Nucleation-controlled Polymerization of Human Monoclonal Immunoglobulin G Cryoglobulins*

The kinetics of the polymerization of human mono- clonal cryoimmunoglobulins at low temperature was investigated in temperature jump experiments by monitoring the changes in turbidity resulting from the scat- tering of incident light by the polymers. Above a critical concentration between 2 and 3 mg/ml, depending on the ionic strength, the kinetics were characterized by a concentration-dependent lag phase and initial rate of self-assembly. Under equilibrium conditions which fa-vored polymerization, the only stable intermediate de- tected by analytical ultracentrifugation was the dimer. Although purified monomers were unable to self-asso- ciate at 4 "C, addition of trace amounts of autologous dimers promoted polymerization. The apparent rate of polymerization was shown to be slow (k = 4.7 x M" s-'), and the process was governed by an equilib- rium constant of 4.6 X io4 M-'. The initial rate of self-assembly was proportional to the product of the mono- mer concentration and the concentration of promoter (ie. dimer). The rate of depolymerization was three orders of magnitude greater than the rate of polymerization and was proportional to the Concentration of polymers present. These results suggest that the polymerization of monoclonal cryoimmunoglobulins is a nucleation-controlled process in which dimerization is the rate-limiting step. Kinetic studies on the polymerization of Fab and F(ab')2 fragments from cryoimmu- noglobulins and a comparison as a function of cryoglobulin monomer concentration. The experiments were carried out at 4 "C at two different concentrations of autologous dimer: 0.51 mg/ml ( O " 0 ) and 0.35 mg/ml (H), respectively. The initial rates of polymerization were calculated from the increase in A330 with time after the temperature was rapidly lowered to 4 "c. the initial rate of polymerization is directly proportional to the concentration of dimer added. At a fixed concentration of dimer, the initial rate of assembly increases in direct proportion to the concentration of cryoglobulin monomer. The dimeric promoter depolymer-izes upon dilution when the concentration of monomer is below the critical concentration. Finally, the initial rate of depolymerization following a temperature jump at 28 "C is directly proportional to the polymer concentration. Taken together, these results suggest that the cold-induced condensation polymerization of monoclonal cryoglobulins can be described as follows.

The kinetics of the polymerization of human monoclonal cryoimmunoglobulins at low temperature was investigated in temperature j u m p experiments by monitoring the changes in turbidity resulting from the scattering of incident light by the polymers. Above a critical concentration between 2 and 3 mg/ml, depending on the ionic strength, the kinetics were characterized by a concentration-dependent lag phase and initial rate of self-assembly. Under equilibrium conditions which favored polymerization, the only stable intermediate detected by analytical ultracentrifugation was the dimer. Although purified monomers were unable to self-associate at 4 "C, addition of trace amounts of autologous dimers promoted polymerization. The apparent rate of polymerization was shown to be slow (k = 4.7 x M" s-'), and the process was governed by an equilibrium constant of 4.6 X io4 M-'. The initial rate of selfassembly was proportional to the product of the monom e r concentration and the concentration of promoter (ie. dimer). The rate of depolymerization was three orders of magnitude greater than the rate of polymerization and was proportional to the Concentration of polymers present. These results suggest that the polymerization of monoclonal cryoimmunoglobulins is a nucleation-controlled process in which dimerization is the rate-limiting step. Kinetic studies on the polymerization of Fab and F(ab')2 fragments from cryoimmunoglobulins and a comparison of cryogel ultrastructure by electron microscopy suggested that the interaction site between monomers is located in the Fab region. Since the polymerization of monomers was only induced by autologous dimers and not dimers from other cryoimmunoglobulins, it was concluded that the hypervariable regions play a specific role in the condensation reaction. The fact that one cryoimmunoglobulin has a well defined antibody activity against streptolysin 0 argued against a low temperature-induced auto-antiidiotype mechanism. Reduction of the interchain disulfide bonds of the Fab fragments abolished their ability to polymerize, probably b y inducing a conformational change a considerable distance a w a y in the variable domains of the molecules.
Cryoglobulins are a clinically important group of immune-* This work was supported by grants from the Medical Research Council of Canada (MT 4259) and from the Arthritis Society (7-264-80). 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.
*Supported under the terms of the Canada-France Exchange Agreement. Present address, Service de Nephrologie et des Maladies Metaboliques, Centre Hospitalier et Universitaire de Grenoble,38043 Grenoble, France. globulins that reversibly precipitate or form gels upon cooling. Previous immunochemical analyses of purified human cryoglobulins have shown that they may be formed either of polymers of monoclonal immunoglobulins (monoclonal cryoglobulins) or of immune complexes (mixed cryoglobulins) (4,12,19). Correlations have been established between the immunochemical type of cryoglobulins and the clinical symptoms as well as the underlying disease (4).
