Learn more about research at Calvin
All of our full-time professors participate in diverse year-round research. Discover more about each of their current research projects:
Dr. Carolyn Anderson
Dr. Eric Arnoys
Dr. Michael Barbachyn
Dr. Dave Benson
Dr. Ron Blankespoor
Dr. Crystal Bruxvoort
Dr. Roger DeKock
Dr. Herb Fynewever
Dr. Larry Louters
Dr. Mark Muyskens
Dr. Kumar Sinniah
Dr. Chad Tatko
Dr. Doug Vander Griend
The Anderson group is focused on developing new synthetic methodologies for preparing N-alkyl pyridones, including amino acid homologues. N-Alkyl pyridones are interesting motifs due to their prevalence in natural products as well as their potential to serve as amino acid mimics and engage in strong intermolecular hydrogen bonds. As such, the development of a simple means for achieving selective nitrogen alkylation within pyridone motifs continues to be a synthetic goal. To this end, our group has recently disclosed a novel lithium iodide mediated O- to N-benzyl migration, with current studies directed towards elucidating the transformation’s mechanism (Scheme 1, JOC 2008).
Scheme 1. Lithium Iodide-Promoted O- to N-Benzyl Migration.
Extension of the lithium iodide-promoted migration to propargylic systems, such as 7, has lead to not only the expected product 8, but also a wealth of addition new reactions (Scheme 2). Utilizing either a modified lithium iodide method or a gold catalyzed process, we can now access a wide range of synthetically useful, N-alkyl pyridone containing products 8-10 by simply modifying reaction conditions. Further studies to optimize these reactions and determine their scope and mechanism are ongoing in our laboratory.
Scheme 2. Reactivity of Propargyloxypyridines.
Our research is currently funded by the National Science Foundation and the Research Corporation for Science Advancement.
One of our research goals has been to determine how specific proteins shuttle in and out of the nucleus of mammalian cells. We have been using molecular biology, fluorescence microscopy with Green Fluorescent Protein (GFP), and molecular modeling to examine how the polarity of amino acids and the structure of proteins allow them to bind to interact with transport proteins.
Confocal fluorescence microscopy also allows us to selectively bleach GFP in specific regions or compartments within the cell. The rate of return of fluorescence depends upon the protein being studied, the compartment bleached, and the state of the cell. We hope to use this information to help determine how cells regulate protein transport within the cell.
Research includes development of novel synthetic methodology; identification of unique bioisosteres with applicability in pharmaceutical agents and conception and preparation of novel anti-infective agents with actviity against multidrug-resistant pathogens.
Sensors that selectively detect fluxes of small molecules in living cells are being developed. We are primarily focuses on bacterial periplasmic binding proteins, such as maltose binding protein, that undergo ligand dependent changes in protein conformation or tertiary structure (see movie). Proteins that provide the small molecule (e.g. maltose, lead ions, glucose, glutamate) selectivity are engineered to bind semiconductor nanoparticles, called quantum dots. Quantum dots have an intense and photostable fluorescence compared to organic fluorophores. The proteins are also engineered to bind metal complexes or organic fluorophores. In our first generation biosensor a ruthenium complex (top left) was attached to maltose binding protein, which when attached to ZnS coated CdSe nanoparticles (botom left) provided maltose-dependent changes in emission intensity. The mechanism by which the maltsoe-dependent emission intensity changes occurs comes from an electron transfer reaction between the ruthenium complex and the quantum dot (upper right). The majority of projects in the lab are based on this core technology and are focused on designing proteins to bind molecules other than their natural ligands (e.g. lead ion biosensors) or focused on fluorescence microscopy for live cell small molecule imaging and single molecule fluorescence analysis.
We are interested in applying our nanobiosensor technology to imaging fluxes of small molecules inside or on the outer surface of living cells. For instance, calcium ion fluxes are vital to neural synapses and signal transduction and have spawned research into calcium ion selective fluorophores such as Fura-2. Our technology will provide sensors that can be used for hours inside living cells as opposed to minutes with current organic-based fluorophores. An additional feature with our quantum dot-based sensors is that molecular fluxes can be imaged in red blood cells. The figure above and to the left shows InGaP nanoparticle fluorescence from inside rabbit red blood cells. An additional feature of quantum dots is that the emission linewidth is small relative to organic fluorophores. This means that it is possible to image multiple quantum dot sensors using monochromater or filter cube selection (e.g. top, right figure). The ultimate goal is to use these sensors to understand the molecular basis of diseases controlled by small molecule transport (e.g. Diabetes mellitus, lead poisoning, atherosclerosis).
