Oxygen binding to sickle cell hemoglobin.

The extent of oxygen binding and light scattering of concentrated solutions of hemoglobin S have been determined as a function of oxygen partial pressure using a thin film optical cell. Nearly reversible oxygen binding is observed as witnessed by the small hysteresis found between slow deoxygenation and reoxygenation runs. High co-operativity is noted from unusually large concentration-dependent Hill coefficients when aggregated hemoglobin S is present. The application of linkage theory with the inclusion of non-ideal solution properties permits a test of various simple models for oxygen binding to both the monomer (α₂β₂^s) and polymer (aggregated) phase. It is concluded that oxygen binding to the polymer is either negligible or small under present experimental conditions. Phase diagrams of the solution concentration in equilibrium with polymer phase as a function of oxygen partial pressure are derived using best fit values of polymer parameters.     

Fluorescence correlation spectroscopy and Brownian rotational diffusion

A theroy relating rotational Brownian motion to the time autocorrelation function of the intensity of radiation from a fluorescent system composed of spherical rotors is presented. The calculation shows three relaxation times, two associated with the rotational diffusion, and the third associated with the natural decay of the fluorescence. The correlation function contains terms that relax independently of the fluorescence decay time, thus arbitrarily extending the time range over which rotational diffusion can be studied by fluorescence.     

Dynamic light scattering from collagen solutions. II. Photon correlation study of the depolarized light.

The depolarized forward-scattered light from solutions of rat tail collagen has been studied by photon correlation spectroscopy. The measured autocorrelation function is seen to decay on two widely different time scales. The decay time for the fast component is consistent with the rotational diffusion of rodlike collagen monomers. The slowly decaying autocorrelation component is attributed to large nonspecific aggregates of collagen. A substantial fraction of the collagen is in this aggregated form. Extrapolation of the faster decay times to zero concentration yields a value of θ = 1082 ± 30 sec^?1 for the rotational diffusion coefficient of the collagen monomer.     

Ligand binding and the gelation of sickle cell hemoglobin.

The solubility equilibrium between monomer and polymer which has been shown to exist in deoxyhemoglobin S solutions is examined in solutions partially saturated with carbon monoxide. The total solubility is found to increase monotonically with increasing fractional saturation. At low fractional saturations the increase is nearly linear, amounting roughly to an increase of 0.01 g cm^?3 in solubility for each 10% increase in fractional saturation. Linear dichroism measurements on the spontaneously aligned polymer phase are used to examine the composition of the polymer as a function of the fractional saturation of the corresponding solution phase. The dichroism experiments show that the polymer phase contains less than 5% of CO-liganded hemes even at supernatant fractional saturations in excess of 70%. The polymer selects against totally liganded hemoglobin molecules by a minimum factor of 65 and against singly liganded molecules by a factor of at least 2.5. Consequently, polymerized hemoglobin S has a ligand affinity which is significantly lower than that of monomeric hemoglobin S in the deoxy quaternary structure.The kinetics of the polymerization reaction in the presence of CO are similar to those observed in pure deoxyhemoglobin S solutions. The polymerization is preceded by a pronounced delay, the duration of which, t_d, is proportional roughly to the 30th power of the solubility. At low fractional saturations, this amounts to a tenfold increase in t_d for each 10% increase in the fractional saturation.These results show that the polymerization reaction is nearly specific for deoxyhemoglobin. Models for the dependence of the solubility and the polymer saturation on ligand partial pressure demonstrate the importance of solution phase non-ideality in determining the solubility of mixtures. The results require selection against partially liganded species which is significantly greater than is predicted by the two-state allosteric model. The data are compatible with either sequential or allosteric models in which the major polymerized component is the unliganded hemoglobin molecule.     