Monoclonal cryoglobulins are associated with lymphoproliferative diseases and are responsible for severe cutaneous and vascular lesions. Previous studies have shown that cryoprecipitation of the monoclonal proteins is dependent upon initial protein concentration, temperature, pH, and dielectric constant of the solvent (12,17,20). Nevertheless the molecular events underlying cryoprecipitation remain poorly understood. Temperature-induced conformational changes have been proposed as the initial step in polymerization at low temperature for some monoclonal cryoglobulins (17, 20, 31), but such temperature-dependent transitions could not be detected for some others (21,32). Recently, it has been postulated that cryoprecipitation results from a cooperative intermolecular association occurring via a nucleation event (32). Temperature-dependent molecular mechanisms of this type have been described previously for the self-assembly of tubulin (13), actin (15), flagellin (2), and for the concerted gelation of deoxyhemoglobin S (1). The concerted polymerization of these proteins consists of a rate-limiting nucleation step followed by a growth process. In such systems, the addition of a small amount of high polymers promotes or accelerates the polymerization of the monomeric molecules (13, 24).
The sites responsible for the monomer-monomer interaction at low temperature are probably located in the variable regions of the heavy (VH) and/or light (VL) chains. Isolated Fc regions of IgG or IgM cryoglobulins did not cryoprecipitate (22, 30), whereas the peptic F(ab')a fragments of IgG and IgA cryoglobulins retain this property (28,30). A papain Fab fragment from one IgG cryoglobulin exhibited a temperaturedependent self-association (29). Furthermore, it has been shown that the variable domain of two X Bence-Jones cryoglobulins were responsible for the thermal behavior of the parent light chain dimer. Modification of the tertiary structure associated with the interchain disulfide bridge at the COOH terminus of the dimer could modulate the cryoprecipitability associated with the variable domains (17).
In the study reported here, we have analyzed tbe temperature-induced self-assembly of an IgGl monoclonal cryoglobulin, with anti-streptolysin 0 antibody activity, as well as its depolymerization in order to determine whether the kinetic pathway is consistent with a nucleated polymerization mechanism. Furthermore, we have attempted to localize the region of the molecule involved in the intermolecular interactions between self-associated monomers.

MATERIALS AND METHODS
Isolation a n d Purification of Cryoglobulins and Normal Immunoglobulins-Monoclonal human cryoglobulins (IgG1K Cat, IgGzK Zie, and 1gG3~ Pav) were isolated from the sera of myeloma patients by several successive cycles of precipitation a t 4 "C and solubilization at 37 "C. The cryoprecipitates were extensively washed after each cycle in 10 II~M Tris-HC1/0.15 M NaCl, pH 7.8, containing 0.2% sodium azide (Buffer TBS). Noncryoprecipitating monoclonal IgG and polyclonal normal human IgG were prepared by ammonium sulfate precipitation followed by ion exchange chromatography on DEAE-cellulose (DE-52, Whatman) equilibrated in 20 mM NaCl, 10 mM Tris-HCl, pH 7.8.
Preparations of Immunoglobulin Subunits-Fab and Fc fragments were prepared by solid phase tryptic cleavage, according to Ellemon et al. (7). F(ab'h fragments were prepared by peptic digestion as described by Nisonoff et al. (23). Monoclonal immunoglobulins at 10 mg/ml were mildly reduced at 37 "C with 10 mM dithioerythritol (Sigma) in Buffer TBS, pH 8.6, for 30 min under nitrogen and alkylated with 24 mM iodoacetamide (Sigma) or with ['4C]iodoacetamide (Amersham Corp.). Heavy and light chains were separated by gel fitration on a column of Sephadex G-100 equilibrated in 1 M acetic acid and were renatured by extensive dialysis against 4 mM Na acetate buffer, pH 5.4 (36). Hinge peptides were obtained by trypticpeptic digestion of '%-labeled H chains and analyzed by high voltage electrophoresis according to Frangione et al. (9).
Covalent a n d Noncovalent Reassembly of IgGlK Cac-The noncovalent reassociation of reduced and alkylated H and L chains was achieved by dialyzing an equimolar mixture of H and L chains in 1 M acetic acid against 4 mM acetate buffer, pH 5.4, at room temperature. The reassembled molecules were concentrated and dialyzed against Buffer TBS at room temperature. The oxidative reassembly of the molecule was achieved in two ways. IgGlK Cac was reduced at 7 mg/ml with 10 mM dithioerythritol a t 37 "C and reoxidized by dialysis against Buffer TBS, pH 8.6, at room temperature. Alternatively, H and L chains were separated from the reduced but not alkylated molecule as previously described, recombined, and then renatured and reoxidized by progressive dialysis against Buffer TBS, pH 8.6, in the presence of a disulfide interchange system (oxidized and reduced glutathione), as described by Petersen and Dorrington (25).
