J. Mol. Biol. (1990) 211, 693-698
Length Distributions
of Hemoglobin
S Fibers
Robin W. Brieh11s2,Eric S. Mann’ and Robert Josephs3 ‘Departments
of Physiology & Biophysics and ‘Biochemistry Albert Einstein College of Medicine 1300 Morris Park Avenue Bronx, NY 10461, U.S.A. 3Department of Molecular Genetics and Cell Biology University of Chicago 920 East 58th Street Chicago, IL 60637, U.S.A. (Received 10 October 1989)
Electron microscopy of sickle cell hemoglobin fibers fixed at different times during gelation shows an exponential distribution of fiber lengths, with many short fibers and few long ones. The distribution does not change significantly with time as polymerization progresses. If this distribution of lengths reflects kinetic mechanism of fiber assembly, it complements information from studies of the progress of average properties of the polymers and, as has been done for other rod-like polymerizing systems, permits testing of models for the mechanism of fiber assembly. In this case, the results are consistent with the double nucleation model of Ferrone et al. or with a related alternative model based on fiber breakage. However, other possible causes of this microheterogeneity exist, including: breakage due to solution shearing of the long, rod-like, fibers; the presence of residual nuclei; equilibrium relations governing polymerization; and breakage of solid-like but weak gels that develop early and adhere to the grid. The arguments against the first three of these possibilities suggest that they are not responsible. However, breakage of entanglements or cross-links in a solid-like and adherent gel is consistent with the distributions.
Pathogenesis in sickle cell disease arises from the polymerization of deoxyhemoglobin S into long, rod-like, fibers that induce gelation and alter intraerythrocytic rheology. The salient feature of the kinetics of polymerization is the presence of a highly concentrationand temperature-dependent delay time before evidence of aggregation appears (Hofrichter et al., 1974; Malfa & Steinhardt, 1974). In addition, reaction progress is exponential in its early stages and the exponential rate also exhibits high concentration and temperature dependences (Ferrone et al., 1985a; Briehl & Christoph, 1987). Finally, the kinetics exhibit stochastic properties arising from individual nucleation events (Ferrone et al., 1980; Hofrichter, 1986). The double nucleation model of Ferrone et al. (19856) suffices to explain all these properties. According to this model, fibers are initiated homogeneously in bulk solution and heterogeneously on the surfaces of pre-existing fibers, and then the fibers grow by independent of hemoglobin monomers (i.e. tx2B2 addition tetramers. M, 64,500). 002~~8836/90/040693-06
$03.00/O
All kinetic studies of polymerization to date have been done by techniques that measure average properties of the system (e.g. turbidity, calorimetry, birefringence, light-scattering, viscometry). Such approaches cannot reveal the detailed distribution of fiber lengths in polymerizing solutions. Yet any kinetic mechanism implies a particular length distribution during assembly. The distribution of fiber lengths, were it available, would add much information about the kinetic mechanism. Thus, kinetic studies and polydispersity studies are complementary: each offers information not available from the other. Here we show that the length distribution as obtained from electron microscopic observation of grids of gelling hemoglobin S is a negative exponential and independent of time as the reaction progresses. We then consider possible mechanisms for this distribution including artefacts of preparation and mechanisms dependent on the equilibria and the kinetics of gelation. Gelation of deoxyhemoglobin S was induced by a temperature jump from 2°C to 20°C. Grids were
693 0
1990 Academic
Press Limited
694
R. W. Briehl
et al.
Figure 1. (a) Hemoglobin S fibers at high magnification (the bar represents 50 nm). (b) A section of a typical distribution of fibers from which length distributions were obtained (the bar represents 5 pm). Hemoglobin 8 obtained from therapeutic exchange transfusions was purified and prepared in @l M-potassium phosphate (pH 7.0), as described (Briehl & Ewert, 1973, 1974), placed in an anerobic glove chamber, diluted to 14 mM (in heme; range 13.95 to 1409 mM), and deoxygenated at 2°C by addition of sodium dithionite to 4-fold excess over heme. Hemoglobin portions placed on formvar and carbon-coated 366 mesh copper grids (Huxley & Zubay, 1966; Hanson & Lowy, 1963; Kawamura & Maruyama, 1970) were blotted, fixed immediately with 2% (w/v) glutaraldehyde, stained with 2% (v/v) phosphotungstic acid (pH 7.0) and examined with a JEOL 1OOCX electron microscope at 80 kV. The portions were taken while the preparation was still fluid.
