In the Laboratory
Lysozyme Thermal Denaturation and Self-Interaction: Four Integrated Thermodynamic Experiments for the Physical Chemistry Laboratory Jeffrey J. Schwinefus,* Nathaniel J. Schaefle, Gregory W. Muth, and Gary L. Miessler Department of Chemistry, St. Olaf College, Northfield, MN 55057; *
[email protected] Christopher A. Clark 3M Drug Delivery Systems Division, St. Paul, MN 55144
There is growing interest in building undergraduate science curricula at the interface of chemistry and biology (1). The recent Bio2010 report recommends enhanced investigative experiences and integration of quantitative physical sciences, mathematics, and biology to foster student interdisciplinary thinking (2). Our department has long recognized thermodynamics as one of the most fundamental and powerful subjects encountered in the undergraduate physical sciences and its central role in both chemical and physical change. We feel thermodynamics provides the vehicle to develop laboratories at the chemistry– biology interface since thermodynamics has truly undergone a rebirth in the last two decades with numerous applications in the burgeoning field of biophysical chemistry (3, 4). We present a physical chemistry laboratory suite of four thermodynamic experiments investigating the thermal denaturation (or unfolding) and self-interaction of hen egg white lysozyme in aqueous solution as functions of pH and ionic strength. Laser light scattering (LLS) and gel permeation chromatography (GPC) are used to measure the second virial coefficient of lysozyme, while differential scanning calorimetry (DSC) and UV absorbance thermal denaturation are used to investigate the unfolding thermodynamics of lysozyme. By dividing these experiments into two sets that use complementary techniques, we give students the opportunity to validate their experimental results. These experiments have been used in our physical chemistry laboratory required for chemistry majors. We find that physical characterization of a protein piques the intellectual curiosity of students who have an interest in science at the chemistry–biology interface. Additionally, lysozyme is relatively inexpensive and its unfolding (5, 6) and self-interaction (7, 8) have been subjects of significant research. These experiments enable students to develop connections between thermodynamic concepts developed in physical chemistry lecture and biopolymer inter- and intramolecular interactions studied in the laboratory. Each lab provides students with an impetus for performing the given experiment and clear instructions for completing the experiment and analyzing the data. However, interpretation of the data emphasizes the investigative nature of the project (9), encouraging students to look for patterns in the class data to speculate on the dependence of lysozyme folding and self-interaction on pH and ionic strength. At the same time, this set of experiments introduces students to the physical chemistry of polymers and the techniques used to characterize them, a component of the physical chemistry laboratory we have stressed in the past (10). Experimental Measurements Students work in pairs throughout the sequence of experiments. The instructor assigns each pair of students one of four
available 45 mM sodium acetate buffers: pH 3.6 with either 0 mM or 60 mM NaCl or pH 4.6 with either 0 mM or 60 mM NaCl. The low solution pH values ensure sufficient positive charge on lysozyme to avoid lysozyme aggregation without any added NaCl (8). Hen egg white lysozyme was purchased from Sigma and used without further purification. Freshly prepared stock 6–10 mg/mL lysozyme solutions are provided to students for gravimetric dilution. All experiments can be completed in the standard four hour period. Instructions for lysozyme solution preparation, operation of the instruments, and data analysis are given in the online supplement. Visualizing Lysozyme Using Protein Explorer As an introduction to the sequence of lysozyme experiments, we have students complete an exercise using Protein Explorer (11) to visualize the three-dimensional structure of lysozyme. This exercise is especially beneficial to those students who have not had a biochemistry course. During this exercise, we emphasize the distribution of cationic and anionic residues on the surface of lysozyme and how lysozyme’s overall positive charge depends on pH. Understanding the dependence of lysozyme charge on pH is critical for students to understand the dependence of lysozyme unfolding and self-interaction on pH and ionic strength. Lysozyme Interactions Monitored by LLS In our first experiment designed to quantify lysozyme selfinteraction in solution, students use static LLS to determine the second virial coefficient A2. Positive values of A2 correlate with strong solvent–solute interactions, whereas negative values correlate with strong solute–solute interactions. To facilitate student understanding of nonideal solutions, we develop LLS theory by first considering the familiar virial expansion of the ideal gas law. We then introduce students to ideal and nonideal solutions by developing an analogous expression of the virial expansion of van’t Hoff ’s law describing osmotic pressure (12). Introducing students to nonideal solutions using discussions of osmotic pressure is a straightforward and familiar practice to develop student comprehension of A2 (see p 26 in the online supplement for this discussion). Since the intensity of scattered light is proportional to the magnitude of polymer concentration fluctuations, we can derive the expression for static light scattering from a polymer solution,