Using a microscope outfitted for total internal reflected fluorescence (above, left) we are examining the fluorescence from single protein-quantum dot assemblies. Single qunatum dots have intermittent fluorescence (click here for a movie), called "blinking." Fluorescence intermittency is modulated by electron transfer reactions with the excited states of fluorophores. From a series of experiments, we expect our nanobiosensor systems function through an analyte-dependent ground state electron transfer reaction that effects the character of fluorescence intermittency. This concept is shown above (right), where maltose (analyte) introduction changes not only the average emission intensity but also the deviation of the emission intensity. We are developing methods for analyzing maltose binding to single maltose biosensors to characterize the heterogeneity of maltose affinities and lower limits of detection in these systems. We expect that reporducible heterogeneity will increase the analyte sensitivity by orders of magnitude from solution measurements.
We have used a computer algorithm (Dezymer) to introduce side chain repalcements that allow phosphate binding protein to selectively bind lead ions. The coordination sphere (above, top, left) whose geometric parameters were used for Dezymer calculations was selected due to the preference for a stereochemically active lone pair (SALP). An interaction with a pre-existing, positively-charged arginine residue from the phosphate binding site (above, top, right) seems to still allow lead ion binding but (presumably) repels zinc, cadmium, and copper ion binding. There is also a quicktime movie of the simultated binding site provide. Introduction of the redesigned phosphate binding protein into the nanobiosensor system provides a 100 nM lower limit of detection for lead ions (above, bottom) that can be performed in the presence of red blood cells.
Crosslinked Protein Derived Cofactors
Cofactors generated through posttranslational redox reactions are best known from green fluorescent protein. However, a series of smaller cofactors (above) are formed by association with metal centers in proteins and participate in concert with these metal centers often times for enzymatic function. Our lab is investigating this relatively new class of protein cofactors using computational modeling, protein design, and small molecule synthesis.
Our research is currently funded by the Office of Naval Research.
One of our research projects involves the use of a commercially available chiral catalyst in allylic substitution reactions with amines as nucleophiles and carbonates as leaving groups. When racemic carbonates are reacted with one-half equivalents of amines in the presence of this rhodium catalyst, not only are the secondary amine products obtained in high enantioselectivity, the unreacted carbonates are also obtained as a single enantiomer. Thus, this method can be used can be used for the kinetic resolution of racemic carbonates and for the synthesis of secondary amines in large enantiomeric excesses. We are studying the mechanism for this reaction and exploring the scope of this reaction with respect to substrates, nucleophiles, and leaving groups.
Research in scientific reasoning, conceptual change, nature of science and inquiry-based science teaching.
We model molecules using the tools of computational chemistry. Some of our chemical projects are:
1) Hydrogen atom migration in organometallic complexes.
2) Relative energy of molecular and ionic forms of NH3(H2O)7
3) We are examining methods to extract "effective" nuclear charges from atomic ionization energies.
My particular research focus is on the role of formative assessment inside and outside of the classroom. By formative assessment, I mean a process in which students receive feedback regarding their thinking and understanding while they are doing the work associated with learning. To further illustrate what I mean by formative assessment, contrast it with the more typical summative assessment. Often in schools, most assessment is summative: the teachers’ feedback is in the form of a grade and comments after students complete the test, paper, or homework. In this way, the assessment measures the result of learning but does not contribute (in any direct way) during the learning process.
Figure 1: Summative assessment (only) model
In summative assessment there is no opportunity for the student to make thinking visible until the summative exam. At this point, it is too late for the instructor use data from the student’s thinking to adjust content delivery, student’s preconception lens. There is also no opportunity for the student to learn from their mistakes (i.e. to process again in light of the final grade).
In formative assessment, the student’s thinking is made visible early and repetitively during the course. The instructor can use the data from the student’s thinking to adjust instruction priorities and new content delivery. The instructor and/or the student’s peers can give the student feedback to correct any misconceptions in the student’s lens and the feedback serves as input for further student processing. A summative grade can also be assigned.