prepared from 10-/d portions removed serially as polymerization progressed until gross solidification occurred. Preparations were then blotted and fixed with glutaraldehyde. In control studies glutaraldehyde prevented and stopped assembly (as judged by the absence of a turbidometric progress curve at 800 nm) when added before and during the delay period, respectively. A few preparations were made with modifications of the method: (1) addition of glutaraldehyde to the hemoglobin on the grid prior to blotting and (2) addition of 1 ml of glutaraldehyde to 10 ~1 of hemoglobin, with vigorous mixing in a pipette prior to placing the preparation on the
grid. Both of these methods produced exponential length distributions similar to (although with fewer fibers than) those of the primary method. The progress of polymerization is exponential in its early stages, corresponding to at least 10 to 15% and as much as 25% of the full reaction, as measured by light-scattering or turbidity (Christoph & Briehl, 1983; Ferrone et al., 1985a; Briehl & Christoph, 1987). Three criteria indicate that the samples used for grid preparation represented these early stages. (1) Turbidometric progress curves under the conditions employed for the electron microscopic studies showed delay times much longer
Communications
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Figure 2. (a) Histogram of length distribution of fibers 10 min after the temperature jump. The distribution peak is at the bin centered at 025 pm: 91 pm bins begin at zero length. The lines are non-linear, least-squares fits of single exponentials to the data: continuous line, data at and to the right of the peak (r2 = 6986, where r is the correlation coefficient for the fit); broken line, data beginning 2 bins to the right of the peak, which provided the best fit (r’ = 6993). Average T* for all micrographs was 0971 (+@025), fitting beginning at the peak. (b) Data in (a) plotted semi-logarithmically. Lines are the non-linear, least-squares fits obtained in part (a), with slopes -B = - 1.55 and - 1.78 pm-’ for fits beginning at the peak and peak +2 bins, respectively. Change of bin size (to 065 and 62 pm) produced insignificant changes in the fitted value of B in all distributions, as did the use of staggered bin starts (commencing bins in increments of 901 pm above 0, designated “running bins”). Therefore, all B values are reported for 91 pm bins commencing at zero with fit beginning at the peak bin. In this distribution the short fiber deficit (see the text) LB = 916 pm. Fiber lengths were measured using a Jandel digitizing tablet. From 209 to 2384 fibers (1537 in this distribution; average 700) were measured in each of 34 distributions from 16 grids.
than the times at which the samples were taken (and the inverse delay times showed a 45th power dependence on hemoglobin concentration, consistent with known behavior of hemoglobin 8). . (2) Light-scattering under similar conditions and with a highly sensitive method and low background (Christoph & Briehl, 1987) showed delay times that were shorter than those obtained by turbidity, but
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Figure 3. (a) The absence of significant time dependence in the length distribution, in the peak location and in number average fiber length from serial portions of a single preparation. The bottom section shows B (filled circles, continuous regression line) and the location of the distribution peak (open triangles, broken regression line) as obtained by “running bins” (see the legend to Fig. 2). Points at the same time represent different regions of the same grid except at 10 min, where 1 point was derived from a separate grid. The slopes are not sufficiently different from 0 to be significant for either parameter. The top section shows the number-average fiber length obtained directly from the data (filled circles, continuous regression line) and the calculated average fiber length from the fitted distribution (open squares, broken regression line). The latter value is the number-average length of an exponential distribution, l/B, plus the length below which there is an absence of fibers, L,. If there are unresolved short fibers, both methods will give too high a value; the lower limit is l/B. (b) B (bottom) and the number-average length (top; directly from data) for all preparations; this confirms the absence of a significant time dependence.
were still of the same order as the times of sampling. Thus, the portions were removed when there was still little polymer present. (3) Sampling was limited to the time in which the preparations were grossly liquid. They subsequently progressed to very rigid and solid gels, suggesting that polymerization progressed substantially after the last portions were removed and therefore that the samples represent early stages of polymerization.
R. W. Briehl et al.
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polymerization reaction, i.e. equilibria and/or kinetic mechanism. The salient and consistent feature in these distributions is their exponential nature. A second matter concerns the possible presence of a deficit of short fibers and the associated peak in the distribution. We consider five possible factors contributing to the exponential length distribution.
0
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---+J-------i-
:
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(1) Shear-induced
breakage of $bers in solution.
Figure 4. The ratio of the length of the longest fiber measured (filled circles, continuous regression line) or the length at which the fitted distribution predicts 1 fiber (open circles, broken line) to the peak of the distribution as a function of time in a single sample. The average ratios are 14.0 : 1 and 9-4 : 1 using the longest measured fiber and the extrapolated distribution, respectively (corresponding standard errors are 698 and @71). All ratios are much greater than 2 : 1, the ratio expected from shear breakage (see the text).
Shear can break polymeric fibers at or near their centers, where tension due to a shear field is greatest (Levinthal & Davison, 1961). If shear were the major factor, distributions should show a maximum, critical breaking, length and breakage to half this length. Figure 4 shows t,hat this relation does not obtain. The ratio of the longest fiber to the peak is much larger than 2. Also, shear-dependent distributions should be sharply truncated at the breaking length rather than falling exponentially to low frequencies of long fibers. Therefore, we conclude that breakage due to shearing of a solution of fibers is not the cause of the distributions.
