A kinetic coupling between protein unfolding and aggregation controls time‐dependent solubility of the human myeloma antibody light chain

Abstract

Protein aggregation is one of the most critical processes affecting protein solubility in various contexts—from protein therapeutics formulation to protein diseases. In general, time‐dependent changes in protein solubility are complex kinetically driven processes that often involve a triggering event that consists of a protein unfolding/misfolding followed by the assembling of aggregation‐competent protein species. In this study, we have examined the relation between stability and time‐dependent solubility of the recombinant human antibody light chain, hLC, which was found to form renal tubular casts in the multiple myeloma patient. To analyze the aggregation quantitatively, the hLC stability and protein solubility assays were performed in vitro at elevated temperatures. A differential acceleration of the processes at high temperatures enabled us to dissect observed kinetics of irreversible hLC unfolding and aggregation. We find that for hLC these processes have different molecularity and activation energy barriers. While the irreversible unfolding of hLC is a unimolecular step with a substantial activation energy barrier of 260 kJ/mol, the aggregation is rate‐limited by the bimolecular reaction, which is characterized by a lower activation energy barrier of 40 kJ/mol. By the combination of experimental assays at different temperatures, different protein concentrations and kinetic modeling using ordinary differential equations, we were able to extrapolate time‐dependent protein solubility to temperatures where both unfolding and aggregation processes are strongly kinetically coupled. Our study enables mechanism‐based evaluation and interpretation of different physico‐chemical factors contributing to the hLC unfolding and aggregation and their effect on the formation of extracellular protein deposits.

Abbreviations

ANS

1‐aniline‐8‐naphthalene sulfonate

CD

circular dichroism

DSC

differential scanning calorimetry

E_a

activation energy

FLCs

free light chains

hLC

human light chain protein

MM

multiple myeloma

nm

nanometer

PBS

phosphate‐buffered saline

SDS‐PAGE

sodium dodecylsulfate polyacrylamide gel electrophoresis

ThT

Thioflavin T

1. INTRODUCTION

Time‐dependent protein solubility plays an important role in highly diverse research fields such as the storage of biopharmaceuticals, industrial enzyme applications, liquid–liquid phase separation, and protein aggregation‐related diseases. At the moment, thermal stability studies are used for a phenomenological description of thermal profiles and much less focus on quantitative analysis. Quantitative analysis often requires mathematical models and solving of differential equations in the case of nonequilibrium processes. Moreover, protein thermal stability and time‐dependent protein aggregation are often complex processes that can be kinetically coupled under arbitrary conditions, which leads to the difficulty of the interpretation of the observed rates and processes. A suitable combination of experimental conditions, solubility assays and mathematical modeling can provide enough information for quantitative analysis of long‐term solubility of proteins. In this study, human immunoglobulin light‐chain from multiple myeloma patient ¹ was taken as a model protein for the development of experimental assays and quantitative analysis.

Owing to their extraordinary ability to bind broad diversity of chemical groups, immunoglobulins (Igs) are an essential part of humoral immunity. In their mature form, Igs are complex molecules; they are assembled in large heteromeric multichain complexes, which are stabilized by the inter/intramolecular disulfide bridges and several post‐translational modifications—highly conserved glycosylation of heavy chain, for example. A canonical immunoglobulin Y structure is a dimer of a heterodimer consisting of two distinct subunits called light chain and heavy chain. In humans, two types of light chain exist: κ‐chains and λ‐chains and five types of Ig heavy chains: α, δ, ε, γ, and μ. At the cellular level, production and assembly of such large protein complexes are tightly regulated in the plasma B‐cells, which are located in the bone marrow and lymph nodes. Dysregulation of the tightly controlled production of complete immunoglobulins can occur due to complex adverse genetics events that can lead to severe pathological states such as amyloid‐light chain amyloidosis and multiple myeloma (MM). ² In the case of MM, clonally expanded B‐cells produce and secrete large excess of free light chains (FLCs), which are then present at abnormally high concentrations in the blood. Because of high free light chain concentration, light chains can self‐assemble and create extracellular fibrillary deposits that can accumulate and damage vital organs such as the kidney, heart, and liver. While under normal conditions dimeric light chains are cleared in 3–6 hr, larger FLC aggregates circulate much longer time and hence over time, they form insoluble protein deposits in the vital organs leading to disease‐characteristic severe symptoms. The understanding of the molecular mechanism behind the formation of light chain deposits is challenging because of large numbers in vivo factors that potentially contribute to the development of these deposits. Using recombinant light chain production combined with simple in vitro assays and conceptual application of mathematical models can help to assess how perturbation such as mutations, post‐translational modifications, and external ligands affect aggregation in vivo.

2. RESULTS

2.1. The hLC light chain protein as a model protein for extracellular protein deposit formation

In this study, we chose two‐domain λ6a light chain protein, hLC as our model. The protein originates from 60‐years old male multiple myeloma patient. ¹ When heated to 55°C, the hLC protein forms large, macroscopic clusters, which are visible by a naked eye (Figure 1b). The microsized‐aggregates can be stained by the Thioflavin T dye and visualized by confocal fluorescence microscopy (Figure 1b). Importantly, while native hLC does not aggregate over a short period of time, ³ thermal denaturation of the protein leads to the acceleration of the unfolding and to the exposure of the aggregation‐prone parts, which can trigger the aggregation. The propensity of the unfolded LC to aggregate can be assessed by several bioinformatics tools such as TANGO. ⁴ Indeed, the TANGO analysis of the hLC sequence predicts four regions of an increased tendency to aggregation (Figure 1c) with the region of the highest aggregation propensity located in the constant domain. Thus, hLC seems to be a suitable system for a quantitative study of the light chain stability.