Fluorescence lifetime spectroscopy in multiply scattering media with dyes exhibiting multiexponential decay kinetics

To investigate fluorescence lifetime spectroscopy in tissue-like scattering, measurements of phase modulation as a function of modulation frequency were made using two fluorescent dyes exhibiting single exponential decay kinetics in a 2% intralipid solution. To experimentally simulate fluorescence multiexponential decay kinetics, we varied the concentration ratios of the two dyes, 3,3-diethylthiatricarbocyanine iodide and indocynanine green (ICG), which exhibit distinctly different lifetimes of 1.33 and 0.57 ns, respectively. The experimental results were then compared with values predicted using the optical diffusion equation incorporating 1) biexponential decay, 2) average of the biexponential decay, as well as 3) stretched exponential decay kinetic models to describe kinetics owing to independent and quenched relaxation of the two dyes. Our results show that while all kinetic models could describe phase-modulation data in nonscattering solution, when incorporated into the diffusion equation, the kinetic parameters failed to likewise predict phase-modulation data in scattering solutions. We attribute the results to the insensitivity of phase-modulation measurements in nonscattering solutions and the inaccuracy of the derived kinetic parameters. Our results suggest the high sensitivity of phase-modulation measurements in scattering solutions may provide greater opportunities for fluorescence lifetime spectroscopy.     

Monomer diffusion into polymer domains in sickle hemoglobin.

The gelation of sickle hemoglobin includes the formation of spherulitic arrays of polymers, known as polymer domains, which are an intrinsic result of the polymer formation mechanism. We have observed the diffusion of monomers into domains as they form, which substantially increases the total concentration of hemoglobin within the domain. The maximum total concentration attained is comparable with the pellet concentration of 0.5-0.55 g/cm3 obtained in sedimentation experiments. The half time for this process is approximately 50 s for domains of 25 microns radius, and is approximately independent of temperature. The shape of the diffusion progress curves as well as the deduced diffusion constants, and their weak temperature dependence are consistent with a simple model of hemoglobin monomer diffusion into the domain.     

Characterization of aggregate structure in mercerized cellulose/LiCl.DMAc solution using light scattering and rheological measurements

The structure of a semidilute solution of mercerized cellulose (CC1m) in 8% (w/w) LiCl.DMAc, which contained some aggregates, was investigated using static and dynamic light scattering measurements. The static scattering function of the polymer solution containing a small amount of aggregates can be separated into fast- and slow-mode components by combining static and dynamic light scattering measurements. The osmotic modulus was identical for the fast-mode component of the CC1m solutions and the native cellulose (CC1) solutions, in which cellulose is dispersed molecularly. This indicates that the molecularly dispersed component of the CC1m solutions has an identical conformation with the cellulose molecules in the CC1 solutions. The correlation length was also identical for the fast-mode components of CC1m solutions and the CC1 solutions, indicating that these solutions have the same mesh size of the polymer entanglement. These observations for the fast-mode components are consistent with the concentration dependence of the zero shear rate viscosity and the plateau modulus estimated in the rheological measurements. The slow-mode component, on the other hand, gave information on the aggregate structure in the CC1m solution. The radius of gyration of the aggregate structure estimated from the slow-mode component was about 70 nm, which is independent of the concentration of the solution. The plots for particle scattering factor of the slow-mode component lay between the theoretical curve of a sphere and a Gaussian chain, implying that the structure of the aggregate in the CC1m solution is like a multiarm polymer. A characteristic time of the slow-mode component calculated with the translational diffusion coefficient and the radius of gyration were almost identical with the relaxation time of the long-time relaxation observed in the rheological measurements. This indicates that the long-time relaxation of CC1m solutions originates in the translational diffusion of the aggregate structure in the solution.     

Mechanism of bovine liver glutamate dehydrogenase self-assembly: III. Characterization of the association-dissociation stoichiometry with quasi-elastic light scattering

The homodyne light-scattering autocorrelation function originating in translational diffusion has been simulated for a polymerization model proposed for a number of self-associating systems: the sequential addition of identical monomer units to a growing aggregate, with identical equilibrium constants for each step. Both spherical and rigid rod structures have been considered. When applied to quasi-elastic light scattering data on glutamate dehydrogenase self-assembly, the simulation results indicate the formation of elongated polymers having equivalent and identical association sites. The weak response of translational diffusion coefficients to solution non-ideality leads to a valuable test of the unique equilibrium constant assumption. On the other hand, it is shown that successful exploitation of quasi-elastic light scattering data on aggregating systems of this type relies heavily on independent information.     

