Analysis of Protein Denaturation Through
Dynamic Light Scattering
An Honors Thesis submitted in partial fulfillment of the requirement
for Honors Studies in Physics
By Jeffrey Andrew Sparks
Spring 2003
Department of Physics
J. William Fulbright College of Arts and Sciences
The University of Arkansas
Acknowledgements
This project could not have happened without the tireless effort, support,
guidance, instruction, prompting, reality doses, and collaboration of Dr. Lin Oliver of the
University of Arkansas Physics Department. The honors theses and research of Nadeem
Akbar, who designed the internal heater I used in my research, and April Fortner, who
gave instrumental guidance on the production of protein, were invaluable as well. I also
incorporated some of their figures in the experimental method portion and their strategy
in deriving the theory of Dynamic Light Scattering. Dr. Wes Stites and Lee Manuel were
also very helpful in offering advice and guidance during the long hours this physicist
spent making protein. Finally, I would like to thank my family, friends, and international
diversions who were always willing to keep my mind off this project.
2
Table of Contents
TITLE PAGE...............................................................................1
ACKNOWLEDGEMENTS.........................................................2
TABLE OF CONTENTS ............................................................3
LIST OF FIGURES .....................................................................4
INTRODUCTION .......................................................................5
Proteins and Cell Biology: From DNA to Protein ..........................5
Protein Structure ..............................................................................8
The Problem With Folding ............................................................12
Protein Denaturation ......................................................................13
Methods of Protein Analyzation ....................................................15
Thermal Denaturation ....................................................................20
Goals ..............................................................................................22
THEORY OF DYNAMIC LIGHT SCATTERING ..................23
PROPERTIES OF STAPHYLOCOCCAL NUCLEASE .........30
EXPERIMENTAL METHOD ..................................................31
Production of Staphylococcal nuclease .........................................31
Dynamic Light Scattering Procedure .............................................32
RESULTS AND DISCUSSION................................................42
CONCLUSIONS .......................................................................52
REFERENCES ..........................................................................54
3
List of Figures
Figure 1 - Generalized structure of an amino acid .........................................................7
Figure 2 - A typical peptide bond ..................................................................................8
Figure 3 - The structure of a sulfhydryl bond between cysteine groups ........................9
Figure 4 - A typical secondary structure of a protein, the ribbon α-helix....................10
Figure 5 - An example of the β-sheet, part of the secondary structure of a protein ....10
Figure 6 - The tertiary structure of ribulose bisphosphate carboxylase (RubisCo) .....11
Figure 7 - The structure of hemoglobin, a good example of quaternary protein
structure............................................................................................................12
Figure 8 - Diagram of DLS incident and scattered wavevectors .................................24
Figure 9 - Structure of Staphylococcal nuclease using X-Ray crystallography ..........30
Figure 10 - Schematic of optics ...................................................................................33
Figure 11 - The filtration system viewed from above..................................................35
Figure 12 - Schematic diagram of internal furnace......................................................37
Figure 13 – Interior and exterior of aluminum can ......................................................38
Figure 14 - The typical setup of the Brookhaven Instruments DLS software .............40
Figure 15 - The optical table during a Dynamic Light Scattering run .........................41
Figure 16 - Viscosity as a function of temperature ......................................................44
Figure 17 - Raw data and our programmed fit for a single exponential at 24ºC …….45
Figure 18 - Raw data our programmed fit for a developed double-exponential
at 44 ºC .............................................................................................................45
Figure 19 - Radius of SNase WT as a function of temperature ...................................46
Figure 20 - Evolution of the unscaled correlation functions at different times at
45 ºC.................................................................................................................47
Figure 21 - Evolution of the scaled correlation functions at different times at
45 ºC.................................................................................................................48
Figure 22 - Time development at 45 ºC of the "molten globule" ................................49
Figure 23 - Time development at 45 ºC of the "floppy chain" ....................................49
Figure 24 - Floppy chain size (the larger radius from a double-exponential) at
different temperatures ......................................................................................51
4
Introduction
Proteins and Cell Biology: From DNA to Protein
The process by which a protein attains a specific three-dimensional ―activated‖
conformation is considered by some to be the last fundamental aspect of cell biology that
is still incompletely understood. The recent success of the Human Genome Project
emphasizes the fact that even though we understand the ―language‖ of biology as
expressed in base pairs and the genetic code, this knowledge can only mean so much if
we cannot interpret the architectural blueprint of structure that arises from this language.
While we now have the entire DNA base sequence for humanity at our disposal, we are
still unsure how or why a specific sequence of DNA nucleotides finally results in
precisely arranged proteins in three dimensions. The process of the amino acids within a
protein finding their particular stable structure is called protein folding.
The mass
movement of scientists now studying the theory of protein folding and contributing to
databases of particular proteins is called proteinomics.
Before focusing specifically on the protein and the problem of why it folds to a
particular state, it is important to understand why this is fundamental to cell biology. The
most fundamental principle of biology lies in the transcription of deoxyribonucleic acid
(DNA).
A DNA molecule consists of a long sequence of combinations of four
nucleotides in a double helix.
A specific nucleotide bonds to another analogous
nucleotide, so that one side of the helix is enough to know the sequence of the other side.
Adenine (A) always bonds to thymine (T); guanine (G) always bonds to cytosine (C).
DNA can be thought of as a long string of four letters: A, C, T, and G.
5
Ribonucleic acid (RNA) comes in several different varieties, and its main function
is to serve as a working template for transferring the information contained on a given
segment of DNA into a specific string of amino acids. RNA polymerase ―unzips‖ the
double-stranded helix of DNA, allowing the mRNA nucleotides (the same as DNA
nucleotides except with uracil, U, replacing thymine, T) to form a complementary string
of letters based on the same principle of base pairs within DNA. This mRNA sequence is
refined by various methods so that some introns are snipped out and not part of the
mature mRNA transcript.1 The entire process of converting a sequence of DNA to a
usable sequence of RNA is called transcription.
The mRNA is formed in the nucleus of the cell, but is free to move to other parts
of the cell. Specifically, the ribosomes often lining the rough endoplasmic reticulum are
an important site for the next stage of protein assembly. Within the cytoplasm, tRNA is a
sort of molecular harness for specific amino acids.
Each tRNA molecule has an
anticodon of three nucleotides. On the surface of the ribosome, each tRNA anticodon
binds to a specific codon in the mRNA sequence, which again consists of three
nucleotides. Each codon therefore corresponds to a specific amino acid. It is interesting
to note that there are conceivably 64 different combinations of codons (43 = 64), but there
are only 20 different amino acids. Some codons act as a ―STOP‖ codon, so that the
amino acid string ceases once these codons are reached. Nature has a built-in mechanism
to avoid errors in that if the third nucleotide in a codon is changed for some reason, it will
result in the same amino acid.2 The system by which specific codons of three nucleotides
correspond to specific amino acids is called the genetic code. This is the Rosetta stone of
cell biology, converting a long string of letters in mRNA into three-letter ―words‖ and
6
meaningful information in amino acids. The process by which an mRNA sequence is
converted to an amino acid sequence is called translation.
Amino acids are often called the building blocks of life, and we have now seen
how the information contained in DNA eventually becomes a sequence of amino acids.
Amino acids make up proteins, one of the most important and most diverse of all
biological molecules. An amino acid is a small organic compound consisting of an
amino group, a carboxyl group (an acid), a hydrogen atom, and one or more atoms known
as an R group (see Figure 1). The R Group is what distinguishes the amino acids from
each other.
Figure 1 - Generalized structure of an amino acid. (From
http://www.bact.wisc.edu/MicrotextBook/BacterialStructure/Proteins.html)
When the tRNA brings each particular amino acid into proximity with the
adjacent amino acids along the mRNA chain, these amino acids bond to each other. An
amino group bonds to the adjacent carboxyl group, so that a regular pattern emerges: -NC-C-N-C-C-. This bond is called a peptide bond, and is extremely durable and stable
(see Figure 2). The initial linkage of amino acids forms a polypeptide chain (distinct
from the term protein because of a lack of three-dimensional structure).
At the most basic level, each protein consists of a specific sequence of amino
acids in its polypeptide chain, and this sequence is called the primary structure of the
protein. The chemical synthesis of proteins ceases once peptide bonds are formed at the
ribosomes, so the rest of the protein story has to do with the three-dimensional
7
Figure 2 - A typical peptide bond. (From
http://www.bact.wisc.edu/MicrotextBook/BacterialStructure/Proteins.html)
arrangement of this polypeptide chain.