Preparation of Cryoglobulin Polymers-Cold-induced polymerization of IgGlK Cac and 1 g G 3~ Pav was achieved by cooling a solution of resolubilized proteins at 25 mg/ml from 40 "C to 22 "C. Alternatively, nonspecific aggregation of cryoglobulins and normal polyclonal IgG was achieved by heating protein solutions at 10 mg/ml for 10 min at 63 "C. The polymer-containing samples were then fractionated on a Sephacryl S-300 superfine (Pharmacia Fine Chemicals) column equilibrated in Buffer TBS at room temperature. The column was calibrated with standards of known molecular weight (IgM pentamer, IgM monomer, F(ab'),, and albumin). Chemically cross-linked oligomers of IgGlK Cac were prepared by treating a 15 mg/ml solution of cryoglobulin monomer with 10 mM dimethyl suberimidate (Pierce Chemical Co.) for 30 min at room temperature. The reaction was stopped by the addition of ethanolamine.
Electrophoresis a n d Immunological Techniques-The purity of the monoclonal and polyclonal proteins and their fragments was assessed by electrophoresis, immunoelectrophoresis, and immunodiffusion, using monospecific and polyvalent antisera and by sodium dodecyl sulfate-polyacrylamide electrophoresis in 7.5% gels containing 0.1% sodium dodecyl sulfate. When cryoglobulins were to be tested, immunoelectrophoresis and immunodiffusion were carried out at 37 "C. The molecular weight of cross-linked oligomers was determined by SDS-polyacrylamide gel electrophoresis in 4% gels.
Analytical Ultracentrifugation-Sedimentation coefficients of native cryoglobulins, cryoglobulin oligomers, and cryoglobulin fragments were measured in a Beckman model E analytical ultracentrifuge operated at 60,000 rpm with a titanium rotor at 37 "C to prevent cryoprecipitation or at lower temperatures in order to monitor the cold-induced formation of high molecular weight components. Sedimentation was followed using schlieren optics at protein concentrations above 2 mg/ml and with the photoelectric scanning system at 280 nm for concentrations below 2 mg/ml. Sedimentation coefficients were calculated in the usual way (5).
Turbidity Measurements-The kinetics of cold-induced polymerization of monomeric cryoglobulins was followed by monitoring changes in the absorbance at 330 nm resulting from the scattering of incident light due to tbe formation of polymers. Measurements were carried out on a Cary 118 spectrophotometer using full scale settings of 0.02 to 2 absorbance units. The temperature of the experimental cell (pathlength, 0.438 or 1.0 cm) was maintained at 4 "C by using thermostated cell holders connected to a circulating water bath (Lauda K2/R), and the temperature was continuously monitored with a Yellow Springs Instrument Co. model 42SC telethermometer equipped with a small nylon-covered thermistor probe. During preliminary studies, a wavelength scan of several solutions of cryoglobulin at different concentrations, polymerized by incubation at 4 "C for 38 h, indicated that the absorbance was proportional to for IgGbc Cac and X-' .' for I g c 3~ Pav. In another series of experiments, 1 -d diquots of solutions of I g G k Cac at different concentrations were polymerized in the cold, and absorbance at 330 nm was measured at 4 "C. The polymers were centrifuged in the cold at 60,000 x g, and the quantity of cryoprecipitate was calculated from the residual absorbance in the supernatant as previously described. Under these conditions, it was shown that A33onrn is an exponential function of the total protein concentration and is proportional to the quantity of high polymers found at 4 "C for protein concentrations ranging from 2-20 mg/ml.
Kinetics of Polymerization a n d Depolymerization-Temperature jump experiments were performed to determine the rates of polymerization and depolymerization of IgGlK Cac and its fragments. To initiate polymerization, 2.0 ml of cryoglobulin in Buffer TBS was warmed to 37 "C for 1 h, rapidly fdtered (Millipore filter, 0.45 pm), and immediately placed in a prechilled cuvette maintained at 4 "C. Thermal equilibration was reproducibly reached in 10 k 1 min. In order to study the polymerization of cryoglobulin monomers promoted by the addition of oligomers, increasing quantities of a solution containing oligomers were added at 37 "C to the cryoglobulin solution so that the final protein concentration would be held constant at 3.5 mg/ml. The solution was then rapidly placed in the prechilled cuvette and the kinetics recorded. To study the kinetics of depolymerization, samples of polymerized cryoglobulin, maintained at 4 "C, were injected with a prechilled syringe into the experimental cell which had been prewarmed at a predetermined temperature so that the final temperature observed after addition of 1 ml of the cold cryoglobulin solution would be identical with that of the cell holder in which the cell was placed. Using this technique, the time required to obtain thermal equilibration was 10-15 s, irrespective of the amplitude of the temperature jump. The cell compartment was flushed with air throughout the experiment in the presence of anhydrous calcium sulfate in order to prevent condensation.
Initial rates of polymerization and depolymerization were determined graphically.
