CHEM 3175 Biophysical Chemistry Fall Semester, 2015
Department of Chemistry and Biochemistry
The University of Texas at Arlington
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TABLE of CONTENTS
Item
Pg.
Course Information…
3
Schedule of Events…
6
Experiment 1 – Particle in a Box
10
Experiment 2 – Electron Paramagnetic Resonance
13
Experiment 3 – Magnetic Susceptability
19
Experiment 4 – Enzyme Kinetics
26
Experiment 5 – Circular Diochroism
36
Experiment 6 – DNA Melt
42
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CHEM 3175 BIOPHYSICAL CHEMISTRY (General Information) INSTRUCTORS: Dr. Brad Pierce Phone: 817‐272‐9066 Office Hours: by appt. TAs and Meeting Times Meeting Time/Place TA Office: SH 300 F e‐mail: [email protected] Office Hours
Contact Thurs. 1‐5pm/CPB 211 Sinjinee Sardar Tues. 1‐3 SH 314 [email protected] Wed. 1‐5pm/CPB 211 Philip Palacios [email protected] Text: Other materials: storage drive Thurs. 1‐3 SH 314 Laboratory Manual, will be distributed electronically Scientific calculator, Laboratory notebook, USB portable Grading: Lab Reports (5) 250 pts. (5 x 50) Notebook Check (2) 50 pts. (2 x 25) Poster Presentation 50 pts. PREPARATION Read the experiment before you come to class. Preparing an outline of the experimental procedures prior to the lab is required before you walk through the door. This means that every calculation for dilutions and all sample preparations must be completed and present in every group member’s notebook prior to coming to lab. THIS ALSO MEANS THAT YOU MUST KNOW THE STOCK CONCENTRATIONS/MOLAR MASS/ECT OF WHAT YOU WILL BE USING. You may need to visit the station you will be attending the next week to write down this information from the reagent bottles. Be prepared to be verbally quizzed by your TA about the experiment you are about to perform. Failure to complete any of these tasks will result in dismissal from the current week’s lab period. If you are dismissed from the lab, you can come the following week to finish as much of the experiment that you can. Use of a computer (spreadsheets and word processors) is an essential component of this course. The university provides numerous sites for free student computer usage with access to various software. It is your responsibility to practice and familiarize Mandatory Online Safety Training: yourself with the software. Ask your TA if you need extra guidance. Page | 3
Students registered for this course must complete the University’s required “Lab Safety Training” prior to entering the lab and undertaking any activities. Students will be notified via MavMail when their online training is available. Once notified, students should complete the required module as soon as possible, but no later than their first lab meeting. Until all required Lab Safety Training is completed, a student will not be given access to lab facilities, will not be able to participate in any lab activities, and will earn a grade of zero for any uncompleted work. 1. You should have received an email from the UTA Compliance Department. Click on the link in the email (or navigate to https://training.uta.edu for the login page) 2. Log on using your network log‐on ID and password (what you use to access email). If you do not know your NetID or need to reset your password, visit http://oit.uta.edu/cs/accounts/student/netid/netid.html. 3. The available courses for completion will be listed. For Chemistry 1441, complete the course entitled ‘Student Lab Safety Training’ 4. Go to ‘Training I’ve Completed’, and print this displayed page for your TA. Verify that it shows clearly your name, that the training is completed/passed and the date when the training was completed. If you have just completed the training but it is not updated on the ‘Training I’ve Completed’ page, try the training again (you should get to the Certificate page). If this does not work, call the training helpline at 817‐272‐5100. 5. If you did not receive the training email and you have not already completed the training you will need to contact the training helpline (817‐272‐5100) or email [email protected]. 6. Students who have not completed the training by census date may be dropped from the lab (and consequently the lecture). Once completed, Lab Safety Training is valid for the remainder of the same academic year (i.e. through next August) for all courses that include a lab. If a student enrolls in a lab course in a subsequent academic year, he/she must complete the required training again. All questions/problems with online training should be directed to the University Compliance Services Training Helpline at 817‐272‐5100 or by emailing [email protected]. Policies and Notes: Dropping: When dropping the course, you are responsible to see that all the proper paperwork is done by checking with the Chemistry Department office and, YOU MUST properly check out of the lab, and account for any missing, broken, or dirty apparatus. Failure to follow these instructions will result in a grade of ‘F’. Drop for non‐payment of tuition: If you are dropped from this class for non‐payment of tuition, you may secure an Enrollment Loan through the Bursar’s office. You may not continue to attend class until your enrollment Loan has been applied to outstanding tuition fees. Grade Replacement: Students enrolling in the course with the intention of replacing a previous grade earned in the same course must declare their intention to do so at the registrar’s office by Census Date of the same semester in which they are enrolled. Page | 4
Pass/Fail: If P or F is a grade option in this class and you intend to take this class for a pass/fail grade instead of a letter grade, you MUST inform me, through the necessary paperwork, BEFORE the census date. Americans with Disabilities Act: The University of Texas at Arlington in on record as being committed to both the spirit and letter of federal equal opportunity legislation; reference Public Law 93112‐The Rehabilitation Act of 1973 as amended. With the passage of new federal legislation entitled Americans with Disabilities Act‐(ADA), pursuant to section 504 of The rehabilitation Act, there is renewed focus on providing this population with the same opportunities enjoyed by all citizens. As a faculty member, I am required by law to provide “reasonable accommodation” to students with disabilities, so as not to discriminate on the basis of that disability. Student responsibility primarily rests with informing faculty at the beginning of the semester and in providing authorized documentation through designated administrative channels. Bomb Threat Policy: In the event of a bomb threat to a specific facility, University Police will evaluate the threat. If required, exams may be moved to an alternate location, but they will not be postponed. UT‐Arlington will prosecute those phoning in bomb threats to the fullest extent of the law. Students with Pregnancies: For students who are pregnant, it is recommended by the Chemistry and Biochemistry Department that you do not enroll into a chemistry lab at this time. If you become pregnant during the semester, we recommend dropping the course as soon as possible and special provisions will be made to assist you in finishing the course at later date. Please see your faculty instructor for assistance. IMPORTANT: Academic Dishonesty: Enrollment in this course implies acceptance of the university policy as outlined in the Regents’ Rules and Regulations and on this course syllabus. “Scholastic dishonesty includes but is not limited by cheating, plagiarism, collusion, the submission for credit of any work or materials that are attributable in whole or in part to another person, taking an examination for another person, any act designed to give unfair advantage to a student or the attempt to commit such acts.” (Regents’ Rules and Regulations, Par One, Chapter VI, Section e, subsection 3.2, Subdivision 3.22). It is the students’ responsibility to be aware of what constitutes academic dishonesty. Any and all accusations or situations which may involve academic dishonesty will be directed to the Office of Judicial Affairs. No warnings will be given. Discipline may range from loss of credit on an exam/quiz/assignment to expulsion from the university. Page | 5
Schedule of Events Week starting
Experiment
Mon, 8/31/15
Lab Check-in: Complete on-line safety training (see p. 7)
Complete first experiment PIB
Mon, 9/7/15
Write up for First Experiment
Mon, 9/14/15
Begin Second Experiment
Mon, 9/21/15
Continue Second Experiment
Mon, 9/28/15
Begin Third Experiment
Mon, 10/5/15
Continue Third Experiment
Mon, 10/12/15
Begin Fourth Experiment
Mon, 10/19/15
Continue Fourth Experiment
Mon, 11/26/15
Begin Fifth Experiment
Due Dates
Exp. 1 Report
Due
Exp. 2 Report
Due
Exp. 3 Report
Due
Exp. 4 Report
Due
Continue Fifth Experiment
Mon, 11/2/15
Mon, 11/9/15
Begin Sixth Experiment
Issue Poster Presentation Assignments
Mon, 11/16/15
Continue Sixth Experiment
Mon, 11/23/15
THANKSGIVING HOLIDAY!!!!
