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Spider Silk:
Examining Biological Sequences
Student Edition
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Spider Silk: Examining Biological Sequences
Stronger than steel and more elastic than rubber: spider silk is unsurpassed in its expandability,
resistance to tearing, and toughness. Spider silk would be an ideal material for a large variety of
medical and technical applications, and researchers are thus interested in learning the spiders’
secrets and imitating their technique.[1]
This unit has a direct purpose and an indirect purpose. Its direct purpose is to explain some of the
amazing properties of spider silk, how a mathematical algorithm called “sequence alignment”
can be used to uncover some of its secrets, and how a computing environment can be employed
to quickly implement this algorithm. Its secondary purpose is to show students that biology and
mathematics are more interdependent now than ever before, and that mathematical skills will
continue to grow in importance as an essential tool for biology research.
Spiders and Silk
Spiders are classified in the animal kingdom as shown below:
• Phylum Arthropoda (which includes insects, arachnids, and crustaceans)
• Class Arachnida (which includes scorpions, mites and ticks)
• Order Araneae (which contains thousands of spider species)
Spiders are found worldwide and most are predators of insects. As predators, spiders play an
important ecological role in controlling insect populations. Spiders have a variety of methods for
capturing prey. Some produce toxins that immobilize prey, some physically catch prey, and
others build webs to trap their prey. The activities in this unit will deal with a few of the webbuilding species.
Most species of spiders produce several types of silk, each having a specific purpose. These
include constructing webs, capturing prey, assisting movement, and protecting eggs. The silk is a
solid fiber composed of different proteins combined to provide the mechanical properties
necessary for each function. The thread of protein forming the silk is released from an internal
gland and passes through structures called “spinnerettes,” located on the abdomen, which remove
moisture, and produce a solid fiber. Usually each species of spider produces several types of silk,
each released by a different silk gland.
In the most familiar type of spider, the orb-weaver, the web is a flat spiral anchored in several
directions to a structure of some sort, perhaps a wall, a branch, or a leaf. Major ampullate or
dragline silk makes up the axes of the web and anchors the web to a support. Minor ampullate
silk is applied to the support in a spiral starting in the middle where the draglines intersect. It is
attached to the dragline silk with a piriform silk that is glue-like. As the spiral increases in
diameter, the silk changes from minor ampullate to flagelliform silk for the part of the web
where insects are likely to impact. Flagelliform is much more elastic than minor ampullate, so
the insect does not bounce off, but becomes ensnared with the forward and backward stretching
of the web.
Spider Silk
Student 1
The strength and mechanical properties of spider silks are extraordinary. They have high tensile
strength (are hard to break), are sticky and very elastic. Dragline silk is stronger than KEVLAR
(used in bullet-proof vests) and the tendons in human joints. Flagelliform is also stronger than
KEVLAR, 40 times more elastic than tendons, and one-third as elastic as rubber. The silks are
also insoluble in water; webs stand up to rain storms and dew quite well. In fact, dragline silk
shrinks when wet to about 50% of its dry length. Because of these properties, artificially
produced spider silk could be used to produce such things as artificial tendons, sutures used in
surgery, lightweight bulletproof vests, and wear-resistant clothes. Unfortunately, spiders are not
social creatures, so it is not possible to have spiders live in colonies in order to harvest their silk
in bulk, as is done with silk worms. Science will have to find a way to make synthetic spider silk
if we are to take advantage of its wonderful properties. The key to this is to look at what spider
silk is made of: protein!
Protein
A protein is a molecule composed of polymers (a compound of several repeating units) of
amino acids bonded together. A protein is like a blob of spaghetti, made up of a very long sticky
spaghetti noodle consisting of a chain of amino acids. Depending on how these amino acids
interact with each other and surrounding water molecules, the protein chain folds up into a three
dimensional shape, which largely determines the properties of the protein. There are 23 different
amino acids, and any number of these can be chained together in any order to form a protein
molecule. Thus there are countless possible protein molecules. Protein chains found in nature
range from just a few to many thousands of amino acids. Each one of these can be completely
specified simply by writing down the order of the amino acids in the chain.
