Decrease in Stability of Human Albumin with Increase in Protein Concentration*

The stability (reflected in denaturation temperature, Td) of defatted human albumin monomer, monitored by differential scanning calorimetry, decreases with increasing protein concentration. This is shown to be compatible with a simple model in which reversible polymerization of denatured monomer promotes un- folding. This model also predicts an increase in transition cooperativity with decreasing protein con- centration whereas experimentally cooperativity decreases because the rate of thermally induced po- lymerization of unfolded monomer is slow relative to the scan rate of the calorimeter. The denaturation of undefatted human albumin monomer, subsaturated with high affinity endogenous long-chain fatty acid (LCFA), was previously observed by differential scan- ning calorimetry to be a biphasic process. T d for the first endotherm, associated with the denaturation of LCFA-poor species, decreases with increasing protein concentration similar to that for defatted monomer whereas Ta for the second endotherm, associated with denaturation of LCFA-rich species, is independent of concentration. The magnitude of the concentration de- pendence of T d relates directly to the extent of polymerization of denatured monomer, which decreases with increasing level of bound ligand. The bimodal thermogram observed for undefatted monomer persists upon simultaneous extrapolation of T d values to low concentration and low scan rate thereby demonstrat-ing that this biphasic denaturation arising from ligand redistribution during denaturation is a true thermo-


Decrease in Stability of Human Albumin with Increase in Protein
The stability (reflected in denaturation temperature, Td) of defatted human albumin monomer, monitored by differential scanning calorimetry, decreases with increasing protein concentration. This is shown to be compatible with a simple model in which reversible polymerization of denatured monomer promotes unfolding. This model also predicts an increase in transition cooperativity with decreasing protein concentration whereas experimentally cooperativity decreases because the rate of thermally induced polymerization of unfolded monomer is slow relative to the scan rate of the calorimeter. The denaturation of undefatted human albumin monomer, subsaturated with high affinity endogenous long-chain fatty acid (LCFA), was previously observed by differential scanning calorimetry to be a biphasic process. T d for the first endotherm, associated with the denaturation of LCFA-poor species, decreases with increasing protein concentration similar to that for defatted monomer whereas Ta for the second endotherm, associated with denaturation of LCFA-rich species, is independent of concentration. The magnitude of the concentration dependence of T d relates directly to the extent of polymerization of denatured monomer, which decreases with increasing level of bound ligand. The bimodal thermogram observed for undefatted monomer persists upon simultaneous extrapolation of T d values to low concentration and low scan rate thereby demonstrating that this biphasic denaturation arising from ligand redistribution during denaturation is a true thermodynamic phenomenon and not an artifact of specific experimental conditions or the method used to induce denaturation.
In an earlier study, undefatted human albumin monomer, subsaturated with high affinity endogenous LCFA,' was found to undergo biphasic denaturation, which was reflected as two endotherms in the DSC thermogram (1, 2). In order to elucidate the mechanism of the denaturation of albumin, the consequence of removing endogenous LCFA (defatting) on the observed biphasic unfolding of undefatted monomer has * The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
$ To whom correspondence should be addressed.
been investigated by DSC in the current study. In addition, the effects of protein concentration on the unfolding process of both undefatted and defatted monomer have been determined. The behavior of the denaturation temperature of defatted monomer as a function of concentration is shown to be compatible with an attendant polymerization of unfolded albumin monomer during thermal denaturation. In order to establish whether the undefatted monomer undergoes biphasic denaturation under conditions that better approximate those of equilibrium with minimal protein-protein interactions, a method is presented for simultaneously extrapolating the denaturation temperatures to low protein concentration and low scan rate.

MATERIALS AND METHODS
Protein Stock Solutions-Undefatted human albumin monomer was prepared by gel filtration chromatography from 7.3% fraction V albumin as before (1). This fraction V starting material was unheated, contained no stabilizers, and contained 0.50 mol of free sulfhydryl/ mol of protein. The monomeric protein was concentrated by diafiltration and dialyzed to give undefatted monomer at 89.1 mg/ml in 150 mM NaC1, pH 7.7.
