Extrapolating Differential Scanning Calorimetry Data for Monoclonal Antibodies to Low Temperatures

Abstract

For irreversible denaturation transitions such as those exhibited by monoclonal antibodies, differential scanning calorimetry provides the denaturation temperature, ${\text{T}}_{\text{m}}$, the rate of denaturation at ${\text{T}}_{\text{m}}$, and the activation energy at ${\text{T}}_{\text{m}}$. These three quantities are essential but not sufficient for an accurate extrapolation of the rate of denaturation to temperatures of 25 °C and below. We have observed that the activation energy is not constant but temperature dependent due to the existence of an activation heat capacity, ${\text{C}}_{\text{p,a}}$. It is shown in this paper that a model that incorporates ${\text{C}}_{\text{p,a}}$ is able to account for previous observations like, for example, that increasing the ${\text{T}}_{\text{m}}$ does not always improve the stability at low temperatures; that some antibodies exhibit lower stabilities at 5 °C than at 25 °C; or that low temperature stabilities do not follow the rank order derived from ${\text{T}}_{\text{m}}$ values. Most importantly, the activation heat capacity model is able to reproduce time dependent stabilities measured by size exclusion chromatography at low temperatures.

Graphical abstract

Introduction

A major concern in the development of monoclonal antibodies (mAbs) as therapeutic agents is the formation of denatured and/or aggregated forms over time [1–3]. While aggregation can originate from many different causes, including self-association of native mAbs, in this paper we will be concerned exclusively with the aggregation triggered by the irreversible denaturation of mAbs. Optimizing the long-term conformational stability of mAbs is an important goal, which would be facilitated by an understanding of the temperature dependence of their rate of denaturation. Attempts at predicting the long-term stability of mAbs have been cumbersome, especially when extrapolating data obtained under temperature stressed conditions, usually 40 °C or higher, down to storage temperatures of 25 °C or lower. In particular, Drenski et al [4] noticed that the rate of denaturation/aggregation of mAbs does not follow traditional linear Arrhenius kinetics, and that a simple linear extrapolation from aggregation kinetics measured between 50 – 60 °C would predict pharmaceutical shelf lives greater than the age of the Earth (see also Brader et al, 2015 [5]).

Differential scanning calorimetry (DSC) has been used profusely to assess the viability and temperature stability of mAbs [5–12]. In addition of being the gold standard for the determination of midpoint denaturation temperatures (${\text{T}}_{\text{m}}$) or onset denaturation temperatures (${\text{T}}_{\text{onset}}$) and denaturation enthalpies [5, 13–15], DSC is uniquely able to determine the rate and activation energy of an irreversible process such as the denaturation of mAbs [16–19], a process that results in the aggregation of the denatured molecules [20]. Knowing the denaturation rate at ${\text{T}}_{\text{m}}\left({\text{k}}_{\text{Tm}}\right)$ and the activation energy at ${\text{T}}_{\text{m}}\left({\text{E}}_{\text{a},\text{Tm}}\right)$ allows calculation of the rate at any other temperature by using the Arrhenius equation; however, in this case also, the rates predicted at 25 °C or below are unrealistically slow in a similar manner as noted by Drenski et al [4]. Also important is the observation that some mAbs tend to aggregate faster at 5°C than 25 °C [20].

In this paper we have taken advantage of a mAb that exhibit faster aggregation at 4 °C than at 18 °C in order to identify and quantitate the thermodynamic variables that account for this behavior. It is shown that the activation energy is not constant but temperature dependent and that this dependence is accounted for by an activation heat capacity, ${\text{C}}_{\text{p,a}}$. Together with the denaturation temperature (${\text{T}}_{\text{m}}$) and activation energy at ${\text{T}}_{\text{m}}\left({\text{E}}_{\text{a},\text{Tm}}\right)$ measured by DSC, these three parameters provide a more accurate quantitative extrapolation of the stability of mAbs at room temperature or below.

For the DSC and aggregation experiments, we have used a chimeric 17b IgG1 monoclonal antibody expressed in a mouse constant domain background. 17b is a monoclonal IgG1 antibody which targets the HIV-1 envelope glycoprotein gp120 from several different strains of HIV-1 [21, 22]. Although, mAb 17b binds with high affinity to a well-conserved structure on the gp120 monomer, it neutralizes most viral isolates poorly and is therefore mainly of experimental importance [2, 23, 24].