Proteins are large, diverse, and obviously
extremely important to any form of life.
They come in many different varieties:
enzymes, structural proteins, transport proteins, nutritious proteins, hormones,
glycoproteins, lipoproteins, and lymphatic proteins. Much of what we are comes from
proteins which amazingly come from just twenty amino acids which come from just four
DNA nucleotides. The key to this variety and to having a protein that is activated and
can actually fulfill its intended purpose is the three-dimensional arrangement of the
protein.
To this point, the mechanisms governing the steps from DNA to protein are for
the most part very well understood. After the primary structure of a protein, though,
scientists are unsure about the exact mechanisms which govern a protein into a specific
form in free space.
Protein Structure
A protein’s structure is the key to its use and function. As already stated, the
primary structure of a protein is the unique sequence of amino acids in its polypeptide
chain. This is the first level of structure and can be written on a page in linear fashion.
The second level of structure is the coiled or extended shape of a protein. This is
primarily due to hydrogen and disulfide bonds on adjacent links of a polypeptide chain.
8
It is not uncommon for hydrogen bonds to form between every third amino acid, for
example.3 The peptide bond allows for a surprising amount of swivel and rotation so that
covalent bonds can form with neighboring atoms.
Sulfhydyrl linkages, or disulfide
bonds, are covalent bonds between cysteine groups. Cysteine has a sulfur group available
for binding to other groups and often forms a covalent link to another cysteine group
within a protein (see Figure 3).
Figure 3 - The structure of a sulfhydryl bond (disulfide bridge) between cysteine groups. (From
http://www.bact.wisc.edu/MicrotextBook/BacterialStructure/Proteins.html)
The secondary structure of a protein often results in two common forms: the αhelix and the β-sheet (sometimes called ―pleated,‖ see Figure 5). The formation of both
arises from hydrogen bonds, disulfide bridges, and hydrophobic interactions of amino
acids with water in solution. The α-helix resembles a ribbon of amino acids wrapped
around a tube to form a staircase-like structure. The structure is very stable yet still
flexible, allowing for other levels of structure. See Figure 4 for an example of an α-helix.
In the β-sheet, two planes of amino acids form, lining up parallel so that hydrogen
bonds form between each sheet. Unlike the α-helix, in the β-sheet hydrogen bonds form
between amino acids very far away from each other within the primary structure. 4 Figure
5 shows an example of the β-sheet. Other variations on these general sorts of secondary
structure are β-turns, random coils, helical wheels, terminal arms, and loops.
9
Figure 4 - A typical secondary structure of a protein, the ribbon α-helix. (From
http://www.bact.wisc.edu/MicrotextBook/BacterialStructure/Proteins.html)
Figure 5 - An example of the β -sheet, part of the secondary structure of a protein. (From
http://www.bact.wisc.edu/MicrotextBook/BacterialStructure/Proteins.html)
The tertiary structure consists of further folding of a coiled chain owing to bendproducing amino acids and interactions among R-groups far apart on a looped-out chain.
Interactions between certain amino acids (such as proline) bend a chain at a certain length
and at a certain angle. R-groups further down the length interact to hold the loop at
characteristic positions.
A tertiary structure can be viewed as a three-dimensional
―packing‖ of secondary structural elements. In many cases it is possible to identify
recurring patterns of secondary structural organization, called motifs.
10
The tertiary
structure is often most important in function.
Proteins with very different primary
structures but similar functions will often have similar tertiary structures. Figure 6 shows
the tertiary structure for RubisCo, an enzyme used in the conversion of carbon dioxide to
carbohydrates.
Figure 6 - The tertiary structure of ribulose bisphosphate carboxylase (RubisCo), an important
enzyme used in the conversion of carbon dioxide to carbohydrates. (From
http://www.bact.wisc.edu/MicrotextBook/BacterialStructure/Proteins2.html)
The final level of protein structure is the quaternary structure. In this level of
interaction, two or more polypeptide chains are linked tightly by hydrogen bonds and
other interactions such as hydrophobia, disulfide bridges, and R-group interaction.
Inorganic cations can also play a role in this level of structure. Figure 7 shows a good
example of the quaternary level of structure in hemoglobin, the oxygen-transporting
protein in blood, which contains a heme group with an iron cation.
11
Figure 7 - The structure of hemoglobin, a good example of quaternary protein structure. (From
http://www.isat.jmu.edu/users/klevicca/isat454/hemoglobin_essay.htm)
The Problem With Folding
The various levels of structure of a protein are explained through principles of
interaction that are well understood by scientists, but I prefaced this discussion by saying
that the problem of predicting the three-dimensional structure of proteins is the
fundamental area of cell biology still eluding an understood framework. The problem
lies mostly in the astronomically large numbers of different conformations (or specific
states in free space) a protein may undertake. Even a small protein of only 150 amino
acids (the size of the protein used in this project) each with two rotatable bonds and with
three possible orientations each, would have between 4150 and 9150 possible
conformations. If such a protein were able to sample one million of these conformations
per second, it would take longer than the lifetime of the universe to find the ―correct‖
conformation.5 Understandably, scientists are having great difficulty predicting higher
levels of protein structure given a primary sequence of amino acids. This is quite
frustrating since the three-dimensional structure of a protein is what makes that protein
12
useful. All of the knowledge we have acquired concerning DNA and transcription and
translation can only go so far. We are able to read the language of biology with the
genetic code, but we are still unable to interpret this blueprint to build and manipulate
proteins from scratch.
The protein folding problem is so fundamental to biology that the benefits to
understanding it would be so vast and broad as to be immeasurable. Engineering proteins
to have a specific shape and function would go a long way toward controlling cancer,
viral infections, and aging affects.
Several ailments are already related to the
―misfolding‖ of proteins, where a particular protein simply does not fold correctly so that
metabolic pathways or disease resistance methods are halted. These illnesses include:
Alzheimer’s disease, Mad Cow disease (Bovine Spongiform Encephalopathy or BSE),
Lou Gehrig’s disease (Amyotrophic Lateral Sclerosis or ALS), Creutzfeldt-Jakob disease,
and Parkinson’s disease.6
Protein Denaturation
The conformation of a protein when it is in its activated or functional state is also
called the ―native state‖ of the protein. After synthesis at a ribosome, a protein typically
―finds‖ its specific natured state (out of the billions of billions of possible states) on the
timescale of a few minutes. This is quite amazing, obviously, since scientific models at
this point cannot even usually predict the final tertiary and quaternary states of a protein
on any timescale.
Since starting from the primary structure of a protein is quite
impractical given the number of possible conformations, scientists usually start in
analyzing a protein by how it unfolds or denatures from its natured state.
13
A protein has very specific pH, temperature, and pressure ranges where it is
folded such that it is functional. When these values are varied slightly, the weaker bonds
in the higher levels of structure are the first to break. In this way, the process by which a
protein reaches its natured state can be studied by watching the way bonds break. Some
theorists contend that bonds should break in the reverse order that they are formed. An
important known exception to this is in proteins that contain the disulfide bond, which
only fold properly in the presence of an oxidant.7 When a protein is denatured, it no
longer functions as it is intended. An everyday example of denaturation is the protein
lysozyme contained in uncooked chicken eggs. As the egg is cooked, the heat destroys
the weaker bonds contributing to the three-dimensional structure, but does not disrupt the
strong covalent bonds of the primary structure. This is what gives cooked eggs its texture
and white foamy appearance.
A major hurtle in denaturation is that much of the time when a protein is
denatured, there is no way for the protein to fold back to its original state. There is no
way to uncook an egg, and it is often not possible recover the long-range interactions that
form the higher orders of protein structure. It seems to me that the hypothesis that a
protein unfolds in the reverse order that it folds is not necessarily true for many proteins.
For proteins that do refold to their natured state after denaturation, this hypothesis seems
more feasible. For this project, Staphylococcal nuclease was chosen because it readily
refolds to its natured state after denaturation and contains no disulfide bonds.
