2+ M ∙EDTA Binding Affinities: A Modern Experiment in Thermodynamics for the Physical Chemistry Laboratory Leah C. O’Brien*, Hannah B. Root, Chin-Chuan Wei, Nahid Shabestary, Cristina De Meo, and Douglas J. Eder† Department of Chemistry, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1652 ABSTRACT Heat to Reference Cell (μJ) -151 -153 -155 -157 0 1000 2000 3000 4000 Time (s) 5000 As a part of reporting their results, students were asked to infer on the basis of their observation and chemical knowledge what they might observe at different pH values (strongly acidic and strongly basic) and in a different (phosphate) buffer also at pH = 7.4. All lab reports (n=20) from the Physical Chemistry Laboratory course in Fall 2011 were reviewed by an external assessment expert (DJE) to assess four aspects of critical thinking, which are based fundamentally on the critical thinking theories of Richard Paul . Critical thinking is good [effective] when it is: -154 -156 -158 1. Clear (communicates effectively) -160 2. Logical (relevant and coherent) -162 3. Broad (asks "What else?") 4. Deep (asks "What next?") -164 0 6000 1000 Ca2+ + EDTA 2000 3000 Time (s) 4000 5000 6000 0 c) How well does the discussion in the lab report recognize the potential influence of the buffer itself and consider how a phosphate buffer might change the thermodynamics (an indicator for property #3 above)? 500 Schematic diagrams for the ITC apparatus can be found online [e.g., 24-27]. Briefly, a reference cell and a sample cell are submerged in an adiabatic chamber as shown in Figure 1. One reagent is contained in the sample cell, and the other reagent is loaded into a syringe injector. Both reagents are in the identical buffer solution to minimize mixing/dilution enthalpy. In a standard ITC experiment, the automatic injector introduces a known amount of solution into the sample cell using a programmable series of small titrations. A sensitive thermocouple on each cell activates feedback electronics which will increase or decrease the electrical current to the reference cell and maintain the cells at the exact same temperature. A graph of current vs. time produces the ITC isotherm. ΔH is obtained by integrating the area under the curve, and both exothermic and endothermic reactions can be monitored. Each titration peak is integrated separately, and these values are used to create the sigmoid-shaped curve of the integrated isotherm. The equilibrium binding constant Kb can be determined by the severity of the sigmoid curve, and the mole ratio n can be determined using the inflection point of the sigmoid curve. The experimentally determined ΔH and Kb from the ITC analyses can be used to calculate ΔG, and ΔS based on the well-known thermodynamic relationships, ΔG = -RT ln(Kb) = ΔH - TΔS. It should be noted that n is used as a float number to evaluate the acceptance of the data; a value that deviates significantly from 1 indicates problems in determining the sample concentrations. THERMODYNAMICS OF M2+ + EDTA BY ITC Micro-ITC has for the most part been utilized only in biophysical research laboratories, due in part to the equipment expense (micro-ITC >$70k) and the reagent costs (i.e., enzymes). However, the importance of hands-on experience with micro-ITC is growing, since this is one of the few ways to study the weak biochemical interactions that often correlate with a biological response. Thus experience with ITC is important for students seeking further research opportunities and employment in the broad fields of pharmaceutical and biochemistry. This experiment studied the [M2+ + EDTA] reaction for M2+ = Ca2+ and Mg2+ using ITC. Ethylenediaminetetraacetic acid, often abbreviated as EDTA or H4Y, is a useful chelating agent. EDTA has a high affinity for metal cations, and binds to metal atoms in a hexadentate fashion with a 1:1 mole ratio. Students first prepared a 10.0 mM HEPES buffer trimmed to pH=7.4, then made 2.0 mM Mg2+, 2.0 mM Ca2+, and 0.3 mM EDTA solutions using the buffer as solvent. The laboratory handout developed for our students is available from the “Supplementary Materials” available online from this Journal. The handout includes instruction on careful handling and loading of the ITC, and gives suggestions for the preparation of quantitatively accurate, dilute solutions. The handout gives the pKa,n values for HEPES (n=1,2) and EDTA (n=1-6). Associated with this work is a companion paper that describes a lysozyme∙NAG3 binding experiment using competitive inhibition developed for the Biochemistry Laboratory at our institution . Due to the delicate nature of that experiment (e.g., enzyme costs, enzyme purification requirements, and careful microscale techniques), a more robust and inexpensive experiment (described in this manuscript) was also developed to be used as the initial introduction to ITC. This work describes experiments using isothermal titration calorimetry to study the binding of EDTA with M2+ cations, suitable for a two-week experiment in an upper level Physical Chemistry Laboratory course. Representative isotherms and integrated isotherms from student work are shown in Figures 2 and 3. The thermodynamic values obtained from the experiments are given in Table 1 and are compared with literature values [1,2]. Students found that [Ca2+ + EDTA] binding is an exothermic process (see Figure 2), whereas [Mg2+ + EDTA] binding was an endothermic process (see Figure 3). Table 1. Thermodynamic properties for [Mg2+ + EDTA] and [Ca2+ + EDTA] binding obtained from student experiments (rows 1, 2 top) and comparison with literature values in various buffers (rows 1-5) [1,2]. 