Materials and Methods

Proteins and Reagents:

Human monoclonal antibody 17b was obtained from SDIX, LLC (Newark, DE, USA). The chimeric 17b IgG genes, comprising the variable domains from human 17b with sequences obtained from PDB ID: 1G9N, and the constant domains of mouse IgG1, were synthetized (Gene Universal) and subsequently cloned into the pVRC8400 expression vector. The chimeric 17b IgG was expressed using the Expi293 cell expression system (Thermo Fisher Scientific) following the manufacture’s protocol. The plasmids expressing the heavy chain and the light chain were combined with Turbo293 transfection reagent (SPEED BioSystems), and the mixture was then added to a liter of cells at a density of 2.5 × 10⁶/ml and incubated overnight in a shaker incubator set at 120 rpm, 37 °C, and 9% CO₂. Cell cultures were further incubated under the same conditions for an additional 4 days. On the 5th day post-transfection, the antibody was harvested by collecting the supernatant through centrifugation. To purify the antibody, protein A resins (Cytiva) were placed in a chromatography column (Bio-Rad), washed with elution buffer (Fisher Scientific), and equilibrated with PBS washes. The supernatant, filtered through a 0.22 μm filter unit (Fisher Scientific), was then loaded onto the Protein A column, washed with PBS, and the antibody was eluted using elution buffer. The eluted antibody was adjusted to a neutral pH with 1 M Tris-HCl at pH 8.0 (Thermo Fisher Scientific), dialyzed against PBS overnight, and confirmed for purity using SDS-PAGE.

The buffers used in the DSC and aggregation experiments were 10 mM sodium formate, pH 4.0, with zero or 300 mM NaCl. For DSC experiments performed in urea, a stock solution of 10 M urea in buffer was first prepared and the required volume of this solution was added to sample and reference solutions to final concentrations of 1.0 and 2.0 M urea. Urea and buffer components were from Sigma-Aldrich (St. Louis, MO, USA).

Differential Scanning Calorimetry:

Differential scanning calorimetry experiments were performed using a MicroCal capillary cell microcalorimeter from Malvern Panalytical (Northampton, MA, USA). The total volume of the calorimeter cell is 0.138 mL. Temperature scans were conducted from 10 °C to the indicated final temperature at a rate of 1 °C/min. Data collection and processing of raw data were performed using the software provided with the instrument. Data analysis was performed using software developed in this laboratory implementing the mixed model equations described before [19].

Aggregation Measurements:

The 17b antibody was dialyzed against 10 mM sodium formate, pH 4.0, with 300 mM NaCl and 0.02% sodium azide, at 20 °C. The protein was filtered and diluted to 1.5 mg/mL and finally dispensed into vials of 300 μL each. The vials were incubated at 4, 18, 25, and 37 °C. Protein aggregation was followed by static light scattering using a Cary Eclipse fluorescence spectrophotometer (Agilent Technologies, Mulgrave, Victoria, Australia) at 25 °C with both the excitation and emission wavelengths set to 500 nm. The excitation and emission bandwidths were set to 2.5 nm and the readings were averaged over 5 s. At each incubation temperature, the change in light scattering was measured as a function of time. The rates of aggregation were calculated from the slope of the data up to 8 days of incubation.

Results and Discussion

DSC of Human and Chimeric IgG Antibodies.