Defatted albumin monomer was prepared by the method of Chen (3, 4) from the above 7.3% fraction V material, concentrated by diafiltration, purified by the same gel filtration chromatography procedure used above, reconcentrated, and dialyzed to yield 75.9 mg/ml defatted monomer in 150 mM NaCl, pH 7.7.
Protein concentration was determined by using 5.50 and 5.45 for A g n m for undefatted monomer and defatted monomer, respectively.
These values were obtained from spectrophotometric absorbance measurements at 280 nm of dilutions in 0.10 M NaPO,, pH 7.0, of solutions the concentrations of which had been determined by differential refractometry at 546 nm with a value of 0.186 ml/g for dn/dc (5). The undefatted and defatted albumin preparations contained 1.43 and 0.084 mol of endogenous LCFA/mol of albumin monomer, respectively, which were determined by the method of Bergmann et al. (6). High pressure liquid chromatography analysis with a Spherogel-TSK 3000 column (Beckman Instruments, Inc.) and polyacrylamide gel electrophoresis in sodium dodecyl sulfate under reducing and nonreducing conditions demonstrated that both the undefatted and defatted albumin preparations were 299% monomer. Cellulose acetate electrophoresis showed that >99% of both the undefatted and defatted monomer preparations migrated as albumin.
Solutions for Calorimetry-Solutions for DSC were prepared by dilution of the appropriate albumin monomer stock solution with 150 mM NaCl; concentrations of diluted solutions were determined from the weight and densities of the solvent and the protein stock solutions by using a partial specific volume of 0.733 ml/g for albumin (7). The amount of sample placed in the calorimeter was determined from the weight and appropriate density (8).
Calorimetry-Design, operation, and calibration of the differential scanning calorimeter, which is of the heat flow type, are described elsewhere (9,10). In a typical experiment, 1.482 g of protein solution was loaded into the sample cell with the reference cell remaining unfilled and heated from 30 to 95 "C at 14.7 K/h. The solvent contribution to the heat capacity was determined separately and subtracted from the protein scan.
The differential voltage signal, V, was converted to excess heat capacity, Ce=, in cal/(K. g protein) by the relation ( (1) where c(T) is the calorimeter calibration constant in watts/V, V is the differential voltage in V, r ( T ) is the time constant in s, dV/dt is the first derivative of the differential voltage with respect to time in V/s, @ is scan rate in K/s, and w is the mass of protein in g.
Enthalpy of denaturation values was determined by integrating the thermogram over the temperature interval of denaturation with respect to a linear base line drawn throughout this region from where the transition was judged to have started as evidenced by departure of the excess heat capacity curve from the sloping predenaturation base line to where it meets the nearly flat postdenaturation base line. This approach has been shown to be a good approximation for transitions characterized by a change in heat capacity (12) and is appropriate for thermograms comprised of multiple endotherms.

RESULTS
Experimental Conditions and Uncertainties-DSC experiments were performed on defatted and undefatted (1.4 eq of LCFA/monomer) human albumin monomer in 150 mM NaC1, pH 7.0. The protein undergoes irreversible thermal denaturation at all concentrations.
