3240
J. Phys. Chem. B 2008, 112, 3240-3250
Immunoglobulin Dynamics, Conformational Fluctuations, and Nonlinear Elasticity and Their Effects on Stability Tim J. Kamerzell,† Joshua D. Ramsey, and C. Russell Middaugh* Department of Pharmaceutical Chemistry, UniVersity of Kansas, Lawrence, Kansas 66047 ReceiVed: October 16, 2007; In Final Form: December 20, 2007
The relationships between protein dynamics, function, and stability are incompletely understood. Two external perturbations (temperature and pH) were used to modulate the flexibility and stability of an IgG1κ monoclonal antibody (mAb) in an attempt to better understand the possible correlations between flexibility and stability. Ultrasonic velocimetry, densitometry, differential scanning calorimetry (DSC), and pressure perturbation calorimetry (PPC) were used to experimentally determine the adiabatic and isothermal compressibility, expansibility, fractional volumes of unfolding, and various nonlinear thermoacoustical parameters as a function of pH and temperature. By combining these results, state parameter fluctuations were calculated from fundamental statistical mechanical relationships. The most dynamic and rigid mAb ensemble is measured at pH 4 and 6, respectively, based on state parameter fluctuations and compressibility. The effect of pH appears to couple mAb dynamics to solvent fluctuations, which control its dynamics and stability. A nonlinear response to mechanical perturbation, comparable to that seen with many polymers, is observed for this monoclonal antibody at pH 4-8. This behavior is characterized as strongly anisotropic and anharmonic, especially at pH 4. The midpoint of thermal unfolding as measured by DSC does not necessarily correlate with flexibility.
Introduction The effect of varying solution conditions (e.g., pH, temperature, concentration) on protein dynamics is important for understanding the molecular determinants of protein stability and function. The physicochemical stability and biological functions of proteins are thought to be intimately related to their flexibility, fluctuations, and other internal motions. Direct relationships between protein flexibility, function, and stability, however, have not been established. While the interest in ascertaining such relationships is not new, limited experimental measurements over a wide range of protein motions has limited the available data. Numerous methods, including NMR, ultrafast and single molecule spectroscopy, isotope exchange, and molecular dynamics simulations among others are quickly advancing our understanding in this area.1-7 A popular approach toward understanding the relationship between protein flexibility and stability compares homologous thermophilic proteins to their mesophilic counterparts, typically concluding that an inverse correlation exists. A growing amount of evidence, however, argues against such a simple relationship and points toward a much more complicated inter-relationship of the coupling between both rigid and flexible regions of a protein and correlation of various motions across extended networks.8-11 It has also been shown that the solvent plays a significant role in protein fluctuations and stability.12-15 The fluctuations in enthalpy, volume, and the electric dipole moment of some proteins are critically dependent on solvent fluctuations and are considered to be slaved to solvent motions.12-14,16 Therefore, methods that measure both hydration and protein * To whom correspondence should be addressed. Address: University of Kansas, Department of Pharmaceutical Chemistry, 2030 Becker Drive, Lawrence, Kansas 66047. Phone: (785) 864-5813. Fax: (785) 864-5814. E-mail:
[email protected]. † Current Address: Genentech, Inc., 1 DNA Way, South San Francisco, CA 94080.
fluctuations should provide a more detailed understanding of the relationships between protein flexibility, fluctuations, and stability. Multidimensional NMR and isotope exchange experiments have been instrumental in describing the dynamics and regional flexibility differences of protein molecules. In addition, measurements of protein compressibility and expansibility using ultrasonic spectroscopy,1,17-30 densitometry,31 and pressure perturbation calorimetry32-36 are promising methods capable of describing the relationships between protein flexibility, stability, and hydration. For example, Mitra, Winter, and co-workers characterized the unfolding and solvation of ribonuclease A, staphylococcal nuclease, and various tripeptides in the presence of various cosolvents, based on measurements of thermal expansion, with the interesting conclusion that various solvent conditions dramatically influence the conformation, stability, and void volumes of the polypeptides studied.35 Similarly, numerous other groups have advanced our understanding of protein conformational substates, protein flexibility, and hydration using ultrasonic velocimetry.1,17,23-29,37-41 Statistical thermodynamics describes all dynamic systems in terms of fluctuations around some mean value and bridges the gap between macroscopic experimental thermodynamics and microscopic ensemble representations.41,42 Thus, a protein in solution can be viewed as a statistical distribution of conformational microstates with differential degrees of flexibility and conformational excursions described by time-independent equilibrium statistical ensembles using a simple Boltzmann probability distribution.41-43 The equilibrium fluctuations of protein structural states is one measure of protein flexibility, and using established statistical thermodynamic relationships, experimental measurements of volume and enthalpy fluctuations are readily accessible. Equilibrium fluctuations have previously been measured using isotope exchange and neutron scattering and calculated theoreti-
10.1021/jp710061a CCC: $40.75 © 2008 American Chemical Society Published on Web 02/20/2008