Exp. 5 Report
Due
Exp. 6 Report
Due
Poster Presentations
Mon, 11/30/15
Make Up Week
Mon, 12/7/15
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Laboratory Exercises Expt. No. Title # Lab Periods 1 Particle in a Box 2 2 Electron Paramagnetic Resonance 2 3 Magnetic Susceptibility 2 4 Enzyme Kinetics 2 5 Circular Dichroism 2 6 DNA Melt 2 SAFETY a. YOU MUST COMPLETE THE ON‐LINE SAFETY BRIEFING PRIOR TO BEGINNING THE EXPERIMENTS! (Ideally, during first week of classes) https://training.uta.edu b. You must wear approved safety goggles at all times in the lab! Any student not wearing safety goggles in lab when experiments are in progress will be asked to leave the lab for the remainder of the period. Repeat offenders will be denied access to the lab for the remainder of the semester. c. No sandals! d. YOU ARE NOT ALLOWED TO USE CELL PHONES IN THE LAB! e. NO HEADPHONES! f. No Food in Lab ‐ EVER! g. Know where the showers, eye‐wash fountains, and fire blankets are located. h. Use the hoods when instructed or whenever in doubt. i. NOTIFY THE LAB INSTRUCTOR OF ANY INJURIES. j.
For your safety, wash your hands after each lab. Page | 7
EQUIPMENT a. NEVER put spatulas, glass pipets or anything else into any community reagent vessel. NEVER put any excess reagents back into these vessels. Take only what you need. b. Instruments are sensitive and expensive. Treat them accordingly. Don’t touch any knobs, switches, etc. until you know what you’re doing. An abused instrument will yield inaccurate results for everyone. c. Use the pipets correctly. If you are unsure how to operate the pipets, please ask you TA. JACS COMMUNICATION LAB REPORT FORMAT Each lab report should follow JACS Communication format. This has a three page maximum (anything over three pages will receive penalty), needs to look like it blends into a magazine (make it look nice), and follow specific guidelines for JACS Communications (found on the Journal of the American Chemical Society webpage). The grading will be a composition of three categories (weighted differently): Presentation (10/50) – How aesthetically pleasing is your overall paper? How nice do your figures look? How relevant are the figures you showed? Did you leave out material that would have been more appropriate? Writing (15/50) – How readable is your paper? Did you use correct grammar with proper use of the English language? Was the background information adequately presented with citations correctly formatted? Interpretation of Results (25/50) – Did you answer the fundamental questions implied in the experiment, use correct calculations to obtain desired results, and show an understanding of content (you can do this, even with incorrect results)? You will notice that it is difficult to fit in all the information and figures that you have in the 2‐3 pages allotted. It is up to you to decide what information is relevant to the lab report (your instructor or TA will not tell you what information you should and shouldn’t put in it). The overall clarity, readability, attention‐to‐detail, and presentation of your lab report will affect the score of your paper. PROOFREAD!!!! Page | 8
GRADING POLICY All lab reports should be submitted electronically to your TA (Submit with file name: “3175_Title_LastName_First Initial.pdf” ex: “3175_Electron Paramagnetic Resonance_Pierce_B.pdf”) before 1 pm on the date due. The title should be Particle in a Box, Magnetic Susceptibility…ect. Lab write‐ups turned in after 1 pm will be assessed a 10% penalty. An additional 10% penalty will be assessed per 24 hours that the lab report is late. Because you are turning reports in electronically, weekends count. Five laboratory reports will be submitted and the lowest score can be replaced by your poster presentation if you adequately completed all 5 labs. In addition to the lab reports, your lab notebooks will be collected at two random dates during the semester. These will be on days we are starting new experiments so that everyone will be there. If you miss the day notebooks are collected, or are significantly late and miss it, you will take a zero without a chance to make up this grade. Finally, at the end of the semester, your group will choose one of the experiment topics to present as a poster. Remember these are scientific posters. Your TA and instructor will be able to assist you with resources to help create your poster. Page | 9
EXPERIMENT 1
‘PARTICLE IN A BOX’ ESTIMATION OF CONJUGATED
BOND DISTANCES
LAB PREPARATION
Read the attached publication [J. Chem. Ed. 74, 985 (1997)]
EXPERIMENT
Use a chemical drawing program to produce bond-line drawings of the molecules of
interest for your report. All of the conjugated double bonds are in the “trans”
configuration.
Determine the particle in a box quantum numbers for each HOMO and LUMO. For each
molecule, count the number of -electrons in the conjugated system (the phenyl rings
don’t count). Your bond-line drawing will help. Using this electron count, determine the
1-D particle in a box quantum number of the highest occupied molecular orbital (HOMO)
for each molecule, assuming that a pair of electrons goes into each orbital. For example,
if your system has two -electrons, then the particle in a box quantum number for the
HOMO is n = 1. The corresponding 1-D particle in a box quantum number of the lowest
occupied molecular orbital (LUMO) is one more than that of the HOMO. Therefore, the
particle in a box quantum number for the lowest unoccupied molecular orbital (LUMO)
in this example is n = 2.