Kc 1 2 A2 c RQ PQ M w
(1)
where K is an optical constant; c is the polymer concentration in mass/unit volume; Rθ is the Rayleigh factor and a measure of the
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 1 January 2008 • Journal of Chemical Education
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In the Laboratory
(Kc/R90p) / (10ź5 mol/g)
8.8
8.4
8.0
7.6
7.2
1
0
2
3
4
5
6
7
c / (10ź3 g/mL) Figure 1. Representative student LLS plots of hen egg white lysozyme at an angle of 90º according to eq 1. Lysozyme dissolved in a 45 mM sodium acetate, pH 3.6 buffer with 0 mM (●) and 60 mM (○) NaCl. Linear regression yields 103 × Kc/R90 = (2.14 ± 0.19)c + (0.0718 ± 0.0007) (0 mM NaCl data) and 103 × Kc/R90 = (0.11 ± 0.18)c + (0.0719 ± 0.0007) (60 mM NaCl data). The second virial coefficient A2 is given by one-half the slope of the best-fit line. 0.6
A
lysozyme
Absorbance
0.5 0.4 0.3 0.2
AMP BD
0.1 0.0 ź0.1 0
5
10
15
20
Time / min
B
ln KD
ź0.145
ź0.150
ź0.155
ź0.160
0
5
10
15
[Ȳciȵ(1 − KD)] / (10ź5 g/mL) Figure 2. (A) GPC of blue dextran (BD, 0.4 mg/mL), lysozyme (1 mg/mL), and adenosine monophosphate (AMP, 0.05 mg/mL). Blue dextran (Mw ≈ 2,000,000 g/mol) is excluded from the pores in the stationary phase and elutes first while AMP (Mw = 347 g/mol) explores the entire column volume and elutes last. (B) Representative student plots of the natural logarithm of the GPC lysozyme distribution coefficient KD according to eq 2. Lysozyme dissolved in a 45 mM sodium acetate, pH 3.6 buffer with 0 mM (●) and 60 mM (○) NaCl. Linear regression yields ln KD = (88.8 ± 3.9)(1 − KD) − (0.158 ± 0.001) (0 mM NaCl data) and ln KD = (21.9 ± 7.1)(1 − KD) − (0.150 ± 0.001) (60 mM NaCl data). Second virial coefficients A2 are proportional to the slopes of the best-fit lines.
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intensity of scattered light at a given scattering angle and distance from the detector; Pθ is the form factor describing the scattering of light from large polymers; and Mw is the polymer weight-average molar mass (12). Because of the small molar mass of lysozyme, 14,320 g/mol by amino acid sequencing (8), Pθ ≈ 1. Students gravimetrically dilute the stock lysozyme solution to prepare five samples ranging from 1–6 mg/mL. Students measure the intensity of scattered light from each solution at angles of 75°, 90°, and 105° on a Brookhaven Instruments BI200-SM light scattering apparatus. Figure 1 contains plots of eq 1 for representative lysozyme light scattering data sets using pH 3.6 sodium acetate buffers with 0 mM and 60 mM NaCl. Linear regression of the data in Figure 1 yields the slope, 2A2, for each solution. The intercepts in Figure 1 can be used to determine Mw of lysozyme using eq 1. Positive and negative values of A2 indicate repulsive and attractive lysozyme–lysozyme interactions, respectively. As seen in Figure 1, the addition of NaCl attenuates A2 significantly. Lysozyme Interactions Measured by GPC In our second experiment to determine A2 for lysozyme– lysozyme interactions, we measure the lysozyme concentration dependence of the GPC distribution coefficient (7). This novel application of GPC allows us to introduce students to thermodynamic nonideality of solutions using lysozyme activity coefficients in the mobile and stationary phases. Assuming lysozyme equilibrium in the stationary and mobile phases, equating free energies yields (7), ln K D = 2 A2 Mw ci (1 − KD ) − ln Ko (2) where KD is the concentration-dependent lysozyme distribution coefficient; 〈ci〉 is the average lysozyme concentration in the mobile phase; and Ko is the distribution coefficient in the limit of infinite dilution. Students are required to gravimetrically prepare four lysozyme solutions from 1–4 mg/mL. Each solution is spiked with adenosine monophosphate and blue dextran as standards to measure the retention times of molecules completely included in and excluded from the stationary phase pores, respectively. The retention times of all three analytes are used to construct KD (7). Our Agilent 1100 Series chromatographs use hydrophilically modified 5 μm silica bead columns from YMC (YMC-Diol-200AMP, 30 cm × 0.6 i.d.), a flow rate of 0.5 mL/ min, and UV absorbance detection at 278 nm. Linearity of the absorbance signal with lysozyme concentration indicates little, if any, lysozyme–blue dextran complexation (13). A typical chromatogram is shown in Figure 2A. Figure 2B shows representative lysozyme GPC data sets fit to eq 2 for pH 3.6 sodium acetate buffers with 0 mM and 60 mM NaCl. The slope of each plot is equal to 2A2Mw. Thermal Denaturation of Lysozyme Monitored by UV Absorbance Spectroscopy In the first experiment studying lysozyme unfolding, students review the van’t Hoff relation between the equilibrium constant Kd and the van’t Hoff enthalpy, ∆Hvo for thermal denaturation (14), which we express as $ Hvp $S o ln K d (3) RT R where R is the ideal gas constant, T is absolute temperature, and ∆S o is the entropy change for the unfolding transition.