Electron Microscopy-The native IgGK Cac and its proteolytic fragments were allowed to gel at 4 "C. About 1 ml of each gel was shaken by a sharp blow, and gel fragments of approximately 1 mm' were transferred into cold fixative containing 3% glutaraldehyde. Fixation was allowed to proceed overnight and was followed by extensive washing in three changes of 0.1 M cacodylate buffer, pH 7.4, at 4 "C. The gel fragments were then post-fixed with 1% OS04 in the previous buffer for 1 h at 4 "C. After this second fixation, the samples were washed and dehydrated in solutions of increasing ethanol concentrations and finally embedded in Epon. Ultrathin sections of about 50 nm were cut and stained on the grids with uranyl acetate followed by lead citrate. Sections were made conductive with a carbon layer about 5 nm thick in a high vacuum evaporator and were examined in a Philips EM 200 electron microscope equipped witb an anticontamination device.

oglobulins-The IgGh
Cac used in the present study has a well documented antibody activity against streptolysin 0 (34). The V region subgroups of its y and K chains were determined by sequence analysis and were shown to be VHIII and VJI, respectively. The V region subgroups of the I~G~K Zie were VHIII and VJ, whereas PAV 1gG3~ Pav belongs to the VHIII and V,I variable frameworks. The 14C-labeled hinge peptides, obtained by tryptic-peptic digestion of the H chains of the IgGs were identical with their normal counterparts, as judged by mobility in high voltage electrophoresis performed at two pH values (6.5 and 3.5). The general physical-chemical parameters influencing the cryoprecipitation of IgGlK cryoglobulins have been previously reported (16, 20). The optimal pH for cryoprecipitation for the three cryoglobulins was near 7.4, and the amount of precipitate decreased when the ionic strength increased above physiological conditions. The IgGlK and the I~G~K gave a cryogel when cryoprecipitation was induced by cooling an aggregate-free solution of these proteins at high molar concentrations ( M). The I~G~K cryoglobulin crystallized. Ultrastructural Studies-Electron microscopy of the cryogels obtained with the native IgGlK Cac and its F(ab')2 and Fab fragments revealed a periodic tubular structure.
The native IgG gave well aligned bundles of microtubules with a periodic structure and, in cross-section, the annuli were formed of a double ring with an external diameter of 30 nm and an internal diameter of 11 nm. These rods, following gel disruption, were homogeneous in diameter but varied in length. These tubular structures tended to form tangled bundles of long filaments. In contrast, the proteolytic fragments yielded disordered microtubules which in cross-section were formed of a single annulus composed of 12-14 globular subunits with an external diameter of 19 nm. Although a similar structure was observed for the Fab cryogel, the ring structures appeared to be more fragile and to have an external diameter significantly smaller than that observed with the native cryoglobulin or its F(ab'):! fragment (Fig. 1).
Kinetics of Cold-induced Polymerization-The kinetics of the cold-induced polymerization of the IgGlK cryoglobulin at 4 "C was studied under physiological conditions a t different protein concentrations (Fig. 2 A ) (-) and subsequently depolymerized by rapid rewarming to 37 OC (---). Cycles of polymerization-depolymerization were rcpeated twice.
were used to monitor the cryoprecipitation phenomenon. Turbidimetric measurements have been successfully used to monitor the temperature-dependent polymerization reactions of different proteins, such as tubulin (13) and cryoglobulins (32,33). Below a critical concentration of approximately 2 mg/ml, no cryoprecipitation was observed with IgGlK Cac. Above this critical concentration, a monotonic increase in absorbance was observed after a short concentration-dependent lag phase following thermal equilibration (10 min for the lowest cryoglobulin concentration). The duration of the initial lag phase decreased as the protein concentration increased and correspondingly, the initial rate of the reaction determined graphically after the lag period increased. As shown in Fig. 2B, the polymerization phenomenon a t 4 "C was completely reversible at 37 "C during three successive cycles of temperature change.
At long reaction times, the observed decrease in absorbance results from the sedimentation of high polymers. Therefore, since the final AR:)Onm value could not be precisely determined, the order of the reaction could not be established. Furthermore, for a fixed molar concentration of cryoglobulin, the initial rate varied when different preparations of the same cryoglobulin were compared under identical experimental conditions. Nevertheless, the occurrence of a critical concentration below which polymerization did not occur and the existence of a lag phase are suggestive of a slow thermodynamically unfavorable initiation process for self-nucleating polymerization.
Analytical ultracentrifugation analysis of a sample of native cryoglobulin a t 9 mg/ml warmed to 37 "C for an hour showed the presence of two distinct peaks. The major peak corresponded to the IgG monomer (s20.a = 6.7) and a second peak corresponding to the presence of less than 10% of a species corresponded to the dimer (sSlr. = 9) (Fig. 3A). This observation suggested that dimer formation might be the nucleation event which promoted the growth of large polymers. A nucleation event was further supported by the following experiments. The polymerization of the native IgGk at 16 m g / d was induced by lowering the temperature from 37 "C to 20 "C in less than 5 min. This relatively small drop in temperature was chosen in order to induce a slow polymerization. The turbidity of the solution was continuously monitored at 330 nm, and 0.5-ml aliquots were withdrawn every second hour during the initial polymerization phase and analyzed at 20 "C in the analytical ultracentrifuge. High polymers responsible for the light scattering sedimented to the bottom of the ultracentrifuge cell, and the dimer was the only stable intermediate detected in significants amounts during polymerization (data not shown).