Using the expression for the energy of a particle in a one dimensional box, derive an
equation for the energy difference between two 1-D particle in a box energy levels. For
each molecule, find the peak in the spectrum that corresponds to the HOMO-LUMO
transition. Use the Planck-Einstein equation for the energy of a photon to find the E
corresponding to the absorption of light with this wavelength. Plug this E and the
relevant particle in a box quantum numbers from
The theoretical box length
Determine the ‘through-bond’ phenyl-phenyl bond length. Note: this is not simply the
through-space distance from one ring to the next. Work out the sum of each bond
distance based on the known bond distances and angles. Include these values as your
expected value for comparison to what you determine from the UV-visible absorption
spectrum as illustrated in Table 1.
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Table 1: Through space phenyl-phenyl distances
Dye
1,4-diphenyl-1,3-butadiene
1,6-diphenyl-1,3,5-hexatriene
1,8-diphenyl-1,3,5,7-octatetraene
Experimental (Å)
Theoretical (Å)
Report
Start with a brief, simple introduction. Briefly recount how you took the spectra,
including what concentration of each molecule you used and any other relevant
explanation, such as what you used as a blank. Include publication quality bond-line
drawings of the molecules of interest. Present the spectra in a publication quality figure in
your report.
Explain how you determined the HOMO and LUMO particle in a box quantum numbers
for each molecule. Explain which peaks you used in your calculations and how the
calculations were done. Present the results of your calculated experimental box lengths
for each molecule. How do your experimental box lengths compare to the theoretical box
lengths? End with a brief, coherent conclusion.
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EXPERIMENT 2
CHEMICAL MOTIONS MONITORED BY SPIN-SPIN EXCHANGE
AND ELECTRON PARAMAGNETIC RESONANCE
SPECTROSCOPY
LAB PREPARATION
Read the attached publication [J. Chem. Ed. 59, 677-679 (1982)] for the theory of spin
exchange and diffusion.
EXPERIMENT
OVERVIEW
Molecules possessing a magnetic moment, either nuclear or electronic, can exchange
their moment with a corresponding molecule upon collision. This phenomenon is referred
to as spin spin exchange and it can be utilized to study the rates of chemical reactions and
motions. The rate of spin-spin exchange between molecules can be determined in NMR
or EPR experiments. In this experiment, we will use electron paramagnetic resonance
(EPR), also called electron spin resonance (ESR), spectroscopy to measure the collision
frequency of nitroxide free radicals in solution and compare the result to that expected
from a simple diffusion process. If the spin exchange is governed by the rate of
collisions, the observed rates of spin exchange can give kinetic information for reactions.
The nitroxide EPR spectrum originates from a single unpaired electron which couples
magnetically to a nitrogen atom. A collision between nitroxide molecules may allow an
exchange of electron spins, but not the nitrogen nuclear spins. As the collision rate
increases, the electron-nuclear coupling information is lost and the spectrum broadens.
The collision rate will be varied in this experiment by changing the concentrations of
nitroxide in solution. The corresponding changes in the EPR line width will be measured
to give the spin exchange rate.
THEORY
For nitroxide free radicals, the single unpaired electron (S = 1/2, mS = ±1/2) usually has a
significant density at the 14N nucleus (I = 1, mI = -1, 0, +1), i.e. the electron spend a
fraction of time at N. This electron-nuclear contact gives rise to a hyperfine coupling, A,
between S and I, with energy,
Ehf = AmSmI.
The electron spends most of its time on O, but 16O has no nuclear moment (I=0) and
therefore no hyperfine interaction. The total energy of a state is given by the sum of the
three terms: electron Zeeman, nuclear Zeeman, and hyperfine, respectively,
E = geμBBmS - gNμNBmI + AmSmI
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where μB = 9.274 x 10-24 J/T and 1T (Telsa) = 104 G (Gauss).The following diagram gives
the relative positions of the states mS, mI and their energies for a nitroxide free radical.
The EPR spectrum can be predicted from this energy level diagram. To observe a
resonance, the microwave energy, hν, of the radiation must match one of the above
energy differences, ΔE. In addition, resonances are only allowed in accordance with the
selection rules, ΔmS = ±1, ΔmI = 0. These rules means that only the three transitions
shown by arrows in the above figure are allowed. The energy differences of these
transitions are
ΔE = geμBB - A (mI = -1)
ΔE = geμBB (mI = 0)
ΔE = geμBB + A (mI = +1).
In most EPR experiments, ν is fixed near 10 GHz and B is varied. Using ΔE = hν, we
expect to find three resonances at magnetic field values of
B2 = hν/geμB B3 = (hν + A)/geμB
B1 = (hν - A)/geμB
and the corresponding spectrum is shown below.
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The hyperfine constant A (in MHz) can be determined from the field separation between
any two adjacent resonance lines a (in Gauss). The conversion is A = 2.802 a.
Read the attached publication [J. Chem. Ed. 59, 677-679 (1982)] for the theory of
spin exchange and diffusion.
Your objective in this experiment is to compare the spin exchange rates observed by
EPR spectroscopy with the theoretical diffusion rates, and explain any differences.
EXPERIMENT:
Prepare a 50mM stock solution (3mL) of PADS in K2CO3 buffer. Once the PADS is
added to solution the clock is ticking. The free radical has a finite half-life in solution;
therefore, you will need to keep the solution on ice and complete measurements within
the hour. Make 4 more samples (1mL) by diluting an aliquot of the PADS stock solution
into K2CO3, covering the concentration range of approximately 5-50 mM. Be sure to
accurately determine the dilution factors you have used. Ask your TA to teach you how
to record the spectra of the different concentrations of PADS solutions and measure the
linewidth, ΔH, of the central resonances. You will need to expand the central resonance
to accurately measure the width. To determine ΔH0, plot ΔH vs. Concentration and
compare to the value used in the following paper.
Follow the analysis of the data as given in the JCE paper. The correction factor f* is due
to the electrostatic repulsion of the charged radical ions. For a species without charge, f*
= 1, but for our experiment with potassium nitrosodisulfonate [PADS, (KSO3)2NO], f* <
1. You can determine f* for your particular concentrations by interpolating between the
values given in the table of the JCE paper. Plot f* vs. PADS concentration and fit this
with a second order polynomial. You do not need to calculate f* as suggested in the
paper.
For the value of ΔH0, use the lesser of your value and that given in the JCE paper. Since
your sample was not deoxygenated, the linewidth may not reflect a true minimum value.
For a solution in water at 20ºC, the viscosity, η, is 0.001 Pa-s. Use MKS units for the
calculations of the spin exchange rate and diffusion rates. Put units on your numbers and
make sure they cancel properly to give either sec or sec-1. Note the typo in the JCE paper:
γ = 1.76 x 10+7 sec-1Gauss-1 (not x 10-7).
