ABSTRACT

1. Bomb calorimetry and differential scanning calorimetry

In calorimetry, the heat (q) released by a system to its surroundings as a result of chemical and physical phenomena is measured and used to draw conclusions about a system under study. By measuring this heat exchange, other thermodynamic properties such as enthalpy (ΔH) and entropy (ΔS) can be determined, which ultimately allows one to determine the properties that are important in stabilizing or driving the reactions in a given system and the overall potential of a given process through the relationship between these parameters along with free energy ΔG. Applied to nutrition, calorimetry can be used to measure the energy content, kilocalories (Calories), of different foods. An earlier report of a similar experiment involved the use of exploring the energy content of pizza to analyze the nutritional content (12). However, when a chemically defined food item is used, such as a sugar cube, the data can be used to compare and contrast the information reported on a standard nutrition label. For this experiment, a standard bomb calorimeter can be used along with a food sample. The food sample is carefully situated inside the bomb, which is sealed, filled with oxygen, and subsequently placed inside a water bath (at constant volume). The sample is ignited, and afterwards, the temperature of the surrounding water reservoir (surroundings) is monitored until there is no longer an appreciable change. With the change in temperature and the known calorimeter constant, previously determined by combusting a sample with a known enthalpy (benzoic acid, −3226 kJ/mol), ΔH can be determined (13). This experiment can be carried out with commercial food samples such as sugar (sucrose), candies, or other food items with a sufficient caloric content. For these experiments, it is recommended that foods richer in caloric density be used so that a sufficient temperature change can be observed and recorded.

From the constant volume conditions described above, the following is accepted to be true, (1) $$\Delta U_{\text{v}}=q_{\text{sys}}$$ where ΔU_v is the internal energy of the system at constant volume and q_sys is the heat given off by the system at constant volume. Because the change in pressure under these conditions is also considered to be negligible, it can safely be assumed that the internal energy of the system is approximately equal to the enthalpy: ΔU = ΔH. In a bomb calorimeter, q_sys is measured and thus can be used to calculate ΔH on a per mole basis for a chemically defined food item such as sucrose or on a per mass basis for artificial foods for which the chemical content is not specifically defined (e.g., candy).

Because the bomb calorimeter is isolated from the rest of the universe, the reactants constitute the entire system, and the rest of the calorimeter (water bath) is defined as the surroundings. When combustion takes place, the heat released q_sys is subsequently absorbed by the surroundings C_surr and can be determined by (2) $$q_{\text{sys}}=C_{\text{surr}}\times \Delta T$$ where C_surr is the heat capacity of the surroundings or calorimeter constant, previously determined with benzoic acid, and ΔT is the temperature change of the water bath. If the range of ΔT is small (3–5 °C), it can be assumed that C_surr is nearly independent of temperature (14, 15).

Differential scanning calorimetry (DSC) is a method that can be used to measure the thermodynamic stability of a protein such as lysozyme. Lysozyme is a relatively small protein, 14.3 kDa, with a reported temperature transition peak, T_m, at approximately 73 °C (the temperature at which the protein is thermally denatured). The denaturation process for lysozyme is reversible, making lysozyme highly stable relative to other proteins and especially well-suited to this experiment. This lab can be easily adapted to illustrate how factors such as pH or salt content can affect the thermal stability of lysozyme. The experiment and sample preparation are straightforward when the protein, mutants, or both are made ready ahead of time, and the analysis illustrates important thermodynamic considerations related to protein folding and unfolding at a specified or experimentally determined temperature, T_m. From the T_m and the area under the curve (both of which can be extracted from the software program used to operate the DSC, e.g., VP-DSC MicroCal (Malvern Panalytical, Westborough, MA) equipped with Origin Lab by Malvern Panalytical. other thermodynamic parameters can be calculated and conclusions can be drawn about the relative stability of lysozyme and related physiological implications (Fig 2) (16).

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A typical DSC melting curve for lysozyme at pH ∼ 5.0 may look similar to Figure 3. Under these conditions lysozyme exhibits a 2-state model for unfolding reflected by the morphology (width of the temperature transition) and the number of peaks displayed in the DSC thermogram (16–18).