Universal metastability of sickle hemoglobin polymerization

Sickle hemoglobin (HbS) polymerization occurs when the concentration of deoxyHbS exceeds a well-defined solubility. In experiments using sickle hemoglobin droplets suspended in oil, it has been shown that when polymerization ceases the monomer concentration is above equilibrium solubility. We find that the final concentration in uniform bulk solutions (i.e., with negligible boundaries) agrees with the droplet measurements, and both exceed the expected solubility. To measure hemoglobin in uniform solutions, we used modulated excitation of trace amounts of CO in gels of HbS. In this method, a small amount of CO is introduced to a spatially uniform deoxyHb sample, so that less than 2% of the sample is liganded. The liganded fraction is photolyzed repeatedly and the rate of recombination allows the concentration of deoxyHbS in the solution phase to be determined, even if polymers have formed. Both uniform and droplet samples exhibit the same quantitative behavior, exceeding solubility by an amount that depends on the initial concentration of the sample, as well as conditions under which the gel was formed. We hypothesize that the early termination of polymerization is due to the obstruction in polymer growth, which is consistent with the observation that pressing on slides lowers the final monomer concentration, making it closer to solubility. The thermodynamic solubility in free solution is thus achieved only in conditions with low polymer density or under external forces (such as found in sedimentation) that disrupt polymers. Since we find that only about 67% of the expected polymer mass forms, this result will impact any analysis predicated on predicting the polymer fraction in a given experiment.     

Vascular response to infusions of a nonextravasating hemoglobin polymer.

The clinical utility of cross-linked tetrameric hemoglobin solutions is limited by peripheral vasoconstriction thought to be due to scavenging of nitric oxide. In addition, transfusion of crude preparations of hemoglobin polymers can cause arterial hypertension. We tested the hypothesis that eliminating low-molecular-weight components from the polymer solution would prevent extravasation and its associated pressor response. A zero-link polymer of bovine hemoglobin was developed without chemical linkers left between the tetramers. Transfusion of unprocessed preparations of these polymers in rats resulted in appearance of the polymer in the renal hilar lymph. However, eliminating the low-molecular-weight components with a 300-kDa diafiltration resulted in an average hydrodynamic radius of 250 A and in undetectable levels of polymer in hilar lymph. Exchange transfusion in anesthetized rats and cats and in awake cats produced no increase in arterial pressure. In anesthetized cats, exchange transfusion with an albumin solution reduced hematocrit from 30 to 18%, increased cerebral blood flow, and dilated pial arterioles. In contrast, reducing hematocrit by transfusing the diafiltered polymer did not increase cerebral blood flow as pial arterioles constricted. These results are consistent with the hypothesis that the increase in arterial pressure associated with cell-free hemoglobin transfusion depends on hemoglobin extravasation. Constriction observed in the cerebrovascular bed with a nonextravasating hemoglobin polymer at low hematocrit is presumably a regulatory response to prevent overoxygenation at low blood viscosity.     

Quasielastic light-scattering study of polyadenylic acid solutions. II

Quasielastic light scattering is used to study saline solutions of polyadenylic acid with varying polymer concentrations and molecular masses. These experiments clearly show the existence of two relaxation times. For dilute solutions, when the chains are mutually independent, the fast mode is due to the free diffusion of the polymer chains. For concentrations above the overlap concentration C*, the fast mode is due to the propagation of collective excitations of the pseudolattice of polymer chains. The slow modes are observed when the polymer concentration is in the vicinity of the overlap concentration C*. A series of experiments shows that both their relaxation time and amplitude depend only on the polymer concentration and not on the polymer molecular mass. This result rules out any previous explanation based on individual chain motion. Furthermore, since the amplitudes depend on the time elapsed from the preparation of the solution, the slow modes are due to the diffusion of concentration inhomogeneities in the pseudolattice.     