**Your objective in this experiment is to compare the spin exchange rates observed by
EPR spectroscopy with the theoretical diffusion rates, and explain any differences.
Estimate the error in the measurements as they are recorded so that you can determine
whether or not the difference between the two rates is within experimental uncertainties.
If not, is there some theoretical reason for the difference?
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EXPERIMENT 3
MAGNETIC SUSCEPTIBILITY AND MAGNETIC MOMENT FOR
TRANSITION METAL COMPLEXES
LAB PREPARATION
Find and read the publication [Microscale techniques for determination of magnetic
susceptibility J. Chem. Ed. 69, A176-A179 (1992)] along with the attached paper for a
description of the Evan’s method for determination of magnetic susceptibility.
EXPERIMENT
SUMMARY
The spin associated with each electron gives rise to a magnetic moment. As a result of
this spin (S), electrons within a molecular orbital will impart a net magnetic moment to a
molecule. If the sum of electronic moments is not cancelled out by pairing the molecule
will exhibit a net paramagnetic moment. For example, consider the electronic
configuration of oxygen in its ground (3Σg) state shown in Figure 1. The two outer most
electrons reside in the degenerate π*2py, and π*2pz molecular orbitals and thus the
magnetic moment of these electrons are not quenched by pairing. Therefore, O2 in its
ground state has a net magnetic moment.
Figure 1. Molecular orbital scheme for the valence
electrons
of
molecular
oxygen.
Electronic
configuration (σ1s2, σ∗1s2, σ2s2, σ∗2s2, π2py2,
π2pz 2, σpx 2, π2*py 1, π∗2pz 1). The total spin of
molecular oxygen is the sum of two unpaired
electrons; S = ½ + ½ = 1
Molecules in which all electrons are paired are termed diamagnetic. Application of a
strong magnetic field to a diamagnetic material will induce rotation of the electrons
within the material to produce an opposing magnetic field. As a result of the induced
diamagnetic repulsion a sample will appear to weigh less in a magnetic field as compared
to its true mass in the absence of a magnetic field. Alternatively, molecules with more
than one unpaired electron (S > 0) are termed paramagnetic. If a paramagnetic material is
placed in a magnetic field it will experience an attraction to the field due to the alignment
of the permanent paramagnetic moment of the substance with that of the applied field. As
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a result paramagnetic materials will appear to weigh more in the presence of an applied
magnetic field.
By definition, transition metals have incompletely filled d- or f-shells in at least one of
their possible oxidation states. As a result, transition metals may be diamagnetic in one
oxidation state and paramagnetic in another. In fact biological systems take advantage of
the paramagnetic nature of transition metals to catalyze a variety of chemical reactions
with would be spinforbidden for a diamagnetic material. For example superoxide
dismutase isolated from the mitochondria (SOD2) has a mononuclear Mn-active site
which follows a classic ‘Ping-Pong’ mechanism. This reaction is named because the
enzymatic active site oscillates between two active forms, the oxidized SOD1 which
contains Mn(III) and the reduced form with contains Mn(II).
(A)
(
(B)
( )
)
+
+
−•
2
−•
2
→
→
( )
(
)
+
2
+
2 2
By exploiting these opposing forces generated by diamagnetic and paramagnetic
substances on a permanent magnet, one can measure the mass magnetic susceptibility
(χg) of a given substance. From this the molar magnetic susceptibility (χM), and the
spin-only or effective magnetic moment (μeff) can be determined. Since μeff is
proportional to the number of unpaired electrons (Spin, S) in a given substance this
method can be very useful in determining the electronic structure of a new or unknown
material. Therefore a variety of techniques have been developed to measure the bulk
magnetic susceptibility of a substance. In this experiment we will use the Evans method
to determine the molar magnetic and the spin-only magnetic moment of a variety of
transition metal complexes.
EXPERIMENT
You will be given 4 compounds in order to test magnetic susceptibility:
Fe(SO4)2(NH4)2·6H2O
CuSO₄·5H₂O
K₂Fe(CN)₆
CaCl₂
First, grind each compound into a fine powder. Weigh capillary tube before and after
addition of 2.5 cm of compound to obtain weight of sample. Record Ro and R for each
solid sample. Second, make 5 dilutions of CuSO4·5H20 ranging from 50-500 mM, again
only adding 2.5 cm of each into capillary tube. Measure Ro and R values.
(The instructor will demonstrate how to operate the MSB).
If you are having trouble with your calculations, you may want to search other
publications, similar to the one below and compare tactics with them.
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EXPERIMENT 4
ENZYME KINETICS: OXIDATION OF L-LACTIC ACID
LAB PREPARATION
Read this handout and have all of the calculations for the preparation of your samples
complete before coming to class.
1. Derive integrated rate laws for the oxidation of l-lactate that are first order and zeroth
order in lactate.
2. Assume you are monitoring the concentration of lactate as a function of time during
which it undergoes an oxidation to form pyruvate. What quantities would you plot to
determine whether the reaction is zeroth order or first order in lactate?
EXPERIMENT
1. Theory
The reaction studied in this experiment, the enzyme-catalyzed oxidation of
lactate, illustrates the simplest mechanism for a catalytic reaction. The substrate lactate S
reacts reversibly with the enzyme E to form an unstable complex ES which can revert
back to E and S or can decompose to the product P and release the enzyme for use in
another cycle.
E
+
S
k1
k-1
ES
k2
E
+
P
The forward and reverse reactions in the first step are very fast and the rate-controlling
step forming product is very much slower. The concentration of complex is always very
small, with the consequence that a minute amount of enzyme can catalyze conversion of
an indefinitely large amount of substrate to product.
Though there is in general no direct relation between the kinetic order of a
chemical reaction and the overall stoichiometry, in some simple cases, as in this one, the
stoichiometry does correspond to the reaction mechanism and the kinetic rate equations
can be written by inspection: i.e.
d[S]
dt = -k1[E][S] + k-1 [ES]
(1)
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d[ES]
dt
= -k-1[ES] + k1[E][S] - k2[P]
(2)
dP
dt = k2[ES]
(3)
Here [...] denotes the concentration of a reagent. The system of kinetic equations can be
solved easily if an approximation is made. SGN (p. 265) employ the steady-state
approximation: i.e. that the small concentration of complex ES is effectively constant so
that d[ES]/dt is zero. Combining this condition and the conservation of enzyme,
[E] + [ES] = [E]o = constant
(4)
with eq. 3, they obtain, after some algebra, the Michaelis-Menten equation for the rate of
oxidation of lactate:
d[P]
v = dt
=
k 2 [E]o [S]
K m  [S]
(5)
where the Michaelis constant Km = (k-1 + k2)/k1. The rate of loss of S (or the rate of
accumulation of P) is measured, and the initial concentration of enzyme [E]o is known.