Figure l(a) shows fibers at high magnification; Figure l(b) shows a portion of a low magnification array used to obtain length distributions. Figure 2 shows a typical length distribution. It is well fitted at lengths above the peak by a negative exponential with semi-logarithmic slope -B = All length distributions, including -1.6pm-‘. control studies under a variety of preparative conditions, were well fitted by negative exponentials. The average value of B was 2.2 (+@6)pm-‘. Figure 3(a) shows (bottom section) that B and (top section) average fiber length change insignificantly with time within a single sample. Figure 3(b) shows the absence of significant time dependence in all samples. An additional feature of these distributions, seen in Figure 2, is the deficit of short fibers as compared to a distribution that is exponential at all lengths. This might be due to limited resolution in the micrograph, or poor staining and/or poor adherence of short fibers to the grid. Or it might represent a true deficit of fibers. We have expressed the deficit as the location of the distribution peak and also as a median length, L,, in the region of the distribution cutoff (this is the length, defined assuming that the cutoff is sharp, that produces the same number of missing fibers as the measured distribution shows when it is compared to the fitted exponential distribution extrapolated to zero length). Both values are usually higher than the resolution limit of the micrograph (i.e. the minimum length at which almost all fibers can be discerned, usually about 61 pm). However, the difference is not large and therefore we cannot assign the deficit a definite cause. Length distributions of polymeric fibers may arise from artefacts of the invasive process of grid preparation as well as from intrinsic properties of the
Helical polymers characteristically produce exponential length distributions at equilibrium (Oosawa, 1970; Kawamura & Maruyama, 1970). Our distributions were prepared from samples of deoxyhemoglobin S that were still liquid and had not yet produced gels as judged by gross mechanical properties. Hence final equilibrium was not established. Therefore, if equilibrium factors are to be implicated as a cause of these distributions, it must be assumed that polymerization itself is complete and reaches its own equilibrium rapidly while the preparation is still liquid; and that subsequent gelation depends only on fiber interactions, entanglement and/or domain packing without further polymerization (except for polymerization driven by fiber interactions and the phase change itself (Briehl & Herzfeld, 1979; Herzfeld & Briehl, 1981a,b)); i.e. that polymerization is totally separable in time from subsequent phase change and gelation. Although the present results of themselves do not exclude this possibility, much previous work on the kinetics of polymerization and gelation argues against it. For example, the close association of calorimetric progress, reflecting only polymerization (Ross et al., 197.!i), and birefringence (Hofrichter et al., 1974), depending only on phase change, is not consistent with the sequential hypothesis. The assignment of viscosity change and related delay times to degree of polymerization (Malfa & Steinhardt, 1974) would also be in question. And the simultaneity of progress curves obtained from turbidity, birefringence and nuclear magnetic resonance observations (Eaton et al., 1976) could not be readily encompassed. (3) Pre-existing or residual nuclei. Kinetic fiber length distributions often depend on the presence of a fixed number of pre-existing nuclei (or added seeds) in the absence of continuing spontaneous nucleation (Oosawa & Asakura, 1975). As fibers in the initial spike in the frequency distribution
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Communications become longer, the spike broadens in accordance with a Poisson distribution. That the peak frequency in these distributions does not move to greater length with time argues against pre-existing seeds playing a significant role in the polymerization of hemoglobin S. In addition, the good fit to an exponential is not consistent with the increasingly steep semi-logarithmic slope of Poisson distributions as the number of events increases. (4) Kinetic control of length distribution. Length distributions governed by polymerization kinetics have the potential for testing proposed mechanisms of fiber assembly. Assuming fibers grow at a rate independent of fiber length, length reflects the time of fiber nucleation. At time t the number of fibers of length L is the number nucleated at prior time t’ = t-(L/k,), where k, is the rate of elongation. If reaction progress is exponential in time, as is the case for hemoglobin S (except extremely early in the reaction when homogeneous nucleation dominates) (Ferrone et al., 1980, 1985a,b; Briehl & Christoph, 1987), new fibers are nucleated at a rate proportional to the extent of the reaction. Therefore, the length distribution must also be exponential containing many recently nucleated short fibers and few long, old fibers. In the double nucleation model of Ferrone et al. (1980, 1985b) heterogeneous nucleation dominates except at the very earliest times. The nucleation rate is proportional to the extent of reaction (measured as fiber mass). Progress is exponential, as observed, and the length distribution should be exponential. It can also be predicted that the distribution should be independent of time. The total number of fibers increases with time, but the number at each length increases in the same proport,ion. Therefore, the normalized distribution and average length should not change, consistent with Figure 3. Under double nucleation, depletion of monomeric hemoglobin in solution should markedly slow the highly co-operative nucleation rate as polymerization progresses. If the short fiber deficit is real, it might be explained by this mechanism, since fibers were nucleated late, when monomers are depleted. However, under this mechanism the distribution peak should move to the right with time, contrary t,o the observations shown in Figure 3(a). nucleation predicts Double budding and branching of new fibers from old ones, with many short, new branches and fewer long, older, branches. Our micrographs fail to show buds and branches as X-shaped or Y-shaped junctions with the frequency and length distribution predicted. If, however, branches break free while they are still very short they will be rare and also difficult to resolve. Our micrographs do not exclude this possibility. Alternatively, heterogeneous nucleation might occur by the formation of new fibers parallel to old ones. Such alignments are occasionally seen in our micrographs, but it cannot be ascertained if they result from spontaneous, entropy driven, alignment