Immunoglobulin Conformational Fluctuations cally by computer simulations.44 Through a combination of experimental measurements, including adiabatic and isothermal compressibility, coefficients of thermal expansion, heat capacity, and density, a wealth of protein flexibility information may be ascertained. Recently, compressibility and expansibility were used to study the effects of ligand binding on the equilibrium fluctuations of fibroblast growth factor-10,34 with the surprising result that ligand binding increases the transition temperature of thermal unfolding while increasing global fluctuations. Similarly, by combining the aforementioned techniques, thermoacoustical parameters may be calculated which describe many physical properties of interest. Some of these parameters have not been previously evaluated for proteins but have found widespread use describing the mechanical properties, elasticity, and molecular motions in polymers and condensed matter. The use of these parameters in describing the physical properties of proteins may be of a previously unrecognized significance. Various aspects of the flexibility of immunoglobulin G (IgG) and its fragments have been characterized using fluorescence anisotropy45-47 and resonance energy transfer,48 NMR,49,50 and X-ray and neutron scattering51 among other techniques. Many of the methods used to study monoclonal antibody flexibility, however, are limited by the specific time scales and types of flexibility that may be monitored and by the large size of IgG molecules. For example, external probes are typically used for anisotropy analysis and provide information concerning only the reorientational dynamics of specific internal domains (e.g., hinge bending), while the size of monoclonal antibodies (mAb’s) limits their analysis by NMR. Global fluctuations and the internal flexibility of monoclonal antibodies are equally important for understanding their solution stability and function and provide complementary information. In this work, a combination of experimental methods is used to monitor the effects of pH and temperature on the conformational flexibility and stability of a monoclonal IgG1κ antibody. A comprehensive description of the global fluctuations and flexibility of this antibody and its solvent dependence is presented. The transition midpoints of thermal unfolding (Tm) and reversible enthalpy of unfolding (∆H) of the Fc region were measured as a function of pH using differential scanning calorimetry (DSC). High-resolution ultrasonic spectroscopy was used to determine the change and attenuation in ultrasonic velocity of mAb solutions as a function of pH and temperature. The adiabatic and isothermal compressibilities of these solutions were calculated from sound velocity, density, and thermal expansion measurements. Compressibility is directly related to fluctuations in volume and is a measure of global protein flexibility.41,42 The coefficient of thermal expansion was also measured and reflects changes in solvation and enthalpy as well as volume fluctuations. Monoclonal antibody state parameter fluctuations were calculated as a function of pH and temperature using fundamental statistical mechanical relationships. Finally, thermoacoustical parameters describing the physical, thermal, and mechanical properties of this IgG1κ have been calculated from measurements of density, heat capacity, sound velocity, and thermal expansion. Experimental Methods
J. Phys. Chem. B, Vol. 112, No. 10, 2008 3241 Scientific (Pittsburgh, PA). All solutions were prepared in 20 mM citrate phosphate buffer, ionic strength ∼ 0.15 adjusted with NaCl, pH 4.00-8.00, and dialyzed overnight. Protein concentration was determined at room temperature by absorbance measurement at 280 nm ( ∼ 1.5 mL/mg‚cm) using an Agilent 8453 UV-visible spectrophotometer (Palo Alto, CA) fitted with a Peltier temperature controller. The concentration used in all experiments was 5.00 ( 0.01 mg/mL. Methods. High-Resolution Ultrasonic Spectroscopy (HR-US). Ultrasonic measurements were conducted with an HR-US 102 Spectrometer (Ultrasonic Scientific, Dublin, Ireland) with full sample and reference cell volumes (1 mL). The frequencies used for analysis were 5 and 12 MHz, while the frequency range of the instrument extends from 2 to 18 MHz. The resolution of the HR-US instrument is (0.2 mm/s and 0.2% attenuation. Reference cells were filled with buffer. All solutions were degassed prior to measurement. HRUS v4.50.27.25 software was used for analysis of all samples. Temperature control was achieved with a Phoenix P2 Circulator (Thermo Haake). The coefficient of adiabatic (βS) compressibility was calculated using the following relationships:38,52
βS ) -
1 ∂V ) -(1/ν)(∂ν/∂P)S ) V ∂P S (β0/νc)[β/β0 - (F - c)/F0] (1)
( )
where
ν ) (1/c)[1 - (F - c)/F0]
and β is the adiabatic compressibility of the solution, β0 the adiabatic compressibility of the solvent, F the density of the solution, F0 the density of the solvent, c the concentration of protein, and ν the partial specific volume of the solute. The Laplace equation, β ) 1/Fu2, was used to calculate the adiabatic compressibility of the solution (β) and solvent (β0) from the sound velocity (u) and density (F) of the solution and solvent. Similarly, the isothermal compressibility (βT) was calculated using eq 3:53
βT ) -
1 ∂V ) βS + R2T/FCp V ∂P T
( )
(3)
where T is the absolute temperature, Cp the specific heat, and R the thermal expansion coefficient. It should be noted that apparent molar values were not used for the calculation of βT and that the units of βS and βT are Pa-1. Pressure Perturbation Calorimetry (PPC). The heat changes resulting from pressure changes above each solution were measured with a Microcal VP-DSC microcalorimeter equipped with a PPC accessory (MicroCal, Northampton, MA). A detailed description of this technique is provided elsewhere.54,55 Briefly, the coefficient of thermal expansion (R) is related to the pressure coefficient of the heat exchange (∂Q/∂P)T through the following relations:
(∂Q ∂P )
T
(∂P∂S) , using Maxwell’s relation (∂P∂S) ) ∂V ∂Q ∂V -( ) and substituting ( ) ) -T( ) ) -TVR (4) ∂T ∂P ∂T )T
T
P
Materials. A highly purified immunoglobulin G1 kappa light chain (IgG1κ), monoclonal antibody (mAb) was kindly provided by MedImmune, Inc. (Gaithersburg, MD) and stored in its formulation buffer at 2-8 °C. All chemicals were of reagent grade and were obtained from Sigma (St. Louis, MO) and Fisher
(2)
T
T
P
where V is the volume, T is the temperature, and R is the coefficient of thermal expansion, R ) (1/V)(∂V/∂T)P. Reference and sample cells were filled with identical volumes (0.5 mL). Applied pressures were ∼5 atm. An average of 15 pressurization
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Kamerzell et al.