Figure 2: Formative (+ summative) assessment model
There are many ways to structure a classroom and assignments to incorporate formative assessment into student learning. Below I will briefly describe my recent, current, and future work.
Web-based homework — Recently I published a paper examining the effect of feedback immediacy on my General Chemistry students1. In particular, I conducted a controlled experiment comparing the learning outcomes for students with traditional “paper” homework assignments versus students with web-based assignments. The critical difference between these class sections was that those students who turned in paper homework experienced a two-day delay in receiving their graded homework back again while the students who submitted their homework online received their grades with feedback instantaneously. The data from this experiment show that web-based homework was as effective as paper-based homework for student learning. One shortcoming of the web-based homework is that some students are likely to “game the system,” which can reinforce poor problem solving practices. This limitation, also seen in physics education research2, warrants future research.
Small group inquiry activities — In a recent paper3 I examined the effectiveness of inquiry laboratory work in juxtaposition to “cookbook” laboratory work. Formative assessment is implicit in inquiry as it is defined by the National Science Education Standards4. During an inquiry activity, amongst other things, a learner:
- determines what constitutes evidence and collects it;
- formulates explanation after summarizing evidence;
- forms reasonable and logical argument to communicate explanations.
When these tasks are conducted in an environment of interaction with a small group of peers and a roving instructor, they naturally lead to continuous feedback for the students while they are learning. My research showed that students’ thinking is on a deeper level with inquiry activities in comparison to “cookbook” laboratories where most questions served only to clarify details of how to follow lab manual instructions.
Current and future directions
Students will learn best during a class period if they continuously assess their understanding of the material. For most students, copying notes off the board is woefully insufficient interaction - students simply rush to copy down the notes, postponing interaction with the material until later. In her book Tools for Teaching, Davis cites research indicating that the typical student’s attention span is only 10 to 20 minutes5. To keep students engaged, I have tried the following formative assessment techniques to form an interactive classroom.
Questions PLUS a minute to think — I try to avoid a typical classroom pitfall: many teachers, after asking a question, rarely wait for more than a few seconds before giving prompts6. In this case, most students will not engage themselves in thinking through the question asked, but will instead wait for the instructor or their fellow students to answer the question for them. As a result, students are getting no feedback on whether or not they could answer the question (this again returns to my theme of formative assessment). In contrast, I’ll often preface a question for my class with the request “Please don’t say anything yet. Think about the problem and write down how you’d solve it.” Then I stand in front of the class in utter silence for a full minute or more! I find that with this method nearly every student interacts with the problem and is therefore invested in the subsequent discussion of the solution. Measuring the impact of this technique is an area of current and future research.
Peer instruction — To include peers in the students’ sources of feedback, I use Eric Mazur’s technique outlined in his book Peer Instruction7. Using this method, the instructor uses a classroom response system (“clickers”) or hands out index cards with the letters A, B, C, and D on them. Then a multiple-choice conceptual question is presented with these four choices. The students have some time to think about the problem. After an appropriate amount of time, the students simultaneously vote. Now that they’ve committed to one answer, the students turn to their neighbor and discuss their answer and get feedback. Then they vote once more. Most likely, the class converges towards the correct answer. I plan to investigate what impact this peer feedback has on long term memory of the concepts taught.
Directed peer-led discussion — An important skill for upper-division students to acquire is the ability to talk about chemistry to experts and non-experts alike. The extent to which students can talk about chemistry tells them pretty quickly whether or not they really understand what they’re talking about. What better way then, to integrate a vigorous cycle of formative assessment, than to have each upper-division student lead class discussion on a topic in chemistry, fielding questions and comments from non-expert classmates?
In my upper-division classes I assign each student with the task of leading class discussion centered on a particular topic for a given week. In preparation, all students must read a journal article supplied by the student leader in advance of the discussion and answer a set of questions related to it. Included in these is the question “Write down two good questions about the article which do not know the answer to.” These questions are written on the board prior to the first day’s discussion and the class works together over the subsequent days to formulate the answers. While the leader guides the investigation, all of the students are learning very actively as they puzzle through their own questions. Importantly, the leader is learning the most of all as he or she utilizes the very depths of their understanding to fulfill the role of expert.
Role of undergraduate researchers
Research in chemical education is interdisciplinary in nature often sharing aspects with research in the social sciences. This requires well-rounded investigators, such as those found amongst Calvin students. Working collaboratively with me, students engage in:
- Experiment design Educational research requires careful planning. Student researchers examine the literature and propose educational experiments designed to avoid common pitfalls.