Then Km is obtained by fitting the data to eq. 5.
An alternative simplifying approximation that leads to the same result, and seems
a bit more direct, is the assumption that the reaction step that produces the product does
not appreciably perturb the equilibrium among E, S, and ES. Then we write
[E] [S]
Km = [ES]
(6)
so that [ES] = [E] [S] Km. Eliminating [E] between eqs. 4 and 6, solving for [ES], and
substituting in eq. 3, gives the desired result, eq. 5.
Looking at eq. 5 we see that
v =
k 2 [E]o [S]
Km
(7)
at the limit with [S] << Km and
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Vmax = k2[E]o
(8)
with [S] >> Km. Thus at the first limit, v is first-order with respect to [S]; and at the
second it is zero-order with respect to [S] (i.e. independent of [S]).
This behavior corresponds to physical intuition. If most of the enzyme molecules are
unoccupied, the rate of formation of P is increased proportionally by adding more
substrate; and when all enzyme molecules are combined with substrate, adding more
substrate does nothing. This behavior is shown schematically in the plot of v versus [S]
on p. 265 of SGN.
The usual approach in studying enzyme kinetics is to measure the initial rate vo of
the reaction, so that the concentrations [E] and [S] do not change substantially from the
initial values [E]o and [S]o: i.e.
vo =
[P]
k [E] [S]
= 2 o
t
K m  [S]o
(9)
Traditionally, eq. 9 is rearranged in the Lineweaver-Burke (L-B) form
Km
1
1
1

=
k 2 [E]o k2[E]o [S]o
vo
(10)
showing that the intercept of a linear plot of 1/vo versus 1/[S]o is 1/k2[E]o and the slope is
Km/k2[E]o. Hence from these two quantities Km is determined: Km = slope/intercept.
A more recent innovation is the Eadie-Hofstee (E-H) plot of vo/[S]o versus vo, which
corresponds to another rearrangement of eq. 9:
k [ E]
vo
vo
= 2 o Km
[S ] o
Km
(11)
Here again slope and intercept of a straight line determine the Michaelis constant Km..
With perfect data conforming exactly to eq. 9, the information from the L-B and
E-H plots would be exactly equivalent. However, the E-H method is said to have some
practical advantages in analyzing real (imperfect) data.
The rate constant k2, which can also be determined from the initial-rate data is
called the turnover number. It is the number of substrate molecules reacted per second
per molecule of enzyme when the enzyme is saturated with substrate: i.e. [S]o >> Km so
that eq. 8 holds and vo has its maximum value.
Inhibition of Enzymes:
Page | 28
In enzymatic reactions, the activity of the enzyme can be decreased through
noncovalent binding of inhibitors. Studies of this type can often help to elucidate the
mechanism of the overall enzymatic reaction.
The most common types of reversible inhibition are competitive, non-competitive,
uncompetitive, and mixed. Only the first two cases will be of significance in this
experiment.
Competitive inhibition occurs when another molecule which resembles the
substrate can compete for the enzyme’s active site with the substrate. This has the effect
of preventing the substrate’s access to the catalytic site, thus raising the observed Km
(K’m). Since the inhibitor is not altering the enzymes active site, the rate of the reaction
once substrate is bound does not change. Therefore the Vmax is unaltered in the case of
competitive inhibition. Mechanistically, the incorporation of a competitive inhibitor into
the Michaelis-Menten formulation is written:
E
+
+
S
k1
k-1
ES
k2
E
+
P
I
k-3
k3
EI
From this, the new apparent Michaelis-Menten constant K’m is given by:

[I] 

K' m  K m  1 
K i 

(12)
where [I] is the inhibitor concentration and Ki is the dissociation constant for the enzymeinhibitor complex. Following a similar logic as for Km, Ki is defined as:
Page | 29
Ki 
k  3 [E][I]

k3
[EI]
(13)
In the case of competitive inhibition, the Lineweaver-Burke and Eadie-Hofstee
equations take the form:
L-B:
K  1 
1
[I] 
1
 
 m 
1 
v o Vmax  [S] 
K i  Vmax
E-H:
 v 
[I] 
  Vmax
v o   K m  o 1 
K i 
 [S] 
(14)
(15)
Noncompetitive Inhibition occurs when the inhibitor does not compete with the
substrate for the active site. Both inhibitor and substrate can bind to the enzyme
simultaneously to form a temporary complex. This can be accomplished by (1) a
permanent (irreversible) modification of the enzyme; (2) reversible binding of the
inhibitor to the enzyme but not within the active site; (3) reversible binding of the
inhibitor to the enzyme substrate complex. Typically, this form of inhibition does not
affect the enzyme’s affinity for the substrate (Km), but instead lowers the Vmax. Because
a portion of the enzyme molecules are effectively inactivated, the maximum velocity of
the reaction is decreased, but the binding constant of the functional enzymes remains
unchanged. Mechanistically, the incorporation of a noncompetitive inhibitor into the
Michaelis-Menten formulation is written:
E
+
S
k1
ES
k-1
+
+
I
S
k-3
EI
k3
k'-3
+
S
k4
k-4
k2
E
+
P
k'3
EIS
Page | 30
In the case of noncompetitive inhibition, the Lineweaver-Burke and EadieHofstee equations take the form:
L-B:
[I] 
1  Km  1 
1 
1 

 


K i 
v o  Vmax  [S]  Vmax 
(16)
E-H:
 v 
[I] 
  Vmax
v o   K m  o 1 
K i 
 [S] 
(17)
2. Laboratory Procedure:
Lactate dehydrogenase is a hydrogen transfer enzyme which catalyzes the 2
electron oxidation of l-lactic acid to pyruvate. -Nicotinamide adenine dinucleotide
(NAD+) functions as the electron acceptor and serves as a cofactor for the enzyme. The
reduction of NAD+ is easily observed at 340 nm using a uv-vis spectrophotometer.
(You’ll need to look up the extinction coefficient for NADH at this wavelength prior to
making your calculations).