and 15 depressurization peaks from each of three separate experiments were integrated and used to calculate the coefficient of thermal expansion over the temperature range 20-100 °C. The relative volume changes upon unfolding were calculated by integrating alpha over the appropriate temperature range according to eq 5:
∆V ) V
∫T R dT Tf
(∂∂ lnln Vν)
Γ)(5)
)-
T
(21) + (21)(∂∂ lnln Vβ) ) 2 + (2RT)
0
Statistical Thermodynamic Analysis of Protein Fluctuations. From well-known statistical thermodynamic relationships, the probability distribution (Pi) can be described in terms of its mean value and the moments about the mean for any parameter Xji (volume, energy) in state i. At thermodynamic equilibrium, the entropy of the system is maximized and defined by the Boltzmann law:
S ) kB ln W ) -kB
∑i pi ln pi
where S is the entropy, kB is Boltzmann’s constant, and W is the multiplicity. The average, mean, or expected value is therefore 〈Xj〉 ) ∑PiXji. Higher moments leading to the calculation of the actual distribution function may be obtained from the lower moments. The nth moment of a continuous probability distribution function 〈xn〉 is
〈xn〉 )
temperature and pH are not shown but have been used to calculate other thermoacoustical parameters and have been compared to other polymers with excellent agreement. From the volume expansivity (R) and temperature (T), the lattice Gruneisen parameter (Γ) was obtained from the relation56-58
∫
b n x p(x) a
Γj )
T,µi
d ln νj d ln νj )d ln F d ln V
The thermodynamic Gruneisen parameter (Γ′) is an average over all modes and includes both inter- and intramolecular vibrations and is calculated by the equation
Γ′ )
RV RV u 2R ) ) βTCV βSCp Cp
(10)
in which
β T Cp ) )γ βS C V
Second moments describe mean square deviations and the width of the probability distribution, while the higher moments describe the shape and symmetry of the distribution. Mean square volume fluctuations and enthalpy fluctuations for the second moments of the distribution are given by41,42
(∂P∂V)
( ) ( )
dx
∑i (Xji - 〈Xj〉)n × Pi
〈δV2〉 ) -kBT
2 + RT 3 (9)
which describes the anharmonicity of the normal-mode frequency (ν) of vibrations and molar volume (V), where β is the compressibility. The utility of this equation may be further expanded using statistical mechanics and describing each lattice frequency (νi) with the coupled Gruneisen constant defined by59
and for discrete probability distributions
〈δXnj 〉 )
-1
) kBTVβT
〈δH2〉 ) kBT2Cp
(6) (7)
Similarly, mixed moments are required to describe fluctuations in more than one state parameter. The mixed moment of volume and enthalpy fluctuations was calculated from
〈δHδV〉 ) kBT2VR
(8)
where kB is Boltzmann’s constant, V is the volume, and R is the coefficient of thermal expansion. Thermoacoustical and Anharmonic Parameter Calculations. A number of thermoacoustical parameters, including the thermodynamic (Γ′) and lattice (Γ) Gruneisen parameters, MoelwynHughes parameter (C1), Sharma parameter (S*), isochoric temperature coefficient of internal pressure (X), isobaric (K) and isothermal acoustical parameter (K′), the specific heat capacity ratio (γ), and acoustic impedance (Z), were calculated, based on measurements of sound velocity, density, coefficients of thermal expansion, and specific heat, as a function of temperature and pH. The plots of X, K, and K′ as a function of
(11)
where γ is the specific heat capacity ratio, βS and βT are the adiabatic and isothermal compressibility, u is the sound velocity, and Cp and CV are the heat capacities at constant pressure and volume, respectively.57,58,60 For the equation with sound velocity squared, alpha and heat capacity were used. The Moelwyn-Hughes parameter (C1) is closely related to the Gruneisen parameters and is defined as the dimensionless pressure coefficient of the isothermal bulk modulus or the reciprocal of isothermal compressibility in partial derivative form as61
C1 )
(β1)(∂ ∂Pln β) ) (∂∂ lnln Vβ) T
T
while Sharma expressed C1 in terms of the coefficient of thermal expansion (R) as62
C1 )
(133) + (RT) + (34)(RT) -1
(12)
In this work, Sharma’s expression of the Moelwyn-Hughes parameter was used to calculate C1. Sharma has also introduced another dimensionless parameter, S*,63,64 in an attempt to show that thermal expansion dominates the thermoacoustical parameters. The Sharma parameter was calculated as a function of temperature at each pH by the equation
S* ) 1 +
4RT 3
(13)
The isochoric temperature coefficient of internal pressure (X), isobaric (K), isothermal (K′), and isochoric acoustical param-
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eters, due to Rao65 and Carnevale and Litovitz,66 may also be calculated from the following equations:
X)
K)-
-2(1 + 2RT)
( ) ( ) [ ( ) [
1 d ln u R dT K′ )
)-
P
d ln u d ln V
)
P
]
S*(1 + RT) 1 1+ 2 RT
]
(15)
S*(1 + RT) + X 1 3+ 2 RT
(16)
1 d ln u 1 d ln u X ) )1+ R dT V β dp V 2RT
(17)
1 d ln u β dP
K′′ )
(14)
V ˜ C1
(
)
T
)
V ˜)
(
)
+ 1) (1RT/3 + RT
K′′ ) K′ - K
3
(18) (19)
where all symbols are defined as above. Finally, the acoustic impedance (Z) which describes the resistance to ultrasonic wave propagation and depends only on the physical properties of the material is calculated from the density (F) and ultrasonic velocity (U), from Z ) FU (eq 20). Differential Scanning Calorimetry (DSC). All DSC thermograms and absolute heat capacities were measured using a Microcal VP-Capillary DSC with autosampler (MicroCal, Northampton, MA) and calculated using Microcal subroutines. Experimentally measured partial specific volumes and coefficients of thermal expansion were included in the calculation. The scanning rate for all experiments was 60°/h, and a filtering period of 16 s was used. The DSC thermograms were recorded up to the temperature of reversibility at all pH values and were rescanned 2-3 times. The full DSC trace (higher temperatures) was also obtained in a separate experiment from which the transition midpoints were obtained. Reversible absolute heat capacities were used in all calculations of statistical thermodynamic and thermoacoustical parameters. A Levenberg-Marquardt nonlinear least-squares method was used to fit the reversible transition utilizing a two-state model. Density Measurements. Measurements of density were conducted using a precision density meter, DMA-5000 (Anton Paar, Graz, Austria), with a precision of 1 × 10-6 g/cm3 and 0.001 °C. Solvent and sample solution densities were measured at 2.5 °C intervals from 20 to 55 °C for pH 4 and from 20 to 75 °C for all other pH values. The density meter was calibrated with dry air and water for all temperatures prior to analysis. Results DSC. Differential scanning calorimetry was used to measure the transition midpoint of thermal unfolding (Tm) of the mAb (Figure 1). Fab and Fc fragments of the mAb were produced by papain digestion, and the corresponding DSC profiles were obtained. Based on a comparison of these Tm values, the first transition at all pH values corresponds to the unfolding of the mAb crystallizable fragment (Fc) while transitions at higher temperatures are due to unfolding of the mAb antigen binding fragment (Fab). The Fc unfolding transition was reversible at all pH values used in these experiments; however, Fab unfolding was irreversible. Therefore, a rigorous thermodynamic analysis of Fab unfolding was not possible. The pH affects the transition temperature (Tm) of the mAb Fc region to a greater extent than