Kinetics of the polymerization of hemoglobin in high and low phosphate buffers

Diluted solutions of deoxyhemoglobin S in concentrated phosphate buffer form aggregates or gels with a clear exhibition of a delay time. The aggregates can be liquified by cooling, bubbling with O2 or CO gas, or the dilution of phosphate buffer with water. These properties can be used as a simple method for studying the mechanism of polymerization and depolymerization of hemoglobins. The advantages of this method are: 1) The amount of hemoglobin sample required is only 1% to 5% of that required for the gelation of deoxy-Hb S in low phosphate buffer. 2) The kinetics can be measured turbidimetrically using an ordinary spectrophotometer. 3) The solubility of hemoglobin can be directly determined by taking the absorption spectrum of the supernatant solution after polymerization. 4) The polymer phase can be easily separated from the solution so that the amount and composition of the polymers can be analyzed. 5) The volume of the polymer phase is so small that excluded volume effect can be neglected. 6) The method can be applied to the study of polymerization of non-sickle hemoglobins and that of mixtures of sickle and non-sickle hemoglobins. The major question is whether the polymerization of hemoglobin in concentrated phosphate buffer is the same as that of deoxy-Hb S in low phosphate buffer. To answer this question, we studied the polymerization of Hb S, Hb A, Hb C Harlem, and Hb C in phosphate buffers of different molarities. We also studied the mechanism of the conversion of gels of these hemoglobins into crystals.     

Kinetics of sickle hemoglobin polymerization. II. A double nucleation mechanism

A double nucleation mechanism for the polymerization of sickle hemoglobin is described. The mechanism accounts for all of the major kinetic observations: the appearance of a delay, the high concentration dependence of the delay time, and the stochastic behavior of slowly polymerizing samples in small volumes. The mechanism postulates that there are two pathways for polymer formation: polymerization is initiated by homogeneous nucleation in the solution phase, followed by nucleation of additional polymers on the surface of existing ones. This second pathway is called heterogeneous nucleation. Since the surface of polymers is continuously increasing with time, heterogeneous nucleation provides a mechanism for the extreme autocatalysis that is manifested as an apparent delay in the kinetic progress curves. In this mechanism, each spherulitic domain of polymers is considered to be initiated by a single homogeneous nucleation event. The mechanism explains the irreproducibility of the delay time for single domain formation as arising from stochastic fluctuations in the time at which the homogeneous nucleus for the first polymer is formed. Integration of the linearized rate equations that describe this model results in a simple kinetic form: A[cosh(Bt)-1] (Bishop & Ferrone, 1984). In the accompanying paper (Ferrone et al., 1985) it was shown that the initial 10 to 15% of progress curves, with delay times varying from a few milliseconds to over 10(5) seconds, is well fit by this equation. In this paper, we present an approximate statistical thermodynamic treatment of the equilibrium nucleation processes that shows how the nucleus sizes and nucleation equilibrium constants depend on monomer concentration. The equilibrium model results in expressions for B and B2A as a function of monomer concentration in terms of five adjustable parameters: the bimolecular addition rate of a monomer to the growing aggregate, the fraction of polymerized monomers that serve as heterogeneous nucleation sites, the free energy of intermolecular bonding within the polymer, and two parameters that describe the free energy change as a function of size for the bonding of the heterogeneous nucleus to a polymer surface. This model provides an excellent fit to the data for B and B2A as a function of concentration using physically reasonable parameters. The model also correctly predicts the time regime in which stochastic behavior is observed for polymerization in small volumes.     

Evidence for carbon monoxide binding to sickle cell polymers during melting.