Figure 1 shows the heat capacity function of the chimeric 17b IgG at pH 4.0, 300 mM NaCl. For comparison, the DSC of the human 17b IgG is also shown. In both cases the denaturation transition is characterized by three peaks corresponding to the CH2 domain (low temperature peak), a large peak corresponding to the Fab domain and another small peak corresponding to the CH3 domain [11, 25, 26]. While the overall denaturation transition is irreversible, the CH2 transition of the human construct is reversible [19]. Most notably, the midpoint for the CH2 domain of the human construct is 45.5 °C whereas that of the chimeric construct is 5.5 °C higher and centered at 51.0 °C. Contrary to the CH2 domain, the Fab domain in the chimeric construct has a ${\text{T}}_{\text{m}}$ 4.9 °C lower than in the human construct (62.1 °C versus 67.0 °C) and also a calorimetric enthalpy (area under the curve) somewhat smaller (550 versus 800 kcal/mol). Also noticeable, the Fab peak of the chimeric construct is broader than that of the human construct. The CH3 domain exhibits very similar ${\text{T}}_{\text{m}}$ in both cases (62.8 and 63.1 °C). It is clear in the DSC scans that there is a strong overlap between the CH2 and Fab peaks in the chimeric construct whereas they are largely separated in the human construct. The overlap between the peaks of the CH2 and Fab domains implies that denatured Fab can interact with native CH2, a situation that is precluded when the peaks do not overlap. This lack of overlap may explain the reversibility of CH2 in the human construct, since it also becomes irreversible once the Fab domain undergoes denaturation [19].

Figure 1.

The heat capacity function versus temperature of the human (top panel) and chimeric constructs (bottom panel) of 17b. The DSC scans were performed at pH 4.0, 300 mM NaCl at a scanning rate of 1°C/min. The mixed denaturation model deconvolution of the data is also shown for both samples (red and blue lines).

The deconvolution analysis of the DSC data was performed using the mixed denaturation model described before [19]. This model assumes a mixture of reversible [27–29] and irreversible transitions[16, 17, 19]. (The equations are summarized in the Appendix). For the chimeric construct three irreversible transitions (CH2, Fab and CH3) were used in the analysis, whereas for the human construct one reversible (CH2) and two irreversible (Fab and CH3) transitions were used. Table 1 summarizes the results of the analysis. Since the CH2 domain of the human construct is reversible, the van’t Hoff enthalpy is reported rather than the activation energy. The CH3 domains in both constructs behave in a similar manner. For the Fab domains, in addition to the differences in ${\text{T}}_{\text{m}}$ mentioned above, the most notable observation is the large difference between their activation energies (70 kcal/mol for the chimeric construct and 111 kcal/mol for the human construct). A lower activation energy is consistent with a faster denaturation rate at lower temperatures.

Table 1.

	$T_{m,CH2}$ (°C)	$\Delta H_{,\mathit{CH}2}$$E_{a,CH2}$ (kcal/mol)	$T_{m,Fab}$ (°C)	$E_{a,Fab}$ (kcal/mol)	$T_{m,CH3}$ (°C)	$E_{a,CH3}$ (kcal/mol)
Human	45.4±0.05	130.0±3†	67.0±0.05	111.0±2	62.8±0.1	110.0±1
Chimeric	51.0±0.1	82.5±2†	62.1±0.04	70.0±1	63.1±0.1	145.0±5

^†The value for the human CH2 domain is $\Delta H_{,\mathit{CH}2}$, the van’t Hoff enthalpy, and for the chimeric CH2 domain is $E_{a,CH2}$, the activation energy (see Appendix).

Low Temperature Aggregation.

Storage in the refrigerator at 4 °C resulted in aggregation of the chimeric construct but not of the human construct (Figure 2). This unexpected observation prompted us to perform a time course aggregation experiment of the chimeric construct at different incubation temperatures between 4 and 37 °C. The results of the aggregation experiment using static light scattering are shown in Figure 3. Aggregation was not observed for the human construct; also, no aggregation was observed for the isolated chimeric CH2 domain, suggesting that interaction with denatured Fab is the aggregation trigger. In this figure, the initial rate of change of the light scattering signal has been plotted as a function of temperature. It is clear that the rate of aggregation is maximal at the highest temperature, it reaches a minimum at around 18 °C (the inversion temperature) and increases again at 4 °C.

Figure 2.

The chimeric construct (mouse CH domains) of 17b shows aggregation at 4 °C whereas the human construct does not. This observation permits the measurement of the aggregation time dependence using light scattering.

Figure 3.