Journal of Chemical Education • Vol. 85 No. 1 January 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
In the Laboratory
Thermal Denaturation of Lysozyme Monitored by DSC As a complementary technique to UV absorbance spectroscopy, students use a MicroCal VP-DSC calorimeter to determine both the model-independent calorimetric enthalpy ∆Hcalo (16) and ∆Hvo (17) for denaturing lysozyme. Figure 4 shows a representative DSC scan for lysozyme where the excess heat capacity Cp,ex for the sample is plotted versus temperature. In Figure 4, the area between the lysozyme and baseline scans represents ∆Hcalo while ∆Hvo is determined by the peak-width (17). Students attempt to verify that the two-state model for lysozyme unfolding is applicable under our conditions by showing ∆Hcalo = ∆Hvo (18). If the instructor wishes, the step in heat capacity between the native and denatured states can serve as a starting point for discussion of the hydrophobic effect (17). Hazards Lyophilized hen egg white lysozyme is a fine powder and users should avoid inhalation. The buffers used are acidic, so skin contact and ingestion should be avoided. Students working with the LLS apparatus are equipped with laser goggles. Results: Putting It All Together As part of a peer reviewed report, students must identify trends in thermodynamic variables for lysozyme thermal denaturation and self-interaction with pH and ionic strength. To facilitate this, students must first pool class data, averaging the results from all groups for each buffer. Tables 1 and 2 give averaged one-semester class data for the four experiments. As seen in Table 1, values of A2 determined by GPC are generally larger
1.0
ln Kd
0.5
0.0
ź0.5
ź1.0 2.870
2.880
2.890
(1/T ) / (10
2.900 ź3
2.910
2.920
ź1
K )
Figure 3. Representative student plots of the natural logarithm of the two-state equilibrium constant Kd for lysozyme unfolding determined from UV absorbance as a function of reciprocal absolute temperature. Lysozyme dissolved in a 45 mM sodium acetate, pH 3.6 buffer with 0 mM (●) and 60 mM (○) NaCl. Linear regression yields ln Kd = (‒66.6 ± 1.0) × 103/T + (192 ± 3) (0 mM NaCl data) and ln Kd = (‒63.3 ± 0.6) × 103/T + (184 ± 2) (60 mM NaCl data). The slopes of the best-fit lines are proportional to the van’t Hoff enthalpy and x intercepts occur at the denaturation temperatures, Td (eq 3).
80
Cp,ex / kJ/(mol pC)
For construction of Kd from absorbance versus temperature scans, we invoke the two-state model for lysozyme unfolding, which assumes that lysozyme transitions reversibly between native and denatured states (14). Hence, Kd = [U]/[F] = fU/ fF where fi denotes the fraction of protein in unfolded (U) and folded (F) states. We stress to students that Kd, as well as ∆Hvo and ∆S o, are model-dependent. We and others (5) have found lysozyme denaturation to be reversible, as evidenced by nearly identical absorbance versus temperature curves for consecutive heating and cooling cycles. However, the degree of reversibility is dependent on the final temperature used in the experiment. Solutions heated to higher final temperatures (e.g., 100 oC) are more susceptible to aggregation (14) and lack the degree of reversibility seen in absorbance versus temperature curves with lower final experimental temperatures (e.g., 85–90 oC). Students measure the absorbance at 301 nm of a nitrogendegassed 0.50 mg/mL lysozyme solution as a function of temperature from 30–100 °C using a Cary 100 UV–vis spectrophotometer equipped with a Peltier temperature controller. To avoid concentration-dependent enthalpies, we urge students to dilute the stock lysozyme solution to 0.50 ± 0.05 mg/mL. Plots of eq 3 are shown in Figure 3 for representative lysozyme thermal denaturation data sets using pH 3.6 sodium acetate buffers with 0 mM and 60 mM NaCl. Students determine ∆Hvo and ∆S o at the denaturation temperature, Td, where ln Kd = 0 and half the lysozyme molecules are in the native state while half are in the denatured state. We limit student analysis to a small temperature region around Td (approximately Td ± 2 oC) since ∆Hvo and ∆S o for protein unfolding are strongly dependent on temperature (15). Negative slopes and positive intercepts indicate ∆Hvo > 0 and ∆S o > 0 for lysozyme unfolding.