the Fab region (Figure 1, Table 1). The transition temperatures of the Fab and Fc regions are greatest at pH 6, 7, and 8 and lowest at pH 4 and 5 (Table 1). Adiabatic and Isothermal Compressibility. High-resolution ultrasonic spectroscopy measures the velocity and attenuation of high-frequency sound waves as they are passed through a sample and reference. Ultrasonic waves probe intramolecular forces through compressions and decompressions of the material of interest. The elasticity, density, and internal interactions are determined through measurement of the ultrasonic velocity, while energy changes in compression and decompression are probed through changes in attenuation of the wave. Attenuation is determined by the scattering of ultrasonic waves in nonhomogeneous samples and fast relaxation processes. Protein fluctuations and their coupling to the solvent as well as contribution from compressible cavities and voids in the protein interior can be detected by this technique. The compressibility is directly related to fluctuations in volume, thus reflecting dynamic behavior.41 The relative change in ultrasonic velocity and attenuation between the sample and reference was measured using HRUS. The monoclonal antibody at all pH values displays a decrease in relative ultrasonic velocity and an increase in absolute velocity as a function of temperature (data not shown). Rigid molecules possess a higher elastic modulus compared to less rigid species, resulting in a more rapid velocity of sound through the more rigid sample. The adiabatic compressibility (βS), calculated using eq 1, of the mAb at all pH values increases as a function of temperature with the lowest and highest values observed at pH 6 and 4, respectively (Figure 2A). The compressibility of pH 4 mAb solutions was dramatically altered at temperatures above 30 °C compared to pH 5-8. The isothermal compressibility (βT) was calculated from βS using eq 3, R, and the specific heat. The isothermal compressibility increases in a similar manner to βS as a function of temperature (Figure 2B). Differences in mAb βT values are clearly observed and significant at pH 4 and 6. Coefficient of Thermal Expansion. Pressure perturbation calorimetry (PPC) measures the heat produced or absorbed when a pressure change is applied simultaneously to a sample and reference cell.54 The differential heat change can be used to calculate the thermal coefficient of expansion (R) of the partial volume of the sample. PPC also permits the measurement of macromolecule solvation, accessible surface area, and solvent structure. Large values of R may indicate a greater magnitude of volume fluctuations, a larger magnitude of enthalpy fluctuations, or both.67 The addition of ligands and excipients has been shown to modulate the expansibility, volume of unfolding, and hydration layer of a variety of proteins.34,54 Coefficients of thermal expansion as a function of temperature plots display major differences between pH 4 and pH 8 (Figure 4). Alpha increases at pH 4 and 5 and decreases at pH 7 and 8 with little to no slope at pH 6 as a function of temperature. Two distinct transitions are observed at pH 7 and 8, one is observed at pH 5, and no easily observable transition is seen at pH 4 as measured by this technique. Hydration contributions may be estimated from the relative slope of plots of alpha versus temperature from 20 to 40 °C. The values of ∆(R)/∆T20-40 °C as well as the change in volume upon unfolding at all pH values are compared in Table 1. Because the unfolding transition of the Fc region (in the thermogram of the intact IgG) was reversible, volumes of unfolding for this region of the mAb were obtained and found to decrease in the order pH 6 > 7 > 8 > 5.
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Figure 1. Monoclonal antibody midpoints of thermal unfolding: (A) Tm1, (B) Tm2, (C) Tm3, and (D) absolute heat capacity as a function of pH. The numbers represent the data corresponding to the indicated pH. The width of the lines indicates the error associated with the measurement. (E) Full DSC thermograms at each pH indicated within the inset.
State Parameter Fluctuations. Enthalpy and volume fluctuations of the mAb as a function of pH and temperature were calculated from a combination of experimental techniques including PPC, DSC, HR-US, and density measurements using eqs 7 and 6, respectively. Root-mean-square enthalpy fluctuations (〈δH2〉1/2) increase as a function of temperature prior to and decrease past the midpoint of thermal unfolding at all pH values (Figure 5A). Volume fluctuations increase as a function of temperature at all pH values with the largest root-mean-square fluctuations occurring at pH 4 and the smallest at pH 6 (Figure
5B). The mixed second moments of enthalpy and volume fluctuations, obtained from eq 8, are shown in Figure 5C as a function of pH and temperature. All 〈δHδV〉 fluctuations increase as a function of temperature with the lowest values and greatest slope measured for pH 4 solutions and the largest mixed moment fluctuations at pH 7 for all temperatures. Thermoacoustical and Anharmonic Parameters. Specific Acoustic Impedance (Z). The specific acoustic impedance (Z) describes the resistance to propagation of an ultrasonic wave and is only dependent on the physical properties of the material
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TABLE 1: PPC and DSC Thermodynamic Parametersa pH
∆V/V Fc
∆VFc (mL mol-1)
∆R20-40
Tm1
Tm2
Tm3
Tm4
4 5 6 7 8
6.16 × 10-5 1.40 × 10-4 1.05 × 10-4 1.03 × 10-4
1.01 × 10-4 5 × 10-7 -3.6 × 10-5 -4.3 × 10-5 -3.6 × 10-5
53.9 ( 0.1 64.1 ( 0.1 70.0 ( 0.1 70.8 ( 0.1 70.6 ( 0.1
71.5 ( 0.1 82.9 ( 0.2 82.7 ( 0.1 81.4 ( 0.1 79.4 ( 0.2
80.9 ( 0.1 87.1 ( 0.1 85.6 ( 0.1 83.9 ( 0.1 82.0 ( 0.2
84.0 ( 0.2
7.1 15.4 12.1 11.5
a
∆H1 (kcal mol-1) 111.6 ( 0.8 127.2 ( 1.0 137.3 ( 1.1 102.5 ( 1.9 114.1 ( 1.3
Fc ) Fragment crystallizable. ∆VFc ) Fractional volume of unfolding. Tm ) Midpoint of thermal unfolding. ∆H1 ) Enthalpy of unfolding.