Observed aggregation rates of chimeric 17b at different temperatures at pH 4.0 (10 mM sodium formate, 300 mM NaCl). The experimental values are shown as squares. The solid line is the predicted line using the Fab denaturation parameters (${\text{T}}_{\text{m}}$ = 62.1 °C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70.0 kcal/mol determined by DSC) together with an activation heat capacity, ${\text{C}}_{\text{p,a}}$, of 1.55 kcal/K*mol.

Attempts were made to fit the data in Figure 3 to the energy activation parameters summarized in Table 1. It was found that the only way to fit the data was by assuming that the Fab denaturation is the trigger for aggregation and by using the Fab denaturation parameters (${\text{T}}_{\text{m}}$ = 62.1 °C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70.0 kcal/mol) together with an activation heat capacity, ${\text{C}}_{\text{p,a}}$, of 1.55 kcal/K*mol. ${\text{T}}_{\text{m}}$ and ${\text{E}}_{\text{a},\text{Tm}}$ were fixed to the experimental values and ${\text{C}}_{\text{p,a}}$ adjusted to obtain the best fit. The spread of ${\text{C}}_{\text{p,a}}$ values that account for the data is very narrow +/− 0.1 kcal/mol. The solid line in Figure 3 was calculated by using these parameters. The heat capacity of activation creates the upward curvature in the temperature dependence of the denaturation rate, preventing it to become infinitely small. If ${\text{C}}_{\text{p,a}}$ were zero, the denaturation rate will continue to drop and the halftime at 4 °C would be 6 × 10⁶ days instead of the observed 2.5 days.

The Activation Heat Capacity Model.

According to the activation heat capacity model, the basic equation to calculate the denaturation rate at any temperature is:

$$lnk=-\frac{E_{a,Tm}+C_{p,a}\times \left(T-T_m\right)}{RT}+\left(\frac{E_{a,Tm}}{R{T}_m}\right)+\ln \left(k_{Tm}\right)+\frac{C_{p,a}}{R}\ln \left(\frac{T}{T_m}\right)$$ (1)

Figure 4 panels a, b and c provide a visual depiction of the effects of the three parameters ${\text{T}}_{\text{m}}$, ${\text{E}}_{\text{a},\text{Tm}}$ and ${\text{C}}_{\text{p,a}}$ on the temperature dependence of the rate of denaturation. In all cases, the reference curve (shown in red) was calculated using the parameters obtained for the chimeric construct: ${\text{T}}_{\text{m}}$ = 62.1 °C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70 kcal/mol and ${\text{C}}_{\text{p,a}}$ = 1.55 kcal/K*mol.

Figure 4.

Panel a: The effects of ${\text{C}}_{\text{p,a}}$ on the temperature dependence of the rate of denaturation. Red line ${\text{T}}_{\text{m}}$ = 62.1°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 1.55 kcal/K*mol. Blue line ${\text{T}}_{\text{m}}$ = 62.1°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 0.775 kcal/K*mol. Green line ${\text{T}}_{\text{m}}$ = 62.1°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 0.0 kcal/K*mol.

Panel b: The effects of ${\text{T}}_{\text{m}}$ on the temperature dependence of the rate of denaturation. Red line ${\text{T}}_{\text{m}}$ = 62.1°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 1.55 kcal/K*mol. Blue line ${\text{T}}_{\text{m}}$ = 65.1°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 1.55 kcal/K*mol. Green line ${\text{T}}_{\text{m}}$ = 68.1°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 1.55 kcal/K*mol. Panel c: The effects of ${\text{E}}_{\text{a}}$ on the temperature dependence of the rate of denaturation. Red line ${\text{T}}_{\text{m}}$ = 62.1°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 1.55 kcal/K*mol. Blue line ${\text{T}}_{\text{m}}$ = 62.1°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 90 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 1.55 kcal/K*mol. Green line ${\text{T}}_{\text{m}}$ = 62.1°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 110 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 1.55 kcal/K*mol. See Results and Discussion for details. In all panels the red line corresponds to the parameters determined for the denaturation of chimeric 17b.