Denaturation temperature, Td, is defined as the temperature at which a local maximum occurs in the excess heat capacity, Cex. The reproducibility in the denaturation temperatures for the sharper endotherms (Td in Tables I and 111 and Tg' in Tables I1 and IV) is estimated as f0.03 "C and that for the broader endotherms (Ti2' in Tables I1 and IV) Tables I and I1 is estimated as +3%. The estimated uncertainties in C F (maximum excess heat capacity) and HHW in Tables I and I11 are k2% and k0.05 "C, respectively. Variation of Td and A& with Protein Concentration-Thermograms for defatted human albumin monomer were measured as a function of protein concentration from 1.4 to 74 mg/ml at a scan rate of 14.7 K/h. Defatted monomer shows a single endotherm at all concentrations; a typical thermogram at 30 mg/ml is presented in Fig. 1, thermogram A. Values of Td, Cp,"', and HHW at each concentration are given in Table I. With decreasing albumin concentration, Td increases monotonically from 63.9 "C at 74.1 mg/ml to 66.4 "C at 1.43 mg/ml, whereas M d appears to be constant with an average value of 4.18 cal/g. In addition, with decreasing protein concentration, the endotherm decreases in amplitude and broadens, i.e. e","" decreases and HHW increases.
Thermograms for undefatted albumin monomer were measured as a function of concentration from 1.3 to 64 mg/ml at a scan rate of 14.7 K/h. At all protein concentrations studied, the thermogram for undefatted monomer is bimodal (Fig. 2); the lower denaturation temperature is designated Ti1) and the higher Ti2'. Both Tf' and A& appear independent of protein concentration with average values of 78.2 "C and 5.16 cal/g, respectively (Table 11). With decreasing albumin concentration, Ti1' increases monotonically from 66.3 "C at 64.1 mg/ml to 71.1 "C at 1.25 mg/ml (Table 11). Thus, at a constant scan rate of 14.7 K/h, the two denaturation peaks tend to merge with decreasing protein concentration; however, even at 1.25 mg/ml the thermogram for undefatted monomer is bimodal (Fig. 2).
Sturtevant and co-workers (13-15) have demonstrated that a plot O f the logarithm of protein concentration versus 1 / T d with Td in K is linear with a negative slope when an oligomeric  protein dissociates on denaturation. The positive slope observed for a similar plot of the data reported here for defatted monomer (Fig. 3, line A) suggests that albumin undergoes polymerization on denaturation. A simple model for such a chemical reaction may be described by where NL,, is the native protein unit with n ligands bound that undergoes reversible two-state unfolding with an attendant dissociation of ligand and polymerization of m denatured  (4) where A€€"H, van't Hoff enthalpy, is assumed to be temperature independent and ( L ) has been set equal to total ligand   (Table I). The experimental data (0) were fitted by linear least squares with ln(N)o as the independent variable and 1 / T d as the dependent variable to give a slope of +2.00 X lo5 K and correlation coefficient of 0.957. Line B, Thl' data for undefatted monomer ( Table   11). The experimental data (W) were fitted by linear least squares as above to give a slope of 9.76 X lo' K and correlation coefficient of 0.997. Line C, T$*' data for undefatted monomer ( Table 11) ( m / ( m -1)).
( A€€,H/R). Such a plot for defatted monomer is linear and has a positive slope (Fig. 3, line A ) .
For undefatted monomer, T d data (Table 11) are plotted as ln(N)o uersus 1/Td in Fig. 3 also. A straight line with a positive slope results for Ti1) (Fig. 3, line B ) , and a straight vertical line corresponding to 78.2 "C represents Tf' (Fig. 3, line C).
Effect of Polymerization on Endotherm Shape-The effect on the endotherm of attendant polymerization during denaturation is obtained from C.,(T) = AH.da(T)/dT (5) (13,16) where LW is taken as the calorimetric enthalpy, m d , and da/dT is the rate of change of the extent of reaction, a(T), with respect to temperature. For defatted monomer da/dT can be expressed as a function of a, m, and A K H by considering the van't Hoff temperature dependence of the overall equilibrium constant in the absence of ligand (Equation 3 with n = 0). This permits the calculation of the excess heat capacity for the denaturation/polymerization reaction for defatted monomer from  + a(T).(rn -1))' R . T 2 (6) where a H v H is assumed to be temperature independent. For given values of (N),,, m,  The experimental thermogram for defatted monomer at 30.4 mg/ml (Fig. 1, thermogram A ) has a slightly elongated tail on the high temperature side with a of 0.926 cal/(g . K) and a HHW of 3.46 "C. The calculated endotherm for the denaturation/polymerization reaction at 30.1 mg/ml protein (Fig. 1, thermogram B ) , computed with the input parameters determined above, is skewed to the high temperature side with a of 0.948 cal/(g.K) and a HHW of 3.86 "C. By contrast the endotherm calculated for the two-state denaturation involving no polymerization (Fig. 1, thermogram C) is essentially symmetric with a C F of 1.28 cal/(g.K) and a HHW of 2.88 "C.