697
(Onsager, 1949; Flory, 1956; Minton, 1974; Briehl & Herzfeld, 1979; Herzfeld & Briehl, 1981a,b) or from nucleation. Under double nucleation the reaction progresses exponentially because the heterogeneous nucleation rate is proportional to polymer mass. An alternative explanation attributes exponential progress to breakage of newly forming segments at the ends of existing fibers rather than to surface nucleation. The rate of new fiber creation is then proportional to the fiber growth rate and to the number (rather than the mass) of fibers. Exponential progress depends on the proportionality of the rate of new fiber formation to the number of fibers (i.e. ends). The high concentration dependence of reaction progress and inverse delay time derive from the proportionality between breakage rate and fiber growth rate, requiring growth rate to be highly cooperative in respect to monomer concentration. This last assumption, differing from the assumed independent addition of monomers under double nucleation is reasonable for a solid, rope-like (as opposed to a hollow helical), fiber such as hemoglobin S (Dykes et al., 1978, 1979). In contrast, the addition of monomers to a hollow helical fiber can be expected to proceed independently for each monomer, since each monomer added makes identical contacts (unless the helix consists of stacked discs). On the other hand, in a solid fiber such as hemoglobin S there is a source for co-operative energy of interaction in the side-side contacts that occur between double strands when more than one is elongated; addition of groups of monomers is much favored over single additions. Both models predict an exponential length distribution and its time independence and are consistent as well with the known properties of exponential reaction progress and its marked temperature and concentration dependences. (5) Breakage of jibers in an entangled or crosslinked, solid-like gel. Viscometry suggests that there exists a small number of long fibers early in the progress of gelation of hemoglobin S (Kowalczykowski & Steinhardt, 1977). Therefore, a preparation that is liquid to gross observation might in fact possess weak solid-like properties. The development of a stress that is held when shear is relaxed (Briehl, 1980) long before gelation is complete is consistent with this possibility. If grid preparation, and particularly blotting, are carried out under these conditions the entangled or crosslinked structure will necessarily be ruptured and some fibers must be broken, in contrast to the relatively non-invasive nature of blotting applied to a solution of independent rod-like fibers. A relatively simple model for this breakage predicts an exponential length distribution. If p is the probability of breakage at a given site (i.e. within a small length interval I the probability that a break will occur at a distance nl from an existing break is ~(1 -p)“- ‘. Thus, the slope of the histogram on a semi-logarithmic plot, d In N/dn (where N is the number of fibers within a length interval l), has the
698
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constant value In (1 -p) and the length distribution is exponential. We conclude that the most likely mechanisms for the production of a time-independent exponential distribution of fiber lengths are (1) the double nucleation mechanism (or a related mechanism) for the kinetics and assembly of hemoglobin S fibers or (2) breakage of a solid-like gel during preparation of grids of gelling hemoglobin S. This work was supported by grants HL07451 and HL28203 (to R.W.B.) and HL22654 (to R.J.) from the National Heart, Lung and Blood Institute. E.S.M. was supported by a Medical Scientist Training Program award from the National Institute of General Medical Sciences. We thank Joel Hirsch, Colleen Randall, Barry Gross and Patty Wu for technical assistance and Dr Samuel Charache of Johns Hopkins School of Medicine for generous gifts of sickle cell blood.
References Briehl, R. W. (1980). Nature (London), 288, 622-624. Briehl, R. W. & Christoph, G. W. (1987). In Pathophysiological Aspects of Sickle Cell Vaso-Occlusion (Nagel, R. L., ed.), pp. 129-149, Alan R. Liss, New York. Briehl, R. W. & Ewert, S. (1973). J. Mol. Biol. 80, 445-458. Briehl, R. W. & Ewert, S. (1974). J. Mol. BioE. 89, 759-766. Briehl, R. W. & Herzfeld, J. (1979). Proc. Nat. Acad. Sci., U.S.A. 76, 2740-2744. Christoph, G. W. & Briehl, R. W. (1983). Biophys. J. 41, 415a. Dykes, G. W., Crepeau, R. H. & Edelstein, S. J. (1978). Nature (London), 272, 506-510. Edited
et al.
Dykes, G. W., Crepeau, R. H. 6 Edelstein, S. J. (1979). J. Mol. Biol. 130, 451472. Eaton, W. A., Hofrichter, J., Ross, P. D., Tschudin, R. G. & Becker, E. D. (1976). Biochem. Biophys. Res. Commun. 69, 538-547. Ferrone, F. A., Hofrichter, J., Sunshine, H. R. & Eaton, W. A. (1980). Biophys. J. 32, 361-380. Ferrone, F. A., Hofrichter, J. & Eaton, W. A. (1985~). J. Mol. Biol. 183, 591-610. Ferrone, F. A., Hofrichter, J. & Eaton, W. A. (19856). J. Mol. BioZ. 183, 611-631. Flory, P. J. (1956). Proc. Roy. Sot. ser. A, 234, 73-89. Hanson, J. & Lowy, J. (1963). J. Mol. Biol. 6, 46-60. Herzfeld, J. & Briehl, R. W. (1981a). Macromolecules, 14, 397-404. Herzfeld, J. & Briehl, R. W. (19815). Macromolecules, 14, 1209-1214. Hofrichter, J. (1986). J. Mol. Biol. 189, 553-571. Hofrichter, J., Ross, P. D. & Eaton, W. A. (1974). Proc. Nat. Acad. Sci., U.S.A. 71, 48644868. Huxley, H. E. & Zubay, G. (1960). J. Mol. Biol. 2, 10-18. Kawamura, M. & Maruyama, K. (1970). J. B&hem. 67, 437-457. Kowalczykowski, S. & Steinhardt, J. (1977). J. Mol. Biol. 115, 201-213. Levinthal, C. & Davison, C. F. (1961). J. Mol. Biol. 3, 674-683. Malfa, R. & Steinhardt, J. (1974). Biochem. Biophys. Res. Commun. 59, 887-893. Minton, A. P. (1974). J. Mol. Biol. 82, 483-498. Onsager, L. (1949). Ann. N. Y. Acad. Sci. 56, 627-659. Oosawa, F. (1970). J. Theoret. Biol. 27, 69-86. Oosawa, F. & Asakura, S. (1975). Thermodynamics of Protein Polymerization, Academic Press, New York. Ross, P. D., Hofrichter, J. & Eaton, W. A. (1975). J. Mol. Biol. 96, 239-256.
by D. DeRosier
Note added in proof. Since submission of this manuscript we (R. E. Samuel, E. D. Salmon & R. W. Briehl) have examined unperturbed polymerizing hemoglobin S in real time by video-enhanced differential interference contrast microscopy. We find that a cross-linked gel occurs very early, nucleation conforms to the double nucleation model and nucleation by fiber breakage is not seen if the system is not perturbed. We conclude that the most likely basis of the present length distributions lies in breakage of solid-like gels that adhere to grids.