CH3
H
NAD
OH
Lactate Dehydrogenase
H3C
+
O
+
pH 8.8 to 9.8
O
O
O
NADH
+
H
O
Michaelis-Menten and Enzyme Inhibition Kinetics:
Necessary Reagents: (Provided)






1.0 M lactic acid solution, 50 mM CHES, pH 9.2
About 5 M lactate dehydrogenase (LDH), 50 mM CHES, pH 9.2
20 mM -NAD, 50 mM CHES, pH 9.2
50 mM CHES buffer, pH 9.2
250 mM Borate solution, 50 mM CHES, pH 9.2
20 mM EDTA solution, 50 mM CHES, pH 9.2
Page | 31
Protocol:
From the 1000 mM stock lactic acid solution, prepare a series of 6 samples with a
lactate concentration (in the cuvette) of 1, 5, 10, 50, 100, and 250 mM. Each sample
should have .75-mL of NAD solution, 5-L of enzyme (added last to initiate the reaction
in the cuvette), and a ratio of stock lactate to buffer solution to give the appropriate
substrate concentration. The samples should have a final volume of 1.5-mL. Use the pH
9.2 50 mM CHES buffer provided to dilute the lactate stock solution.
Using both the stock 250 mM borate solution, and 1000 mM lactic acid solution,
prepare another set of 6 samples of lactic acid at their previous concentrations. Into each
sample, spike in an appropriate volume of borate solution such that the final borate
concentration is 20 mM in each vial. Again, use the buffer solution to dilute the solutions
to their final volumes as done in the previous step.
Using both the stock 20 mM EDTA solution, and 1000 mM lactic acid solution,
prepare another set of 6 samples of lactic at their previous concentrations. Into each
solution spike in the appropriate volume of EDTA solution such that the final EDTA
concentration is 2 mM in each vial. Again, use the buffer solution to dilute the samples
to their final volume of 1.5-mL.
The spectrophotometer should be blanked vs. .75-mL of 20 mM NAD + .75-mL
of the buffer. Once the instrument is blanked, each sample run should start with .75-mL
of the 20 mM NAD solution and .75-mL of the lactic acid solution prepared. The addition
of 5 L of the enzyme solution starts the reaction. Make sure to measure the
absorbance at 340 nm prior to the addition of the enzyme for a t=0 reading. This
value should be subtracted from all subsequent readings within that run. Measure
the absorbance of the sample after the addition of the enzyme solution at
t = 0, 10, 20, 30, 40, 50, 60, and 120 seconds. Repeat the above procedure for all 6
concentrations of lactic acid and in the presence of each inhibitor.
Analyze your kinetic data on the enzymatic oxidation of lactate by the method of
initial rates. Make Lineweaver-Burke (1/vo vs. 1/[S]o) and Eadie-Hofstee (vo vs. vo/ [S])
plots before you leave the lab. (Make sure to calculate the initial rate using the slope of
the linear portion of the [S] vs. time curve). From the Lineweaver-Burke and EadieHofstee plots of the enzymatic reaction in the presence of borate and EDTA you should
be able to determine the type of inhibition for both borate and EDTA.
Page | 32
Determining the order of an enzymatic reaction:
From the uninhibited 1.0 and 250 mM lactate solution data, determine whether the
rates are zero or first order in substrate. Analyze your data from these runs with the use of
integrated rate laws that are zero-order and first-order in pyruvate concentration. In you
experimental write-up, you should discuss the results of the these plots, and compare
your data to the results found in the Michaelis-Menten section. In particular, given you
experimentally derived Km, does the observed order of the reaction for each substrate
concentration make sense. Also, assuming that the Km for the pyruvate is ~25 M,
explain how measuring first order kinetics for lactate might be problematic and how this
could be overcome.
3. Enzyme Lab Analysis
Analysis of rate of lactate oxidation with time. Attempt to answer the question: is the
reaction zeroth order or first order in substrate concentration?
Zeroth order means that the rate is independent of substrate concentration:
-d[S]/dt = +d[P]/dt = ko (the zeroth order rate constant)
Integrating both sides over time yields:
[P] = kot or [S] = [S]o – kot
where [S]o is the concentration of substrate at zero time (remember, [P]o is zero). A plot
of [S] versus time should give a straight line with slope –ko.
First order means that the decay of the substrate or the formation of the product are single
exponential in time, where the differential equation describing a first order reaction is as
follows:
d[S]

 k1 [S]
dt
where k1 is the first order rate constant. By rewriting the equation in order to separate
variables, the equation takes the form:
d[S]
 k1dt
[S]
Page | 33
Then, through integration of both sides of the equation, the formula takes the form:
d[S]
 [S]
 k1  dt
ln[S] = -k1t + C
Where C is the constant of integration. In order to evaluate this the concentration has to
be known at a particular time. For instance, if [S]o is the concentration at time zero, then
it must satisfy the condition, ln[S]o = C. This implies that the concentration of the
substrate decreases exponentially as a function of time. Therefore at time zero, ln[S]o =
1 and will decay in a linear fashion to zero as t   . Note: ln[S] must also satisfy
ln[S] = C, therefore, you can also plot the following formula in terms of product:
ln
[ P] - [P]obs
  k1 t
[P]
where [P]obs is the concentration of product at each time measured and [P] is the
asymptote for product formation. A plot of ln ([S]/[S]o) vs. t will generate a straight line
with slope –k1 for first-order kinetics.
(Note: You should derive these equations in your write-up)
Plot your experimental data as [S] vs. t and ln([S]/[S]o) vs. t for both the 1.0 and 250 mM
lactate runs. From these, you should be able to determine the enzymatic rate law for both
high and low substrate concentration. Calculate both the zeroth and first order rate
constants (ko and k1).
Activity. Using data from , calculate specific activity which is given by:
(# micromoles substrate oxidized) / [(minute)x(grams of enzyme)].
Turnover Number (# substrate molecules oxidized)/[(seconds)x(# of enzyme
molecules)]. Use 134,000 g/mol as the molecular weight of the enzyme. Compare the
value obtained from the fit to a zero order plot to the value of the turnover number that
you obtain from the Lineweaver-Burke and Eadie-Hofstee plots (below).
Analysis of Enzyme Kinetics via methods of initial rates. In this set of runs, you vary
the initial substrate concentration, [S]o, and measure the initial rate, [P]/minute, at each
[S]o. This data can be analyzed in (at least) two ways in order to determine both k2, the
rate of dissociation of the enzyme-substrate complex (or the rate determining step in an
enzyme catalyzed reaction) and the Michaelis-Menten constant (Km). Also, for the runs
in the presence of an inhibitor, calculate the effective Michaelis-Menten constant (K’m)
and inhibitor constant (Ki) based on equations (12) through (17). Make sure to identify
the type of inhibition occurring in the presence of both EDTA and borate.