In panel a, the effects of changing ${\text{C}}_{\text{p,a}}$ are shown. If ${\text{C}}_{\text{p,a}}$ were zero, the denaturation rate at 4 °C would be 1.6 × 10⁻⁷ days⁻¹, corresponding to a halftime of 6 × 10⁶ days. The effect of increasing ${\text{C}}_{\text{p,a}}$ is to introduce an upward curvature in the rate of denaturation as the temperature decreases. Even though at 4 °C, a ${\text{C}}_{\text{p,a}}$ of 1.55 kcal/K*mol causes a rate increase close to six orders of magnitude, the effect of ${\text{C}}_{\text{p,a}}$ becomes significant only below 50 °C, i.e. about ten degrees below ${\text{T}}_{\text{m}}$.

In panel b, the effects of changing the ${\text{T}}_{\text{m}}$ are shown. Increasing the ${\text{T}}_{\text{m}}$ shifts the entire curves to higher temperatures while maintaining their shapes. The inversion temperature also shifts to higher temperatures. The immediate consequence of this behavior is that a mAb with a higher ${\text{T}}_{\text{m}}$ might be less stable (faster denaturation rates) at low temperatures than a mAb with a lower ${\text{T}}_{\text{m}}$; i.e. the stability rank order at 5 or 20 °C is not necessarily the same as the rank order derived from ${\text{T}}_{\text{m}}$ or ${\text{T}}_{\text{onset}}$ depending on the value of ${\text{C}}_{\text{p,a}}$. This lack of correlation is well documented in the literature [4, 5, 30, 31].

In panel c, the effects of increasing the activation energy at ${\text{T}}_{\text{m}}$ are shown. A higher ${\text{E}}_{\text{a},\text{Tm}}$ mitigates the effects of ${\text{C}}_{\text{p,a}}$ by shifting the inversion temperature to much lower values, improving the low temperature stability of the mAb. For example, the Fab of the human construct studied in this paper has a higher ${\text{T}}_{\text{m}}$ and a higher ${\text{E}}_{\text{a},\text{Tm}}$ than the chimeric construct (Table 1) and does not aggregate at low temperature. Figure 5 illustrates the difference in denaturation rates between the chimeric and human constructs using the experimental thermodynamic parameters in Table 1. For the human construct the same ${\text{C}}_{\text{p,a}}$ of 1.55 kcal/K*mol was assumed.

Figure 5.

Comparison of the simulated rates of denaturation for chimeric (red line) and human (blue line) 17b. Assuming that the human 17b has the same ${\text{C}}_{\text{p,a}}$ as the chimeric construct, it is shown that the higher ${\text{T}}_{\text{m}}$ and ${\text{E}}_{\text{a},\text{Tm}}$ prevent denaturation at low temperatures. Red line ${\text{T}}_{\text{m}}$ = 62.1°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 70 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 1.55 kcal/K*mol. Blue line ${\text{T}}_{\text{m}}$ = 67.0°C, ${\text{E}}_{\text{a},\text{Tm}}$ = 111 kcal/mol, ${\text{C}}_{\text{p,a}}$ = 1.55 kcal/K*mol.

Predictions of the Activation Heat Capacity Model.