FIGURE 1.

(a) 3D structure of light chain dimer 17 (PDB ID: 6MG4) presented by chain A (red ribbon) and chain B (blue ribbon), connected by a disulfide bond between two Cys216 (zoom in the circle), gray spheres represent amino acids with a tendency to aggregation. (b) Aggregates of the light chain formed by heating and stained by Thioflavin T. (c) Dependence of the position of amino acid on the tendency to aggregation (black line) calculating by Tango algorithm and accessibility of amino acids to solvent (gray line). The upper line shows the secondary structure of LC—β strands (green arrows) and α helices (orange ribbon)

2.2. Monitoring irreversible thermal denaturation of hLC using intrinsic and extrinsic probes

In vitro, isolated light chain denatures irreversibly. First, we asked whether our two‐domain light chain unfolds cooperatively and whether the two‐state irreversible model is a suitable description of the thermal denaturation of hLC. To this end, thermal transitions were measured using various spectroscopic/nonspectroscopic probes that can sense unfolding processes at different levels of the hLC structure. First, thermal transitions of the secondary structure were measured using circular dichroism (CD) in the far UV region (Figure 2a,b). CD signal in this so‐called peptide region is highly sensitive to the microenvironment of peptide groups. The first thermal profile of LC shows a transition temperature T _m of ~53.7°C. After cooling to 20°C, the second re‐heating scan shows no visible cooperative transitions indicating that under given conditions, hLC unfolds irreversibly. Under native conditions, hLC is a covalently linked homodimer, and at the same time, at high temperature, a large number of hLC molecules form macroscopic clusters. To assess whether unfolding is coupled to processes with different molecularity, we measured thermal transitions of LC between 5–25 μM. Within the range of investigated concentrations, the transition temperatures of the hLC protein does not depend on protein concentration (Table 1). Above 5 μM concentration, post‐transition baselines became highly distorted, which has precluded quantitative analysis using this method (Supporting Information).

FIGURE 2.

CD measurements: (a) Thermal denaturation curve of hLC (heating rate 1 K/min, PBS, pH 7.4)—red markers represent the first scan; the black line represents fit and black markers represent the second scan after cooling sample. (b) Concentration dependence of thermal transition for 7.5 μM (green), 15 μM (blue), and 25 μM (red) of protein. Fluorescence measurements: (c) Change of Trp fluorescence by thermal denaturation (heating rate 1 K/min, PBS, pH 7.4)—fluorescence signal at 360 nm (red), 330 nm (black), the ratio of F ₃₆₀/F ₃₃₀ multiplied 200× (blue) and fit of F ₃₆₀/F ₃₃₀ (black line). (d) Thermal transition curves for 5 μM (red), 15 μM (green), and 25 μM (blue) of protein. DSC measurements: (e) Thermal transition of the light chain (heating rate 1 K/min, PBS, pH 7.4)—black line represents the first scan, and the red line represents the second scan after cooling sample. (f) Concentration dependence 10.7 μM (black), 21.4 μM (blue), and 32.0 μM (red)

TABLE 1.

The overview of the temperatures of transition and activation energies for unfolding of hLC obtained by various methods

	[Protein] (μM)	Scan rate (K/min)	Model free	Two‐state irreversible model
			T m (K)	E a (kJ/Mol)	T* (K)
Differential scanning calorimetry (DSC)	42.7	2.0	331.4 a	257.0 a	333.5 a
	42.7	1.5	330.6	267.1	333.5
	42.7	1.0	329.7	291.0	333.3
	42.7	0.5	328.5	327.6	333.2
	32.0	1.0	329.7	323.1	333.0
	21.4	1.0	329.9	293.6	333.4
	10.7	1.0	329.8	291.8	333.3
	5.3	1.0	329.7	305.7	333.2
Tryptophan fluorescence	0.5	1.0	326.1 a , b	222 ± 90	341.0 ± 3
	2.5	1.0	327.9	196 ± 90	345.5 ± 3
	5.0	1.0	326.7	238 ± 90	340.4 ± 3
	7.5	1.0	327.8	246 ± 90	338.9 ± 3
	10.0	1.0	327.8	251 ± 90	338.4 ± 3
	15.0	1.0	327.6	260 ± 90	337.8 ± 3
	25.0	1.0	328.5	230 ± 90	340.3 ± 3
ANS fluorescence	7.5	1.0	326.6 ± 0.3	263.3	338.8 ± 1
Thioflavin T fluorescence	7.5	1.0	327.6 ± 0.3	ND	ND
Circular dichroism (CD)	5	1.0	327 ± 1.2	260 ± 60	342 ± 2.5

Note: Data obtained from DSC was analyzed by RateCon (software for a two‐state model) and calculated parameters were used for fitting of CD and fluorescent data by trapezoid integration.

^a SDs for T _m ± 0.2 K, E _a ± 20–30 kJ/mol, T* ± 0.3 K.

^b Temperatures of transition (T _m) from measurements tryptophan fluorescence (fluorescence intensities ratio) were evaluated by a correction algorithm TCORE (https://degbioresearch‐tcore.sk/). TCORE provides correction of the mathematical issues due to the analysis of the fluorescence intensity ratio. ⁵ ND—not determined. The analysis of tryptophan and CD thermal denaturation experiments displays large SDs due to irregular distortion of post‐transition baselines and, hence, they must be taken with caution.

