chem 3175 biophysical chemistry - uta.edu · experiment 4 – enzyme kinetics 26 experiment 5 –...
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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 Office: SH 300 F
Phone: 817‐272‐9066
Office Hours: by appt. e‐mail: [email protected]
TAs and Meeting Times
Meeting Time/Place TA Office Hours Contact
Thurs. 1‐5pm/CPB 211 Sinjinee Sardar Tues. 1‐3 SH 314 [email protected]
Wed. 1‐5pm/CPB 211 Philip Palacios Thurs. 1‐3 SH 314 [email protected]
Text: Laboratory Manual, will be distributed electronically
Other materials: Scientific calculator, Laboratory notebook, USB portable
storage drive
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.
Mandatory Online Safety Training:
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
yourself with the software. Ask your TA if you need extra guidance.
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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
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.
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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.
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Schedule of Events
Week starting Experiment Due Dates
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 Exp. 1 Report Due
Mon, 9/21/15 Continue Second Experiment
Mon, 9/28/15 Begin Third Experiment Exp. 2 Report Due
Mon, 10/5/15 Continue Third Experiment
Mon, 10/12/15 Begin Fourth Experiment Exp. 3 Report Due
Mon, 10/19/15 Continue Fourth Experiment
Mon, 11/26/15 Begin Fifth Experiment Exp. 4 Report Due
Mon, 11/2/15 Continue Fifth Experiment
Mon, 11/9/15 Begin Sixth Experiment
Issue Poster Presentation Assignments Exp. 5 Report
Due
Mon, 11/16/15 Continue Sixth Experiment
Mon, 11/23/15 THANKSGIVING HOLIDAY!!!! Exp. 6 Report Due
Mon, 11/30/15 Poster Presentations
Mon, 12/7/15 Make Up Week
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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.
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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!!!!
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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.
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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 Experimental (Å) Theoretical (Å) 1,4-diphenyl-1,3-butadiene 1,6-diphenyl-1,3,5-hexatriene 1,8-diphenyl-1,3,5,7-octatetraene
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
B1 = (hν - A)/geμB B2 = hν/geμB B3 = (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, π2py
2, 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) ( ) + 2−• → ( ) + 2
(B) ( ) + 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 ES E + Pk1 k2
k-1 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)
dPdt = 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:
v = d[P]dt =
[S] K
[S][E]k
m
o2
(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
Km = [E] [S][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 = m
o2
K
[S][E]k (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]t
= om
o2
[S] K
[S][E]k
(9)
Traditionally, eq. 9 is rearranged in the Lineweaver-Burke (L-B) form
ov
1=
oo
m
o2 S][
1
k2[E]
K
[E]k
1 (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:
o
o
]S[
v=
m
o2
K
E][k -
m
o
K
v (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:
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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 ES E + P
+
I
EI
k1 k2
k-1
k3k-3
From this, the new apparent Michaelis-Menten constant K’m is given by:
imm K
[I]1KK' (12)
where [I] is the inhibitor concentration and Ki is the dissociation constant for the enzyme-inhibitor complex. Following a similar logic as for Km, Ki is defined as:
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[EI]
[E][I]
k
kK
3
3i
(13) In the case of competitive inhibition, the Lineweaver-Burke and Eadie-Hofstee equations take the form:
L-B: maximax
m
o V
1
K
[I]1
[S]
1
V
K
v
1
(14)
E-H: maxi
omo V
K
[I]1
[S]
vKv
(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 ES E + P
+
I
EI
k1 k2
k-1
k3k-3
+ S EIS
+
S
k'3k'-3
k4
k-4
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In the case of noncompetitive inhibition, the Lineweaver-Burke and Eadie-Hofstee equations take the form:
L-B:
imaxmax
m
o K
[I]1
V
1
[S]
1
V
K
v
1 (16)
E-H: maxi
omo V
K
[I]1
[S]
vKv
(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).
O O
H OH
CH3
O O
OH3C
NAD NADH H+
+ +pH 8.8 to 9.8
Lactate Dehydrogenase
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
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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 Eadie-Hofstee 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.
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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:
[S]kdt
d[S]1
where k1 is the first order rate constant. By rewriting the equation in order to separate variables, the equation takes the form:
dtk[S]
d[S]1
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Then, through integration of both sides of the equation, the formula takes the form:
dtk[S]
d[S]1
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:
tk[P]
[P] - P][ln 1
obs
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.
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** 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 plot vo versus vo/[So] slope = -Km y-intercept = Vmax Report Writing: 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.
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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) 624-628(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 Myoglobin Lysozyme Poly-L-Lysine
Helix () 68 29 100
Sheet () 5 11 0
Random Coil (r) 27 60 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 ()]
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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 high-voltage 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?
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Table 2 Sample Baseline Series Test Series
Lysozyme (mMol/L)
Gdn-HCl (mMol/L)
Lysozyme (uMol/L)
Gdn-HCl (Mol/L)
1 - 5 5 5 2 - 2.5 2.5 2.5 3 - 1.25 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), 218(Beta), 222(Alpha) For Myoglobin = 20,000 -22,000 -24,000 For Poly-L-Lysine = 25,000 -36,000 -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)
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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
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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.
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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.
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