- Intervention design Often experiments include design of new instructional practices. Students have insights and intuition that are a welcome addition to the plans of faculty who may not remember what it is like to begin on the journey of learning chemistry.
- Implementation and data collection There is a large amount of legwork needed to conduct educational research. This includes meeting ethical regulations for work with human subjects, recruiting subjects, collecting artifacts of learning outcomes, interviewing subjects, etc.
- Data analysis Both quantitative, statistical analysis and qualitative, thematic analysis are used in my research. Students learn tools of the trade which will serve them well in many types of future research.
- Writing. I work collaboratively with the students to communicate our work through peer-reviewed publications.
1 H. Fynewever, The Chemical Educator 13, 264 (2008).
2 A. M. Pascarella, in National Association of Research in Science Teaching (Vancouver, BC, 2004).
3 P. Meyer, H. H. Hong, and H. Fynewever, The Chemical Educator 13 (120-124) (2008).
4 National Science Education Standards. (National Research Council National Academy Press, Washington, D.C., 2000).
5 B. G. Davis, Tools for Teaching. (Jossey-Bass, San Francisco, CA, 1993).
6 M. B. Rowe, in Questions, Questioning Techniques, and Effective Teaching, edited by W. W. Wilen (National Education Association Washington, D.C., 1987).
7 E. Mazur, Peer Instruction (Prentice Hall, Upper Saddle River, NJ, 1997).
Regulation of Glucose Uptake
Overview: Our research focuses on glucose transport into cells and how that rate of transport rapidly adjusts as the cells’ environment changes. Glucose is arguably the most important energy source in biological systems. Proper glucose uptake is critical to the maintenance and health of a wide variety of organisms. For example, in humans, diabetes is a disease in which glucose uptake is compromised either due to the insufficient production of insulin (type 1) or compromised response to insulin at peripheral tissues (type 2). The uptake of glucose across biological membranes is mediated by a family of proteins called GLUTs (GLUcose Transporters). Our lab is particularly interested in the regulation of two of these transporters—GLUT 4, which is responsive to insulin, and GLUT 1, which is found in a variety of tissues and is responsible for basal or background uptake. Acute regulation of GLUT 4 by agents such as insulin and exercise is primarily mediated by a translocation of the transporter from internal stores to the cell surface, thereby increasing glucose uptake. GLUT 1 was initially viewed to be responsible for basal uptake and therefore not acutely regulated by environmental conditions. However, recent data from our lab and others have indicated that cell stressors such as azide, hyperosmolarity, and methylene blue can quickly increase the transport of glucose through GLUT 1. Our current research focus is to understand the acute regulation of glucose uptake with a focus on the activity of GLUT 1. GLUT1 is a membrane glycoprotein of about 55 kD, (see Figure from Lehninger (Freeman)) which transports glucose in and out of the cell. Its proposed structure is shown below. We are currently exploring three plausible mechanisms for the activation of GLUT1.
Our lab works with several cell types—intact mouse muscle (soleus and epitrochlearis), cultured fibroblast cells (L929, which contain only GLUT 1), and cultured myoblast cells and myotubes. Glucose uptake is measure by scintillation spectrometry using the radioactive glucose analog, 2-deoxyglucose or 3-O-methylglucose.
Recent Student Projects
Project: Genetic engineering of GLUT1
We have generated a genetic construct consisting of the GLUT1 gene with the green fluorescent protein attached to the C-terminus. We have transformed L929 fibroblast cells and have shown that the chimeric protein is expressed and locates to the Golgi and cell surface as expected. This fluorescentGLUT1 will be used in FRAP and FRET assays to study changes location or mobility that may result from activation of the transporter. We will also generate a chimeric protein with GFP attached to the N-terminus should the C-terminus GLUT1-GFP prove to be either not able to transport glucose or not able to be activated.
Project: Role of Adjacent Sulfhydrals in the Activation of GluT1
A family of membrane imbedded proteins, known as GluT, transport glucose into cells. Phenylarsine oxide, chemical that binds tightly to the sulfur atoms of neighboring cysteine residues, has a dual action on glucose uptake. At low concentrations (3µM) it activates glucose uptake, and at higher concentrations (10µM) it blocks the activation of glucose transport initiated by either methylene blue treatment or glucose starvation.