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At the transition temperature, or T_m, it can safely be assumed that [protein_natured] = [protein_denatured]; therefore, the denatured protein is approximately 50% by mole. The free energy, ΔG, for the denaturation (u = unfolding) is related to temperature T, enthalpy ΔH (area under the curve), and entropy of denaturation ΔS by the equation: (3) $$\Delta G_{\text{u}}^{\text{o}}=\Delta H_{\text{u}}^{\text{o}}-T\Delta S_{\text{u}}^{\text{o}}$$

By Eq. 3, temperature and enthalpy are known or measured, and entropy can be calculated at T_m where ΔG = 0. The heat capacity, C_p, is defined over a temperature range and can be expressed as: (4) $$C_{\text{p}}={\left(\text{d}H\text{/d}T\right)}_{\text{p}}$$

It is worth noting that the ΔC_p values for the denaturation of proteins compared with oligonucleotides are distinctly different from one another (Fig 2). The molecular forces that give rise to these differences are significant and should be highlighted.

2. Ultraviolet spectroscopic analysis of DNA melting

To explore nucleotide interactions and the interactions that give rise to secondary structure, one powerful approach is the use of inherent chromogenic shifts in ultraviolet absorbance at various temperatures to track the denaturation of complementary nucleotide strands. Nucleotides can adopt various secondary structures, such as hairpin loops and non–self-complementary and complementary structures, to name a few. Compared with their single-stranded counterparts, double-stranded DNA and RNA have an attenuated absorbance intensity at 260 nm, the typical absorbance wavelength for nucleotides. When applying heat to double-stranded DNA/RNA, the absorbance at 260 nm increases in intensity. This change can be tracked and used to calculate thermodynamic properties depending on the type of predicted secondary structure 2 single-stranded pieces of DNA can form: self-complementary versus non–self-complementary (where [strand A] = [strand B]). The thermodynamic properties underlying this interaction can be determined both experimentally and theoretically. After experimentally determining the thermodynamic parameters for this process, it can be compared by the nearest neighbor prediction method, which is based on theoretical calculations established from previous experiments (19–21). In the lab, students work with small complementary DNA oligonucleotide sequences (heptamers). The solutions of double-stranded DNA are gradually heated to denature the 2 strands and the temperature at which this occurs is recorded by tracking the change in the absorbance intensity at 260 nm with a standard benchtop spectrophotometer equipped with a Peltier temperature controller. A plot of absorbance versus temperature can be generated from the raw absorbance data and the T_m can be used to determine other thermodynamic parameters (22–25).

The general equation for free energy is expressed by (5) $$\Delta G^{\text{o}}=\Delta H^{\text{o}}-T\Delta S^{\text{o}}=-RT\text{ln}{K}_{\text{eq}}$$ where R = 1.987 K⁻¹ mol⁻¹ and K_eq represents the equilibrium constant for the denaturation process. For self-complementary strands, K₅₀ = 1/[C_T]. Therefore, when T = T_m, then K_eq = K₅₀ = 4/[C_T] and gives (26): (6) $$\Delta H-T_{\text{m}}\Delta S=-R{T}_{\text{m}}\text{ln}\left(4/\left[C_{\text{T}}\right]\right)$$

Experimental values can subsequently be compared with theoretical values (27). This exercise can also be extrapolated to other types of DNA strands, adapted to different lengths of DNA or RNA, and used to show differences in thermal stability for GC-rich versus AT-rich strands. Reagents are readily available and can be easily prepared. Oligonucleotides can also be commercially synthesized on a milligram scale from multiple commercial sources (e.g., Integrated DNA Technologies, IDT, Eurofins, Thermo Fisher Scientific).