1 2 3 4 5 Mg2+ + EDTA in HEPES* pH=7.4 Lit value from  Ca2+ + EDTA in HEPES pH=7.4 Lit value from  Ca2+ + EDTA in TRIS* pH=7.5  Ca2+ + EDTA in MOPS* pH=7.5  Ca2+ + EDTA in PIPES* pH=7.5  Kb (x 106 M-1) ΔH (kJ/mol) n 1.27 +19.0 .88 0.60 +18.4 1.0 Buffer Ionization Enthalpy (in kJ/mol) [1,29] 21.7 30 -21.0 .92 44 -25.0 1.0 198 -50.0 1.0 47.4 235 -24.0 0.99 21.9 104 -13.9 1.01 11.5 *HEPES=4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid: TRIS=tris(hydroxymethyl)aminomethane: MOPS=3-(N-morpholino)propanesulfonic acid: PIPES=piperazine-N,N′-bis(2-ethanesulfonic acid). 21.7 -200 -300 -400 -500 400 On a three-point scale (3 = way better than good enough, 2 = good enough, 1= not good enough), the observations are recorded below in Table 2. The rubrics that describe the scale of 3, 2, 1 follow thereafter in Table 3. The analysis reported above was not used to grade the student lab reports or to record correctness of student calculations or interpretations. Rather, it was a separate analysis of student critical thinking based on the experimental observations available to them and on background knowledge of chemistry appropriate to the level of the exercise. 300 200 100 -600 0 0 2 4 6 8 10 Injection # 12 14 16 Figure 2. Isotherm (top) and integrated isotherm (bottom) for [EDTA + Ca2+] binding by ITC. -1 1 3 5 7 Injection # 9 11 13 Figure 3. Isotherm (top) and integrated isotherm (bottom) for EDTA + Mg2+ binding by ITC. EDTA binds stronger to Ca2+ than Mg2+ due to the favorable size match between the EDTA and Ca2+ ionic radius, and most students expected different binding enthalpies. However, all of the students (to date) have been surprised by the endothermic reaction of [Mg2+ + EDTA]. A series of post-lab discussion questions helped to guide students through the reaction for a better understanding of their results. These included, “Identify the conjugate acid/base pair for HEPES at pH=7.4”, “Identify the exact chemical formula of EDTA at this pH”, “Where does the proton from the EDTA go?”, and “Identify all bonds that are broken and all bonds that are formed during the reaction.” At a pH of 7.4, all carboxyl groups are deprotonated to carboxylate groups, one amino nitrogen with pKa,5 = 6.16 is neutral (not protonated), while the other amino group with pKa,6 = 10.3 is protonated, leaving EDTA (pH=7.4) triply ionized as HY3- [26,27]. EDTA therefore must shed a proton to the buffer prior to chelating metal cations and creating the [M2+∙Y4-]2- complex. Thus the observed binding enthalpies are strongly dependent on pH and buffer ionization enthalpy [1,29,30]. Table 3. Rubric for the Assessment Scores Shown in Table 2. Table 2. Summary of Scores for Critical Thinking Assessments (n=20). a. Effect of ionic size on ΔH of chelation b. Inferences about effect of pH on binding enthalpy c. Inferences about phosphate vs. HEPES buffer effects Score=3 Score=2 Score=1 5 6 9 8 8 4 1 3 16 Score=3 a. Effect of ionic size on ΔH of chelation Accordingly, and with respect to the isothermal calorimetry exercise, inferential questions below were considered: b) To what degree does the discussion in the lab report deal effectively with how pH might change the affinity of EDTA for divalent ions due to deprotonation (an indicator for property #4 above)? 600 -100 5. Discriminating (arrives at evidence-based conclusions) a) To what extent does the discussion in the lab report make inferences as to the effect of ionic size on chelation (an indicator for property #4 above)? Mg2+ + EDTA Integrated Energy (μJ) Isothermal titration calorimetry (ITC) is a relatively new technique that is used to determine thermodynamic parameters for a reaction. Modern, ultrasensitive micro-ITC (< 1mL scale using mM and nM solutions) has found many applications in Biochemistry and Pharmaceutical research: protein-protein, protein-drug, protein-DNA, protein-ligand and metal-ligand interactions are examples of intermolecular interactions that can be studied by ITC [1-20]. Despite the explosion of micro-ITC in physical biochemistry research and in the pharmaceutical industry in the past decade, only a few articles related to this important analytical method have appeared in the science education literature. Three papers from the Journal of Chemical Education  were identified that describe ITC undergraduate experiments. The 2001 JCE paper  describes an isothermal heat conduction calorimeter and offers several ideas for undergraduate experiments. The 2008 and 2011 JCE papers [22,23] describe the construction of a low-cost, home-made isothermal calorimeter and an [Ba2+ + 18-crown-6] binding experiment. These experiments show the great variety in applications of calorimetry at the mL scale: however, the equipment described does not offer the ultrasensitivity of the modern micro-ITC systems that is needed for enzyme binding studies, which are normally conducted at the sub-mL scale. Heat to