Next, the thermal transition of the tertiary structure was examined using tryptophan fluorescence after selective excitation. hLC contains three tryptophans unevenly distributed along the protein sequence. Hence, Trp fluorescence can be used to monitor changes in the close environment of these residues. Thermal profiles of hLC were measured after excitation at 290 nm. hLC tryptophan's emission was recorded at two wavelengths: 330 and 360 nm. Individual thermal profiles of individual emissions show a highly nonlinear behavior (Figure 2c,d). However, the ratio of fluorescence intensities at these wavelengths shows a typical sigmoidal‐like thermal transition. One should stress out, that the thermal profiles based on fluorescence intensity ratio should be analyzed carefully. ⁵ Thermal transitions of hLC measured at 5–25 μM concentrations show no significant/systematic changes in transition temperatures (Table 1).

In the case of thermal unfolding of tertiary structure, tryptophan fluorescence measure specifically microenvironment of tryptophans and hence may or may not sense the unfolding of the overall hLC tertiary structure. Differential scanning microcalorimetry (DSC) was used to measure heat endotherm generated during the hLC unfolding. DSC thermogram at 1 K/min shows a single cooperative, slightly asymmetric endothermic peak (Figure 2e). After the cooling of the sample, the re‐heating of the hLC‐sample shows no visible endotherm indicating complete irreversibility of the thermal unfolding. Again, we measured thermal transitions of hLC in the range of concentrations 5.3–42.7 μM. Within this concentration range, the melting temperatures used do not change significantly (Table 1), while the overall shape of the transition change only slightly.

All the methods mentioned above are based on some intrinsic spectroscopic/nonspectroscopic probes; hence, we asked whether extrinsic probes can reveal some additional silent unfolding events. Namely, some extrinsic dyes bind to partially/fully unfolded species such as molten‐globule states and, hence, these dyes enable detection of otherwise invisible intermediates. ⁶ As the first extrinsic probe, we used 1‐aniline‐8‐naphthalene sulfonate (ANS). In general, this dye binds to exposed hydrophobic regions and is used frequently to detect molten‐globule states of proteins. ⁷ , ⁸ For example, the Fab fragment unfolding step during IgG unfolding can be selectively detected using ANS. ⁹ For native hLC, below the transition temperature, the ANS fluorescence is relatively low, but increases during heating of the protein in a sigmoidal fashion. The thermal transition monitored by the ANS fluorescence shows a single cooperative thermal transition with T _m of ~53.5°C (Figure 3a). After cooling of the sample, the ANS fluorescence remains high. The re‐heating of the thermally denatured hLC in the presence of ANS shows a flat curve with a tiny sigmoidal‐like shape. We also recorded the thermal transition of hLC in the presence of Thioflavin T (ThT). ThT dye binds to β‐sheet‐rich proteins and is often used for staining/detecting amyloid fibrils. ¹⁰ , ¹¹ The thermal transition of hLC in the presence of the excess of ThT was measured by ThT fluorescence (Figure 3b) and showed a single thermal unfolding with a transition temperature of ~54.5°C. After cooling the sample, the second re‐heating cycle shows no thermal transition.

FIGURE 3.

(a) Change of fluorescence signal of light chain labeling by ANS probe with the change of temperature (heating rate 1 K/min, PBS, pH 7.4, ANS is in 100‐fold excess to the protein)—red markers represent the first scan, the black line represents the fit of the first scan and black markers represent the second scan after cooling sample. (b) The thermal transition of LC monitored by fluorescence of Thioflavin T (heating rate 1 K/min, PBS, pH 7.4, ANS is in 100‐fold excess to protein)—black line represents the first scan, and the red line represents the second scan after cooling sample. (c) Microscopy analysis of LC aggregates formed by heating at 60°C for 30 min and staining by ThT (overnight)—white line represents scale bar 50 μm (upper figures); 3D display of aggregate—color scale represents z line of aggregate red‐0 μm, blue‐67 μm (lower figure)

2.3. Fluorescence imaging of light chain aggregates after ThT staining

Aggregation‐sensitive extrinsic ThT fluorescent dye can be used to visualize the higher‐order structures of hLC aggregates. First, hLC was incubated for 30 min at 60°C, then cooled, mixed with 100‐fold ThT, and incubate overnight at room temperature.

The samples were then measured by scanning confocal fluorescence microscopy using excitation at 488 nm (Figure 3c). Several clusters of aggregated hLC can be identified [green clusters, Figure 3c]. A set of 2D images was collected. In these images, several irregular structures of the aggregates are visible, including fine structures within. In the next step, we reconstruct a 3D image of hLC aggregate particles by scanning the sample at different z‐depth (color‐coded in 3D image). After the reconstruction of the 3D image, we found that observed hLC aggregates are relatively large, with many pores and cavities (Figure 3c). We asked whether the ThT dye alone can contribute to the thermal denaturation process and hence may influence the structure of hLC aggregates. Thermal denaturation experiments at super‐stoichiometric concentrations 750 M ThT showed that even at such high ThT concentration, the transition temperature is not significantly affected by the ThT dye. Besides, the microscopy results obtained upon ThT staining did not depend on the order when the dye was added (before/after hLC aggregates were formed). In summary, the ThT dye does not induce/or change aggregation structures of the hLC protein.