The pathway a protein takes to its natured state is a hotly debated subject, with
several plausible explanations available. Some think proteins nature all-at-once or at
least into discernable stages corresponding to their order of structure. There is some
14
evidence for denaturation in stages, because proteins can form intermediate
conformations called molten globules. It is likely some proteins fold rapidly and some
less rapidly and in stages. Most agree that the Thermodynamic Hypothesis is critical in
the formation of protein structure. This was proposed in the 1960s by one of the pioneers
in protein analysis, C. B. Anfinsen.8 This hypothesis states that the native conformation
of a protein is adopted spontaneously to ―the global minimum of [Gibbs] free energy.‖9
Gibbs free energy is a thermodynamic property used to determine whether a process is
spontaneous or not. A system seeks out a minimum in Gibbs free energy according to the
Second Law of Thermodynamics (entropy increases for any process).
Further
complicating the study of folding is the influence of nucleation, which is a specific event
that triggers rapid folding.10
Methods of Protein Analyzation
Common methods of analyzing the denaturing process include: Nuclear Magnetic
Resonance spectroscopy (NMR), X-Ray crystallography, fluoroscopy and fluorescence
correlation spectroscopy, and Dynamic Light Scattering (DLS).
NMR spectroscopy utilizes the magnetic spin of the nuclei of atoms within a
protein and aligns them with a strong external magnetic field. Nuclei with an odd
number of protons or neutrons will have a net magnetic moment. This net magnetic field
is then analyzed by pulsing radiofrequency (RF) radiation to excite the nuclei which will
then emit specific frequencies of radiation depending on their position relative to other
atoms in the protein. By using RF pulses at several angles, intensities, and frequencies, a
three-dimensional picture of the protein can then emerge. A complicated process called
sequential assignment is also used based on the amino acids known to be present. The
15
technique is quite time-consuming, and sequential assignment’s complexity means that
NMR spectroscopy can only be used on small proteins (less than 200 amino acids in
primary structure). Also, the environmental conditions of the protein must be held
constant over long periods of time, lending high temperature and pressure studies
impractical. Another newer method of NMR spectroscopy involves halting the protein
folding process while it is occurring through a sudden change in pH and switching the
solution to ―heavy water‖ or D2O. This ―paints‖ the protein at a specific point midfold so
that each area of a protein can be marked as folding either before or after the process.
This promising avenue does have its difficulty in controlling uniformly the point in the
folding process at which the solution switch happens since the folding process is so rapid.
Also, the sudden change in pH is enough to invasively disrupt the folding process and can
alter the natural folding process. This data are also notoriously difficult to interpret.
In X-Ray crystallography, proteins are first crystallized.
This hinders the
adaptability of the technique from the start since conditions must be very controlled and
cannot vary. Crystallization is ―as much an art as a science . . . countless attempts to
determine molecular structures have failed at this stage.‖11 Once a crystal is finally
obtained, a diffraction pattern is produced by X-irradiation. This pattern consists of
thousands of spots which are the raw data. The position and intensity of each spot is
relatively easily determined, but the phases of the waves which formed each spot must
also be determined in order to produce an electron density map. Once the phase problem
is solved, a very accurate model of the protein’s structure can emerge, though the primary
structure of the protein must already be known. X-Ray crystallography can be utilized
16
for any size protein, but does not give information about denatured proteins or even
thermal conformational variability within a natured protein.
In fluoroscopy, a few specific amino acids are excited by visible light and release
electromagnetic radiation as they return to their ground states. The stereochemistry of the
polypeptide chain and other environmental factors affect the fluoroscopy in ways that can
be analyzed to follow changes in folding conformations.
Fluoroscopy can give
information about a protein’s conformation state, binding sites, solvent interactions,
degrees of flexibility, internal motions, rotational diffusion coefficient, and other
parameters.12 Fluoroscopy utilizes residues within a protein so that the fluorescence
intensity from a solvent-exposed amino acid will be higher than that of the inner residue.
This yields some information about how a protein unfolds by interpreting the changing
amount of exposure to the residue and to the solvent. This method is somewhat crude
compared to other methods and the residue may affect a protein’s folding, but
fluoroscopy can provide a rough picture of the unfolding process.
The technique used for this project is Dynamic Light Scattering (DLS), also
known as Photon Correlation Spectroscopy (PCS).
DLS does not yield as much
structural information as NMR spectroscopy or X-Ray crystallography, but its strengths
lie in versatility. NMR spectroscopy relies on a concentrated sample with very precisely
managed environmental factors and can only study small proteins.
X-Ray
crystallography can only study proteins that are crystallized and therefore the amount of
environmental factors affecting protein folding that can be studied is extremely limited.
Also, both of these methods rely on very complex analysis. Fluoroscopy gives only a
crude sense of protein unfolding and the residue and technique make the process
17
unnatural and invasive. DLS studies protein unfolding by shining coherent light upon a
protein solution and analyzing the individual photons that are scattered off the protein. A
detector transforms the signal from the individual photons into an electronic signal that
can be analyzed by a computer quickly and without intrusion on the protein. The
technique allows for great flexibility of the environment of the protein and does not
involve any additives that might affect denaturation. The objective of DLS is to analyze
the seemingly random properties of the scattered light intensity by calculating
correlations in this time-dependent signal.
When a coherent beam of light, such as a laser beam, passes through a solution,
the solute particles scatter some of the light in all directions. When these particles are
small compared to the wavelength of light used, the intensity of the scattered light is
uniform in all directions. This is known as Rayleigh scattering. For larger particles, Mie
scattering occurs where the intensity of the scattered light is angle- and wavelengthdependent. In this project, 514.5-nm coherent laser light is scattered on much smaller
proteins or polystyrene spheres, and Rayleigh scattering occurs.
In this project, coherent and monochromatic laser light is scattered by a solution
of protein (or polystyrene spheres). A time-dependent fluctuation in the intensity of the
scattered light at a particular angle is observed because the particles are small enough to
undergo random thermal Brownian motion, so the distance between each protein
molecule is constantly varying. At each instant, the light scattered from neighboring
particles interferes either destructively or constructively so the Rayleigh scattering
undergoes fluctuations in intensity. Since this fluctuation arises from properties of the
solution, we can analyze the scattered light to yield information on the size of particles
18
within the solution. In particular, an analysis of the time-dependence of the intensity
fluctuations yields the diffusion coefficient of the particles from which their
hydrodynamic radius can be determined via the Stokes-Einstein equation. Thus, DLS is a
quick and non-intrusive method of determining the size of a protein at a particular set of
conditions.
A photomultiplier tube (PMT) is used to detect single scattered photons within
specific time intervals. A PMT consists of a series of plates so that a single photon is
amplified into a cascade of electrons. Richard Feynman explains further how a PMT
works: ―when a photon hits the metal plate A . . . , it causes an electron to break loose
from one of the atoms in the plate. The free electron is strongly attracted to metal plate B
(which has a positive charge on it) and hits it with enough force to break loose three or
four electrons. Each of the electrons of plate B is attracted to plate C (which is also
charged), and their collision with plate C knocks loose even more electrons. The process
is repeated ten or twelve times, until billions of electrons, enough to make a sizable
electron current, hit the last plate.‖13 This electric current is fed directly into a computer
processor where a program can interpret the data. DLS therefore allows for precise and
quick measurement of single photons by a PMT.
DLS is extremely useful in protein folding studies of larger proteins and of
proteins undergoing thermal, chemical, or pressure denaturation. The volume used can
be small and relatively dilute and no foreign constituents need to be added to the solution
for the process to occur. DLS is a method of actually watching the protein as it unfolds,
and this voyeurism does not affect the folding or unfolding of the protein. DLS is
19
literally where physics and biology intersect, so that the mysteries of life can be studied
according to the calculated objectivity of physical equations.
Thermal Denaturation
Dynamic Light Scattering can be used to study the particular effects on
denaturation of almost any environmental stimulus. The goal of this project is to refine
the DLS apparatus for thermal denaturation and to study the particular protein
Staphylococcal nuclease. The focus of much of the rest of the discussion will thus be
about temperature-dependence of protein denaturation, an area that is notoriously
difficult to study with NMR spectroscopy and X-Ray diffraction. Thermal denaturation
is important biologically because small changes in temperature can affect a protein’s
solubility, enzymatic activity, and deactivate the protein, often irreversibly. For example,
raising body temperature after the onset of a sickness activates certain enzymes within
the immune system while raising the metabolism and helping to hinder proteins within
the pathogens.