Page | 34
** Keep in mind that Vmax = k2[E]o **
Lineweaver-Burke:
1/vo = Km/Vmax(1/[S]) + 1/Vmax)
plot 1/v0 versus 1/[S0]
slope = Km/Vmax
y-intercept = 1/Vmax
k2 is the turnover number which can be obtained if [E]o is known. Report this value. The
turnover number is the number of lactate molecules oxidized per second when the
enzyme is saturated with substrate or, in other words, when [E]s = [E]o .
Eadie-Hofstee Plot:
vo = Km(vo/[S]) + Vmax
Report Writing:
plot vo versus vo/[So]
slope = -Km
y-intercept = Vmax
One final note of clarification: Whether or not you choose to use a spreadsheet program such as EXCEL to do your calculations
(and we strongly advise that you do), you must show a sample calculation for the operations that you are performing so that it is clear what
equations you are using and what values you are plugging into them. This will allow both you and us to check your work. Only include tables
that are relevant and included in the discussion. The tables that list your data must be numbered, with a title, and must be properly labeled
showing correct units.
Page | 35
EXPERIMENT 5
Circular Dichroism
LAB PREPARATION
Read the attached publication [J. Chem. Ed. 87, 891-893 (2010)] and find and read the
publication, How to Study Proteins by Circular Dichroism. Biochimica et Biophysica
Acta, 1751, 119-139 (2005). The following papers will may also be useful in your
discussion [Biochemistry 8(10), 4108-16 (1968); and Macromolecules 2(6) 624628(1969)]. Use these as a guide to determine the relative secondary structure of an
unknown protein and follow the denaturation of lysozyme.
EXPERIMENT
The CD spectra of two protein samples will be collected and processed into mean residue
ellipticity (deg* cm2 decimol-1). The observed ellipticity, [], in the 190-240 nm range is
diagnostic of the macromolecular chirality due to a protein’s secondary structure (alpha
helix, beta sheet, or random coil) as described by equation 1. For any protein, the
observed CD spectra within this region can be used to determine the relative fraction of
secondary structure [alpha helix (), beta sheet () and random coil (r)] by comparing
the mean residue ellipticity for a specific wavelength to samples of known secondary
structure. In addition to the polypeptide poly-L-lysine, the proteins lysozyme and
myoglobin are frequently used as protein standards for CD spectroscopy.
Table 1. Secondary structure of selected proteins and polypeptides.
2° Structure
 Helix ()
 Sheet ()
Random Coil (r)
Myoglobin
68
5
27
Lysozyme
29
11
60
Poly-L-Lysine
100
0
0
Equation 1 indicates that the observed CD spectra for any protein can be described as the
sum of molar ellipticities at a fixed wavelength () for alpha helix, beta sheet and random
coil ( () ,  () , and r ()) weighted by the relative fraction of each secondary structure
(, , and r). For accurate structural prediction, it is important to select wavelengths
appropriate for each secondary structure basis set. For example, the observed molar
ellipticity at 222 nm is predominately due to alpha helix. Using this approach, the
secondary structure of an unknown protein can be determined by simultaneously solving
a series of 4 linear equations based on the three standard proteins and one unknown.
Equation 1
[()] = ·[ ()] + ·[ ()] + r·[r ()]
Page | 36
Alternatively, using the given data for myoglobin and poly-L-lysine, along with the data
you receive from your lysozyme standard, you can create calibration curves for each
secondary structure to compare with your unknown.
CD spectroscopy can also be utilized to observe changes in protein conformation due to
denaturating conditions. In these experiments, the change in the mean residue ellipticity
is monitored as secondary structure is lost by protein unfolding. Also, in this experiment,
you will see lysozyme denatured with 5 M guanidine hydrochloride and subsequently
refolded by serial dilution into an appropriate buffer. The calculated secondary structure
composition should return to reported values.
In review, you will acquire one sample for Lysozyme under normal conditions, three
samples of Lysozyme under different acidic conditions, and one sample for your
unknown.
PROCEDURE
Instrumentation. Jasco 715 UV-visible circular dichroism spectrometer. The highvoltage UV-lamp is capable of producing ozone and thus the lamp is purged by a
continuous flow of N2 gas. Prior to igniting the lamp, make sure to purge the lamps for at
least 10-minutes. Note: The lamp will also need approximately 10-minutes to warm up
after ignition. To ensure accurate measurements, make sure that the HT[V] is below
7000 for the entire spectrum.
Materials:
Buffer -10 mM Sodium Phosphate pH 6.9. Filtered to remove any particles.
Guanidine HCL - 6 M solution.
Quartz cuvette - 0.1 cm circular, holds ~0.3 mL and can be filled using pipettes.
Procedure (Be sure to obtain baseline scans for all 5 scans that you run.)
A. Lysozyme (4 samples): 1) Prepare a sample of buffer to acquire a baseline
spectrum for your Lysozyme sample and unknown, 2) and prepare samples for the
baseline series containing three different concentrations of Gdn-HCl described in
Table 2. If you make enough of sample 1, this can be diluted to make baseline
samples 2 and 3. The Lysozyme sample for your calibration should be made in
buffer and at a concentration of 2.5uM (the concentration of stock Lysosyme will
be given at the beginning of lab). You MUST know the molecular weight and
number of peptide bonds (residue-1) for Lysozyme from chicken egg white (look
in the literature).
B. Unknown (1 sample): Prepare a sample of buffer to acquire a baseline spectrum
for your unknown sample. You will be given an unknown sample of protein. On
the vial, you will find the number of residues, molecular weight, and
concentration of your unknown protein. Using the known values of the three other
proteins, what is the relative % of alpha helix, beta sheet, and random coil for the
unknown?
Page | 37
Table 2
Sample
1
2
3
Baseline Series
Lysozyme
Gdn-HCl
(mMol/L)
(mMol/L)
5
2.5
1.25
Test Series
Lysozyme
Gdn-HCl
(uMol/L)
(Mol/L)
5
5
2.5
2.5
1.25
1.25
a. Dilutions from 5 mM Gdn-HCl were given at least 10 minutes for folding
to occur.
CD Measurements and Data Analysis. Prior to measuring samples, baseline
measurements should be made using 1) a buffer solution and 2) the three baseline series
samples from table 2. Carefully load the cuvette using a transfer pipette (~0.3 mL),
avoiding air bubbles. Prior to running sample ensure the baseline correction is selected
and parameters are correct. CD scans are collected in  (milli-degrees) and should be
converted to mean residue ellipticity. The conversion requires the exact concentration of
the sample, molecular weight, the number of peptide bonds (# of amino acids-1) and the
path length of the cuvette (0.1 cm). Export data as a text file with listed wavelengths and
measured mean residue ellipticities. Thoroughly clean the cuvette with deionized water
between measurements.