Length Distributions
of Hemoglobin
S Fibers
Robin W. Brieh11s2,Eric S. Mann’ and Robert Josephs3 ‘Departments
of Physiology & Biophysics and ‘Biochemistry Albert Einstein College of Medicine 1300 Morris Park Avenue Bronx, NY 10461, U.S.A. 3Department of Molecular Genetics and Cell Biology University of Chicago 920 East 58th Street Chicago, IL 60637, U.S.A. (Received 10 October 1989)
Electron microscopy of sickle cell hemoglobin fibers fixed at different times during gelation shows an exponential distribution of fiber lengths, with many short fibers and few long ones. The distribution does not change significantly with time as polymerization progresses. If this distribution of lengths reflects kinetic mechanism of fiber assembly, it complements information from studies of the progress of average properties of the polymers and, as has been done for other rod-like polymerizing systems, permits testing of models for the mechanism of fiber assembly. In this case, the results are consistent with the double nucleation model of Ferrone et al. or with a related alternative model based on fiber breakage. However, other possible causes of this microheterogeneity exist, including: breakage due to solution shearing of the long, rod-like, fibers; the presence of residual nuclei; equilibrium relations governing polymerization; and breakage of solid-like but weak gels that develop early and adhere to the grid. The arguments against the first three of these possibilities suggest that they are not responsible. However, breakage of entanglements or cross-links in a solid-like and adherent gel is consistent with the distributions.
Pathogenesis in sickle cell disease arises from the polymerization of deoxyhemoglobin S into long, rod-like, fibers that induce gelation and alter intraerythrocytic rheology. The salient feature of the kinetics of polymerization is the presence of a highly concentrationand temperature-dependent delay time before evidence of aggregation appears (Hofrichter et al., 1974; Malfa & Steinhardt, 1974). In addition, reaction progress is exponential in its early stages and the exponential rate also exhibits high concentration and temperature dependences (Ferrone et al., 1985a; Briehl & Christoph, 1987). Finally, the kinetics exhibit stochastic properties arising from individual nucleation events (Ferrone et al., 1980; Hofrichter, 1986). The double nucleation model of Ferrone et al. (19856) suffices to explain all these properties. According to this model, fibers are initiated homogeneously in bulk solution and heterogeneously on the surfaces of pre-existing fibers, and then the fibers grow by independent of hemoglobin monomers (i.e. tx2B2 addition tetramers. M, 64,500). 002~~8836/90/040693-06
$03.00/O
All kinetic studies of polymerization to date have been done by techniques that measure average properties of the system (e.g. turbidity, calorimetry, birefringence, light-scattering, viscometry). Such approaches cannot reveal the detailed distribution of fiber lengths in polymerizing solutions. Yet any kinetic mechanism implies a particular length distribution during assembly. The distribution of fiber lengths, were it available, would add much information about the kinetic mechanism. Thus, kinetic studies and polydispersity studies are complementary: each offers information not available from the other. Here we show that the length distribution as obtained from electron microscopic observation of grids of gelling hemoglobin S is a negative exponential and independent of time as the reaction progresses. We then consider possible mechanisms for this distribution including artefacts of preparation and mechanisms dependent on the equilibria and the kinetics of gelation. Gelation of deoxyhemoglobin S was induced by a temperature jump from 2°C to 20°C. Grids were
693 0
1990 Academic
Press Limited
694
R. W. Briehl
et al.
Figure 1. (a) Hemoglobin S fibers at high magnification (the bar represents 50 nm). (b) A section of a typical distribution of fibers from which length distributions were obtained (the bar represents 5 pm). Hemoglobin 8 obtained from therapeutic exchange transfusions was purified and prepared in @l M-potassium phosphate (pH 7.0), as described (Briehl & Ewert, 1973, 1974), placed in an anerobic glove chamber, diluted to 14 mM (in heme; range 13.95 to 1409 mM), and deoxygenated at 2°C by addition of sodium dithionite to 4-fold excess over heme. Hemoglobin portions placed on formvar and carbon-coated 366 mesh copper grids (Huxley & Zubay, 1966; Hanson & Lowy, 1963; Kawamura & Maruyama, 1970) were blotted, fixed immediately with 2% (w/v) glutaraldehyde, stained with 2% (v/v) phosphotungstic acid (pH 7.0) and examined with a JEOL 1OOCX electron microscope at 80 kV. The portions were taken while the preparation was still fluid.
prepared from 10-/d portions removed serially as polymerization progressed until gross solidification occurred. Preparations were then blotted and fixed with glutaraldehyde. In control studies glutaraldehyde prevented and stopped assembly (as judged by the absence of a turbidometric progress curve at 800 nm) when added before and during the delay period, respectively. A few preparations were made with modifications of the method: (1) addition of glutaraldehyde to the hemoglobin on the grid prior to blotting and (2) addition of 1 ml of glutaraldehyde to 10 ~1 of hemoglobin, with vigorous mixing in a pipette prior to placing the preparation on the
grid. Both of these methods produced exponential length distributions similar to (although with fewer fibers than) those of the primary method. The progress of polymerization is exponential in its early stages, corresponding to at least 10 to 15% and as much as 25% of the full reaction, as measured by light-scattering or turbidity (Christoph & Briehl, 1983; Ferrone et al., 1985a; Briehl & Christoph, 1987). Three criteria indicate that the samples used for grid preparation represented these early stages. (1) Turbidometric progress curves under the conditions employed for the electron microscopic studies showed delay times much longer
Communications
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Figure 2. (a) Histogram of length distribution of fibers 10 min after the temperature jump. The distribution peak is at the bin centered at 025 pm: 91 pm bins begin at zero length. The lines are non-linear, least-squares fits of single exponentials to the data: continuous line, data at and to the right of the peak (r2 = 6986, where r is the correlation coefficient for the fit); broken line, data beginning 2 bins to the right of the peak, which provided the best fit (r’ = 6993). Average T* for all micrographs was 0971 (+@025), fitting beginning at the peak. (b) Data in (a) plotted semi-logarithmically. Lines are the non-linear, least-squares fits obtained in part (a), with slopes -B = - 1.55 and - 1.78 pm-’ for fits beginning at the peak and peak +2 bins, respectively. Change of bin size (to 065 and 62 pm) produced insignificant changes in the fitted value of B in all distributions, as did the use of staggered bin starts (commencing bins in increments of 901 pm above 0, designated “running bins”). Therefore, all B values are reported for 91 pm bins commencing at zero with fit beginning at the peak bin. In this distribution the short fiber deficit (see the text) LB = 916 pm. Fiber lengths were measured using a Jandel digitizing tablet. From 209 to 2384 fibers (1537 in this distribution; average 700) were measured in each of 34 distributions from 16 grids.