Spider Silk
Student 2
Scientists have developed a variety of technologies for synthesizing, or producing by artificial
means, proteins. They continue to develop new and better techniques. For example, given a
protein sequence that we would like to synthesize, it is possible to “program” microorganisms to
synthesize these proteins for us. Scientists do this by building a DNA sequence that codes for the
desired protein sequence. The ability to build this sequence is a technological achievement of no
small note. They then insert the sequence into the genome of some bacteria such as E. coli
(another major technological achievement) and allow the bacteria to build the protein.
Because of significant laboratory research, we already know the amino acid sequences for many
silk proteins. Additionally, research suggests that the technology to manufacture spider silk is not
too far off. But perhaps we could do even better. What if we changed the amino acid sequence?
Could we find a better sequence of amino acids that would yield even better silk, or make some
other material with even more amazing properties? How can we determine a good amino acid
sequence?
One answer is to compare the amino sequences of different types of silk proteins and between
different species of spiders. By doing this, it may be possible to identify patterns in the sequences
that contribute toward specific properties of spider silk. We can then use this information to
design better proteins!
In this unit, we will study an algorithm called sequence alignment, which allows us to
efficiently compare different sequences in a biologically meaningful way. This algorithm is one
of the fundamental tools of bioinformatics—a field that has revolutionized biological research
through the use of mathematics and computer science. While the main ideas of sequence
alignment can be described in purely mathematical terms, getting the details right requires some
understanding of molecular biology.
Spider Silk
Student 3
Unit Goals and Objectives
Goal: Understand protein sequences and their role in identifying relationships among various
species and organisms
Objectives:
 Describe protein sequences in relation to DNA.
 Explain why the alignment of protein sequences is of importance to biologists.
 Understand the methods used by researchers to align protein sequences.
Goal: Understand the use of lattices to represent the alignments of genetic sequences.
Objectives:
 Represent a pair of sequences to be aligned as an appropriate labeled lattice.
 Interpret any path in that lattice as a particular alignment.
 Apply an algorithm to a labeled lattice to generate one or more optimal alignments of two
given sequences.
Goal: Use technology tools and resources to examine and analyze alignments of genetic
sequences.
Objectives:
 Be able to access and use the Biology Student Workbench (BSW) Internet resource to
carry out alignments.
 Analyze output from the BSW program.
Spider Silk
Student 4
Lesson 1
Molecular Biology Essentials
DNA
Deoxyribonucleic acid (DNA) is the well-known double helical molecule that is the basis of
heredity. DNA contains all of the information used in the development and functioning of all
living organisms.
The information in DNA is encoded using four different nucleotides: adenine (A), guanine (G),
cytosine (C), and thymine (T). These nucleotides are connected together sequentially along a
phosphate-sugar backbone. The order of these nucleotides in this sequence determines the
information that can be used to manufacture ribonucleic acid RNA and protein molecules,
which perform all of the functions of the organism. This information can be represented
succinctly simply as a string of letters from the four letter alphabet A, G, C, T.
The structure of a DNA molecule is like a spiral staircase, as illustrated in Figure 1.1. The
molecule consists of two nucleotide strands. The phosphate-sugar backbones of the two strands
form the sides of the spiral staircase. In the middle, each nucleotide from one strand is
connected to a nucleotide from the other strand to form a base pair, which is analogous to a
“step” of the spiral staircase. Notice that the figure shows only two types of base pairs: A-T, and
C-G. This is because nucleotides come in complementary pairs: ‘G’ pairs only with ‘C’ and
‘A’ pairs only with ‘T’.
Figure 1.1: Cartoon drawing of DNA.
Illustration by Cornell University [Public domain], via Wikimedia Commons
Because of this complementary pairing, the sequence of nucleotides on one strand is completely
determined by the sequence on the other strand. In this sense, both strands contain exactly the
same information. But only one of the strands is used to make RNA or protein. This strand is
called the coding strand; the other is called the complementary strand.
Spider Silk
Student 5
The following figure shows the two strands of a DNA molecule, but some of the entries in the
complementary strand are missing. Can you fill in the missing entries?
coding strand:
complementary
strand:
C
G
A
T
A
T
G
C
T
A
A
T
A
T
C
G
G
C
G
C
C
G
A
_
A
_
T
_
G
_
G
_
C
_
The complementary base pairing enables the DNA molecule to be replicated. During cell
division, the two strands of the DNA molecule are separated. Each of these strands serves as a
template from which a copy of the other strand is reconstructed by attaching the complementary
nucleotide to each nucleotide in the template. This results in two copies of the original DNA
molecule. Sometimes mistakes, or mutations, happen during DNA replication. There are
three main types of mutations: substitutions, insertions, and deletions. These three types of
mutations play a big role in how the sequence alignment algorithm works.