Project: Investigating GluT1 Activity in Cardiac and Muscle Cells
We have shown that cell stress, such as glucose starvation can quickly activate the glucose transport activity of GluT1 in fibroblast cells. We are interested in understanding this mode of activation extends to other cell lines. This study investigated the effects of insulin and glucose starvation on a muscle cell line, L6 cells, and on a cardiac cell line, H9c2 cells. In both types of cells, glucose starvation stimulated glucose uptake suggesting activation of GluT1. In L6 muscle cells the effects of insulin, which activates GluT4, was additive to the effects of glucose starvation, again suggesting that insulin and cell stress activated different glucose transporters.
Project: Effects of Cinnamon on the Activity of GluT1 Glucose Transporter
Cinnamon has been recommended as a nutritional aid for patients with type 2 diabetes. In this study, we investigated the effects of a cinnamon extract on the glucose transport activity of GluT1 in fibroblast cells. Surprisingly, we found that the extract potently inhibited glucose transport. The extract was separated into 6 fractions using chromatography. The inhibitor compound was isolated in fraction #4. The purified compound, cinnamaldehyde, mimicked the inhibitory effects of the extract. A systematic study of the cinnamaldehyde and related analogs reveal that low concentration actually active transport and higher concentration inhibit. The activity of cinnamaldehyde can be blocked by prior reaction of cinnamaldehyde with a sulfhydral compound. This provides evidence of the importance of sulfhydrals (cysteine residues) to the activity of GLUT1.
We are using a laser-based photochemical technique to study the elimination of hydrogen fluoride (HF) from fluorine containing organic molecules in the gas phase. Our focus recently has been on two molecules, formyl fluoride and trifluoroacetylacetone, which give remarkably different results. The goal is to learn fundamental details about how ultraviolet laser-excited molecules fall apart. Our infrared laser probe technique gives us information about how much vibrational and rotational energy is released into the HF molecule produced in the reaction. Ultimately, our experimental data is used to test theoretical approaches to modeling these kinds of light-based reactions.
Our laser-based photochemical technique allows us to study the elimination of hydrogen fluoride (HF) from fluorine containing organic molecules in the gas phase. We will continue our investigation of two molecules, formyl fluoride and trifluoroacetylacetone, which give remarkably different results. This summer represents a unique opportunity to use a new, NSF-funded, tunable laser system, which greatly expands our ability to use ultraviolet laser pulses to initiate chemical reactions. The summer work continues our ongoing research program investigating photoelimination. Students working with us on the experiment will gain experience in gas synthesis and gas handling, several types of lasers, data acquisition, analysis and modeling. As part of the training the Calvin student(s), along with other students in our research consortium, will be trained in use of the new laser system by Purdue University laser specialist Hartmut Hedderich. The student(s) will also have an opportunity to meet with the other research groups in the consortium, possibly including a trip to Purdue University.
Single Molecule Studies of Biological Systems by Atomic Force Microscopy (AFM)
My research group uses single molecule force spectroscopy to understand the interactions between molecules in biological systems. Single molecule measurements can track an individual molecule over a period of time or measure many single molecule events one at a time. A single molecule can therefore act as a probe to map the local environment around it.
Our group uses an Atomic Force Microscope (AFM) to investigate single molecule interactions. An AFM is typically used to visualize objects on a surface at nanoscale resolution in three-dimensions (see AFM Gallery ). However, the AFM can also measure very small forces. A force measurement always involves tethering the molecules of interest to a cantilever and to a surface, then using a piezoelectric scanner to move the surface towards the probe to allow the molecules of interest to interact before pulling them apart to measure the rupture force.
We are particularly interested in understanding the interactions between carbonic anhydrase enzyme and its inhibitors. An overactive carbonic anhydrase produces excess fluid in the eye, leading to the increase in intraocular pressure resulting in possible damage to the optic nerve in the eye. This process, also known as glaucoma, is a serious eye disease. It can be partly treated using inhibitors that bind to the carbonic anhydrase enzyme.
To measure biomolecular forces, we attach the carbonic anhydrase enzyme to a positively charged surface and the inhibitor to an AFM probe via a long tether. The rupture between the inhibitor and the enzyme leads to a specific shape on a force curve measurement referred to as the rupture event in the cartoon below. All other interactions are considered non-specific and result in a large adhesion curve.