Nucleation-controlled Polymerization
Since the approach to equilibrium of the polymerization reaction seemed to involve a dimer as the stable intermediate acting as a putative promoter, it was necessary to isolate a preparation of aggregate-free monomer capable of polymerizing onto preformed oligomers as well as preparations of oligomers of various sizes which could be assessed for their ability to initiate the growth process. T o this end, a solution of solubilized native cryoglobulin at 15 mg/ml was cooled to room temperature and applied to a calibrated Sephacryl S-300 column. The elution profie (Fig. 4) showed a distinct peak of high polymers, larger than IgM, followed by a major peak of monomer eluting a t V J V , = 0.6, characterized by a marked shoulder (fraction 11) on its ascending limb corresponding to a VJV, smaller than that of 8 S IgM. As shown in Fig. 4, the fractions corresponding to the first peak (fraction I), the shoulder (fraction II), and the descending portion of the monomer peak (fraction 111) were concentrated and analyzed by analytical ultracentrifugation a t 37 "C in Buffer TBS. The high molecular weight fraction consisted of a heterogenous population of polymers as judged by UV scanning a t 2 mg/ml (data not shown). The schlieren pattern of fraction I1 concentrated to 5 mg/ml revealed the presence of symmetrical peaks with sedimentation rates of 6.7 S and 9 S (Fig. 3 0 . The first component was identified as monomer (48%) and the second as dimer (52%) in slow equilibrium with the monomer. The descending portion of the monomer peak isolated by gel fitration was concentrated to 8 mg/ml and was shown to be totally devoid of oligomers (Fig. 3B). Both the polymer and dimer preparations were able to cryoprecipitate in the cold. In contrast, the monomer preparation was unable to precipitate at 4 "C within the time course of the polymerization experiments. When this preparation was concentrated to over 20 mg/ml (i.e. half the serum concentration of the native monoclonal cryoglobulin), a small amount of cryoprecipitate was observed after 1 week at 4 "C.
Rate of Polymerization as a Function of Initiator and Monomer Concentrations-When high molecular weight polymers were added a t 37 "C to a final m a s concentration of 1% to a solution of monomer a t a concentration as low as 2 mg/ml, the low temperature-induced polymerization was restored.
One characteristic of a self-nucleated condensation polymerization is that the initial rate of polymerization is directly proportional to the concentration of the initiator (13, 24). In order to test this prediction and to determine the minimal size of the promotor, increasing quantities of native dimer were added to a fixed concentration of monomer (Fig. 5A), and the temperature was reduced to 4 "C. No change in Axw~,,, was observed in the absence of dimer, whereas a typical condensation polymerization reaction was observed upon addition of increasing concentrations of dimer. Above a critical concentration of dimer, the initial lag period rapidly decreased, and the initial rate of the reaction increased as a linear function of the dimer concentration. Similar findings were observed with 1 g G 3~ Pav (Fig. 5B). The various samples were allowed to stand a t 4 "C for 1 week, and the cryoprecipitates formed were collected by centrifugation; the amount of cryoglobulin contained in the precipitate or remaining in the supernatant was determined spectrophotometrically after dilution in 0.25 M acetic acid. The data clearly indicated that the quantity of cryoprecipitate could only be accounted for if co-precipitation of the monomer had occurred.
An additional prediction of a condensation-polymerization reaction is that the initial rate of elongation is directly proportional to the monomer concentration above a critical concentration (13, 24). In order to verify this property, a fixed quantity of purified dimer was added at 37 "C to increasing concentrations of monomer. The mixture was then rapidly cooled, and the polymerization reaction was monitored a t 330 nm. As shown in Fig. 6, the initial rate of polymerization, determined graphically for two different initiator concentrations (1.7 X 10"' and 1.1 X 10"' M, respectively), increased as a linear function of the molar concentration of monomer. A 1.54-fold increase in the dimer concentration resulted in a 1.58-fold increase in both the slope and the y intercept of the curve obtained for the lowest seed concentration.
Assuming that the polymerization-depolymerization reaction occurs at the end of the linear polymer of cryoglobulin, the initial rate of assembly is the sum of the rates of polymerization and depolymerization and can be described by the following equation

k-[D], and the slope is given by ( l / c ) k + [ D ] .
Therefore, the fiist order rate constant for depolymerization ( k -) and the second order rate The initial rate of assembly kinetics as a function of cryoglobulin monomer concentration. The experiments were carried out at 4 "C at two different concentrations of autologous dimer: 0.51 mg/ml ( O " 0 ) and 0.35 mg/ml (H), respectively. The initial rates of polymerization were calculated from the increase in A330 with time after the temperature was rapidly lowered to 4 "c.
constant for polymerization ( k + ) could be determined graphically and were found to be 1.02 X s-l and 4.72 X k+/kwas, therefore, 4.6 X lo4 M-'. The monomer concentration at which the rate of polymerization is equal to the rate of depolymerization corresponds to the x intercept and was found to be 2.17 X M (i.e. 3.25 mg/ml) and independent of the promotor concentration. This point represents the equilibrium monomer concentration Me at which d[MJ/dt = 0. Thus, Me = k-/k+ = 1/K, where K is the equilibrium association constant (ie. 4.6 X lo4 I C 1 ) . When similar polymerization reactions were carried out at lower ionic strength (ie. 50 mM uersus 150 mM NaCl) which was known to enhance the cryophenomenon, the equilibrium monomer concentration was decreased to about 6.7 X M (1 mg/ml), and the initial rates of polymerization were increased by one order of magnitude (data not shown).