than the times at which the samples were taken (and the inverse delay times showed a 45th power dependence on hemoglobin concentration, consistent with known behavior of hemoglobin 8). . (2) Light-scattering under similar conditions and with a highly sensitive method and low background (Christoph & Briehl, 1987) showed delay times that were shorter than those obtained by turbidity, but
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Figure 3. (a) The absence of significant time dependence in the length distribution, in the peak location and in number average fiber length from serial portions of a single preparation. The bottom section shows B (filled circles, continuous regression line) and the location of the distribution peak (open triangles, broken regression line) as obtained by “running bins” (see the legend to Fig. 2). Points at the same time represent different regions of the same grid except at 10 min, where 1 point was derived from a separate grid. The slopes are not sufficiently different from 0 to be significant for either parameter. The top section shows the number-average fiber length obtained directly from the data (filled circles, continuous regression line) and the calculated average fiber length from the fitted distribution (open squares, broken regression line). The latter value is the number-average length of an exponential distribution, l/B, plus the length below which there is an absence of fibers, L,. If there are unresolved short fibers, both methods will give too high a value; the lower limit is l/B. (b) B (bottom) and the number-average length (top; directly from data) for all preparations; this confirms the absence of a significant time dependence.
were still of the same order as the times of sampling. Thus, the portions were removed when there was still little polymer present. (3) Sampling was limited to the time in which the preparations were grossly liquid. They subsequently progressed to very rigid and solid gels, suggesting that polymerization progressed substantially after the last portions were removed and therefore that the samples represent early stages of polymerization.
R. W. Briehl et al.
696 20
2 z $ zl J
polymerization reaction, i.e. equilibria and/or kinetic mechanism. The salient and consistent feature in these distributions is their exponential nature. A second matter concerns the possible presence of a deficit of short fibers and the associated peak in the distribution. We consider five possible factors contributing to the exponential length distribution.
0
0 10. +-----we---
---+J-------i-
:
5.
(1) Shear-induced
breakage of $bers in solution.
Figure 4. The ratio of the length of the longest fiber measured (filled circles, continuous regression line) or the length at which the fitted distribution predicts 1 fiber (open circles, broken line) to the peak of the distribution as a function of time in a single sample. The average ratios are 14.0 : 1 and 9-4 : 1 using the longest measured fiber and the extrapolated distribution, respectively (corresponding standard errors are 698 and @71). All ratios are much greater than 2 : 1, the ratio expected from shear breakage (see the text).
Shear can break polymeric fibers at or near their centers, where tension due to a shear field is greatest (Levinthal & Davison, 1961). If shear were the major factor, distributions should show a maximum, critical breaking, length and breakage to half this length. Figure 4 shows t,hat this relation does not obtain. The ratio of the longest fiber to the peak is much larger than 2. Also, shear-dependent distributions should be sharply truncated at the breaking length rather than falling exponentially to low frequencies of long fibers. Therefore, we conclude that breakage due to shearing of a solution of fibers is not the cause of the distributions.