60
40
20
0 20
30
40
50
60
70
80
90
100
110
Temperature / pC Figure 4. Student DSC scan of the excess heat capacity, Cp,ex, as a function of temperature for lysozyme in a 45 mM sodium acetate, pH 3.6 buffer. The dotted curve is the buffer baseline.
Table 1. Student Lysozyme Laser Light Scattering (LLS) and Gel Permeation Chromatography (GPC) Results LLS
GPC
pH
[NaCl]/ mM
3.6
0
14390 ± 360
11.3 ± 1.7
24.0 ± 2.1
4.6
0
13610 ± 380
7.5 ± 2.0
10.1 ± 0.5
3.6
60
13910 ± 140
1.8 ± 1.0
8.4 ± 2.2
4.6
60
14250 ± 320
–1.4 ± 1.8
–0.3 ± 1.1
Mw/ (g mol−1)
A2/ A2/ (10−4 mL mol g−2) (10−4 mL mol g−2)
Note: Each value an average from 2–4 different student groups with standard errors. Experiments conducted in a 45 mM sodium acetate buffer.
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In the Laboratory
Table 2. Student Lysozyme UV Absorbance Thermal Denaturation and Differential Scanning Calorimetry (DSC) Results UV Absorbance Thermal Denaturation
pH
[NaCl]/mM
3.6
0
73.4 ± 0.2
4.6
0
3.6 4.6
Td/oC
∆Hvo/(kJ
mol−1)
DSC
o
∆Hcalo/(kJ
mol−1)
∆Hvo/(kJ mol−1)
∆S /(J mol−1 K−1)
Td/oC
537 ± 17
1550 ± 50
72.8 ± 0.1
512 ± 1
532 ± 2
77.8 ± 0.2
566 ± 37
1620 ± 60
76.6 ± 0.1
523 ± 1
547 ± 2
60
72.9 ± 0.2
522 ± 12
1510 ± 30
72.1 ± 0.1
509 ± 2
521 ± 2
60
77.3 ± 0.2
557 ± 15
1590 ± 40
76.2 ± 0.1
522 ± 1
537 ± 1
Note: Each value an average from 2–4 different student groups with standard errors. Experiments conducted in a 45 mM sodium acetate buffer.
than those determined by LLS, potentially due to assumptions in our GPC analysis model. However, the attenuation of A2 with increasing pH and ionic strength is observable with both techniques. As pH increases, the positive charge on lysozyme decreases, attenuating repulsive electrostatic forces between lysozyme molecules (8). With NaCl, the repulsion between lysozyme molecules is screened sufficiently to decrease A2 near or below zero (8). Values of Mw agree favorably with Mw determined from amino acid sequencing (8). Values of ∆Hvo in Table 2 for both UV spectroscopy thermal denaturation and DSC are in excellent agreement with similar investigations (5, 6). With all buffers studied, ∆Hcalo/∆Hvo ≈ 1, validating application of the two-state unfolding model (18). The increase in Td, ∆Hvo, and ∆Hcalo with increasing pH is the result of less electrostatic repulsion between amino acid residues on folded lysozyme molecules. Students are required to present class results and their interpretation of the trends in the thermodynamic variables with pH and ionic strength in a journal-style report, mimicking manuscript submission to the Journal of Physical Chemistry B. To facilitate peer review of the reports, students are required to complete a grading rubric assignment that directs them to the author guidelines for the Journal of Physical Chemistry B. Students must identify the requirements and assign maximum points to be awarded for each section of the report. The grading point distributions in the class grading rubrics are averaged to provide a grading scale for peer review. We feel the journal-style report is a fitting capstone to the investigative and integrated lysozyme experiments and provides most students their first exposure to manuscript submission and peer review. These experiments are readily adaptable. Gel permeation chromatography and UV absorbance spectroscopy are generally lower cost alternatives to LLS and DSC, respectively, and provide enough information for students to observe the dependence of lysozyme thermal denaturation and self-interaction on pH and ionic strength. Even a single experiment could be used to explore lysozyme denaturation or self-interaction based on the instructor’s interest or available instrumentation. To prevent results from one year being shared with subsequent years, the instructor could change protein or buffer conditions. Acknowledgments The light scattering apparatus and differential scanning calorimeter were funded through a National Science Foundation Department of Education CCLI Adaptation and Implementation grant (#0511529). St. Olaf College provided matching funds.
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Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Jan/abs117.html Abstract and keywords Full text (PDF) Links to cited URLs and JCE articles Supplement Student handouts Instructor notes containing: Theory behind each experiment Instructions for lysozyme solution preparation Use of the instruments Data analysis
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