2.4. Colloidal stability measurements of light chain at high temperatures

Confocal microscopy of hLC aggregates showed a formation of large porous aggregates. How are these structures stabilized? Light chains contain several reactive cysteine residues, and their structures are stabilized by disulfide bridges. Additionally, hLC light chain homodimers are covalently linked by terminal cysteine residues. We speculated that after heating, higher‐order structures and aggregates can be stabilized and cross‐linked by the intermolecular formation of disulfide bridges. We used SDS‐PAGE in reducing and nonreducing conditions to distinguish between different quaternary structure forms of hLC. The protein was incubated at 60°C, and at variable times, a protein aliquot was taken from the tube and cooled immediately. Using centrifugation, large insoluble aggregates (pellets) were separated from the soluble protein in the supernatant. The SDS‐PAGE analysis of the supernatant and the pellet fraction was performed under oxidizing and reducing conditions (Figure 4b). Under reducing conditions, both supernatant and pellet show a major single band corresponding to the expected molecular weight of light chain proteins (Mw of 23.4 kDa). As expected, the amount of soluble protein decreases over time of incubation at 60°C.

FIGURE 4.

(a) Graphical illustration of steps for colloidal stability analysis. (b) Analysis of soluble (supernatant) and insoluble (pellet) form of LC by SDS PAGE in different times of heating—5, 25, and 60 min at 60°C in reducing (+ β‐mercaptoethanol) and nonreducing (− β‐mercaptoethanol) conditions. (c) Temperature dependence of colloidal stability of light chain—the amount of soluble protein form after heating at 60 (red), 70 (black), and 80°C (blue). (d) Dependence of colloidal stability of light chain to the initial concentration of protein—the amount of soluble protein form for initial 23.5 (red), 34.2 (black), and 64.1 μM (blue) of protein after heating at 60°C

Interestingly, under oxidizing conditions, which retain disulfide bridges, dimeric and higher‐order molecular weight hLC proteins are also visible in the supernatant fraction. The native protein is a mixture of monomer and dimer forms, which has been published before. ¹² Prolonged exposure at high temperatures, higher‐order structure are visible (Figure 4b). In the pellet fraction, we were not able to solubilize hLC heat‐aggregates using SDS detergent only (empty lanes, Figure 4b). While in the previous analysis, we focused on intermolecular disulfide bridges, we next applied a sedimentation assays to monitor the amount of soluble protein over time. The amount of soluble protein form was evaluated using centrifugation assay, and protein concentration were determined by UV–VIS spectroscopy. Examples of how the amount of soluble protein change at 60, 70, 80°C is shown in Figure 4c. Within the resolution of this endpoint‐based method, the amount of soluble protein decreased in a monoexponential fashion and show time constants of 606 ± 60 s at 60°C, 310 ± 20 s at 70°C and 270 ± 40 s at 80°C. As expected, the amount of soluble protein vanishes faster at higher temperatures. Because aggregation is per definition a multimolecular reaction, one could expect that such kinetics will depend on protein concentration. At high hLC concentrations, the amount of the soluble protein decreases faster. Examples at 60°C are shown in Figure 4d. These measurements show that at 23.5, 34.2, and 64.1 μM of hLC, a monoexponential decrease of soluble protein is described by following time constants of 570 ± 96 s, 300 ± 42 s, and 198 ± 20 s. Because of significant concentration dependence of the observed time constants, we concluded that the hLC soluble‐insoluble transformation process is a multimolecular process (for quantitative analysis, see later).

2.5. Temperature‐dependent unfolding and aggregation kinetics

Thermal denaturation of hLC are scan‐rate dependent and irreversible. Scan rate dependence indicates that the hLC denaturation process is under kinetic control. In the following step, we analyzed the data assuming a two‐state irreversible model between the native (N) and unfolded state (U):

$$N\stackrel{k_{\text{unf}}}{\to }U$$ (1)

where k _unf is a first‐order irreversible unfolding rate constant, which describes the irreversible transformation of the native hLC to the unfolded state. Temperature dependency of the unfolding rate constant follows the Arrhenius equation. Using well‐established numerical analysis, ¹³ , ¹⁴ our DSC data can be fitted very well and show in activation energy of ~260 kJ/mol and T* (the temperature at which microscopic rate constant, k, is equal 1 min⁻¹, see Equation 7) of 60°C. Solid lines in Figure 2e are the best‐fit for the DSC data. Activation energies, E _a, and T* are listed in Table 1. Importantly, different scan rates yielded similar E _a and T* (Table 1); the values for activation energies were between 250 and 300 kJ/mol. The DSC analysis supports the two‐state irreversible model. A similar analysis was performed on thermal denaturation data using tryptophan fluorescence, ANS, and CD spectroscopic signals. Values for E _a and T* are listed in Table 1. We found that the analysis of spectroscopic signals results in similar values of E _a and T*, however, robustness of CD and fluorescence assays is lower, and data showed larger variances. In addition, in the case of the fluorescence, the spectroscopic ratio of two emission wavelengths is used, which is known as a not absolutely reliable approach to determine thermodynamic/kinetic parameters. Therefore, we consider DSC parameters as more robust and they were used for the analysis. Based on the obtained parameters from the DSC experiments, Arrhenius plot ln k _unf vs. 1/T was constructed and is shown in Figure 5a (N → U). From this plot, the calculated activation energy for N → U process is 260 ± 20 kJ/mol. Apparent rate constant obtained from the solubility assay, which monitors the rate of the aggregation (nU → Un), shows a smaller temperature dependence; the activation energy for the aggregation of the unfolded hLC is 40 ± 20 kJ/mol (Figure 5a).

FIGURE 5.

(a) Arrhenius plot for the temperature dependent aggregation and irreversible unfolding. (b) Protein concentration dependence of the aggregation reaction and conformational stability. N state represents the native form of protein, U state is an unfolded form, and Un represents insoluble fibrils or aggregates. Data for the transition of N to U was obtained from DSC measurements. The transition of U to fibrils/aggregates was detected by the analysis of the soluble fraction of hLC

In summary, irreversible hLC unfolding is strongly temperature‐dependent while protein aggregation has significantly lower temperature dependence.