Figure 4. Coefficient of thermal expansion (R) as a function of temperature for the mAb at pH 4 (9), pH 5 (b), pH 6 (2), pH 7 (1), and pH 8 ([). The numbers represent the data corresponding to the indicated pH.
Figure 2. (A) Adiabatic and (B) isothermal compressibility as a function of temperature for the mAb at pH 4 (9), pH 5 (b), pH 6 (2), pH 7 (1), and pH 8 ([).
Figure 3. Adiabatic (0) and isothermal (O) compressibility as a function of pH at 25 °C.
of interest. Acoustic impedance is defined by the relationship Z ) FU, where F is the density and U is the ultrasonic velocity. The specific acoustic impedance of mAb pH 4 solutions is clearly distinguished from the resistance to ultrasonic wave propagation of pH 5-8 solutions (Figure 6A). Gruneisen Parameters (Γ, Γ′). The effect of temperature and pH on the thermodynamic (Γ′) and lattice (Γ) Gruneisen parameters is shown in Figure 6B and C. The thermodynamic Gruneisen parameters are relatively temperature independent
from 20 to 55 °C at pH 5, 7, and 8, with a characteristic dip near the thermal unfolding transition (Figure 6B). The temperature dependence of Γ′ is significant at pH 4 and 6 as defined by a positive and negative slope as a function of temperature, respectively. Furthermore, the absolute value of Γ′ ranges from 0.2 to 0.9. The lattice Gruneisen parameters are temperature independent at pH 6, 7, and 8; however, pH 4 and 5 (Γ) parameters decrease as a function of temperature (Figure 6C). Lattice Gruneisen parameters range from approximately 4 to 11 with the most dramatic difference observed at pH 4. Moelwyn-Hughes Parameter (C1). The Moelwyn-Hughes parameter is closely related to the Gruneisen constant and has been related at a fundamental level to the coefficient of thermal expansion (see eqs 4, 9, 11, and 12).61,62 The effects of pH and temperature on the Moelwyn-Hughes parameters and Gruneisen constants are very similar (Figure 6D). Temperature independence is observed at pH 6, 7, and 8, while pH 4 and 5 solutions decrease as a function of temperature. Sharma Parameter (S*). The parameter introduced by Sharma, S*, is similarly related to C1 and Γ, Γ′ with the coefficient of thermal expansion and temperature being the only variables used to calculate S* (see eq 13). The Sharma parameter is temperature independent at pH 6, 7, and 8 up to the thermal unfolding event. In contrast, S* is temperature dependent with a positive slope for pH 4 and 5 mAb solutions (Figure 6E). An abrupt increase in S* at temperatures near the thermal unfolding transition is seen at pH 6, 7, and 8, while this increase is absent at pH 4 and 5. Specific Heat Ratio (γ). The specific heat capacity ratios as a function of temperature and pH are shown in Figure 6F as defined by the ratio of isothermal compressibility to adiabatic compressibility or the ratio of constant pressure heat capacity to constant volume heat capacity. The ratio is near 1.00 at pH 4 and increases in the order pH 4 < 5 < 8 < 7 < 6. An increase in γ as a function of temperature is observed for all pH
3246 J. Phys. Chem. B, Vol. 112, No. 10, 2008
Figure 5. Root-mean-square (A) enthalpy, (B) volume fluctuations, and (C) mixed moment fluctuations for the mAb at pH 4 (0), pH 5 (O), pH 6 (4), pH 7 (3), and pH 8 (]).