Figure l(a) shows fibers at high magnification; Figure l(b) shows a portion of a low magnification array used to obtain length distributions. Figure 2 shows a typical length distribution. It is well fitted at lengths above the peak by a negative exponential with semi-logarithmic slope -B = All length distributions, including -1.6pm-‘. control studies under a variety of preparative conditions, were well fitted by negative exponentials. The average value of B was 2.2 (+@6)pm-‘. Figure 3(a) shows (bottom section) that B and (top section) average fiber length change insignificantly with time within a single sample. Figure 3(b) shows the absence of significant time dependence in all samples. An additional feature of these distributions, seen in Figure 2, is the deficit of short fibers as compared to a distribution that is exponential at all lengths. This might be due to limited resolution in the micrograph, or poor staining and/or poor adherence of short fibers to the grid. Or it might represent a true deficit of fibers. We have expressed the deficit as the location of the distribution peak and also as a median length, L,, in the region of the distribution cutoff (this is the length, defined assuming that the cutoff is sharp, that produces the same number of missing fibers as the measured distribution shows when it is compared to the fitted exponential distribution extrapolated to zero length). Both values are usually higher than the resolution limit of the micrograph (i.e. the minimum length at which almost all fibers can be discerned, usually about 61 pm). However, the difference is not large and therefore we cannot assign the deficit a definite cause. Length distributions of polymeric fibers may arise from artefacts of the invasive process of grid preparation as well as from intrinsic properties of the
Helical polymers characteristically produce exponential length distributions at equilibrium (Oosawa, 1970; Kawamura & Maruyama, 1970). Our distributions were prepared from samples of deoxyhemoglobin S that were still liquid and had not yet produced gels as judged by gross mechanical properties. Hence final equilibrium was not established. Therefore, if equilibrium factors are to be implicated as a cause of these distributions, it must be assumed that polymerization itself is complete and reaches its own equilibrium rapidly while the preparation is still liquid; and that subsequent gelation depends only on fiber interactions, entanglement and/or domain packing without further polymerization (except for polymerization driven by fiber interactions and the phase change itself (Briehl & Herzfeld, 1979; Herzfeld & Briehl, 1981a,b)); i.e. that polymerization is totally separable in time from subsequent phase change and gelation. Although the present results of themselves do not exclude this possibility, much previous work on the kinetics of polymerization and gelation argues against it. For example, the close association of calorimetric progress, reflecting only polymerization (Ross et al., 197.!i), and birefringence (Hofrichter et al., 1974), depending only on phase change, is not consistent with the sequential hypothesis. The assignment of viscosity change and related delay times to degree of polymerization (Malfa & Steinhardt, 1974) would also be in question. And the simultaneity of progress curves obtained from turbidity, birefringence and nuclear magnetic resonance observations (Eaton et al., 1976) could not be readily encompassed. (3) Pre-existing or residual nuclei. Kinetic fiber length distributions often depend on the presence of a fixed number of pre-existing nuclei (or added seeds) in the absence of continuing spontaneous nucleation (Oosawa & Asakura, 1975). As fibers in the initial spike in the frequency distribution
0
I
5
IO
15
I
20
Time (mid
(2) Equilibrium
properties of the polymerization.
Communications become longer, the spike broadens in accordance with a Poisson distribution. That the peak frequency in these distributions does not move to greater length with time argues against pre-existing seeds playing a significant role in the polymerization of hemoglobin S. In addition, the good fit to an exponential is not consistent with the increasingly steep semi-logarithmic slope of Poisson distributions as the number of events increases. (4) Kinetic control of length distribution. Length distributions governed by polymerization kinetics have the potential for testing proposed mechanisms of fiber assembly. Assuming fibers grow at a rate independent of fiber length, length reflects the time of fiber nucleation. At time t the number of fibers of length L is the number nucleated at prior time t’ = t-(L/k,), where k, is the rate of elongation. If reaction progress is exponential in time, as is the case for hemoglobin S (except extremely early in the reaction when homogeneous nucleation dominates) (Ferrone et al., 1980, 1985a,b; Briehl & Christoph, 1987), new fibers are nucleated at a rate proportional to the extent of the reaction. Therefore, the length distribution must also be exponential containing many recently nucleated short fibers and few long, old fibers. In the double nucleation model of Ferrone et al. (1980, 1985b) heterogeneous nucleation dominates except at the very earliest times. The nucleation rate is proportional to the extent of reaction (measured as fiber mass). Progress is exponential, as observed, and the length distribution should be exponential. It can also be predicted that the distribution should be independent of time. The total number of fibers increases with time, but the number at each length increases in the same proport,ion. Therefore, the normalized distribution and average length should not change, consistent with Figure 3. Under double nucleation, depletion of monomeric hemoglobin in solution should markedly slow the highly co-operative nucleation rate as polymerization progresses. If the short fiber deficit is real, it might be explained by this mechanism, since fibers were nucleated late, when monomers are depleted. However, under this mechanism the distribution peak should move to the right with time, contrary t,o the observations shown in Figure 3(a). nucleation predicts Double budding and branching of new fibers from old ones, with many short, new branches and fewer long, older, branches. Our micrographs fail to show buds and branches as X-shaped or Y-shaped junctions with the frequency and length distribution predicted. If, however, branches break free while they are still very short they will be rare and also difficult to resolve. Our micrographs do not exclude this possibility. Alternatively, heterogeneous nucleation might occur by the formation of new fibers parallel to old ones. Such alignments are occasionally seen in our micrographs, but it cannot be ascertained if they result from spontaneous, entropy driven, alignment