2.6. Concentration‐dependent unfolding and aggregation kinetics of the hLC protein

In principle, the concentration dependence of the reaction rate bears information on the molecularity in the process. One of the possible ways to obtain information on the molecularity of the process is to measure reaction half‐lives. Reaction half‐times and order‐of the reaction can be obtained using the following equation ¹⁵ :

$$\log {\mathrm{\tau }}_{1/2}=\text{const}.-\left(n-1\right)\log {\left[\text{Protein}\right]}_{t=0s}$$ (2)

where n is the reaction order, const. is a reaction‐specific constant. First, we analyzed our DSC data at different hLC concentrations using a two‐state irreversible model. Even though, hLC is a mixture of monomers and dimers; the half‐times obtained from DSC at different concentrations are independent of protein concentration. The slope of ln τ _1/2 versus ln [hLC] is −0.0003, which corresponds to first‐order kinetics (Figure 5b). Hence, during the hLC thermal denaturation, monomer/dimer equilibrium does not play a significant role. In opposite, the aggregation reaction shows strong concentration dependence of τ _1/2. The slope of ln τ _1/2 versus ln [hLC] is −0.9 ± 0.17, which corresponds to apparent second‐order kinetics. One should note that the τ _1/2 is observed half‐time and does not specify the nature of the kinetic specie associated with the rate‐limiting step. In summary, the unfolding rate constant does not depend on initial protein concentration, and the aggregation rate constant depends strongly and support the notion that the association of two critical molecular species is needed.

2.7. Quantitative modeling of the overall colloidal stability of hLC light chain at 37°C

In our previous analysis, unfolding kinetics and aggregation kinetics of hLC were analyzed separately. This is possible in the time regime when both processes are well separated in time, which is the case at 60°C and above. Now, based on the individual analysis of these two different processes, we combined both analysis and suggest following minimal mechanism, where the unfolding and aggregation processes are modeled at the same time and under conditions when they can affect each other, for example, at ambient temperatures. At high temperature, hLC unfolding is always faster than aggregation kinetics, but as temperature goes down, unfolding slows down much dramatically compared to the hLC aggregation, which has smaller temperature dependence (Figure 5b). Here a quantitative analysis is needed. From our experimental data at high temperatures, we assume the following reactions:

$$N\stackrel{k_{\text{unf}}}{\to }U$$ (3)

$$U\stackrel{\text{very fast}}{\to }X$$ (4)

$$2X\stackrel{k_{\text{agg}}}{\to }{X}_2$$ (5)

and,

$$n{X}_2\stackrel{\text{very fast}}{\to }{X}_{2n}$$ (6)

where X is a critical aggregation‐competent molecular specie that needs to associate in the rate‐limiting step to form the X ₂, and X _n is a full aggregate. The identity of the X specie is unknown, for simplicity, and without any significant loss of generality, we can assume X as U. Assuming a very fast unimolecular reaction U to X, the reaction can be neglected without any significant effect.

Similarly, very fast kinetics of X ₂ transformation to large aggregates X _n can be neglected, and X _n is formed by the rate‐determining step k _agg. Species N, U, and X belong to the soluble molecular species, and X ₂ and X _2n are insoluble hLC molecules.

In these microscopic steps, the N‐to‐U reaction is fully described by the DSC thermal denaturation experiment, while 2X and X ₂ are monitored by the solubility/aggregation assay (Figure 4c,d). The set of the ordinary differential equations (ODEs) describing the reactions above was numerically integrated. In this mechanism, set of the initial conditions and basically two microscopic rate constants describe the system completely. Unfolding microscopic rate constant was obtained independently from the DSC thermal denaturation analysis. In the case of k _agg, the value was obtained from the nonlinear regression analysis of the solved ODEs, where k _agg was set as a free parameter, and the unfolding rate constant was obtained from the DSC. From the temperature dependence, we were able to estimate k _agg at 37°C. At this temperature, we were able to simulate how the amount of the soluble hLC molecules change over time, which we termed as “observed aggregation” to distinguish from the microscopic aggregation process (Figure 6a). The observed half‐time decreases exponentially as total protein concentration increases (Figure 6b). Based on our analysis, we can roughly estimate that at 1 nM hLC, nearly 10 years are needed for aggregation. At 1 μM hLC, >4 weeks are needed to transform half of the hLC into an insoluble form.

FIGURE 6.

(a) Kinetic simulation time‐dependent solubility of hLC at 37°C and at various hLC concentrations (see b). (b) half‐time of protein solubility as a function of protein concentration

3. DISCUSSION

In vivo IgG, light chain aggregation can lead to life‐threatening pathological states. Direct observation of the aggregation process in vivo is, however, highly challenging—experimental and ethical as well. Here, we have developed a simple model that connects conformational unfolding and limiting steps in protein aggregation, that is, a transformation of the soluble protein into insoluble, macroscopic aggregates. We could show that these two processes can be dissected within a specific range of conditions (high temperatures) when the unfolding and aggregation occur at different time scales and hence are kinetically uncoupled. The choice of higher temperatures for the dissection of the kinetics is a natural one; temperature‐dependent kinetics can be easily measured and analyzed using Arrhenius equation, for example. Extrapolating the rates from higher to lower temperature can oversimplified the real situation, for example, when several other kinetic channels exist that operates at lower temperatures but are not frequent at high temperatures because of different temperature coefficient or they simply vanish for other reasons. Example for such case can be the presence of a fast refolding reaction, U → N. In the case that refolding rate is faster than aggregation rate, our time‐dependent solubility calculations will be invalid. A fast refolding of U results in a decrease of the effective concentration of U and hence hLC will be soluble over longer time scales.