An increase in temperature means that bonds within the protein molecule are
strained and weakened. The weakest bonds are affected first and most severely. These
are the bonds that form the tertiary (or quaternary, if present) levels of protein structure.
The protein literally changes its shape as hydrogen bonds are broken and different areas
of the molecule are exposed to the solvent. Water forms new hydrogen bonds with the
amide nitrogen and carboxyl oxygen of the peptide bonds. Hydrophobic portions once on
the interior of the folded protein are also exposed to the solvent. This increases the
amount of water bound to each protein molecule. Thermal denaturation thus results in an
increase in the hydrodynamic radius of the molecule affecting the viscosity and
20
solubility.
The protein responds according to the Thermodynamic Hypothesis to
minimize its Gibbs free energy by exposing as many polar groups and burying as many
hydrophobic (literally ―water-fearing‖) groups as possible. This greatly affects internal
polypeptide interaction so that the protein unfolds and gives a structure quite different
than the activated protein at lower temperature.
If the temperature returns to its original state, the protein may not return to its
original structure even though the original state was likely lower in Gibbs free energy.
Irreversible bonds, along with kinetic factors, may have formed so that the protein is
unable to attain the necessary activation energy to return to its native state. The protein
may only return to its natured state if all levels of structure except the primary one are
broken. The hydrophobic groups of a protein contribute to an energy barrier that possibly
inhibits a protein in returning to its natured state once the temperature returns to a normal
range. If hydrophobic interactions are minimized and disulfide bridges are not present, a
protein may return to its natured state after thermal denaturation (as is the case with
Staphylococcal nuclease, the protein utilized in this project).
Goals
This research is part of a bigger project between several research groups to use
Dynamic Light Scattering techniques to study protein folding in general and
Staphylococcal nuclease and its mutants specifically. The primary goal of this thesis
project involved refining the system apparatus for thermal denaturation and then using
this apparatus to improve upon earlier incomplete thermal measurements on
Staphylococcal nuclease.
A new furnace design was successfully implemented that
21
allowed for the successful attainment of this goal as well as a study of the kinetics of
unfolding in Staphylococcal nuclease.
This study used 21-nm polystyrene spheres for test runs and to test the thermal
DLS apparatus and Staphylococcal nuclease wild-type (abbreviated ―WT‖, the most
common form of Staphylococcal nuclease) to obtain more reliable data about its thermal
denaturation. Further projects are intended to study how substituting specific amino
acids for Staphylococcal nuclease wild-type will affect thermal denaturation and other
types of folding. Reliable high temperature data on Staphylococcal nuclease is not
available, and this information will help in the development of this project and on the
frontline of proteinomics in eventually being able to predict how a protein will fold under
conditions given only the primary structure of a protein.
22
Theory of Dynamic Light Scattering
Dynamic Light Scattering in its fundamental form consists of shining coherent
electromagnetic radiation upon a solution, collecting the scattered photons at a certain
angle, and using this data to uncover characteristics of the solution. The technique is not
limited to biological systems, though it is fast becoming a convenient tool for medical
diagnostics. For example, DLS has been proven to be extremely effective in the very
early detection of cataracts in the eye, an ailment responsible for half the cases of
blindness and prevalent in 34 million people aged over 65.14 Other applications of DLS
include nanoscale engineering, feedback systems for water filtration, diagnostics for the
purity of solutions, and general characteristics of solutions. Its main use is the noninvasive determination of solute particle size in the dilute limit of a solution, which of
course lends itself well to protein denaturation research.
When a coherent (in phase) laser beam illuminates a solution, the distribution of
charges within the molecules in solution is subjected to an oscillating electric field, and
the charges are therefore accelerated. Classical electromagnetic theory proves that an
accelerated charge will radiate electromagnetic radiation. If the solution is optically
similar (its dielectric constant is homogeneous throughout the solution), the light radiated
from each region of the solution differs only by a phase factor (i.e., the wavelength of
light will be the same, but there will be patterns where the light destructively or
constructively interferes). If the dielectric constant fluctuates within the medium, as
happens when molecules move within a solution (e.g. Brownian and thermal motion),
light will be scattered in all directions and undergo frequency shifts.
23
DLS depends primarily on quasi-elastic scattering, which deals with light
scattered from the translational and rotational degrees of freedom of solutes in a solution.
―Quasi-elastic‖ means that the scattered light has almost the same wavelength as the
incident light.15 When frequencies are separated by a very small amount, this gives rise
to a beating of light where the intensity seems to wax and wane with time. This beating
of light can be detected by the PMT.

In DLS, coherent incident laser light of wavevector  i (the incident beam) passes

through the scattering volume (the protein sample). Light with wavevector  s (the
scattered beam) is scattered by this sample and measured by the PMT at some known
angle θ (in our case 90°) with respect to the exiting incident beam (see Figure 8 below).
Figure 8 - Diagram of DLS incident and scattered wavevectors. For this project θ=90º. The incident
beam is scattered in all directions, and the bottom arrow emphasizes this.
The PMT transforms intensity fluctuations from the scattered light into a
corresponding fluctuating voltage as described before. A computer records the output
and calculates from it an intensity-intensity autocorrelation function. The computer can
also analyze these correlation functions to yield physical data about the solution.
24
If the scatterer in solution moves (such as the Brownian and thermal motion for
proteins), the dielectric constant fluctuates over time and a correlation function can be
used. A correlation function is a way to interpret seemingly random data. In this
application, light intensities defined to be similar to each other over a time interval are
said to be correlated, and those that are not are considered not to be correlated.
The following derivation of how the scattered light intensity that the PMT
measures can correspond to the radius of particles in solution is normally calculated
through Brookhaven Instruments DLS control software or on a mathematics program
such as Mathcad or SigmaPlot.
From advanced electromagnetic scattering theory, the intensity of scattered light
from one molecule is
4 2 M 2 sin 2  ( dn / dc) 2 I 0
I (1) 
,
N A2  4 R 2
(1)
where M is the molecular weight of the molecule, υ is the angle of the scattered beam
with respect to the polarization of the incident beam, R is the distance from the scattering
medium to the detector, (dn/dc) is the rate of change of the index of refraction as the
concentration of the solution changes, I0 is the intensity of the incident beam, NA is
Avogadro’s number, and λ is the wavelength of light in the solution.16
To interpret light scattered by the solution, we need to calculate the intensity due
to a large number of molecules. We need to calculate the electric field due to each
molecule, and the total intensity will be proportional to the square of the sum of each
individual electric field. The average intensity of a light beam given in terms of its
maximum electric field is
25
2
E max
I
in W/m2.
2(3.77 )
(2)
Assuming all scattering molecules are identical, so that electric fields vary in phase but
not magnitude, the scattered electric field that is in phase with some reference beam is
E si  E s  cos  i ,
(3)
i
while the electric field out of phase with the same beam is
E so  E s  sin  i ,
(4)
i
where Es is the maximum magnitude of each scattered electric field, the sum is over the
number of scattering molecules, and σi is the phase of the scattered field due to the i-th
particle. Combining these equations gives
2
2
 N
1
  N
 
2 
I (N ) 
E s   cos  i     sin  i   ,
2(3.77 )  i 1
  i 1
 
(5)
which, through trigonometry and substitution of Equations (1) and (2), becomes
N


I ( N )  I (1)  N  2  (cos( i   j ) ,
j i 1


(6)
where N is the number of scattering particles. The terms that vary as the molecules move
in solution are the σi’s and σj’s. The second term in Equation (6) will vary over time and
so will the net intensity of scattered light.17 This time of fluctuation between maximum
and minimum intensity is strictly dependent on the properties of the scattering molecule,
and this is the key to understanding how Dynamic Light Scattering works. By measuring
the macroscopic fluctuations in the intensity of light scattered by a solution, we can
determine microscopic properties of the solution.
26
Intensity fluctuations in DLS are usually studied via correlation functions.
Consider an arbitrary function F(t). The time autocorrelation function of F is defined as:
1
T  T
F (0), F ( )  lim

T
0
F (t ) F (t   )dt .
(7)
This function measures how correlated the function F is at time τ compared to F at time
0. It is useful to convert the integral to a discrete small interval Δt, where F changes
negligibly, t=iΔt, τ=jΔt, and T=NΔt, so Equation (7) becomes
F (0), F ( )  lim
N 
1
N
N
F F
i
i j
,
(8)
i 1
where Fi is the value of F at the start of the i-th interval and N is the number of
molecules. In the case of DLS, the function is the number of photons collected by the
PMT, Δt is called the sample time and τ is called the delay time. The number of photons
incident on the tube during the i-th interval of Δt duration is ni, and the autocorrelation
function is then defined as18
1
N  N
G ( 2 ) ( jt )  lim
N
n n
i
i j
 ni ni  j .