conditions, although the heat ratios at pH 6 and 7 plateau at intermediate temperatures. Discussion Understanding the effect of solution conditions such as pH and temperature on protein dynamics and stability should provide a more complete understanding of the inter-relationships of protein flexibility, stability, and function. Similarly, measurements of compressibility, expansibility, state parameter fluctuations, and thermoacoustical and volumetric parameters, which compliment dynamic measurements of varying time scales and amplitudes, have the potential to provide a more in depth understanding of protein motions. Indeed, such analyses help provide a more complete picture of immunoglobulin flexibility. The types and amplitudes of protein motions measured here are diverse and may reflect important modes of structural fluctuations that strongly influence protein stability. The cou-
Kamerzell et al. pling and dependence of the mAb dynamics on solvent fluctuations are of particular interest. Perhaps most strikingly, the previously hypothesized inverse relationship between protein flexibility and stability does not seem to adequately describe this IgG. It is well-known that antibodies are highly flexible molecules and that this plays a role in their ability to bind a diverse number of antigens of various shapes and sizes. In solution, several aspects of IgG dynamics have been studied and include Fab elbow bending, arm waving, and rotation as well as Fc wagging among others. Solvent and environmental effects upon the conformational fluctuations of IgG have, however, not yet been comprehensively described. The types of motions observed in this study are a superposition of many dynamic modes including protein breathing and swelling, conformational fluctuations, and domain displacements. These are expected to be the types of motions that dominate antibody stability and molecular recognition. Protein compressibility reflects both internal protein motions and hydration. Increased dynamic motions, elasticity, cavities, and void volumes (from imperfect packing of amino acid side chains), as well as small conformational fluctuations, will result in positive contributions to protein compressibility. That is, more dynamic, flexible protein ensembles manifest higher compressibilities compared to less dynamic, more restricted ensembles. In contrast, increased hydration contributes negatively to protein compressibility. Higher intramolecular densities tend to restrict fluctuations and lower compressibility. Positive protein compressibilities may be rationalized as resulting from flexibility and dynamics dominating hydration effects as described by βS° ) -(1/ν°)[∂νcav/∂P + ∂∆νsol/∂P] (eq 21), in which ∂υcav/∂P and ∂∆υsol/∂P are the contributions from cavities and hydration, respectively.68 The most dynamic state of the mAb studied here is observed when the pH is lowered to 4, while the most compact ensemble is present at pH 6. Compressibility measurements may not clearly reflect hydration contributions if the internal motions are large, as shown by eq 21. A more informative measure of hydration contributions to protein dynamics can be obtained from the thermal expansion coefficient (see below). At low temperatures (20-25 °C), an initial sharp increase in isothermal compressibility and volume fluctuations followed by a more shallow positive slope is observed. Thus, antibody motions appear to be somewhat suppressed at 20 °C, although small changes in temperature under these conditions still strongly influence its behavior. These dynamic changes at low temperature may be influenced by solvent damping to a greater extent compared to the motions at higher temperatures. A distinct trend in compressibility as a function of pH is observed with a minimum at pH 6 (Figure 3). Interestingly, the least compressible or most rigid ensemble is not the most thermostable based on a comparison of the three deconvoluted Tm values (Figure 1, Table 1). This same trend, as a function of pH, is observed for the Fc volume and enthalpy of unfolding (Table 1), confirming the compressibility results and consistent with the interpretation provided here. Additional explanations of the difference in compressibility between pH 4 and 6 include the neutralization of acidic titratable groups such as aspartic and glutamic acid side chains. Chalikian, Sarvazyan, and others have investigated the change in protein compressibility resulting from differences in hydration of charged, polar, and apolar amino acid side chains.18,28,69,70 It was concluded from this work that water solvating charged groups is less compressible than bulk water, water molecules
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Figure 6. Experimentally determined (A) specific acoustic impedance, (B) thermodynamic Gruneisen constant, (C) lattice Gruneisen constant, (D) Moelwyn-Hughes parameter, (E) Sharma parameter, and (F) specific heat ratio as a function of temperature for the mAb at pH 4 (0), pH 5 (O), pH 6 (4), pH 7 (3), and pH 8 (]). See text for calculations.
solvating aliphatic groups are less compressible than bulk water, and hydration of polar groups depends on their position relative to other polar and charged groups. The neutralization of charged groups (e.g., Asp, Glu), therefore, may explain the increased compressibility at pH 6. The compressibility at higher pH values (∼8) or at the isoelectric point of the protein (∼8.4), however, would be much higher than that at all other pH values if hydration was a major contributor to the protein’s compressibility. The compressibility at pH 8 is actually decreased compared to pH 6, suggesting that the neutralization of charge is not the primary contribution to compressibility in this case. In addition, the coefficient of thermal expansion data is in direct contrast to the neutralization of charge explanation (see below). Recent work by Kamerzell et al. suggests that both changes in the protonation state of aspartic and glutamic acid residues as well as increased dynamics influence the stability of this same IgG.71 Using two-dimensional FTIR correlation spectroscopy
and H/D exchange, the solution pH was shown to modulate stability, conformational heterogeneity, and flexibility. It was concluded that a very complex inter-relationship between differential flexibility and conformational coupling initiated by changes in pH greatly influence the stability of this IgG. Coefficients of thermal expansion are dependent on protein hydration, solvent exposed surface area, cavities and void volumes, conformational fluctuations, and mechanical elasticity.35 In the case of this mAb, the coefficient of thermal expansion (R) as probed by changes in temperature and pH appears to be more sensitive than compressibility to changes in hydration (Figures 2 and 4). This is not surprising, since it has been shown that R is composed of a large temperature-dependent solvation contribution.54 Higher expansion coefficients and greater temperature dependence (steeper slopes) of R as a function of temperature have been proposed to indicate greater solvation.54 The slope of (R) vs temperature plots changes from