The melting of sickle cell hemoglobin (HbS) polymers was induced by rapid dilution using a stopped-flow apparatus. The kinetics of polymer melting were monitored using light scattering. Polymer melting in the absence of any hemoglobin ligand was compared to melting when the diluting buffer was saturated with carbon monoxide (CO). In this way the role of CO in polymer melting could be assessed. The data were analyzed using models that assumed that melting occurs only at the ends of polymers. It was further assumed that CO could only bind to HbS in the solution phase. However, our data could not be fitted to this model, where CO cannot bind directly to the polymer. Thus, CO probably binds directly to the polymers during our melting experiments. This result is discussed in terms of oxygen induced polymer melting and polymerization processes in sickle cell disease     

Application of a thermodynamic model to the prediction of phase separations in freeze-concentrated formulations for protein lyophilization

Many of the compounds considered for use in pharmaceutical formulations demonstrate incompatibilities with other components at high enough concentrations, including pairs of polymers, polymers and salts, or even proteins in combination with polymers, salts, or other proteins. Freeze concentration can force solutions into a region where incompatibilities between solutes will manifest as the formation of multiple phases. Such phase separation complicates questions of the stability of the formulation as well as labile components, such as proteins. Yet, phase separation events are difficult to identify by common formulation screening methods. In this report, we use the osmotic virial expansion model of Edmond and Ogston (1) to describe phase-separating behavior of ternary aqueous polymer solutions. Second osmotic virial coefficients of polyethylene glycol 3350 (PEG) and dextran T500 were measured by light scattering. Assuming an equilibrium between ice and water in the freeze-concentrated solution, a degree of freeze concentration can be estimated, which, when combined with the phase separation spinodal, describes a "phase separation envelope" in which phase separation tendencies can be expected in the frozen solution. The phase separation envelope is bounded at low temperatures by the glass transition temperature of the freeze-concentrated solution. Scanning electron microscopic images and infrared spectroscopy of protein structure are provided as experimental evidence of the phase separation envelope in a freeze-dried system of PEG, dextran, and hemoglobin.     

Ionic strength effects on macroion diffusion and excess light-scattering intensities of short DNA rods

Quasielastic and static light-scattering measurements were made on DNA isolated from chicken erythrocyte mononucleosomes as a function of ionic strength between 6 × 10^?4 and 1.0M. A transition from single-exponential autocorrelation functions to markedly non-single-exponential decays was observed around 10^?2M ionic strength and was accompanied by a large decrease in the excess light-scattering intensity. Autocorrelation functions recorded below 10^?2M salt were well fit by the sum of two exponential relaxation which differed by as much as 100-fold in time constants. Apparent diffusion coefficients for the fast and slow processes plateaued around 10^?3M with numerical values approximately 10-fold and 1/10, respectively, of the translational diffusion coefficient for mononucleosome DNA at high ionic strength. This behavior is similar to that observed with poly(L -lysine), for which the slow decay has been associated with a transition to an extraordinary phase. The strong and complex salt dependence observed here illustrates potential difficulties in deriving structural information from scattering by polyions at low ionic strength.     

Desmin filaments studied by quasi-elastic light scattering.

We studied polymers of desmin, a muscle-specific type III intermediate filament protein, using quasi-elastic light scattering. Desmin was purified from chicken gizzard. Polymerization was induced either by 2 mM MgCl(2) or 150 mM NaCl. The polymer solutions were in the semidilute regime. We concluded that the persistence length of the filaments is between 0.1 and 1 microm. In all cases, we found a hydrodynamic diameter of desmin filaments of 16-18 nm. The filament dynamics exhibits a characteristic frequency in the sense that correlation functions measured on one sample but at different scattering vectors collapse onto a single master curve when time is normalized by the experimentally determined initial decay rate.     

Kinetics of the polymerization of hemoglobin S: studies below normal erythrocyte hemoglobin concentration.