(9)
i 1
The intensity autocorrelation function is the signal measured during DLS
experiments, but the properties of the scattered molecules are more easily calculated from
the electric field autocorrelation function. To obtain this, we need to normalize the
intensity autocorrelation function with respect to a baseline value to get the net intensity
autocorrelation function:
g ( 2 ) (t ) 
G ( 2 ) (t )
,
G ( 2 ) ( )
27
(10)
where G(2)(∞) is the baseline signal measured over a long period of time. This is
converted to the Electric Field Autocorrelation function g(1)(t) using the Siegert
Relationship19:
2
g ( 2) (t )  1   g (1) (t ) ,
(11)
where 0<β<1 is dependent on experimental values (e.g. properties of the laser beam,
detection optics) and is calculated during data fitting. The electric field autocorrelation
function is determined by Fourier transform of the number density of the scattered light20:

g 1 (r , t )  nˆ d (k , t ), nˆ d (k ,0) .
(12)
The Siegert relationship is based on the assumption that the scattered electric field has a
Gaussian distribution and is valid whenever the system is ergodic, when the timeaveraged properties of the system are equal to the ensemble-averaged properties.
Computer algorithms often help in finding a functional fit for g(1)(t) since it is notoriously
difficult to calculate in general.
Consider the case for a dilute solution of rigid, monodisperse spheres undergoing
only translational diffusion, the function g(1)(t) is simply
g (1) (t )  e 2 t ,
(13)
where Γ is called the decay rate, which is related to the translational diffusion constant DT
of the molecule by
  DT q 2 ,
(14)

where q is the scattering vector defined as the difference between the scattered (  s ) and

incident (  i ) wavevectors (see again Figure 8):


 

q   k s  ki ,
28
(15)
where the magnitude of ks = (2/s) and of ki = (2/i). The magnitude of q is
q
4 n
0
 
sin   ,
2
(16)
where n is the index of refraction of the solution, 0 is the wavelength of the incident
light in vacuum, and  is the scattering angle inside the solution. In the dilute limit,
particle interactions can be ignored, and the diffusion constant (DT) for spheres in a
solution with bulk viscosity η is given by the Stokes-Einstein Equation:
DT 
k BT
,
6rh
(17)
where kB is Boltzmann’s constant, T is the temperature of the solution in Kelvin, and rh is
the hydrodynamic radius of the scattering molecule.
The autocorrelation function has thus come full circle to tell us information about
the size of the scatterer with the assumption that they are spheres. We will use this
assumption that in its native state, a protein is roughly a sphere, and that the radius of the
sphere increases as the sphere unfolds. Equation (13) is also valid in the case where
several different size spheres are present. This case gives a correlation function with a
double decay exponential instead of a single decay exponential. When two or more
particles are in a solution, we can extract the spherical radius of these particles by
analyzing the correlation function as a sum of two or more decaying exponentials.
Staphylococcal nuclease is globular in its native state, so the spherical assumption does
yield meaningful data about its size.
29
Properties of Staphylococcal nuclease
Staphylococcal nuclease (sometimes abbreviated ―SNase‖) is a DNA and RNA
cleaving enzyme with the property of transition between its denatured and natured states
along with, stability under relatively extreme conditions. This makes SNase ideal for a
DLS study. SNase contains no disulfide bridges, so it is possible to study the protein’s
folding process by studying its denaturation in reverse. Staphylococcal nuclease consists
of 149 amino acids, has no quaternary structure, and has molecular mass of 16.8 kDa.21
Shortle & Ackerman have recorded its hydrodynamic radius as 1.6 nm in its natured state
and 3.5 nm when denatured.22 SNase can withstand temperatures as high as 65 ºC and is
stable in the presence of other enzymes. This project utilizes the naturally occurring
―wild-type‖ SNase (WT); future projects may use mutants. Figure 9 below shows the
structure of Staphylococcal nuclease.
Figure 9 - Structure of Staphylococcal nuclease using X-Ray crystallography. (From
http://www.rcsb.org/pdb/)
30
Experimental Method
Production of Staphylococcal nuclease
The production of Staphylococcal nuclease wild-type (WT) is fairly timeconsuming, taking about twenty steps over the course of four or five days. The following
will be only a brief qualitative summary of how Staphylococcal nuclease is produced
from scratch in a biochemistry lab. For a more in-depth discussion on the step-by-step
production of WT, see April Fortner’s 2002 University of Arkansas Honors Thesis
entitled: ―Protein Chemical Denaturation and Analysis using Dynamic Light
Scattering,‖23 and supplemented with Dr. Wes Stites’ laboratory protocol for protein
production: ―Nuclease Protein Preparation in λ Expression System.‖24
An ampicillin-resistant strain of E. coli containing a gene for Staphylococcal
nuclease expression is first grown in a broth and agitated at a warm temperature to
produce an abundance of protein. The bacterial E. coli cells are then lysed, so that
protein is released into solution. Ampicillin is added, which prevents other bacteria from
being produced.
Care is taken not to expose the media to air, so that outside
contaminants are not introduced. Once the bacterial cells are lysed, it simply becomes a
laborious process of isolating the WT from the many other contents inside and outside of
the lysed cell. This is achieved through a long series of centrifugations, resuspensions in
buffer, and cation exchange columns. The initial step of the procedure typically begins
with about 3 L of broth containing the bacterial sample and by the end of the process, a
yield of about 60 mg of WT in a buffer solution is the reward for the lengthy torture.
31
Dynamic Light Scattering Procedure
Several critical points need to be kept in mind when undertaking the procedure for
analyzing a protein sample by Dynamic Light Scattering. First, an optical axis needs to
be carefully established so that the incident and scattered angles are accurately known.
Second, all care must be taken to keep the sample as pure as possible so that scattering
from other solutes such as dust and contaminants contained within the solution is kept to
a negligible level.
Third, it is imperative that the only photons reaching the
photomultiplier tube are the photons scattered off the sample solution. This means that
any stray lights need to be off, the glass tubing for the sample needs to be extremely clean
so that stray laser light does not scatter from it, and a method needs to be established of
allowing only the photons scattered along the optical axis into the PMT. After all of this
preparation, a clean signal can reach the PMT, which is converted to an electronic signal
and analyzed by a computer. The procedure to follow is critical for fulfilling the above
criteria.
The optical setup is shown in Figure 10, with a Coherent Innova 306 laser
operating in single mode at a wavelength of 514.5 nm supplying the coherent light. Since
polystyrene spheres and SNase are much less than this wavelength, Rayleigh scattering
will be observed. From the laser, the beam is split into the incident and alignment beams
by a 90/10 beam splitter.
A system of mirrors brings the two beams roughly
perpendicular, and the angle of 90 degrees is finally established by mounting a mirror
where the sample would normally be and orienting it to 45º 0’ (± 5’). The incident beam
is directed onto this mirror such that it counter-propagates along the alignment beam so
that after removing the mirror, the incident beam is at an angle of 90.0º (± .1º) with
32
respect to the alignment beam on the axis with the PMT. Once this angle is established,
there is no need to repeat this procedure each time unless the table or mirrors are bumped
significantly.
Figure 10 - Schematic of optics. M=mirror, L=lens.
Lens L1 (focal length=63.5 mm) is used to focus the incident beam onto the
sample. This focuses the radius of the beam in the focal plane to as little as 5 μm. Lens
L2 (focal length=100 mm) focuses the scattered light onto the 0.05 mm pinhole, which,
along with the iris, helps to reduce the amount of unwanted light that enters the PMT and
establish a single coherence area over the size of the PMT’s photocathode. During
experiments, a black light-tight box is placed over the PMT and black fabric drapes the
cracks to ensure further protection from unwanted photons. Lens L2 was assembled in a
2f-2f configuration meaning that there is a distance of 200 mm (twice the focal length)
33
from the scattering volume to the lens as well as from the lens and to the pinhole. This
means that the magnification is one since the object and image distances are equal. A
microscope was used to aid in finding the scattered beam and for ensuring that light was
collected along a diameter of the cylindrical glass sample chamber to minimize error due
to refraction.