Reference Cell (μJ) ISOTHERMAL TITRATIONAL CALORIMETRY -149 January 23-25, 2013 Washington, DC DISCUSSION AND EDUCATIONAL GOALS Mg2+ + EDTA -147 Integrated Energy (μJ) Isothermal titration calorimetry was used to experimental determine the binding constant and thermodynamic values for the EDTA(aq) + M2+(aq) reactions, for M2+ = Ca2+ and Mg2+. Students showed that for reactions in a HEPES buffer (pH=7.4) the Mg2+ + EDTA reaction was endothermic, while Ca2+ binding to EDTA was exothermic. EDTA is triply ionized at pH 7.4 and therefore must shed a proton to the buffer prior to chelating Ca2+; thus, the observed binding enthalpies were strongly dependent on buffer ionization enthalpy. Assessment results of student laboratory reports are described. Ca2+ + EDTA 2013 TUES/CCLI PI Conference Renaissance Washington DC Hotel 999 Ninth Street NW Washington, DC 20001 Specifically infers ion size effect on chelating affinity Score=2 Suggests a relationship between ion size and chelating affinity Score=1 Makes incorrect inference or ignores the effect altogether b. Inferences about effect Discusses Discusses of pH on chelation protonation/deprotonation protonation/deprotonation of EDTA and infers correct in general terms only direction of the effects Omits or garbles protonation/deprotonation effects c. Inferences about phosphate vs. HEPES buffer effects Does not mention possible interference of phosphate or states that there is no effect as long as pH remains the same Recognizes potential interference of phosphate, with reasons Mentions that phosphate might interfere, but does not describe how so 15 In general, the evidence suggests that students grappled effectively with inferential questions (a) and (b), that is, considering the question, "What next?" For example, 16 out of 20 students successfully predicted more exothermic binding enthalpies at higher pH due since EDTA would be fully deprotonated (see Table 1). Students followed a basic chain of reasoning that linked their observations directly to causes and consequences. In contrast, the evidence suggests that students were less successful in grappling with inferential question (c) about running the same experiment in a phosphate buffer at pH=7.4 (that is, considering the question, "What else?"). 4 out of 20 students considered potential solubility/interference aspects of a phosphate buffer, but no students discussed the buffer ionization enthalpy. In their defense, rarely have students been asked to consider the thermodynamics of the solvent let alone that of the buffer system. However, as a group, they did not bring in much information from elsewhere in their backgrounds (that is, they did not transfer knowledge) that might have been of use to them: a common failing because transference is difficult. This means that people can speculate wildly and entertainingly when constraints are absent, but they find it harder to make good inferences when constrained by existing evidence. Further experiments are being considered to address the transference issues noted above related to H+ sequestration thermodynamics with choice of buffer. For example, a 3rd week could be set aside for students to run the experiments in a TRIS buffer at pH=7.4. To help them make this leap, more emphasis could be placed on the question “Where does the proton from the EDTA go?” Additional material on buffer ionization enthalpies [29,30] would be included in the handout. In summary, the isothermal calorimetry exercise, when paired with inferential questions, brought about observable, effective critical thinking among students. It appears that students were more successful in thinking linearly about direct causes and consequences, but less successful in thinking broadly (suppose conditions were altered…what then?). CONCLUSION The seemingly straight-forward binding process of [M2+ + EDTA] is thus actually very complex and involves many scientific concepts from freshman chemistry to upper level courses: students review and strengthen their understanding of buffers, as well as the relationships between pKb, pH, and protonation; students must consider the displacement of a proton from the binding ligand – a situation that also occurs often in an enzymatic binding pocket; and students must consider the thermodynamics of the displaced proton sequestered by the buffer. Additionally, students gained hands-on experience with the ITC to better prepare them for subsequent ITC experiments encountered in the biochemistry laboratory course . Ideas and suggestions for further development of this experiment include: using several different buffers to illustrate the dependence on buffer ionization; changing the pH of reaction to demonstrate enthalpy of proton displacement in the binding pocket; changing the chelator (e.g., EGTA instead of EDTA) to exhibit different chelator-metal specificities, and using a competitive binding technique to determine more precisely the equilibrium binding constant Kb for the [Ca2+ + EDTA] reaction, such as [Mg2+·EDTA + Ca2+]. Acknowledgments and References The authors gratefully acknowledge the financial support of the NSF Division of Undergraduate Education, through award #0941517. References are available in the associated manuscript available from the presenter.