According to the activation heat capacity model, three parameters (${\text{T}}_{\text{m}}$, ${\text{E}}_{\text{a},\text{Tm}}$ and ${\text{C}}_{\text{p,a}}$) are sufficient to calculate the denaturation rate at any temperature and consequently the population of native and denatured molecules as a function of time. Previously, we have studied the mAb VRC07 by DSC, isothermal calorimetry and size exclusion chromatography at low temperatures [20]. The DSC profile of VRC07 is also characterized by three peaks, but in this case the Fab domain has a lower ${\text{T}}_{\text{m}}$ than the CH2 and CH3 domains [20]. It was determined that the denaturation triggered aggregation was characterized by an activation energy close to 90 kcal/mol at ${\text{T}}_{\text{m}}$, a ${\text{C}}_{\text{p,a}}$ around 1.3 kcal/K*mol and ${\text{T}}_{\text{m}}$ values of 73.1 and 71.9 °C for the best and worst buffers considered [20]. Interestingly, it was concluded that for VRC07 the denaturation/aggregation was driven by the CH domains, especially the CH2 domain, and not by the Fab as is the case for the construct studied in this paper. It seems that denaturation/aggregation at low temperatures is driven by the domain with the lowest activation energy/${\text{C}}_{\text{p,a}}$ combination; i.e. with the combination that yields the fastest rate at low temperatures. Figure 6 shows the predictions of the activation heat capacity model for the best (50 mM histidine, 50 mM NaCl, 5% w/v sucrose, 2.5% w/v sorbitol, pH 6.8) and worst (50 mM histidine, 100 mM NaCl, pH 6.8) buffers at 5 and 25°C [20]. Since the buffers only differ in excipients, the most significant effect is on ${\text{T}}_{\text{m}}$ (73.1 vs. 71.9 °C). For the simulations in Figure 6, the average activation energy for the CH2 domain (87.06 ± 2.5 kcal/mol) was used [20]. The ${\text{C}}_{\text{p,a}}$ was 1.133 ± 0.31 kcal/K*mol which is close to the values of 1.5 and 1.2 kcal/K*mol estimated previously [20]. Also, these values are of the same order as the value of 1.55 kcal/K*mol for chimeric 17b obtained in this paper. In this figure, the decay in the population of native protein up to 400 days is shown together with the data obtained by size exclusion chromatography. It can be seen that the predicted and experimental values are in excellent agreement. These results support the idea that the incorporation of ${\text{C}}_{\text{p,a}}$ greatly improves the accuracy of extrapolating DSC data to low temperatures.

Figure 6.

Experimental (filled circles) and predicted (solid lines) decrease in native population as a function of time for the mAb VRCO7 previously studied by DSC, isothermal calorimetry and size exclusion [20]. The experimental values were determined by size exclusion chromatography. The solid lines were calculated using equation 1 in the main text and the denaturation parameters determined by DSC (Buffer 1: ${\text{T}}_{\text{m}}$ = 71.9 °C, ${\text{E}}_{\text{a},\text{Tm}}$ = 90.8 kcal/mol; Buffer 4 : ${\text{T}}_{\text{m}}$ = 73.1 °C, ${\text{E}}_{\text{a},\text{Tm}}$ = 90.8 kcal/mol). The ${\text{C}}_{\text{p,a}}$ was 1.255 ± 0.42 kcal/K*mol. Buffer 1: 50 mM histidine, 100 mM NaCl, pH 6.8; Buffer 4: 50 mM histidine, 50 mM NaCl, 5% w/v sucrose, 2.5% w/v sorbitol, pH 6.8.

In the present study the activation heat capacity was evaluated by combining DSC and size exclusion chromatography or light scattering data. In principle, ${\text{C}}_{\text{p,a}}$ can be obtained from a single DSC curve, since a positive ${\text{C}}_{\text{p,a}}$ will lower the activation energy at lower temperatures and cause a broadening of the DSC curve. In practice, however, the effect on the shape of the curve is small and does not allow for an accurate evaluation of ${\text{C}}_{\text{p,a}}$. Moreover, the broadening is expected to occur close to the transition onset, the region most affected by baseline subtraction procedures. An alternative strategy to evaluate ${\text{C}}_{\text{p,a}}$ from DSC data is to perform DSC scans under conditions that shift the ${\text{T}}_{\text{m}}$ to lower temperatures; for example, low concentrations of a denaturant that does not affect the pH or salt concentration. To test this idea, DSC experiments were performed in the presence of low urea concentrations. Figure 7 shows three DSC experiments with the isolated 17b Fab domain performed at 0, 1 and 2 M urea. These concentrations lower the ${\text{T}}_{\text{m}}$ by approximately 20°C. A visible broadening is observed at lower ${\text{T}}_{\text{m}}$ values, as expected from a decrease in ${\text{E}}_{\text{a},\text{Tm}}$. Analysis of these experiments confirm that ${\text{E}}_{\text{a}}$ is temperature dependent; in fact, linear least squares of the temperature dependence of ${\text{E}}_{\text{a},\text{Tm}}$ (shown in the inset) yields a ${\text{C}}_{\text{p,a}}$ of 1.4 ± 0.12 kcal/K*mol, in close agreement with the value for the Fab domain within the entire mAb molecule. These preliminary experiments in the presence of urea suggest a potential approach to derive ${\text{C}}_{\text{p,a}}$ from DSC experiments alone. The temperature dependence of ${\text{E}}_{\text{a}}$ accounts for the magnitude of the rate constants observed both at denaturation and at low temperatures. This observation eliminates the need for more complicated models involving different processes with multiple activation energies (see for example [33]).