Hundreds of these rupture events can be measured and displayed as a distribution of forces to discriminate between single molecule interactions and multiple molecule interactions.
Using microscopic models recently developed by Dudko and Hummer models, the force distribution plots can be analyzed at different pulling velocities to estimate kinetic and thermodynamic parameters for the single molecule interaction.
Nanoscale DNA surface features can be constructed on template stripped gold surfaces by using a combination of "nanoshaving" and self assembly. An AFM tip can be selectively used to remove a layer of a short double-stranded DNA in a specific area, and the shaved area can then be refilled with a longer length single-stranded DNA. The single stranded DNA in the shaved area can be hybridized with a complementary strand and the entire process of manipulation can be monitored by AFM in situ. Nanoscale DNA surface features can be constructed on template stripped gold surfaces by using a combination of "nanoshaving" and self assembly. An AFM tip can be selectively used to remove a layer of a short double-stranded DNA in a specific area, and the shaved area can then be refilled with a longer length single-stranded DNA. The single stranded DNA in the shaved area can be hybridized with a complementary strand and the entire process of manipulation can be monitored by AFM in situ.
Our group also attaches short complementary DNA strands to an AFM probe and to a surface and measures the rupture force present in a duplex DNA strand.
We have shown that the magnitude of the rupture force is dependent on the force at which the AFM probe and surface come into contact initially. By varying the initial contact force, we have demonstrated the rupture force from a DNA duplex can vary significantly.
An Alternative to Lewis-Acid CatalysisMutagenesis studies have implicated an aromatic stack as the method of enzymatic activation for the purine salvage pathway in protozoa. Generation of a beta-haripin peptide with diagonally displayed tryptophan residues should mimic the binding pocket yielding glycosidic bond hydrolysis of adenosine
Peptides Mimicking Nature: The Crucial Role of Aromatics
The widespread use of pentachlorophenol (PCP) has resulted in this toxin leaking into the soil and ground water. By using a beta-hairpin scaffold a molecular cleft is engineered to bind PCP. These peptides may be tuned both structurally and electronically to bind additional, related toxins.
Biocatalytic Desulfurization of Diesel Fuel
The burning of sulfur containing compounds in petroleum fuel stocks has been linked with acid rain and cardiopulmonary disease. Bacteria degrade dibenzothiophene (DBT), but not on the macroscale. Introduction of aromatic rich peptides have shown the capacity to bind DBT and may present a novel method of sulfur removal.
The quest for technologically useful materials with nanometer-sized features increasingly relies on synthetic innovations to assemble complex supramolecules. The difficulty in creating intricate structures from smaller molecular building blocks is organizing the pieces in specific pre-designed ways. The difficulty increases with complexity, but so do the rewards. Just as the secondary, tertiary, and quaternary elements of structure endow enzymes with enhanced functionality, so development of nanotechnology aims to harness the efficacy beyond the limits of primary covalent interactions. This area of research has recently spawned applications in catalysis, ion exchange, host-guest interactions, molecular magnets, nanoelectronics, and nanomachines.
We build supramolecules by linking inorganic units (atoms or clusters) with organic ligands. We are working to design, synthesize, and characterize coordination networks of arbitrary size, shape, and symmetry by exploiting mathematical constraints and chemical control. Besides encouraging undergraduate students to invent and execute rational synthetic schemes, this interdisciplinary research aims to advance the limits of self-assembly molecular processes.
At left is a hypthetical supramolecule built from 4 nickel(II) cations, 4 pyrazine molecules and 4 2,2'-bipyridine molecules.
Many inorganic coordination compounds are beautifully colored, and some change color with changing temperature. We want to design systems that can change from any color to any other color at a preset temperature. The study of these compounds involves spectroscopy, thermodynamics, and inorganic synthesis.
It is possible through advanced mathematical computations to obtain information about pure chemical compounds in solution without isolating the compounds themselves. This is a huge advantage to studying solution thermodynamics, which we employ in both of the previous research topics listed. We have written computer protocols which take spectrophotometric data of multiple solutions at equilibrium and solve for the molar absorbtivities of all the species in solution and the equilibrium reactions constants for the reactions between them.
Our research is currently funded by the NSF and the ACS Petroleum Research Fund.