From obtained temperature‐dependent rate constants and by the solving of corresponding differential equations, we can reconstruct the expected time‐course of aggregation at lower temperatures and include the kinetic barrier for protein unfolding as well. In addition to the temperature dependence of the above‐mentioned rates, observed rates for unfolding and aggregation have different protein concentration dependence. The nonequilibrium unfolding of hLC is independent of protein concentration, which might be unexpected as the hLC exists as a mixture of monomers and dimers. In the case of hLC, homodimers are stabilized by the C‐terminal covalent disulfide bridge, and hence dissociation of the monomers does not occur. Our gel filtration results and SDS PAGE results indicate that hLC exists as solely as a homodimer; however, the disulfide bridge is not always formed. From thermal DSC profiles at different concentrations, it is clear that noncovalent homodimers eventually do not contribute significantly; monomer–monomer dissociation possibly occurs after the rate‐limiting step and, therefore, does not affect the thermal denaturation profile.

Aggregation kinetics, on the other hand, is highly dependent on protein concentration, which indicates that bimolecular association is a rate‐limiting in the formation of hLC protein aggregates and after this event, aggregation proceeds by a rapid sequence of reactions. In addition to simulations of observed aggregation kinetics using the results from our experiments, it is also feasible to evaluate the role of activation energies of the individual processes on overall aggregation half‐time (Figure 7). In the simulations, T* was kept constant. Under ambient temperatures, both processes are coupled, as clear from the simulations where the activation energy barrier for conformational unfolding was varied. Increasing the activation energy for the protein unfolding leads to an increase of the observed aggregation half‐time even though the microscopic rate constant for the aggregation was set as a constant. Besides, as the activation barrier increases, the observed aggregation is concentration‐independent because, in this regime, the unfolding of the protein starts to be rate‐limiting. On the other hand, when the unfolding rate is set constant, and the activation energy barrier for aggregation is varied. Obviously, increasing activation energy barrier leads to higher half‐times for observed aggregation in a dose‐dependent manner. At very high protein concentration, the height of the barrier does not play a significant role. As the activation energy barrier decreases, concentration dependence disappears which again indicates that conformational unfolding is becoming rate limiting for the observed aggregation process.

FIGURE 7.

(a) A simplified hLC reaction coordinate and activation energies for individual steps obtained by DSC measurements and colloidal stability analysis. Transformation of the native light chain (N) to unfolding (U) state is rate‐determining unimolecular step and requires activation energy ~260 kJ/mol. The formation of aggregates (Un) is a bimolecular step with activation energy ~40 kJ/mol. (b) The half‐time of protein solubility from the simulations at various activation energies for the unfolding (E _a,unf) and at the constant activation energy of the aggregation (E _a,agg ~ 40 kJ/mol) at 37°C. (c) The half‐time of protein solubility from the simulations at the activation energy of unfolding (E _a,unf ~ 260 kJ/mol) and various activation energies for the aggregation process (E _a,agg) at 37°C

The dissection of the kinetics between these two independent events enabled us a quantitative prediction of time‐dependent light solubility. From our analysis, we assume that time‐dependent solubility of the hLC protein depends on two processes described by the two microscopic rate constants: k _unf and k _agg. To secure long‐term solubility of light chains, several scenarios possible: for a long‐term soluble light chain, both rate constants have to be very slow at the given conditions; this could be achieved, for example, by a large activation energy barrier. The nature of the energy barriers for both processes is different, while the unfolding of the protein requires disruption of the interactions in the native state, aggregation kinetics of the unfolded state can be facilitated by the presence of aggregation‐prone regions and hence is sequence context‐dependent. In the case of hLC, the low activation energy of the aggregation process (~40 kJ/mol) indicates that part of the hLC sequence can interact with other chains easily. By optimizing hLC sequence, the aggregation tendency of unfolded proteins can be effectively inhibited by increasing activation barriers. One of the benefits of sequence optimization is the existence of several software tools, which can predict aggregation‐prone regions (e.g., TANGO ⁴ ). Such bioinformatics analysis can be easily included and tested for their contribution to the aggregation rate. hLC has ~4 aggregation‐prone regions. Interestingly, the region with the highest aggregation tendency is located in the constant domain. Previously, the hLC variable domain was associated with increased aggregation tendency, and then later, both domains of light chains can contribute to the aggregation, which underpinned the role of the constant domain for light chain solubility. ² , ¹⁶ Above 0.1 μM hLC concentration, aggregation kinetics is apparently concentration independent with τ _1/2 ~ 100–300 days. Below 0.1 μM hLC, aggregation starts to be highly concentration‐dependent, and hLC is soluble over years. Concentration dependence indicates that rapid clearance of the free light chain from the blood and maintain hLC concentrations below threshold values can effectively contribute to keeping soluble hLC.

The transition from the soluble hLC into insoluble form can be projected as two consecutive steps controlled by two energy barriers (Figure 7). The first activation energy barrier is the relatively high ~260–300 kJ/mol. After crossing this barrier, the reaction and limiting step is a bimolecular association of critical molecular species, which is, however, controlled only by a relatively small barrier of ~40 kJ/mol. A low activation energy barrier (enthalpy component) and slow aggregation kinetics, indicate that large entropic factors significantly decelerate the observed kinetics. Such unfavorable entropy might be a reason for the necessity to form structured aggregates and/or due to the necessity of having a certain orientation. How differences in enthalpy barrier heights affect hLC soluble form? A theoretical increase in activation energy barriers for both processes shows large differences for the overall reaction (Figure 7). Increasing the activation energy for hLC conformational unfolding increases the lifetime of the soluble form in a gradual, concentration‐independent fashion (Figure 7b). On the other hand, larger enthalpy barriers for rate‐limiting bimolecular association, stabilizes soluble form only at high hLC concentrations, when it becomes rate‐limiting (Figure 7c). It is important to emphasize Figure 7 is a highly simplified view of the events focusing on the major events, it possible that additional microstates are populated during the reactions, but we could not detect them because of our choice of experimental methods and because they are not rate‐limiting steps.