1. Binding kinetics of 8-anilinonaphthalene-1-sulfonic acid with bovine serum albumin (BSA)

In this exercise, 8-anilinonaphthalene-1-sulfonic acid (ANS) is a fluorescent molecule typically used in biochemistry to assess the hydrophobic content of a protein. ANS alone has very weak fluorescence with an emission maximum λ_max near 500 nm when excited at 380 nm. When ANS binds to BSA, its fluorescence increases dramatically and the λ_max shifts to 470–480 nm. This shift in wavelength and relative fluorescence intensity can be used to track ANS binding with BSA by slowly titrating a solution of BSA into a solution of ANS at a fixed concentration. The resulting ratio of fluorescence signal intensity F_r is determined from measurements of the initial fluorescence signal intensity F_i and final fluorescence signal intensity F_f, which has been corrected (corr) for the change in volume on adding BSA by incorporating F_o from the original fluorescence signal intensity (Eq. 7): (7) $$F_r=\frac{{\left(F_{\text{i}}-F_{\text{o}}\right)}_{\text{corr}}}{{\left(F_{\text{f}}-F_{\text{o}}\right)}_{\text{corr}}}$$

The equation for a simple binding isotherm, (8) $$F_{\text{r}}=\frac{N{K}_{\text{A}}\left[{\text{BSA}}_{\text{free}}\right]}{\text{1}+K_{\text{A}}\left[{\text{BSA}}_{\text{free}}\right]}$$ can be used to describe the relationship between the measured fluorescence intensity and concentration of BSA, where K_A is the association constant for ANS and BSA, N are the number of binding sites, F_r is the ratio of the corrected fluorescence signal before and after binding, and [BSA] is the solution concentration. A graphical representation of the data allows one to extract K_A and determine N. Furthermore, diagnostic tools such as a Scatchard plot are used to extract even more information about the nature of binding, such as cooperativity (negative or positive), and the nature of the binding sites in BSA (equivalent or not). Data analysis with a Scatchard plot is described by Healey (29) along with an alternative experiment measuring fluorescence of ligand–DNA binding.

2. Determining binding sites of bromophenol blue with BSA

A similar approach can be used to determine the number of binding sites of bromophenol blue (BB) on BSA. Instead of using a fluorescence signal to detect the level of binding, the absorbance of BB (590 nm) is used to track ligand binding. Here, the bound ligand, BB, is physically separated from the free ligand by size-exclusion chromatography. The BSA-bound BB complex elutes before the free ligand with the use of a Sephadex G15 resin to separate the two after they have been incubated together for a period of time. By preparing a series of samples with known concentrations of BSA and BB at different ratios with respect to one another, the amount of ligand bound to BSA can be mathematically determined and a binding isotherm generated with the calculated values for bound ligand versus known quantities of free BB ligand. Employing similar principles above, kinetic parameters can be extracted and the nature of the ligand–BSA interaction assessed. This exercise demonstrates the practical importance of size-exclusion chromatography and its separation principles while illustrating how binding kinetics can be used to investigate ligand–protein binding interactions (30–34).

1. Crystallizing lysozyme for structural analysis

In this exercise students use the vapor diffusion method to prepare crystals of lysozyme. Although a number of methods can be used to prepare high-quality crystals, here students learn about different parameters that can affect protein crystal growth and how these parameters can be tested simultaneously in a relatively systematic approach. Each group of students sets up a “crystal box” with a cell culture plate—24-well plates work well—in which they can test 24 different conditions to determine which conditions yield the best crystals. Altering parameters such as pH and salt concentration over a range of values gives students a chance to generate a multitude of conditions, all of which can be sampled in their crystal box (37, 38). In practice, a pH range of 4.3–4.9 has worked best with a sodium acetate buffer. Salt concentrations can vary from 0.5 to 2.0 M in the reservoir. Protein concentrations ranging from 20 to 50 mg/mL have been used successfully. A small quantity, 2–5 μL, of the prepared protein solutions are then spotted on the lid of the 24-well plate. These solutions should match the pH and buffer concentration of the reservoir, with a higher salt content in the reservoir. The plate and lid are carefully sealed and incubated at constant temperature (21–25 °C).