Endotherms corresponding to protein concentrations from 1.4 to 74 mg/ml for the denaturation/polymerization reaction of defatted monomer were computed by assuming a temperature-dependent a "~. These calculated endotherms (data not shown) decrease in HHW, a reflection of increasing cooperativity, sharpen, and increase in amplitude with decreasing protein concentration. In contrast, experimental endotherms substantially broaden and decrease in maximum amplitude with decreasing protein concentration ( Table I).

Variation of T d with Scan Rate and Protein Concentration-
The effect. on Td of decreasing both scan rate and protein concentration has been investigated. At constant concentra-* A . Shrake and P. D. Ross, manuscript in preparation.  with Tar, in K (17)(18)(19). E, is the temperature-independent Arrhenius activation energy in kcal/mol of denaturing unit; R is the gas constant in kcal/(K. mol), and the first constant is a positive number. Equation 9 predicts that a plot of In 0 uersus 1/T,a will give a straight line with a negative slope.
Since for defatted monomer at different concentrations and scan rates (Table 111)   At constant scan rate Td increases with decreasing defatted monomer concentration; thus, the effects on T d of decreasing scan rate and protein concentration are in opposition. To extrapolate to low protein concentration and to low scan rate, a method similar to a Zimm (20) plot, used to extrapolate light-scattering data, was utilized. In accord with Equations 9 and 4, both In @ and ln(N)o vary linearly with 1/Td, respectively. Therefore, the sum [ln @ + ln(N)a] also varies linearly with l/Td and provides the functional form for the plot, 1/Td uersu [In 9 + ~I ( N )~] .

Concentration for undefatted human albumin monomer
In Fig. 4 the experimental Td values for defatted monomer at two concentrations, each at two different scan rates (Table III), are plotted as points 1-4 and are extrapolated linearly to the arbitrarily low values of 1 mg/ml and 1 K/h, point E, which corresponds to T d = 64.04 "C.
The experimental Td values for defatted monomer (Table  111) are extrapolated to various scan rates and protein concentrations by using the method described above. These extrapolated T d values are plotted in Fig. 5, curue A. The effect on T d of decreasing scan rate dominates the effect of decreasing protein concentration so that for defatted monomer T d decreases from 65.0 "C at 30 mg/ml and 30 Kjh to 63.1 "C at 0.30 mg/ml and 0.30 K/h.
T d values as a function of protein concentration and scan rate for undefatted human albumin monomer are presented in Table IV. Ti2' is independent of scan rate and concentration, has an average value of 78.1 "C, and is represented as a horizontal line in Fig. 5, curue C. The TL1' values were extrapolated as those for defatted monomer and are plotted in Fig.   5, c u m B. Ti1' for undefatted monomer decreases from 68.3 "C at 30 mg/ml and 30 K/h to 64.8 "C at 0.30 mg/ml and 0.30 K/h in contrast to Ti2'. The important result is that under conditions that better approximate an ideal equilibrium process, Ti1' and Ti2' are further separated than under actual experimental conditions.

DISCUSSION
An earlier study of the stability of undefatted human albumin monomer revealed that the thermal denaturation of this protein is biphasic, i e . the DSC thermogram consists of two peaks (1). The undefatted protein was subsaturated with high affinity LCFA (21, 22). An analysis of this albumin during the course of its irreversible thermal denaturation showed that the endotherm with the lower Ta is associated with denaturation of LCFA-poor protein species whereas the endotherm with the higher T d is associated with denaturation of LCFA-rich protein species. This uneven distribution of bound LCFA was proposed to arise during denaturation due to increasing free ligand concentration (1).