4. CONCLUSION

We conducted a quantitative analysis of the thermal stability and aggregation of human immunoglobulin light chain. After obtaining experimental data, their analysis and extrapolation of the obtained kinetic values, a simple mathematical modeling of the coupled reactions was used for the prediction of the time‐dependent protein solubility at lower temperatures. One of major assumptions is that aggregation‐competent states populate solely from the irreversible kinetics obtained from thermal unfolding. A potential benefit of such approach is that it can be used for other aggregation‐prone proteins as well or can be used for investigating various conditions and effect of mutations.

5. MATERIALS AND METHODS

5.1. Protein expression and purification

The gene sequence of full‐length human λ‐6A light chain hLC () was chosen from a study of stabilization of amyloidogenic immunoglobulin light chain by small molecules, ¹⁷ and the gene was synthesized by GenScript.

The synthetized sequence was cloned into pET‐11a. The plasmid was transformed into E. coli BL21 (DE3). E. coli BL21 (DE3) were grown in LB medium containing 100 μg/ml ampicillin and 0.5% glucose to OD₆₀₀ 0.6. Expression of LC IgG was induced by isopropyl β–d‐1‐thiogalactopyranoside (IPTG) in a final concentration of 1 mM. After incubation of induced culture at 37°C for 5 hr, LC was found as an inclusion body protein. E. coli cells from 1 L of culture were collected by centrifugation (7,500g, 10 min, 4°C) and resuspended in 10 ml of 50 mM TRIS–HCl pH 8.0, containing 100 mM NaCl, 1 mM phenylmethylsulfonylfluoride, 1 mM ethylenediaminetetraacetic acid, 2.4 mg lysozyme, and 60 μg DNase I. Lysate was sonicated at Branson Sonifier 450 (output control 5, duty cycle 60, 30 pulses, 3 repeats) and centrifugated at 20,000g for 30 min at 4°C. The pellet with inclusion bodies was washed with distilled water. Next steps—solubilization and refolding were performed according to Rognoni et al. ¹⁸ LCs were precipitated with (NH₄)₂SO₄ in 70% saturation; the precipitate was collected by centrifugation and resuspended in 50 mM TRIS–HCl pH 8.0 with 20% glycerol. The protein solution was twice dialyzed overnight against 50 mM TRIS–HCl pH 8.0. The solution was filtered, and protein was purified by anion exchange chromatography on a HiTrap Q HP column (GE Healthcare) equilibrated in 50 mM TRIS–HCl pH 8.0, on a Shimadzu HPLC system, and eluted by 0–0.5 NaCl linear gradient in 20–75 min, the flow rate was 2.5 ml/min. The homogeneity of the protein preparation was analyzed by 14% SDS‐PAGE. Fractions containing LC were pooled, concentrated, and purified by size exclusion chromatography on Superdex 75 Increase 10/300 GL (GE Healthcare) in TRIS–HCl pH 8.0 with flow rate 0.7 ml/min. The concentration of fractions was measured by absorbance at 280 nm by Thermo Scientific NanoDrop One Microvolume UV–Vis Spectrophotometer, using the extinction coefficient calculated by the ProtParam website. ¹⁹ Fractions with recombinant LCs were pooled, concentrated, aliquoted, and store at −80°C. Protein purity was detected by cation exchange chromatography on bioZen™ 6 μm WCX, LC Column 150 × 4.6 mm equilibrated in 20 mM MOPS pH 6.0, eluting with 15–65% of 300 mM NaCl gradient in 0–30 min, the flow rate was 1 ml/min. The homogeneity and purity of hLC was detected by SDS‐PAGE in reducing and nonreducing conditions and by MALDI/TOF experiments (see Supporting Information).

5.2. Protein sequence

In the following, cysteine that tends to create disulfide bond with cysteine of another hLC is shown in bold:

• MNFMLNQPHSVSESPGKTVTISCTRSSGNIDSNYVQWYQQRPGSAPITVIYEDNQRPSGVPDRFAGSIDRSSNSASLTISGLKTEDEADYYCQSYDARNVVFGGGTRLTVLGQPKAAPSVTLFPPSSEELQANKATLVCLISDFYPGAVTVAWKADSSPVKAGVETTTPSKQSNNKYAASSYLSLTPEQWKSHKSYSCQVTHEGSTVEKTVAPTECS.