The PMT is connected to a Brookhaven Instruments BI9000 digital autocorrelator
board in a standard PC. A Thorne-EMI PMT is used with a transit time of less than 25
ns, which means the smallest delay time possible is 100 ns. The voltage applied to the
PMT was usually between -1.9 and -2.2 kV giving 25 to 50 kilocounts per second upon
excitation by scattered light. This voltage was tuned to give a stable count rate. The
count rate was also regulated by neutral density filters on the optical table, which filter
the incident laser beam.
Another piece of information that needs to be kept in mind when performing a
DLS experiment is the idea of coherence area. The section of the interference pattern
detected by the photocathode of the PMT needs to be small enough that solitary
fluctuations in intensity are observed, rather than intensity averages over many
fluctuating points. Coherence area is defined as:
Acoh 
2 R 2
,
a 2
(18)
where λ is the wavelength of the laser light, R is the distance from the scattering volume
to the detector (in this case from the scattering volume on the pinhole to the detector,
about 22 cm), and a is the radius of the scattering volume (at most 25 μm). This means
the coherence area is about 2.6 mm. The area viewed by the detector should be less than
34
this value if possible, and certainly not much more. The size of the photocathode is about
5 mm in diameter, so this requirement is filled.
Of utmost importance is a clean sample and this is achieved by filtering the
sample and cleaning the constituent parts of this system. Valves and glassware are
cleaned with a solution of filtered water and Alconox cleaner. The valves and glassware
are then placed in a sonicator for fifteen minutes and cleansed again in deionized water.
The filtration apparatus consists of various Upchurch Scientific valves, two 0.2 μm inline
filters, a thin glass tube where the laser is focused on the sample (outer diameter of 1/8
inch and inner diameter of 3/32 inch). A glass blower heated the ends of the tubing until
their end diameters created a tight seal (sometimes frustratingly too tight) with the 1/16
outer diameter Teflon tubing used to connect various parts of the filter. The pump, a BISFS model from Brookhaven Instruments Corporation, controls the flowrate of the
filtration. Before taking data, the system was filtered for at least twenty minutes to
ensure a clean sample. Once filtered, the valves are closed so that liquid cannot leave or
enter the glass tube. See Figure 11 for an overview of the filtration system.
Figure 11 - The filtration system viewed from above.
35
The heating apparatus consists of an internal furnace where the glass tube holding
the sample is inserted along with an aluminum capped cylinder can to isolate the sample
from room temperature air. Prior attempts at thermal denaturation were plagued by a
lack of stable rate counts at higher temperatures probably due to convection currents, and
the aluminum cylinder encasing the internal heating device eliminated these convection
currents by ensuring that the entire sample contained between closed valves was held at
the same temperature.
The internal furnace used to be exposed to room temperature air, and besides the
troublesome convection currents, it was not as successful at holding a stable temperature
as the new cylinder encasing system is. The internal heater’s design (see Figure 12)
consists of two pieces of circular aluminum 1.5 cm in height and 2.2 cm in diameter both
of which have 0.2-cm holes drilled through their centers. The two pieces are separated
by spacers 0.5 cm in length so that there is a 0.5 cm gap between the top and bottom of
the furnace, so both the incident and scattered beams can enter. Minco heaters were
wrapped around the outside of the aluminum pieces and a thermocouple was placed along
the bottom heater and wrapped in insulation tape. A thermocouple is placed along the
central cavity which measures the temperature against the glass tube holding the sample.
The heaters and thermocouples are connected to a Lake Shore 330 Autotuning
Temperature Control Unit allowing for a digital readout of the temperature at each
thermocouple, along with heating control to the thermocouple near the sample.
36
Figure 12 - Schematic diagram of internal furnace.
The aluminum can encasing the internal heater that Dr. Oliver and I designed is
constructed to be form-fitted on the bottom and top lids to the valves. This ensures that
the entire sample solution is contained within an environment of the same temperature
when the valves are closed. Before, the internal heater was too small to encase the entire
sample tube and valves. The internal furnace is now mounted on the inside of the can so
that it extends along the vertical element of the entire can. The can is 4.5 inches in height
and 2.5 inches in diameter. Half of the cylinder ―shell‖ can be removed allowing for easy
access to the internal part of the can for alignment purposes. Four windows were
constructed ninety degrees apart, so that the incident, scattered, and exiting beams are all
allowed passage out. The fourth window is used for wires to exit the can. Once the
beams and sample are roughly aligned, the other half of the cylindrical shell can be
placed back on to insulate the sample from the room temperature air. Heating tape (of
37
80-Ω resistance) is then wrapped around the can making sure that none of the windows
(besides the wire window) are covered. The heating tape is connected to a 0-130 V
Tenma Variable Auto Transformer, which is used for rough temperature control. Once
the temperature is near what is desired, the internal heating control can ensure minute
control (along with a digital read-out). This temperature controlling system allowed for
little fluctuation (usually less than 0.03 °C) and could be held at the same temperature
for any desired length of time.
Figure 13 shows the aluminum can with the shell
exposing the interior and also the can wrapped in heating tape, as it appeared during a
trial run.
Figure 13 - Left: aluminum can with shell removed revealing the interior heater, thermocouples, and
the glass tube holding the sample. Right: the aluminum can with heating tape wrapped around it
and insulation.
A Staphylococcal nuclease sample is prepared by first diluting the sample to
about 10 mg/mL and thawing it in a 55 ºC water bath for five minutes to remove dimers
(bonding between protein molecules during the freezing process). This solution is then
diluted further with the 0.1 M NaCl, 0.025 M NaPO4 buffer solution. The physical
equations described before are valid in dilute limits, so the more dilute the sample that
38
can be obtained that still gives a strong scattered signal, the better. A final concentration
of about 7 mg of protein per milliliter of solution (about 0.6% by mass) was typical and at
least 5 mL of sample is needed. This solution is introduced into the filtration system
(usually for about half an hour), the can apparatus and heating tape is then installed, the
alignment is checked again, the sample is heated up using the temperature controlling
unit (for fine adjustments and feedback control) and Variable Auto Transformer (for
coarse adjustments), and data is finally taken. 21-nm polystyrene sphere solutions are
prepared by simply adding 3 to 5 drops of Duke Scientific polystyrene sphere solution
(density 1.05 g/mL) to about 15 mL of water or buffer solution and similarly setting up
the system apparatus.
Brookhaven Instruments Dynamic Light Scattering Software records and
interprets data instantaneously as the apparatus is running. Neutral density filters on the
optics table and the voltage are tuned so that at room temperature, the count rate from the
PMT is stable and somewhat low (25 to 35 kcps). Any adjustment of the voltage will
correspond to a change in count rate which the software will interpret as a change
emanating from the sample. For this reason, it is undesirable to change the voltage, and
if this does occur the run must be started over. Since count rates typically increase with
increases in temperature, the count rate gradually increases to around 50 kcps at
temperatures of about 40 °C, so a voltage adjustment is unnecessary if it is set lower at
low temperatures. At higher temperatures, it is somewhat difficult to avoid the need to
change voltage or the neutral density filters. High temperatures also give rise to a
dynamic environment that makes it difficult to obtain a steady count rate. This will be
explained more thoroughly in the Results & Discussion section.
39
The software has many functions that can be utilized, but runs typically consisted
of the four windows shown in Figure 14: the Control window, NNLS (Non-Negatively
Least Constrained Multipass), Count Rate History, and the Correlation Function.
Figure 14 - The typical setup of the Brookhaven Instruments Dynamic Light Scattering software.
Windows, clockwise from top left: Control Window, NNLS, Count Rate History, and Correlation
Function Window. This run is for a 21-nm sphere solution. Notice the smooth correlation function,
steady count rate, and the NNLS distribution of sphere size around 20 nm.
The Control Window gives information about the delay times, the elapsed run
time, the sample rate, the baseline, the baseline differential (less than 5% for meaningful
data and typically under 1%).
It also controls vital settings such as temperature,
viscosity, the wavelength of light, and channel input, among others. NNLS is one of
several standard methods the Brookhaven software uses to interpret the data as a
distribution of particle sizes. It utilizes a complicated algorithm to give the particle sizes
40
while the computer is still collecting data. For the small proteins and polystyrene spheres
used in this experiment, NNLS was found to be the most accurate given our set of
conditions.25 The software gives a distribution of particle sizes, but we typically used the
raw data and interpreted it through programs Dr. Oliver and I created in Mathcad since
the software gives little user control and its built-in viscosity model assumes a dilute
environment which did not match our system.
