrone, "Homogeneous nucleation in sickle hemoglobin: stochastic measurements with a parallel method," Biophysical Journal (1997) 72 343-353
41. Z. Cao, D. Liao, R. Mirchev, J. J. Martin de Llano, J-P Himanen, J. M. Manning & F. A. Ferrone, "Nucleation and Polymerization of Sickle Hemoglobin with Leu beta 88 substituted by Ala" J. Mol. Biol (1997) 265 580-589
42. R. Mirchev & F. A. Ferrone "The Structural Link Between Polymerization and Sickle Cell Disease" J. Mol. Biol. (1997) 265 475-479