In the current investigation, the thermal denaturation of defatted human albumin monomer, which has essentially all endogenous LCFA removed, is found to be monophasic at all concentrations studied. Since no ligand redistribution can occur during denaturation of defatted monomer, the occurrence of a single endotherm with this protein is compatible with the proposed origin of the biphasic denaturation of undefatted monomer (1). Tiktopulo et al. (23) have performed a DSC study of defatted human albumin monomer at pH 7.0 and observed a bimodal thermogram in contrast to the slightly asymmetric single endotherm observed in this study. They have associated this bimodality with three independent domains within the molecule. However, the protein was modified by reacting the free sulfhydryl with L-cystine; in addition, experiments were performed at scan rates of 60 and 120 K/h, generally at low ionic strength and in the presence of low levels of phosphate, which binds to the protein. The bimodality observed in the present work in the thermogram for undefatted albumin monomer does not derive from sequential denaturation of domains within the same molecule (24) but rather from the denaturation of different kinds of molecules, LCFA-poor and -rich species (1).
The thermal denaturation of human albumin is irreversible under conditions used in this study although we have utilized equilibrium thermodynamics to describe the denaturation/ polymerization of albumin. However, Sturtevant and co-workers (14) have demonstrated that treatment of an overall irreversible process (F e U -I) yields results similar to those for the reversible process alone (F + U) when the irreversible step is slow compared to the rates of interconversion of species F and U. In the present study F U corresponds to the reversible denaturation/polymerization reaction of Equation 2 whereas U -I corresponds to the slower irreversible aggregation of denatured albumin polymers. The appearance of the irreversibly denatured albumin in the presence and absence of LCFA was indicative of aggregation.
However, in the presence of high levels of LCFA, reversible polymerization does not occur since Ti2) for undefatted monomer is independent of concentration. Furthermore, since TF) is independent of both scan rate and concentration, the rate of irreversible aggregation (25-27) must be slow compared to the time scale of the calorimeter experiment. Involvement of the denatured protein in polymerization shifts the equilibrium between the native and denatured species in favor of denaturation in accordance with Le Chatelier's principle; therefore, with decreasing protein concentration, the effect of polymerization lessens and as a result Td should increase as is observed. For defatted monomer a plot of In(N)o uersus 1/Td gives a straight line with a positive slope as predicted by Equation 4, which was derived for the denaturation/polymerization reaction of Equation 2. This two-state reaction requires all denatured units to polymerize to the same degree, m. The actual degree of polymerization is not specific; thus, the parameter m represents an average value. The significant result is that during thermal denaturation defatted monomer undergoes concomitant polymerization, which is manifested in a concentration dependence of Td. The thermodynamics and kinetics of the denaturation of proteins may also be perturbed by excluded volume and electrostatic effects (28), but contributions from these effects are probably not large under our experimental conditions.
The thermogram for undefatted albumin monomer is bimodal at all protein concentrations and scan rates studied. Ti2) is independent of concentration and scan rate whereas at constant scan rate Ti1) increases monotonically with decreasing protein concentration; nevertheless, at the lowest concentrations bimodality is still apparent. Ti1) data for undefatted monomer plotted as h(N)o uersuS 1/Td show a straight line with positive slope; this reflects polymerization of these denatured LCFA-poor species. The corresponding Ti" plotted in the same manner are represented by a straight line with infinite slope; this indicates the lack of polymerization of these LCFA-rich species. The presence of increasing levels of fatty acid anion has been observed to correlate with a decreasing tendency to polymerize.' AHd for defatted monomer and that for undefatted monomer, 4.18 and 5.16 cal/g, respectively, appear independent of Td, probably the result of the small temperature ranges involved. Individual thermograms (Fig. 1, thermogram A , and   Fig. 2) indicate that AC, > 0, where AC, is the heat capacity change for denaturation. The higher A& value for undefatted monomer may in part reflect the enthalpy of binding endogenous LCFA. The apparent lack of concentration dependence of the AHd values suggests that the contribution to AHd from polymerization is much smaller than that from denaturation.