Figure 7.

The heat capacity function versus temperature of the isolated 17b Fab domain. The DSC scans were performed at pH 4.0, 300 mM NaCl at a scanning rate of 1°C/min in the presence of 0 (red), 1 M (green) and 2 M (black) urea. The mixed denaturation model deconvolution of the data is also shown (solid lines). The inset shows the activation energies obtained from the deconvolution analysis as a function of ${\text{T}}_{\text{m}}$. Linear regression of the ${\text{E}}_{\text{a},\text{Tm}}$ vs ${\text{T}}_{\text{m}}$ data yields a ${\text{C}}_{\text{p,a}}$ of 1.4 ± 0.12 kcal/K*mol.

Conclusions

Extrapolating mAb structural stability parameters determined by DSC to low temperatures has been difficult at best. The data presented in this paper as well as those presented previously [20] suggest that a key parameter for temperature extrapolation is the activation heat capacity, ${\text{C}}_{\text{p,a}}$. Due to the existence of an activation heat capacity, the energy of activation is not constant and the denaturation/aggregation of mAbs does not obey linear Arrhenius kinetics. The results obtained so far yield ${\text{C}}_{\text{p,a}}$ values on the range of 1.1 – 1.5 kcal/K*mol. A larger database will be required to assess the spread in ${\text{C}}_{\text{p,a}}$ values for different mAbs and their dependence on sequence or solvent parameters.

• Accurate extrapolation of temperature denaturation data to storage temperatures of monoclonal antibodies.

• Temperature dependence of the rate of denaturation of monoclonal antibodies.

• Long term structural stability of monoclonal antibodies.

• The structural stability of monoclonal antibodies is dictated by activation energy and activation heat capacity.

Appendix

The excess heat capacity function of monoclonal antibodies can be represented as the sum of equilibrium denaturation and irreversible denaturation transitions:

$$C_p=C_{p,CH2}+C_{p,Fab}+C_{p,CH3}$$ (1)

The heat capacity function of the CH2 domain when it undergoes reversible denaturation can be represented by the general equilibrium equation [27–29]:

$$C_{p,CH2}=\frac{{\mathit{exp}}^{-\frac{(\text{Δ}H-T\text{Δ}S)}{RT}}}{(1+{\mathit{exp}}^{-\frac{(\text{Δ}H-T\text{Δ}S)}{RT}}{)}^2}\times \frac{\text{Δ}H\text{Δ}{H}_{cal}}{R{T}^2}$$ (2)

In the above equation, $\text{ΔH}$ and $\text{ΔS}$ are the respective van’t Hoff enthalpy and entropy changes, ${\text{ΔH}}_{\text{cal}}$ the calorimetric enthalpy (area under the curve), R the gas constant and T the absolute temperature.

The heat capacity functions of the Fab and CH3 domains and that of the CH2 under conditions in which it is irreversible, will be represented by the irreversible kinetic ${\text{C}}_{\text{p}}$ equation [17,19,20]:

$$C_{p,i}=\left(e^{\frac{E_{a,i}\times \left(T-T_{m,i}\right)}{R{T}_{m,i}^2}}\right)\times E_{a,i}\text{Δ}{H}_{cal,i}\times \frac{e^{-}\left(e^{\frac{E_{a,i}\times \left(T-T_{m,i}\right)}{R{T}_{m,i}^2}}\right)}{R{T}_{m,i}^2}$$ (3)

Where ${\text{T}}_{\text{m,i}}$ is the transition temperature for the ${\text{i}}^{\text{th}}$ transition and ${\text{E}}_{\text{a},\text{i}}$ its activation energy at ${\text{T}}_{\text{m,i}}$.

For each irreversible transition, the rate constant at ${\text{T}}_{\text{m}}$ is given by the equation [17]:

$$k_{Tm}=v{E}_{a,Tm}/R{T}_{m^2}$$ (4)

Where v is the scanning rate.