Specificity of the Cold-induced Polymerization-In order to test the specificity of the polymerization of the IgGlK monomer onto autologous native dimers used as promoters, we tested the ability of other initiators to induce the nucleation-controlled reaction at low temperature. Soluble high molecular weight polymers obtained by heat aggregation of either the autologous cryoglobulin or polyclonal IgG were prepared by gel fiitration. Cross-linked IgGlK oligomers were obtained by reacting IgGh monomers at 10 mg/ml with suberimidate. Under optimal conditions, 50% of the monomer was covalently cross-linked in the form of dimers, trimers, or tetramers, as judged by SDS-polyacrylamide gel analysis (data not shown). None of these preparations was able to initiate the temperature-dependent polymerization, even at appropriate initiator concentrations (i.e. over 10%). Furthermore, 10% IgGlK Cac dimers were unable to initiate the polymerization of two other monomers (1gG2~ Zie and 1gG3~ Pav) known to cryoprecipitate in the presence of their autologous dimers.
It was also shown that the polymerization reaction is Fc independent. Both the F(ab')* and Fab fragments were able to form gel through a nucleation-controlled polymerization in the cold albeit at higher concentrations than the parent molecule (Fig. 7). It was possible to demonstrate that the addition of as little as 1% of IgGh Cac dimers induced an instantaneous polymerization of a 3.9 m g / d solution of F(ab')z monomers which had been previously shown to be unable to cryoprecipitate at 4 "C ( Fig. 7).
Depolymerization of Cryoglobulin Tubular Structures-As shown in Fig. 2B, the cold-induced assembly is totally reversible at 37 "C. The depolymerization kinetics of solutions of cryoglobulins containing various quantities of tubular polymers of an unequal length and diameter were studied by temperature jump experiments (Fig. 8A). Following a brief lag phase of 10-15 s, corresponding to the time required for thermal equilibration, the rate of disassembly was about three orders of magnitude faster tha,l the rate of polymerization. If the initial part of the reaction corresponding to the lag phase was ignored, the kinetics approximately followed pseudo-fist order kinetics with a single relaxation time of 27 s. Nevertheless, curve-fitting analysis using a computer program showed that the reaction was more complex since the experimental data could not be accounted for by the sum of three f i s t order processes (data not shown). The initial rate of depolymerization was directly proportional to the mass concentration of polymer determined at 4 "C ( Fig. 8A). In a second series of experiments, it was shown that the initial rate of depolymerization for a fixed concentration of polymers increased with the amplitude of the temperature jump (Fig. 8B).
Molecular Localization of the Site of Monomer-Monomer Interaction-The previously described experiments strongly suggest that the self-nucleating event is indeed the dimerization of the cryoglobulin monomer. This dimerization step is thermodynamically unfavorable. It was not possible to demonstrate any temperature-dependent conformational changes in the intact IgG molecule or its Fab fragment. The temperature-dependent changes observed by circular dichroism for Fab Cac were not significantly different from those observed for the Fab fragment of a noncryoprecipitating monoclonal IgGk (data not shown). By difference spectroscopy, we showed that lowering the temperature of a solution of IgGlK Cac or its Fab fragment induced red-shifted difference spectra. However, it was shown that the changes in molar absorbance at two different fixed wavelengths varied as a linear function of the temperature, as expected for a solvent effect and not a conformational change (data not shown).
It has been clearly shown that the Fab and F(ab')z fragments of the molecule are capable of cryoprecipitating and mlnutes at 28°C of IgG Cac at different concentrations in Buffer TBS were polymerized at 4 "C and subsequently depolymerized at 28 "C. The depolymerization kinetics were obtained by continuous recording of the absorbance at 330 nm following a rapid temperature jump from 4-28 "C. Inset shows the dependence of the initial rate of polymerization on the total cryoglobulin concentration. The initial rate was graphically determined after the lag phase (approximately 15 s) corresponding to thermal equilibration. Cryoglobulin concentration in mg/ml was: a, 2.85; b, 4.3; c, 5.7; d, 7.2; e, 10. B, dependence of the depolymerization kinetics on the amplitude of the temperature jump. A sample of IgG Cac at 6 mg/ml in Buffer TBS was polymerized at 4 "C and subsequently depolymerized by rapidly raising the temperature to: a, 19 "C; b, 23 "C; c, 33 "C; d, 38 "C. Inset, initial rate of depolymerization as a function at the fiial temperature.