After the lengthy preparation described in this experimental method, the optical
table appears as in Figure 15 and data can be taken.
Figure 15 - The optical table during a Dynamic Light Scattering run after all of the experimental
method has been followed.
41
Results and Discussion
The Theory of Dynamic Light Scattering section showed how a correlation
function can be interpreted to use the Stokes-Einstein equation below by extracting the
diffusion constant and the hydrodynamic radius (rk) assuming spherical scatterers:
DT 
k BT
,
6rh
(19)
where T is the temperature in Kelvin, kB is Boltzmann’s constant, and η is the bulk
viscosity. The diffusion constant (DT) is determined by fitting an exponential to the
correlation function as described before. Solving Equation (19) for the hydrodynamic
radius gives
rk 
k BT
.
6DT
(20)
It is critical to have accurate temperature-dependent viscosity data in order to determine
accurately the hydrodynamic radii of the solute particles. Unfortunately, viscosity varies
greatly depending on slight changes in many factors. Relating to this project, viscosity
changes with temperature, concentration of chemicals within solution, particle
interactions, and electrostatic interactions between the solution and its container. The
buffer solution we use is somewhat dilute, consisting of 0.1 M NaCl and 0.025 M NaPO4.
Nadeem Akbar took viscosity data as a function of temperature of this buffer solution by
using 21-nm spheres and treating this hydrodynamic radius as constant at any
temperature. He was therefore able to extract the buffer solution’s viscosity in much the
same way that we extract particle size. The viscosity data he took was somewhat lower
42
than water for all temperatures. This does not make much physical sense because
dissolution of ions in water (including NaCl and NaPO4) nearly always raises, not lowers,
the viscosity of the solution compared to deionized water.26 Several factors could have
given skewed data including an inflation of size of the spheres at increasing temperatures,
electrostatic interactions between the spheres, glass, and water, and a solution too
concentrated in spheres.
The protein solutions used in this project were typically about 7 mg/mL— much
more concentrated than the buffer solution. This viscosity data is therefore not applicable
to a solution containing large organic molecules, which would likely raise the viscosity
even more than the buffer solution. Given that we could not assume the size of proteins,
we assumed that the Akbar viscosity data held its trend with temperature even if its
values were problematic. Near room temperature, Staphylococcal nuclease is tightly
folded and our data yielded consistent sizes no matter which viscosity value is used. We
decided to scale the Akbar viscosity data so that at room temperatures, our protein size
agreed with Shortle and Ackerman’s data of about 1.6 nm in radius for SNase in its
natured state.
The scaled Akbar viscosity data gives viscosity as a function of
temperature and yields the agreed-upon value for the natured state’s size. Figure 16
shows a graph of the original data and the scaled data, which is the function we utilized.
43
Viscosity vs. T for Buffer
1.6
1.4
Temp (C) vs Visc (cP)
Quadratic Fit
Scaled Fit
Viscosity (cPoise)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
10
20
30
40
50
60
70
80
Temperature (°C)
Figure 16 - Viscosity as a function of temperature. The Akbar data is in red and the scaled data we
used is in blue.
The NNLS window of the Brookhaven software gives a distribution of particle
radii, but we found the software to be somewhat limiting in control, so we used Mathcad
to analyze the raw data ourselves. NNLS used aqueous viscosities so the radii it reported
were off, but its program gave us a good qualitative and even quantitative idea of error
distributions. Temperatures near room temperature (about 23 ºC) all the way up to over
40 ºC gave fairly typical and clean single-exponential decaying correlation functions.
The NNLS program likewise consistently interpreted the data to be a tight distribution of
a very small particle all the way up to 40 ºC. Just before 45 ºC, the correlation function
showed signs of developing a double-exponential—another, longer time decay. Short
time decays mean that the scattering particle is small and longer time decays mean that
the scattering particle is larger. Thus, at lower temperatures, we needed only to interpret
single-exponential decaying functions, while at higher temperatures, a doubleexponential needed to be analyzed. See Figures 17 and 18 for examples.
44
Correlation Function and Fits at 24 ºC
1.45
1.40
Raw C() Data
Single-Exponential Fit
C()
1.35
1.30
1.25
1.20
1.15
100
101
102
103
104
105
106
107
Time in s
Figure 17 - Raw data and our programmed fit for a single-exponential at 24 ºC. The radius is
calculated to be 1.584 nm for this example.
Correlation Function and Fits at 45 ºC
5.4
5.2
C()
Raw C() Data
Double-Exponential Fit
5.0
4.8
4.6
100
101
102
103
104
105
106
107
Time in s
Figure 18 - Raw data and our programmed fit for a developed double-exponential at 45 ºC. The two
radii were calculated to be 2.836 nm and 84.052 nm for this example.
45
Our program allowed us to use either a single-exponential fit or a doubleexponential fit. We also had the ability to choose which data points to fit by hand,
because often at high temperatures, the baseline would have a downward slope due to
thermal factors that were not meaningful to us, namely the count rate generally increases
from the beginning to the end of a particular run at high temperatures. Also, the first few
data points sometimes were scattered and we could sometimes do a better job of fitting
than the computer program.
We carefully analyzed the hydrodynamic radius as a function of temperature for
Staphylococcal nuclease from 23 ºC up to 60 ºC. The enhanced temperature control and
insulating system made it possible to take meaningful data all the way up to this
temperature, whereas the prior system was unable to remain stable above 40 ºC. Figure
19 shows the radius (or smallest radius when double-exponentials arose) for
Staphylococcal nuclease wild-type as a function of temperature.
Radius (nm)
SNase Radius vs. Temperature
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
20
25
30
35
40
45
50
55
60
Temperature (C)
Figure 19 - Hydrodynamic radius of SNase WT as a function of temperature. For higher
temperatures (>43 ºC) the radius plotted is the smaller of the two radii in double-exponential fits.
46
The graph in Figure 19 clearly shows a gradual increase of the radius from 1.6 nm to 2.1
nm until just before 45 ºC. The radius rapidly becomes larger at this point until it settles
just under 5.0 nm.
The system at 45 ºC deserves special attention. As already mentioned, doubleexponentials begin forming just before this temperature. This means that other larger
components emerge at around this temperature that were not in the system before. The
temperature was held constant at 45 ºC and the correlation function was allowed to
evolve to further study the kinetic emergence of large particles. Figures 20 and 21 show
the evolution over time for the correlation function at 45 ºC (scaled and unscaled).
Evolution of the Raw SNase Correlation Function at 45 ºC
10x10
6
8x106
C() after 0-2 mins
C() after 3-5 mins
C() after 6-8 mins
C() after 8-10 mins
C() after 10-12 mins
C()
6x106
4x106
2x106
0
100
101
102
103
104
105
106
107
Time in s
Figure 20 - Evolution of the unscaled correlation functions at different times at 45 ºC. The
background evolution is evidence of an increase in count rate, leveling off after about 12 minutes.
47
Evolution of the Scaled SNase Correlation Function at 45 ºC
1.5
1.0
C() after 0-2 mins
C() after 3-5 mins
C() after 6-8 mins
C() after 8-10 mins
C() after 10-12 mins
C()
X
+
+++++
+
0.5
+
XXXXXX
+
+
X
X
0.0
-0.5
100
++
+
X X +++++++++++++
+++++++++++++++++++++++++++++
XXXXXXXXXXXXXX
+X
+X
+XX
+XX
+X
+X
+X
+X
+X
+XX
+X
+X
+X
X
XXX
+X
+X
+X
+X
+XX
+X
+XX
+X
X
+X
+X
+X
+X
+X
X
X
+X
+X
+X
+X
+X
X
X
+X
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+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
X
X
X
X
X
XX
X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
XXX
X
X
X
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+X
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+X
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+X
X
X
X
+X
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X
X
XX
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+
+X
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X
X
XX
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X
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X
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+X
+
101
102
103
104
105
106
X
+
107
Time in s
Figure 21 – Evolution of the scaled correlation functions at different times at 45 °C. Notice how the
double-exponential develops by 3 minutes and matures by 12 minutes.