3248 J. Phys. Chem. B, Vol. 112, No. 10, 2008 negative to positive as the pH is decreased from 7 to 8 (∼pI) to 4 (Figure 4). It has been shown that aliphatic side chains exhibit a large positive temperature coefficient, while hydrophilic polar or charged side chains exhibit large negative values.54,72 The slopes of alpha as a function of temperature are strongly positive for aliphatic side chains and negative for polar and charged amino acids.54 The temperature dependence of alpha at pH 4 appears to be the result of increased swelling, breathing, and exposure of aliphatic side chains. On the basis of these considerations, it seems probable that, at pH 4, this mAb is highly dynamic and the solvent perturbs its flexibility to a greater extent than at pH 5-8. The slopes of the plots converge at higher temperatures presumably because of similar states of solvation. The unfolding of the IgG Fab region at high temperatures, however, is not reversible and results in protein aggregation. Therefore, conclusions based on the results at high temperatures are not warranted. The enthalpy and volume fluctuations of this mAb are consistent with the idea that, at pH 4, the most dynamic, flexible protein ensemble exists, with the most rigid ensemble present at pH 6 (Figure 5). Decreased enthalpy fluctuations would not necessarily indicate decreased dynamics if two states of very different enthalpies were significantly populated. The maximum in variance occurs at the midpoint of the thermal unfolding transition. Stabilizing the more dynamic state will result in a decrease in the enthalpy fluctuations even though it is more flexible. The state parameter fluctuations increase as a function of temperature under all solution conditions. Thus, the energy landscape of the IgG at pH 4 may be described as rough with multiple excursions in structure with relatively low energy barriers, while at pH 6 small deviations and fluctuations result in primarily native protein ensembles populated. Intermediate dynamics appear to dominate the antibody at pH 5, 7, and 8. The gross effect of pH and temperature on volume and enthalpy fluctuations is not surprising, but the values of the mixed moments of the enthalpy and volume fluctuations as a function of pH are unexpected. The mixed moment fluctuations increase as a function of temperature, as predicted, but decrease in magnitude in the order pH 7 > 8, 6 > 5 > 4. The magnitude of 〈δHδV〉 is surprisingly low at pH 4. One possible explanation is that hydration significantly perturbs the coefficient of thermal expansion term which in turn dominates the calculation of mixed moment fluctuations. This may indicate increased solvent dependence of the conformational fluctuations and slaving of the protein motions at pH 4 and possibly 5. Protein motions may be local or global in nature with varying degrees of damping which tends to reduce the amplitudes of the individual motions through frictional effects. Smallamplitude, fast local motions are more fluidlike and chaotic, as seen in vibrations and torsional oscillations of bonded atoms. In contrast, local collective or group motions of larger amplitude are subject to restoring forces and overdamping. Global protein breathing, compression, and expansion may be either over- or underdamped. Large-scale protein motions are usually of low frequency and involve significant damping (e.g., local unfolding, low-frequency, large-amplitude displacements characterized by the normal modes, or hinge bending). Frauenfelder et al. have shown that large-scale protein motions, such as conformational changes in folded proteins or motions of unfolded polypeptides, are dominated by solvent fluctuations, with local fluctuations at least partially independent of these motions.14,16,73 The types of protein motions detected for this mAb at lower temperatures do not appear to be the result of increased exposure of apolar surfaces or major unfolding events but rather result
Kamerzell et al. from subtle conformational changes and coupling to the solvent. This is further supported by the fractional volume changes upon unfolding (Table 1), intrinsic tryptophan fluorescence, extrinsic fluorescence using the hydrophobic dye ANS, and near and far UV CD measurements (data not shown). Additional support for the presence of subtle differences in conformation and dynamics of this protein is provided by a two-dimensional infrared correlation spectroscopy study using this same IgG and H/D exchange.71 A fractional volume change for unfolding of the Fc region was obtained by integrating alpha as a function of temperature over the region in which the reversible transitions occur (Table 1). As expected, the transitions obtained from DSC measurements occur over the same temperature range as measured by PPC. The values of ∆V are all positive and comparable in magnitude to previously reported volumes of unfolding.36,54,74 The sign of the volume change upon unfolding, however, may be either positive or negative. This has been termed “The Protein Volume Paradox” by Chalikian and Breslauer.26 The transfer of nonpolar groups from apolar to aqueous environments and the hydration of polar and charged groups result in a decrease in volume. Therefore, it is expected that the fractional volume changes upon protein unfolding would be negative.75,76 In fact, the majority of protein unfolding volumes previously determined are negative, in contrast to the positive unfolding volumes measured for this portion of the monoclonal antibody. Both small negative and positive volume changes, however, have previously been seen.77 The large number of negative unfolding volumes previously measured for many proteins may be an artifact of using high-pressure unfolding methods. In the case of this mAb at high temperatures, the thermal expansivity of the unfolded state is greater than that of the folded forms, resulting in positive changes in the volume of unfolding. This has been observed previously with chymotrypsinogen using pressure-temperature modulated ultraviolet difference spectroscopy.78 Protein breathing and swelling may explain the positive ∆V values seen here, as previously postulated for specific solute effects on some small globular proteins as described by Mitra and co-workers.35 The molecular events accompanying the IgG1κ thermal volume of unfolding, however, are very complex, and caution must be exercised in the interpretation of such data. Condensed matter, including polymers and liquids, is generally described by a nonlinear response to mechanical and external perturbations. Nonlinear thermoacoustical parameters have been used to describe the anharmonicity, molecular motions, and elasticity of solids,79,80 liquids,63,81,82 and polymers.57-59,83-85 Thus, describing protein flexibility in terms of condensed matter should be useful. We were, however, only able to identify two previous reports that describe the calculation of the Gruneisen constant for proteins.86,87 Kharakoz calculated Gruneisen constants (Γ) for a variety of proteins combining data from multiple literature values.86 Experimentally determined values of the Gruneisen constant of ∼5 for lysozyme and myoglobin crystals were obtained on the basis of a mechanical nonlinearity index. This is in excellent agreement with our values of 5 at pH 6 and 8, 4.5 at pH 7, and 5.6 at pH 5 (Figure 6). In contrast, the value of 0.6 obtained earlier by Morozov and Morozova88 for Γ may be due to an underestimation of the Gruneisen constant because of structural relaxation in polymers as explained by Kharakoz. The monoclonal antibody thermodynamic and lattice Gruneisen constants are very near the values obtained for a wide range of polymers. For metals and crystals, Γ′ ≈ Γ, but for polymers, this is not the case. The lattice