The endotherm computed for polymerization/denaturation of ligand-free albumin is slightly asymmetric with a slightly elongated high temperature tail (Fig. 1, thermogram B ) and closely resembles the experimentally observed thermogram (Fig. 1, thermogram A ) . In contrast, the calculated endotherm for two-state denaturation without polymerization is essentially symmetric (Fig. 1, thermogram C) with a CY 40% greater than that observed experimentally.
With a temperature-dependent A H V H for the denaturation/ polymerization reaction, the endotherms computed for defatted monomer show with decreasing protein concentration an increase in C F and decrease in HHW, which reflects an increase in cooperativity. These computed results are in accord with expectation since with decreasing protein concentration the effect of polymerization should decrease. Experimentally the opposite effect is observed; with decreasing protein concentration, the endotherm flattens, decreases, and HHW increases ( Table I). We ascribe this behavior to a kinetic effect that derives from the overall rate of denaturation/polymerization being on the same time scale as the scan rate of the calorimeter. The rate-limiting step is probably the polymerization of denatured monomer. The general result is a broadening of the endotherm relative to what would be obtained for an apparent equilibrium process since in the nonequilibrium situation the denaturation takes place over a greater temperature interval. With decreasing protein concentration, the rate of polymerization further slows and thus the tendency for the endotherm to broaden increases as is observed (Table I). On decreasing the scan rate at constant protein concentration, a sharpening of the endotherm is observed (Table 111); this is also consistent with the above interpretation since the kinetic distortion should tend to decrease as the scan rate decreases, i.e. as equilibrium is approached. Thus, the fitted value of A H , H (162 kcal/mol), which is less than the calorimetric enthalpy of denaturation (278 kcal/mol), may result primarily from the kinetic distortion.
The fitted values of m and A H V~ for defatted monomer must be regarded with caution because they derive from experimental envelopes that are influenced by kinetics and because of the oversimplified nature of the model. Nevertheless, the general features of the endotherms computed for denaturation/polymerization are qualitatively correct under experimental conditions devoid of kinetic effects. Thus, the observed slight skewing to the high temperature side of the experimental endotherm of defatted monomer relates to attendant polymerization on denaturation. The principle effect of the kinetic perturbation is a general broadening of the endotherm. Td values appear little affected by the relatively slow rate of polymerization of denatured monomer since a plot of ln(N)o uersus l/Td is linear as predicted by the equilibrium process described by Equation 4.
In order to gauge the significance of the bimodality observed in the thermograms for undefatted monomer, the thermograms must be examined under conditions as ideal and as close to equilibrium as possible. The effects on Td of decreasing protein concentration and scan rate act counter to each other. In order to determine the net result of these two effects, TL1' and Ti2' for undefatted monomer were extrapolated to various scan rates and protein concentrations. T$*' is independent of both concentration and scan rate, as anticipated for LCFA-rich species. However, Ti1' data behave similarly to Td data for defatted monomer, as anticipated for LCFA-poor species, and are extrapolated analogously; on approach to ideal equilibrium conditions, Ti1' also decreases. Thus, the bimodality observed for undefatted monomer at 15 K/h and 30 mg/ml not only persists at low scan rate and low protein concentration but is enhanced. Therefore, the biphasic denaturation of undefatted albumin monomer, reflected by the bimodal thermogram and arising from ligand redistribution during denaturation, is a true thermodynamic phenomenon and not an artifact of high protein concentration or high scan rate or of the means used to effect denaturation.