Our data fits for this time evolution at 45 ºC yield a very developed doubleexponential (to a reasonable approximation) after twelve minutes as well as an increasing
smaller radius which I will refer to as a molten globule. Figures 22 and 23 graph this
data. Gast et al. refer to molten globules as ―nearly as compact as the native state, have
native-like secondary structure, and differ mainly by the lack of a rigid tertiary
structure.‖27 The molten globule can be thought of as a swelling protein that retains some
structure, though the tertiary and secondary structures are dynamically changing, giving a
bigger average radius. I refer to the bigger radius obtained from the double-exponential
curves as a ―floppy chain.‖ Since the larger particles were not in the system below 45 ºC,
I conclude that the larger particles that develop are indeed denatured polypeptide chains
of SNase. Our analysis yielded floppy chains of about 80 nm depending on
48
radius (nm)
SNase molten globule growth
over time at 45 ºC
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
5
10
15
time (min)
Figure 22 - Time development at 45 ºC of the "molten globule," the smaller of the radii obtained
from the correlation function.
SNase floppy chain growth
over time at 45 ºC
radius (nm)
100
75
50
25
0
0
5
10
15
time (min)
Figure 23 - Time development at 45 ºC of the "floppy chain," the larger of the radii obtained from
the correlation function.
49
the temperature and time evolution.
The NNLS program likewise indicated an
emergence of larger particles at high temperatures. Unlike the smaller molten globule
radius, the larger particle had a wide radius distribution (usually about 20 nm), and
yielded an average larger particle size smaller than our own analysis. Like our data,
NNLS interpreted the floppy chains as becoming larger and a greater constituent of the
solution with increases in temperature and developing over time. Given this information,
we can conclude that large floppy chains do indeed form at higher temperatures and as
the system sits at a high temperature, this effect evolves to become more pronounced.
Since we assumed that proteins are approximated as spheres, it makes sense that
long chains of polypeptides entangling with each other in a dynamic environment would
yield a correlation function that consists of an obvious mixture of big particles. The
correlation function of floppy chains would be unable to accurately obtain a spherical
size for them because floppy chains are not spheres and they are constantly folding in on
themselves and interacting with other chains. SNase has 149 amino acids, so a solution
consisting of a turbulent mixture of chains lacking secondary structure and interacting
with other chains could yield a fairly large scattering particle (100 nm). Figure 24 shows
floppy chain size as a function of temperature. The data at 45 ºC is the same time
development from Figure 23. The general trend that floppy chains become bigger and
more pronounced at higher temperatures and after time evolution is valid even if we
cannot interpret the floppy chains as having a specific spherical radius.
50
SNase floppy chain size Vs.
Temperature
250
Radius (nm)
200
150
100
50
0
40
45
50
55
60
Temperature (ºC)
Figure 24 - Floppy chain size (the larger radius from a double-exponential) at different temperatures.
The general trend of larger floppy chains over time at a given high temperature and as temperature
increases is valid even if the calculated sizes of the floppy chains are inaccurate since they are not
spheres and the system is turbulent. The data points at 45 °C are the same from the time evolution
experiments shown in Figures 20-23.
51
Conclusions
This study was successful in analyzing the protein denaturation of Staphylococcal
nuclease wild-type at high temperatures. The redesign of the heating and insulation
system along with improved filtration and strict cleaning were all instrumental in
allowing the system to remain stable at high temperatures and to be able to record
meaningful data.
Especially provocative is the emergence of floppy chains at high temperatures.
Prior attempts to thermally denature SNase could only maintain a stable system up to
about 40 ºC, so the phenomenon of floppy chains could not be accurately studied, only
speculated. The floppy chains took about five minutes to form at 45 ºC and continued
evolving for another ten minutes. This time evolution is an exciting prospect in protein
studies because time evolution studies usually utilize chemical denaturation and the
evolution stops usually after a minute. Thermal denaturation time evolution studies have
not been performed yet to a great extent, and the emergence of floppy chains at times
much greater than one minute is exciting. For SNase, these floppy chains refold into
natured proteins after awhile and after the temperature is lowered. Even at temperatures
lower than 45 ºC, the floppy chains remain when lowering the temperature from a high
temperature, but completely refold to the native state after a few minutes.
The results of this project raise more questions than they answer, interesting as the
results might be. A continuation of this project would first need to obtain more reliable
viscosity data for each specific protein solution that is studied. An interesting study
would be the thermal refolding of the floppy chains as temperature is slowly lowered
52
from a temperature greater than 45 ºC. Thermal, chemical, and pressure or denaturation
or combinations of those, along with mutants of Staphylococcal nuclease would also
yield meaningful data. Analysis of thermal denaturation of single protein molecules
using optical tweezers is also an exciting prospect for the continuation of this project.
The system apparatus for studying protein denaturation through Dynamic Light
Scattering has been greatly improved, allowing for continued studies and more extensive
collaborations between the research laboratories of Dr. Oliver of the Physics Department
and Dr. Stites of the Chemistry/Biochemistry department at the University of Arkansas.
Frontline research in Proteinomics helps in our understanding of how proteins fold and
this knowledge may someday result in being able to predict the final folded state of a
protein given its primary sequence.
Manipulation of protein structure and full
understanding of the principles of cell biology could benefit humanity almost
immeasurably by potentially eliminating diseases, and engineering bionanoparticles,
among a myriad of other possibilities.
53
References
1
Starr and Taggart, Biology: The Unity and Diversity of Life, Eighth Ed., Wadsworth
Publishing Company, Belmont, CA, 231 (1998).
2
Ibid., 232-233.
3
Ibid., 46-48.
4
http://www.bact.wisc.edu/MicrotextBook/BacterialStructure/Proteins.html.
5
Schafer, Lothar, In Search of Divine Reality, University of Arkansas Press, Fayetteville,
73 (1997).
6
Colón, W. and Kelly, J. W., ―Partial Denaturation of Transthyretin is Sufficient for
Amyloid Fibril Formation In Vitro‖ Biochemistry 31, 8564-8660 (1992).
7
Brandon and Tooze, Introduction to Protein Structure, 269-284 (1991).
8
http://info.bio.cmu.edu/courses/03231/LecF02/Lec08/lec08.html
9
Govindarajan, Sridhar and Richard A. Goldstein, ―On the thermodynamic hypothesis of
protein folding,‖ Proceedings of the National Academy of Sciences USA 95, 5545-5549
(1998).
10
http://svr.ssci.liv.ac.uk/~volk/folding/Fasteventsinproteinfolding.htm
11
http://www.rcsb.org/pdb/experimental_methods.html
12
Ladokhinin, Alexey S, ―Fluorescence Spectroscopy in Peptide and Protein Analysis,‖
Encyclopedia of Analytical Chemistry, John Wiley & Sons Ltd, 5762-5779 (2000).
13
Feynman, Richard, QED, Princeton Science Library, Princeton, NJ, 14-15 (1985).
14
http://www.grc.nasa.gov/WWW/RT2001/6000/6712ansari.html
15
Pecora, Robert, Dynamic Light Scattering, Plenum Press, New York, 11-19 (1985).
16
Ibid.
17
Ibid.
18
Brookhaven Instruments Corporation, ―Instruction Manual for BI9000AT Digital
Autocorrelator.‖
19
Berne, Bruce and Robert Pecora, Dynamic Light Scattering, Dover, Mineola, NY,
2000: 10-28.
20
Ibid.
21
Shortle, David and Michael Ackerman, ―Persistence of Native-Like Topology in a
Denatured Protein in 8M Urea,‖ Science 293, 487-489 (2001).
22
Ibid.
23
Fortner, April, ―Protein Chemical Denaturation and Analysis using Dynamic Light
Scattering,‖ University of Arkansas Honors Thesis, Spring 2003.
24
Stites Lab Protocol, ―Nuclease Protein Preparation in λ Expression System.‖
University of Arkansas, Rev. September 2002.
25
R. S. Stock and W. H. Ray, ―Interpretation of Photon Correlation Spectroscopy Data:
A Comparison of Analysis Methods,‖ J. Polymer Science: Polymer Physics Edition 23,
1393 (1985).
26
CRC Handbook for Chemistry and Physics, 1988.
27
Gast, Klaus et al., ―Compactness of the kinetic molten globule of bovine αlactalbumin: A dynamic light scattering study,‖ Protein Science 7, 2004-2011 (1998).
54