The kinetics of polymerization of deoxyhemoglobin S have been studied by measuring transverse water proton relaxation times (T₂) in hemoglobin solutions. As seen by other techniques, the kinetic profile consists of a delay time followed by a decrease in T₂ during polymerization. The length of the delay time can be decreased and the rate of change of T₂ can be increased by increasing the concentration of hemoglobin S or non-gelling hemoglobin or ovalbumin. At a total protein concentration of about 210 mg/ml the kinetic profiles in all three cases are indistinguishable suggesting that a non-specific protein-protein interaction may be involved in the kinetics of polymerization. In addition, it is suggested that no polymer formation occurs during the delay period.     

Calculations of scattered light from rigid polymers by Shifrin and Rayleigh-Debye approximations.

We show that the commonly used Rayleigh-Debye method for calculating light scattering can lead to significant errors when used for describing scattering from dilute solutions of long rigid polymers, errors that can be overcome by use of the easily applied Shifrin approximation. In order to show the extent of the discrepancies between the two methods, we have performed calculations at normal incidence both for polarized and unpolarized incident light with the scattering intensity determined as a function of polarization angle and of scattering angle, assuming that the incident light is in a spectral region where the absorption of hemoglobin is small. When the Shifrin method is used, the calculated intensities using either polarized or unpolarized scattered light give information about the alignment of polymers, a feature that is lost in the Rayleigh-Debye approximation because the effect of the asymmetric shape of the scatterer on the incoming polarized electric field is ignored. Using sickle hemoglobin polymers as an example, we have calculated the intensity of light scattering using both approaches and found that, for totally aligned polymers within parallel planes, the difference can be as large as 25%, when the incident electric field is perpendicular to the polymers, for near forward or near backward scattering (0 degrees or 180 degrees scattering angle), but becomes zero as the scattering angle approaches 90 degrees. For randomly oriented polymers within a plane, or for incident unpolarized light for either totally oriented or randomly oriented polymers, the difference between the two results for near forward or near backward scattering is approximately 15%.     

Quasielastic light scattering study of thermal excitations of F-actin solutions and of growth kinetics of actin filaments.

In the first part of this work we report quasielastic light scattering (QELS) studies of the internal dynamics of transient actin networks over a time range of 10(-6)-10(-2) s, scattering angles between zeta = 20 degrees and 150 degrees, and a concentration range of 0.015 (0.3) to 0.7 mg/mL (15 microM). We confirm our previous result that (1) the dynamic structure factor g(q,t) is determined by the thermally excited undulations of the actin filaments and (2) that the initial decay of g(q, t) scales as g(q, t) varies; is directly proportional to exp(-q alpha t) while the long time decay scales as g(q, t) varies; is directly proportional to exp [-(Aq alpha t) 2/3] with alpha = 2.75. The deviation of alpha from the theoretical value of alpha = 3 predicted for Rouse-Zimm chains is similar to that found for high molecular weight macromolecular solutions by QELS. A refined analysis of the dynamic structure factor showed that it can be interpreted in terms of three relaxation processes (besides the contribution of the residual monomer diffusion): (1) the dominant Rouse-Zimm dynamics, which comprises between 65 (at high concentrations) and 85% of the signal; (2) a fast relaxation process with a decay constant of gamma = 9 x 10(3) s-1, which contributes at all concentrations with the same amplitude; and (3) a nonexponential ultraslow contribution of the form g(us) varies; is directly proportional to exp [(-gamma ust)]1/4. The third contribution appears only at high concentrations and increases strongly with decreasing scattering angles. It is thus attributed to fluctuations of the mesh size of the transient actin network. In the second part we show that high sensitivity QELS may be applied to follow the actin polymerization process at low temperatures (10 degrees C). The apparent diffusion coefficient and the static scattering intensity of the actin filaments were determined as functions of polymerization time tpol. We show that the process consists of the rapid growth of a few filaments that become very long (approximately 10 microns; even at actin concentrations of 0.04 micrograms/mL) near the critical growth concentration of 0.012 micrograms/mL, as is expected for a growth process determined by nucleation. Finally, we studied actin networks polymerized in the presence of complexes of gelsolin with actin. By application of the CONTIN program we could determine the length distribution of the filaments.(ABSTRACT TRUNCATED AT 400 WORDS)