Immunoglobulin Conformational Fluctuations Gruneisen parameters for the mAb are not equal to Γ′ but range from 4 to 6 at pH 5-8, while, at pH 4, Γ exhibits a strong temperature dependence and much higher values near 10 at 25 °C. The magnitude of Γ is an indication of the anharmonicity of the system with values near 0 describing harmonic motion and little thermal expansion. The frequency of anharmonic vibrations depends on their amplitude, in contrast to harmonic motions in which the frequency is independent of amplitude. Thus, the anharmonicity of the IgG is greatest at pH 4, in agreement with the compressibility, expansibility, and state parameter fluctuations of this large protein. Again, the increase in anharmonicity suggests a dominant contribution from the coupling of vibrational motions, which may be the result of a strong solvent dependence. Interestingly, Γ decreases as a function of temperature suggesting the uncoupling of mAb motions from solvent fluctuations at higher temperatures. This seems reasonable considering the increased energetics at higher temperatures, which would increase intramolecular motions while simultaneously decreasing the slaving to the solvent. Sharma and others have measured the lattice and thermodynamic Gruneisen constants for a number of polymers, and the IgG constants are also of similar magnitude to these molecules.57,85,89 The lattice Gruneisen constant of some representative polymers such as poly(methyl methacrylate), polystrene, polybutene-1, and polypropylene were experimentally determined to be 4.0, 4.4, 4.6, and 9, respectively.83 These values are again in accordance with those measured for the mAb (which range from 4 to 6 at pH 5-8). Warfield and co-workers have measured the thermodynamic Gruneisen constants for polybutene-1, polystyrene, poly(methyl methacrylate), and poly(vinyl alcohol) as 0.66, 0.79, 0.82, and 0.87, respectively.83 The values of Γ′ at pH 5-8 for the mAb range from 0.6 to 0.9, while at pH 4 the IgG manifests much lower values near 0.2, suggesting glassy-polymer-like behavior. The Moelwyn-Hughes parameter (C1) is closely associated with the Gruneisen constant and has been calculated for a number of liquids,90,91 polymers,63,85 and crystals,80 and is equal to the nonlinearity index (µ) calculated by Kharakoz from the available literature (µ ) C1 ) (∂ ln β/∂ ln V)T). The mAb parameter (C1) (Figure 6D) is temperature independent at all pH values except 4 which appears very similar to the lattice Gruneisen constant plot. The magnitude of C1 ranges from 9 to 12 at pH 5-8, in contrast to pH 4 where a value of approximately 21 is seen at 20 °C. The nonlinear index of cytochrome c and pancreatic trypsin inhibitor in solution was calculated86 as approximately 12 from high-pressure NMR results92 and compressibility data,93 in excellent agreement with the IgG Moelwyn-Hughes parameters. Again, these results suggest that the mAb is strongly anisotropic and the vibrational anharmonicity is greatest at pH 4. The common assumption that the Moelwyn-Hughes parameter is temperature independent is obviously not valid in the case of the IgG at pH 4. Temperaturedependent Moelwyn-Hughes parameters have, however, occasionally been observed for polymers.85,94 Sharma has introduced the use of another parameter (S*), also related to the Gruneisen constants and Moelwyn-Hughes parameter, that is calculated from expansivity data alone (Figure 6E). Available S* literature values are rare, and currently, there are no estimates of the Sharma parameter for proteins. Strong temperature dependence and S* values near 1 are seen for the mAb in pH 4 solutions. As the pH is increased, S* increases and the temperature dependence disappears with the largest values of ∼1.28 observed at pH 7. Representative polymer S* values from Sharma for poly(methyl methacrylate), polystyrene,
J. Phys. Chem. B, Vol. 112, No. 10, 2008 3249 and polyethylene (high density) are 1.08, 1.09, and 1.20, respectively.84 Again, these values are similar to those measured for the mAb. Conclusions This work provides a comprehensive description of monoclonal antibody flexibility, dynamics, and stability using fundamental thermodynamic relationships from measurements of sound velocity, compressibility, expansibility, density, and heat capacity. Extensive characterization of proteins using nonlinear thermoacoustical parameters as a function of pH and temperature has not previously been reported. These parameters agree quite well with those values calculated for some polymers and estimated for a few proteins. The most flexible and dynamic conformational ensemble is the least thermally stable and exhibits highly anharmonic behavior. The solvent dependence of the conformational fluctuations and anharmonicity at pH 4 are thought to be a major determinant of protein stability in this specific example. The most rigid ensemble is not necessarily the most thermally stable, although the temperature of the average thermal unfolding transition is greatest at pH 6, the highest observed Fc transition occurs at pH 7-8, while the highest Fab transition appears at pH 5. Thus, these studies provide further evidence that protein flexibility and stability are not simply inversely related. Rather, they can be better described as possessing a complex relationship with multiple contributing factors, including the coupling of protein fluctuations with the solvent. Thermoacoustical parameters appear to provide a unique physical description of the mechanical nonlinearity determining protein dynamics. Further information is still needed to better understand the inter-relationships of protein dynamics, function, and stability based on such considerations. With the currently available technology, and increasing simplicity of measuring sound velocity, density, and expansibility, it is expected that this approach toward understanding protein dynamics will complement NMR, computer simulations, ultrafast spectroscopy, and other methods and begin to help unravel the complex interrelationships between protein flexibility and stability. Acknowledgment. The authors would like to thank MedImmune, Inc., for the kind gift of the monoclonal antibody and financial support of these studies. We especially thank Steve Bishop, Nick Harn, Tom Leach, and Cindy Oliver for their comments and support. References and Notes (1) Gekko, K. Biochim. Biophys. Acta 2002, 1595, 382. (2) Karplus, M.; McCammon, J. A. Crit. ReV. Biochem. 1981, 9, 293. (3) Karplus, M.; McCammon, J. A. Annu. ReV. Biochem. 1983, 52, 263. (4) Karplus, M.; McCammon, J. A. Sci. Am. 1986, 254, 42. (5) Mittermaier, A.; Kay, L. E. Science 2006, 312, 224. (6) Johnson, C. K. Biochemistry 2006, 45, 14233. (7) Wales, T. E.; Engen, J. R. Mass Spectrom. ReV. 2006, 25, 158. (8) Bouvignies, G.; Bernado, P.; Meier, S.; Cho, K.; Grzesiek, S.; Bruschweiler, R.; Blackledge, M. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 13885. (9) LeMaster, D. M.; Tang, J.; Paredes, D. I.; Hernandez, G. Proteins 2005, 61, 608. (10) Ferreon, J. C.; Hilser, V. J. Protein Sci. 2003, 12, 982. (11) Ferreon, J. C.; Volk, D. E.; Luxon, B. A.; Gorenstein, D. G.; Hilser, V. J. Biochemistry 2003, 42, 5582. (12) Fenimore, P. W.; Frauenfelder, H.; McMahon, B. H.; Parak, F. G. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 16047. (13) Fenimore, P. W.; Frauenfelder, H.; McMahon, B. H.; Young, R. D. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 14408. (14) Frauenfelder, H.; Fenimore, P. W.; Chen, G.; McMahon, B. H. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 15469.
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