forming tubular structures similar to the parent molecule. This implies that the region involved in the polymerization is contained within the Fab fragment. It should be stressed that higher molar concentrations of Fab fragments were required to initiate the formation of a cryogel, whereas F(ab'), fragments had an ability to cryoprecipitate comparable to that of the intact IgG. The fact that only autologous dimers can induce the specific nucleation of both the IgG monomer (Fig.  5A) and the F(ab'), fragment (Fig. 7) strongly suggests that the region involved in monomer-monomer association is restricted to the complementarity-determining segments of the V regions. Mild reduction of the inter-H-L disulfide bridge of the native IgG and its proteolytic fragments completely abolished this specific interaction. When this bridge was reoxidized in the absence of dissociation of the H and L chains, the cryoprecipitability of the molecule was restored (Fig. 2 A ) . In contrast, the recombinant molecules obtained by noncovalent reassociation and reoxidation of isolated H and L chains were unable to polymerize even at 7 mg/ml, and the addition of autologous dimers to the reduced and alkylated molecule could not trigger polymerization.

DISCUSSION
Although the mechanism of cold-induced polymerization of monoclonal cryoglobulins had not been elucidated, results from previous experiments suggested that the precipitation at low temperatures of these proteins might be a nucleationcontrolled event (32,33). The objectives of the present study were 2-fold: 1) to test for a condensation-polymerization mechanism in order to establish a model for the in vitro assembly of monoclonal cryoglobulins, and 2) to localize the region of the molecule involved in the monomer-monomer interaction promoted at low temperatures. The study of two monoclonal cryoglobulins of different subclasses (IgGbc, 1gG3~) in pardel has clearly shown that cold-induced polymerization is indeed mediated by a nucleation event. The existence of a critical concentration below which the IgGlK cryoglobulin does not polymerize and a concentration-dependent lag phase and initial rate are strongly suggestive of such a mechanism. Similar observations have been made for a monoclonal I~G~K cryoglobulin (32,33). It has been shown that a solution of cryoglobulin monomer, freed of oligomers by gel filtration, is unable to polymerize even at high concentrations, but that the addition of trace amounts of soluble polymers (seeds) at 37 "C initiates the polymerization at 4 "C. It was further demonstrated that the smallest species capable of acting as a promoter is the native dimer obtained by cryoprecipitation of the monomer at 4 "C. The kinetic predictions for a nucleationcontrolled polymerization have been confirmed in the case of monoclonal cryoglobulins by the following findings. Under equilibrium conditions favoring polymerization, the only stable intermediate detectable by analytical ultracentrifugation is the dimer. No other discrete oligomeric species smaller than the large tubular structures are found in significant amounts. At a fixed concentration of monomer, the initial rate of polymerization is directly proportional to the concentration of dimer added. At a fixed concentration of dimer, the initial rate of assembly increases in direct proportion to the concentration of cryoglobulin monomer. The dimeric promoter depolymerizes upon dilution when the concentration of monomer is below the critical concentration. Finally, the initial rate of depolymerization following a temperature jump at 28 "C is directly proportional to the polymer concentration.
Taken together, these results suggest that the cold-induced condensation polymerization of monoclonal cryoglobulins can be described as follows.
1) The dimerization of cryoglobulin monomers constitutes a thermodynamically unfavorable nucleation event. The rate of dimerization depends on the monomer concentration and is the limiting factor in the polymerization kinetics. This accounts for the concentration dependence of the lag phase and of the initial rate of the reaction. This finding explains the irreproducibility of the kinetic data obtained with different preparations of the same molecule which usually contain variable amounts of oligomers and why they depend on the techniques which have been used to isolate, solubilize, and centrifuge the cryoglobulin solution. Nevertheless, the detailed mechanism of the dimerization process remains unclear. The formation of dimers has been shown to be necessary for the cold-induced assembly of an IgGl Fab fragment (29) and for that of a cryoprecipitating human h chain (17). Although a thermal transition has been proposed to explain the initial step of the polymerization pathway (17, 20, 31) circular dichroism and difference spectroscopy studies performed on both the native IgG and its Fab fragment at various temperatures failed to detect significant conformational changes. A similar observation has also been reported by other groups (21,32). Conversely, as reported in this paper, a decrease in ionic strength resulted in a marked increase in the rate of polymerization and a significant decrease in the monomer critical concentration. However, a conformational change occurring in a limited region of the molecule which would not affect the spatial orientation of aromatic chromophores could be missed by these methods of detection. It has been established that an increase in ionic strength can reversibly abolish the monomer-monomer interactions at low temperatures (17,21). These results indicate that electrostatic interactions between Fab fragments are an essential feature of the phenomenon, and since these electrostatic interactions are temperature independent, it is reasonable to assume that a redistribution of charged amino acid side chains have been induced at low temperature.