For all of these measurements, you will record three wavelength values to calculate
percentage of random, beta, and alpha secondary structure.



Wavelengths are:
197(Random),
For Myoglobin =
20,000
For Poly-L-Lysine = 25,000
218(Beta),
-22,000
-36,000
222(Alpha)
-24,000
-36,000
Table 3. CD Instrumental settings for determination of protein secondary structure.
Parameter
Scanning range
190-250 nm
Bandwidth
2 nm
Time constant
2 sec
Scanning Speed
50 nm/min
Sensitivity
Standard 100 mdeg
Accumulation
2
Conversion to mean residue ellipticity. In the Processing menu select optical constant.
Calculate molecular ellipticity. Input path length in the appropriate box but in the molar
concentration box input the mean residue weight shown below:
MRW= (number of peptide bonds) * Concentration (mol/L)
Page | 38
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Page | 41
EXPERIMENT 6
THERMODYNAMICS OF DNA DUPLEX FOMATION
LAB PREPARATION
Read the attached publication [J. Chem. Ed. 77, 1469-1471 (2000)] and download the
journal article Nucleic Acids Research, (28), No. 23 4762-4768 (2000). Use these papers
as a guide for the determination of H°, S°, and G° during the transformation of a
DNA duplex to form two single stranded DNA monomers.
EXPERIMENT
In this lab you will measure thermodynamic properties of a short DNA duplex by melting
the ordered native structure (duplex or double helix) into the disordered, denatured state
(single strands) while monitoring the transition using ultraviolet (UV) spectrophotometry.
As the ordered regions of stacked base pairs in the DNA duplex are disrupted, the UV
absorbance increases. This difference in absorbance between the duplex and single
strand states is due to an effect called hypochromicity. Hypochromicity, which simply
means “less color”, is the result of nearest neighbor base pair interactions. When the
DNA is in the duplex state, interactions between base pairs decrease the UV absorbance
relative to single strands. When the DNA is in the single strand state the interactions are
much weaker, due to the decreased proximity, and the UV absorbance is higher than the
duplex state. The profile of UV absorbance versus temperature is called a melting curve;
the midpoint of the transition is defined as the melting temperature, Tm. The dependence
of strand concentration on the Tm of a melting transition can be analyzed to yield
quantitative thermodynamic data including ΔH°, ΔS°, ΔG° for the transition from duplex
to single strand DNA. Thermodynamic analyses of this type are done extensively in
biochemistry research labs, particularly those involved in nucleic acid structure
determination. In addition to providing important information about the conformational
properties of either DNA or RNA sequences (mismatched base pairs and loops have
distinct effects on melting properties), thermodynamic data for DNA are also important
for several basic biochemical applications. For example, information about the Tm can be
used to determine the minimum length of a oligonucleotide probe needed to form a stable
double helix with a target gene at a particular temperature.
PROCEDURE
You will melt a duplex formed by two complementary synthetic DNA oligomers:
Five separate samples with different concentrations (indicated on cuvettes) have been
prepared for you in buffer (1M NaCl, 10 mM sodium phosphate pH 7.0, 0.1 mM EDTA).
The buffer was carefully degassed by bubbling nitrogen through it before the samples
were made. Oxygen dissolved in the sample will form bubbles at higher temperatures,
which will scatter light and affect the absorbance measurements. The samples (0.4 mL
each) have been placed in 1 cm path length quartz cuvettes that are sealed with teflon
Page | 42
stoppers. One additional 1 cm cuvette filled with buffer will also be provided to act as a
reference cell for the spectrophotometer.
NOTE: the quartz cuvettes are expensive and fragile. Please treat them very carefully.
During your melting experiment you will monitor the change in absorbance at 254 nm
over the temperature range 10°C to 70°C. Your instructor will give you a set of detailed
instructions 2 concerning the spectrophotometer parameters that you will be using.
Please carefully record in your notebook the parameters used to collect your data. To
record the most accurate data in a research laboratory, melting curves of this type would
generally be done slowly (over several hours) at small temperature increments to ensure
complete temperature equilibration at each point. However, your experiment has been
designed to fit into a two lab periods by minimizing the amount of time necessary to
equilibrate at each temperature by the choice of particular DNA duplex and the use of
small sample volumes. Nonetheless, you should be aware that incomplete temperature
equilibration could be a source of error in your measurements.
CALCULATIONS
Your first step will be to make a single graph of temperature versus absorbance that
contains the four melting curves. Melting curves of DNA are commonly described using
standard helix-to-coil transition theory. In our case the "helix" is duplex DNA and the
"coil" is the disordered single DNA strands. The transition from helix to coil is
monitored in our experiment as a function of temperature by UV absorbance. This can be
done because the percentage of hyperchromicity (increase in absorbance as the duplex is
melted) varies linearly with the number of unstacked bases. Thus our melting curve
relates the absorbance to the fraction of paired bases (f) as the temperature is increased.
The Tm is the temperature where f = 0.5. The steep part of the melting curves reflects the
double strand (AB) to single strand (A+B) equilibrium.
(eq. 1)
A + B ⇔ AB
The treatment we used assumes a two-state (all-or-none) model. In a two-state model, f is
the fraction of fully based-paired strands since there are no partially base-paired
intermediates in the melting process. The two-state model has been shown to be a very
good approximation for short (< 12 base pairs) DNA duplexes. Using this model we
must adjust the absorbance data to a normalized scale so that the values range from 0 to 1
(we will call these values relative absorbance). Then a relative absorbance of 0 occurs
when all of the bases are paired (all in the duplex state) and a relative absorbance of 1
occurs when all of the bases are un-paired (all in the single strand state). At a relative
absorbance of 0.5 half of the strands are paired and half are un-paired, thus f = 0.5 and
the temperature at this point is Tm. You will obtain thermodynamic data from the
concentration dependence of the Tm for each of your curves. Next make a van't Hoff plot
of (1/Tm) versus ln(Ct) where Ct is the sum of the molar concentrations of each single
strand.
Page | 43
Using the following relationship.
(eq 2.)
∆ °
ln
∆ °
∆ °
Calculate ΔH° and ΔS°. Finally, calculate ΔG° at 25°C.
Things to include on your lab report.






Normalilzed melting curves. van't Hoff plot. ΔH° and ΔS° for helix formation. ΔG° at 25°C for helix formation. Literature values for ΔH°, ΔS°, and ΔG°. All appropriate errors. Page | 44
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