After 1–2 wk, the crystals can be evaluated with a standard benchtop light microscope, with which students can determine the conditions that produced the best crystals. Lysozyme crystals can range in morphology and shape. To differentiate between salt and protein crystals, subsequent experimentation can be carried out to verify. Typically, lysozyme crystals are tetragonal, whereas sodium chloride produces cubic lattice structures (39–42). A simple flame test can further verify protein from salt crystals, because salt crystals can withstand the intense flame of a Bunsen burner when passed through (43). The exercise is also a great way to get students to investigate the literature to compare their crystals with what has been reported and to compare their growth conditions (44).

2. Computational tools to analyze protein crystal structure

After students have obtained and analyzed the morphology and physical properties of crystals from their growth experiment, the next phase of the exercise encompasses an analysis by guided approach to begin understanding the kinds of questions structural biologists think about when extracting information from their crystal structure data. If one is fortunate enough to have access to an x-ray crystallography facility, one might be able to generate his or her own data; however, the use of PyMOL (or other) and crystal structure data deposited in the PDB is an alternative approach. In this exercise, students are introduced to PyMOL and begin learning how to execute commands to carry out different functions related to the types of questions that concern structural biologists. Such questions include highlighting important features of lysozyme structure, such as its catalytic residues; elements of secondary, tertiary, and quaternary structure; and the distances between residues. Although it is easy enough to spend several class periods learning the nuances of the program, this exercise is intended to introduce students to more of its advanced features to encourage them to explore more of the capabilities of the program. Students can download an educational version of the program, or an institutional site license can be purchased. Published tutorials are readily available from which additional exercises can be adapted (45, 46). PyMOL allows students to explore protein structures at atomic resolution, providing a platform for a broad range of possibilities for structural analysis assignments. Coupled with crystallization techniques at the bench, this exercise approaches the subject of introductory structural biology, facilitating reasoning capabilities based on a previous foundation of biochemical knowledge.

3. A particle-in-a-box approach to studying interactions of light with matter

This exercise demonstrates how theory in spectroscopy and experimentation can be used to solidify the understanding of quantum theory of subatomic particles.

The use of simple pigment molecules such as lutein and beta-carotene illustrates this idea. These 2 compounds can be readily extracted from vegetables such as spinach and carrots with a few milliliters of 200-proof ethanol. Standards are also used to establish the wavelength maxima for each compound and to verify that the compounds extracted are in fact lutein and beta-carotene. Next, a wavelength scan is carried out, and the λ_max is recorded. The experiment described here is simplistic and can be carried out without the aid of a computational math program such as Maple (Maplesoft, Waterloo, ON, Canada), although incorporating this type of program for these problems is encouraged (47).

The value of λ_max can be obtained in this experiment and corroborated with theoretical values calculated with the assistance of the software program, Spartan (version 8.0.6, Wavefunction Inc., Tokyo, Japan) (48–50). With this program, students can import structure files for each molecule and then calculate bond lengths and cumulatively determine the length of the theoretical “box,” or linear molecule. From the calculated length L of the box and theoretical principles of quantum mechanics introduced in the prelab lecture (workshop, Eq. 9), the wavelength of light λ required to initiate an electron transition Δn can be determined from the energy values E calculated for the transition, (9) $$\Delta E=\frac{\left(n_{\text{f}}^{\text{2}}-n_{\text{i}}^{\text{2}}\right)h^{\text{2}}}{\text{8}{\text{mL}}^{\text{2}}}$$ where n is the quantum energy level occupied by an electron, h is Planck's constant, L is the length of the box, and m is the mass of an electron. Conversely, measurements can be used to calculate the theoretical box length of lutein and beta-carotene and be compared to their calculated values by λ_max and Eq. 10, (10) $$E=h\nu =hc\text{/}\lambda$$ where c is the speed of light and ν is the frequency associated with the wavelength of light absorbed. Several things should become clear as students work through this exercise. Molecules do not always behave, in theory, the way they are often expected to, and theoretical models are only as good as the factors used to determine them. Sometimes other important considerations give rise to discrepancies in models compared with experimentally determined values. Other compounds can be readily adapted to this exercise as well (51).