2) This rate-limiting nucleation event initiates the thermodynamically favorable temperature-dependent elongation of the tubular structures, as judged by the electron microscopic studies of the cryoglobulin. These growth processes are nevertheless slow, with an apparent forward rate constant for the elongation step of 4.7 x M" s-'. They probably result from the addition of monomeric subunits, initially onto the dimer and subsequently at the extremities of the growing microtubule. Further interactions between tubular structures lead to the alignment of microtubules into well ordered bundles or to the formation of entangled filaments. These results are analogous to those reported by Wilson and Makinen (40) for the fiber-to-crystal transition of deoxygenated sickle cell hemoglobin. These authors showed that gels consist of randomly oriented groups of fibers in contrast to the well ordered network of fiaments in deoxy Hb S crystals. It is likely that the high viscosity of the gel phase has impeded the crystallization process of the two monoclonal cryoglobulins used in our study. In that respect, it is noteworthy that the crystallization of four human cryoglobulins (IgG1K Dob (35), IgGlK Kol (6), IgGlh Mcg, and I~G~K Zie (8)) has allowed their three-dimensional analysis by x-ray diffraction. Nevertheless, because of these multiple intermicrotubde interactions, any rigorous analysis of the kinetics of polymerization of cryoglobulins becomes extremely complex.
3) The depolymerization step is exceedingly rapid as compared to the polymerization step, and it has not been possible to elucidate the mechanism in detail because of the complexity of the reaction, due to the fact that the initial solution of tubular polymers is not homogeneous. Although the putative depolymerization by release of monomer from the ends of the tubule should obey zero order kinetics, a pseudo-first order rate will be superimposed due to the time-dependent disappearance of tubular structures heterogeneous in length. This explains why the initial rate of depolymerization is apparently a linear function of the initial mass concentration of polymers.
It has been clearly demonstrated by ultrastructural studies and by the use of proteolytic fragments that the cryophenomenon is Fab dependent. One remarkable finding is that the cryogel structure of the F(ab)z fragment is similar to that of the parent molecule, although the external diameter of F(ab'), tubules is significantly smaller than that of IgG rods (19 nm uersus 30 nm). IgG microtubules are formed of two concentric tubes, the smaller one being approximately the size of F(ab')z cross-sections. Therefore, the difference of about 11 nm in external diameter may be accounted for by the lack of the Fc fragment (7 nm), assuming that the IgG molecules are radially arranged within the tube, Fabs forming the internal tube and Fcs the external one. Lateral associations between aligned IgG microtubules might result from Fc-Fc interactions (26), since these well ordered structures are not seen in the cryogels of proteolytic fragments. The dimensions of the annular section of the hollow F(ab')n rods are similar to those previously reported in the literature for other monoclonal cryoglobulins or cryocrystals (3,14,27,37,39). The observation that the Fab fragment can form similar structures, but with a slightly different and more fragile organization, indicates that multivalency is an important factor for stabilization of these supramolecular structures. This Fab-Fab interaction has been clearly demonstrated in the crystal lattice of IgG2 Zie cryoglobulin by electron microscopy (27). These results invalidate the hypothesis that a structural anomaly of the hinge (i.e. deletion (35) or extra S-S bond (33)) forms the molecular basis for the unusual thermal properties of monoclonal cryoglobulin (32,33). Furthermore, the hinge peptides of the three cryoglobulins used in the present study were normal, and the three-dimensional structure of the normal hinge region of Kol IgGl cryoglobulin has recently been established by high resolution x-ray diffraction analysis (18).
In addition, we have shown that the nucleation-controlled polymerization is a phenomenon specifically and exclusively inducible by autologous native promoters. This crucial finding clearly indicates that hypervariable regions are directly involved in the recognition sites between cryoglobulin monomers and that aggregation of the cryoglobulin, chemical modification of lysine groups by bifunctional cross-linking agents, or transient acid denaturation of the polypeptide chains results in an irreversible loss of the thermal properties of the molecule, probably by modifying the limited region(s) involved in the phenomenon. Confirming our previous experiments on a cryoprecipitating human h chain (17), a change in the tertiary structure of the molecule due to the cleavage of the COOH-terminal causes inter H-L disulfide bridge-induced conformational changes at a distance in the variable region of the Fab fragment leading to a loss of its thermal sensitivity. Recently, it has been shown that some monoclonal cryoglobulins may express an autoantibody activity directed against themselves. Along this line, the possible anti-IgG activity of some monoclonal IgG cryoglobulin has been previously reported (11,37), and a cryoprecipitating monoclonal IgM with cold agglutinin activity has been shown to react with its own N-acetylneuraminosyl residues (38). In IgG Kol crystals, the hypervariable segments of one molecule are in close contact with the hinge peptide of a neighboring molecule, as in an antigen-autoantibody complex (18). More recently, the presence of anti-idiotypic antibodies in mixed cryoglobulins has been suggested (10). In the cases of IgGl Cac cryoglobulin, it is most improbable that this molecule, selected for this study because of its known anti-streptolysin 0 activity, is also an auto-anti-idiotype. Therefore, the polymerization of monomers is probably mediated by lateral surface interactions between Fab fragments.