5.3. Conformational stability

For circular dichroism measurements was used Jasco J‐810 spectropolarimeter (Tokyo, Japan) equipped with a Peltier type thermostated single cell holder (PTC‐432S). All CD measurements were performed in 1 mm pathlength cuvette. Spectra were measured in range 250–190 nm at a scanning speed of 100 nm/min with a bandwidth of 2 nm, data pitch 1 nm, D.I.T. 2 s, and accumulation of 20 scans (Supporting information). CD spectra measurements were performed at 20 and 80°C in 2 mM potassium phosphate pH 7.4. The protein concentration was 0.2 mg/ml. Thermal denaturation measurements of LC IgG by CD were performed in temperature range 20–80°C, with a heating rate of 1 K/min. Ellipticity was measured at wavelength 210 nm, bandwidth 4 nm, and D.I.T 16 s. In the experiment was used PBS pH 7.4 and protein at various concentrations (7.5; 15; 25 μM). The fluorescence measurements were performed with a Varian Cary Eclipse fluorescence spectrophotometer (Varian Australia Pty Ltd.) equipped with a Peltier multicell holder. Thermal transitions of LC IgG were monitored by tryptophan fluorescence at 330 and 360 nm with an excitation wavelength of 290 nm. The temperature was changed from 25°C to 80°C, with a heating rate of 1 K/min. The measurements were performed in PBS pH 7.4, at various protein concentrations (0.5; 1; 2.5; 5; 7.5; 10; 15; 25 μM). ANS measurements were performed by the fluorescence of the 8‐anilinonaphathalene‐1‐sulfonate (ANS) probe, as was described previously. ⁹ Protein concentration was 7.5 μM, ANS concentration 750 μM, and PBS buffer pH 7.4, was used. Conformational stability of LC IgG was monitored by the fluorescence of Thioflavin T (ThT) at 490 and 505 nm and with excitation wavelength 450 nm. The temperature range 25–80°C was changed with a rate of 1 K/min. The measurement was performed with LC concentration 7.5 μM, ThT concentration 750 μM in PBS buffer pH 7.4. Differential scanning calorimetry (DSC) experiments were performed with a VP‐Capillary DSC system (Microcal Inc., acquired by Malvern Instruments Ltd.). Light chain concentrations were 42.7; 32.0; 21.4; 10.7; 5.3 μM in PBS buffer pH 7.4, which was used as a reference. The samples were heated from 25 to 90°C at various scan rates 0.5; 1.0; 1.5, and 2.0 K/min with corresponding filtering period (time period during in which the signal is collected), that is, 25; 10; 8 and 5 s. Thermograms were corrected by subtraction of the sigmoidal curve connecting the signal of excess heat capacity of the native and denatured states and normalized to the molar concentration of the protein.

5.4. Colloidal stability

The colloidal stability of the LC protein was determined by the heating of protein in a thermocycler. The aliquots of protein were incubated over a temperature range from 55 to 95°C; at regular points of time, denaturation was stopped by putting the aliquot of sample on the ice. The samples were centrifuged at 20,000g for 15 min, and the LC concentration in soluble form was measured by UV–Vis nanospectrophotometer. Temperature dependence of the soluble protein was measured at protein concentration 0.55 mg/ml in PBS pH 7.4 at 55; 60; 65; 70; 75; 80; 85; 90 and 95°C. Concentration dependence of the soluble protein was determined at 60°C for protein concentration 64.1; 42.7; 34.2; 23.5; 19.2; 15.0; 10.7 and 6.4 μM in PBS buffer pH 7.4. Samples with concentration of 15.0 μM were heating at 60°C for 0; 5; 25 and 60 min, centrifugated, and soluble (supernatant) and insoluble (pellet) form were analyzed by SDS‐PAGE in reducing and nonreducing conditions (β‐mercaptoethanol). Interestingly, time‐dependent colloidal stability curves show a certain soluble concentration threshold, which we assume might be a result of the damaged aggregated protein because of high centrifugation forces, which are needed to separate soluble/insoluble form. Another possible explanation is that several soluble oligomers are still presented in the solution and the process of aggregation is not completely irreversible.

5.5. Data analysis

Thermal transition obtained by DSC and spectral (fluorescence and CD) methods were analyzed from equation for kinetic two‐state irreversible model. Rate constants at any given temperature can be obtained from the Arrhenius equation:

$$k=\exp \left[\frac{E_a}{R}\left(\frac{1}{T^{*}}-\frac{1}{T}\right)\right]$$ (7)

where R is the gas constant (R = 8.314 J/mol/K), T* is the temperature at which a microscopic rate constant, k, is equal 1 min⁻¹) and E _a is activation energy.

5.6. Fluorescence imaging

Light chain (PBS buffer pH 7.4) was heated at 60°C for 30 min and formed microaggregates were overnight stained by ThT (in 100‐fold excess) at laboratory temperature. The aggregate solution (10 μl) was pipetted on a glass slide embedded MatTek Petri dish (MAtTek Life Science) and imaged by confocal fluorescence microscope (ZEISS LSM 700 microscopic system, ZEISS, Germany) equipped with 40× (LD C‐APOCHROMAT, 1.1 W UV–Vis‐IR) water immersion objective (ZEISS, Germany), and AxioCam HRm camera (ZEISS, Germany). Fluorescence was detected in the spectral range >500 nm at 488 nm solid laser excitation. Obtained fluorescence images were analyzed in ZEN 2010 software (ZEISS, Germany).

AUTHOR CONTRIBUTIONS

Veronika Dzupponova: Investigation; methodology; visualization; writing‐original draft. Veronika Huntosova: Methodology; visualization. Gabriel Zoldak: Conceptualization; formal analysis; funding acquisition; investigation; methodology; project administration; resources; supervision; writing‐original draft; writing‐review and editing.

Supporting information

Data S1 The results of purification steps, scan‐rate dependence of DSC traces, CD spectra native/unfolded hLC, curve‐fitting of thermal denaturation curves with different fixed activation energy, CD thermal denaturation curves at different protein concentrations, and MALDI/TOF experiment.

Džupponová V, Huntošová V, Žoldák G. A kinetic coupling between protein unfolding and aggregation controls time‐dependent solubility of the human myeloma antibody light chain. Protein Science. 2020;29:2408–2421. 10.1002/pro.3968