697
(Onsager, 1949; Flory, 1956; Minton, 1974; Briehl & Herzfeld, 1979; Herzfeld & Briehl, 1981a,b) or from nucleation. Under double nucleation the reaction progresses exponentially because the heterogeneous nucleation rate is proportional to polymer mass. An alternative explanation attributes exponential progress to breakage of newly forming segments at the ends of existing fibers rather than to surface nucleation. The rate of new fiber creation is then proportional to the fiber growth rate and to the number (rather than the mass) of fibers. Exponential progress depends on the proportionality of the rate of new fiber formation to the number of fibers (i.e. ends). The high concentration dependence of reaction progress and inverse delay time derive from the proportionality between breakage rate and fiber growth rate, requiring growth rate to be highly cooperative in respect to monomer concentration. This last assumption, differing from the assumed independent addition of monomers under double nucleation is reasonable for a solid, rope-like (as opposed to a hollow helical), fiber such as hemoglobin S (Dykes et al., 1978, 1979). In contrast, the addition of monomers to a hollow helical fiber can be expected to proceed independently for each monomer, since each monomer added makes identical contacts (unless the helix consists of stacked discs). On the other hand, in a solid fiber such as hemoglobin S there is a source for co-operative energy of interaction in the side-side contacts that occur between double strands when more than one is elongated; addition of groups of monomers is much favored over single additions. Both models predict an exponential length distribution and its time independence and are consistent as well with the known properties of exponential reaction progress and its marked temperature and concentration dependences. (5) Breakage of jibers in an entangled or crosslinked, solid-like gel. Viscometry suggests that there exists a small number of long fibers early in the progress of gelation of hemoglobin S (Kowalczykowski & Steinhardt, 1977). Therefore, a preparation that is liquid to gross observation might in fact possess weak solid-like properties. The development of a stress that is held when shear is relaxed (Briehl, 1980) long before gelation is complete is consistent with this possibility. If grid preparation, and particularly blotting, are carried out under these conditions the entangled or crosslinked structure will necessarily be ruptured and some fibers must be broken, in contrast to the relatively non-invasive nature of blotting applied to a solution of independent rod-like fibers. A relatively simple model for this breakage predicts an exponential length distribution. If p is the probability of breakage at a given site (i.e. within a small length interval I the probability that a break will occur at a distance nl from an existing break is ~(1 -p)“- ‘. Thus, the slope of the histogram on a semi-logarithmic plot, d In N/dn (where N is the number of fibers within a length interval l), has the
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R. W. Briehl
constant value In (1 -p) and the length distribution is exponential. We conclude that the most likely mechanisms for the production of a time-independent exponential distribution of fiber lengths are (1) the double nucleation mechanism (or a related mechanism) for the kinetics and assembly of hemoglobin S fibers or (2) breakage of a solid-like gel during preparation of grids of gelling hemoglobin S. This work was supported by grants HL07451 and HL28203 (to R.W.B.) and HL22654 (to R.J.) from the National Heart, Lung and Blood Institute. E.S.M. was supported by a Medical Scientist Training Program award from the National Institute of General Medical Sciences. We thank Joel Hirsch, Colleen Randall, Barry Gross and Patty Wu for technical assistance and Dr Samuel Charache of Johns Hopkins School of Medicine for generous gifts of sickle cell blood.
References Briehl, R. W. (1980). Nature (London), 288, 622-624. Briehl, R. W. & Christoph, G. W. (1987). In Pathophysiological Aspects of Sickle Cell Vaso-Occlusion (Nagel, R. L., ed.), pp. 129-149, Alan R. Liss, New York. Briehl, R. W. & Ewert, S. (1973). J. Mol. Biol. 80, 445-458. Briehl, R. W. & Ewert, S. (1974). J. Mol. BioE. 89, 759-766. Briehl, R. W. & Herzfeld, J. (1979). Proc. Nat. Acad. Sci., U.S.A. 76, 2740-2744. Christoph, G. W. & Briehl, R. W. (1983). Biophys. J. 41, 415a. Dykes, G. W., Crepeau, R. H. & Edelstein, S. J. (1978). Nature (London), 272, 506-510. Edited
et al.
Dykes, G. W., Crepeau, R. H. 6 Edelstein, S. J. (1979). J. Mol. Biol. 130, 451472. Eaton, W. A., Hofrichter, J., Ross, P. D., Tschudin, R. G. & Becker, E. D. (1976). Biochem. Biophys. Res. Commun. 69, 538-547. Ferrone, F. A., Hofrichter, J., Sunshine, H. R. & Eaton, W. A. (1980). Biophys. J. 32, 361-380. Ferrone, F. A., Hofrichter, J. & Eaton, W. A. (1985~). J. Mol. Biol. 183, 591-610. Ferrone, F. A., Hofrichter, J. & Eaton, W. A. (19856). J. Mol. BioZ. 183, 611-631. Flory, P. J. (1956). Proc. Roy. Sot. ser. A, 234, 73-89. Hanson, J. & Lowy, J. (1963). J. Mol. Biol. 6, 46-60. Herzfeld, J. & Briehl, R. W. (1981a). Macromolecules, 14, 397-404. Herzfeld, J. & Briehl, R. W. (19815). Macromolecules, 14, 1209-1214. Hofrichter, J. (1986). J. Mol. Biol. 189, 553-571. Hofrichter, J., Ross, P. D. & Eaton, W. A. (1974). Proc. Nat. Acad. Sci., U.S.A. 71, 48644868. Huxley, H. E. & Zubay, G. (1960). J. Mol. Biol. 2, 10-18. Kawamura, M. & Maruyama, K. (1970). J. B&hem. 67, 437-457. Kowalczykowski, S. & Steinhardt, J. (1977). J. Mol. Biol. 115, 201-213. Levinthal, C. & Davison, C. F. (1961). J. Mol. Biol. 3, 674-683. Malfa, R. & Steinhardt, J. (1974). Biochem. Biophys. Res. Commun. 59, 887-893. Minton, A. P. (1974). J. Mol. Biol. 82, 483-498. Onsager, L. (1949). Ann. N. Y. Acad. Sci. 56, 627-659. Oosawa, F. (1970). J. Theoret. Biol. 27, 69-86. Oosawa, F. & Asakura, S. (1975). Thermodynamics of Protein Polymerization, Academic Press, New York. Ross, P. D., Hofrichter, J. & Eaton, W. A. (1975). J. Mol. Biol. 96, 239-256.
by D. DeRosier
Note added in proof. Since submission of this manuscript we (R. E. Samuel, E. D. Salmon & R. W. Briehl) have examined unperturbed polymerizing hemoglobin S in real time by video-enhanced differential interference contrast microscopy. We find that a cross-linked gel occurs very early, nucleation conforms to the double nucleation model and nucleation by fiber breakage is not seen if the system is not perturbed. We conclude that the most likely basis of the present length distributions lies in breakage of solid-like gels that adhere to grids.