A gene is a segment of the DNA molecule that contains the information needed to make a
particular protein. In humans, genes vary in size from a few hundred nucleotides to more than 2
million nucleotides. There are many thousands of genes in each DNA molecule. It is estimated
that humans have 20,000-25,000 genes.
RNA
The information encoded in a gene is used to construct a protein molecule. The first step is to
copy the information from the DNA into a messenger RNA (mRNA) molecule through a
process called transcription. Like DNA, RNA (ribonucleic acid) is composed of nucleotides.
But there is one difference: RNA uses the nucleotide Uracil (U) instead of using Thymine.
Thus, the alphabet for describing RNA molecules consists of the letters A, G, U and C. Each
RNA nucleotide pairs with a complementary DNA nucleotide: ‘A’ pairs with ‘T’, ‘G’ pairs with
‘C’, ‘U’ pairs with ‘A’, and ‘C’ pairs with ‘G’.
A complex of proteins called an RNA polymerase, which acts like a robot, performs the
transcription process. Starting at the beginning of a gene sequence, the RNA Polymerase moves
along the coding strand of the DNA attaching a complementary RNA nucleotide to a growing
RNA strand (See Figure 1.2). This process is repeated over and over again, producing many
mRNA molecules from a single copy of the DNA.
Spider Silk
Student 6
Figure 1.2: Transcription from DNA to RNA and translation from RNA to protein.
Note in the figure that the RNA molecule is identical to one strand of the DNA (except for the U
replacing T) but is the complement of the strand from which it is actually transcribed. In a
complement, G and C are switched, and A and T are switched.
The following sequences show a piece of the DNA coding strand for a gene, and the mRNA that
is being transcribed. Fill in the missing nucleotides for the mRNA.
DNA coding strand:
mRNA:
C
G
A
U
A
U
G
C
T
A
A
U
A
U
C
G
G
C
G
C
C
G
A
_
A
_
T
_
G
_
G
_
C
_
Proteins
The information in the mRNA is next translated into a protein molecule. Recall that a protein
molecule is a sequence of amino acids. There are 23 principal amino acids, so fortunately there
are enough letters in the alphabet so that each amino acid can be encoded with a single letter.
Translation is performed according to a genetic code. The units of this code are called codons,
which consist of triplets of nucleotides. Figure 1.3 shows the 64 possible codons in a table
format.
Spider Silk
Student 7
Second letter
C
U
C
A
G
Phenylalanine
(F)
UUA
UUG
Leucine (L)
CUU
CUC
CUA
CUG
Leucine (L)
AUU
AUC
AUA
Isoleucine (I)
AUG
Methionine (M);
initiation codon
GUU
GUC
GUA
GUG
Valine (V)
UCU
UCC
UCA
UCG
CCU
CCC
CCA
CCG
ACU
ACC
ACA
ACG
GCU
GCC
GCA
GCG
Serine (S)
U
Tyrosine (Y)
UGU
UGC
Cysteine (C)
C
Stop codon
UGA
Stop codon
A
Stop codon
UGG
Tryptophan (W)
G
CAU
CAC
Histidine (H)
Arginine (R)
CAA
CAG
Glutamine (Q)
CGU
CGC
CGA
CGG
AAU
AAC
Asparagine (N)
AGU
AGC
Serine (S)
AAA
AAG
Lysine (K)
AGA
AGG
Arginine (R)
GAU
GAC
Asparic
acid (D)
GAA
GAG
Glutamic
acid (E)
UAU
UAC
UAA
UAG
Proline (P)
G
U
Alanine (A)
A
G
Threonine (T)
GGU
GGC
GGA
GGG
C
U
C
Third letter
First letter
U
UUU
UUC
A
A
G
U
Glycine (G)
C
A
G
Figure 1.3: The genetic code.
To use the table, start with any DNA nucleotide triplet (for example CCT). Transcribe this to a
mRNA codon by replacing all the Ts with Us (to get CCU). Read the triplet from left to right
(first letter C, second letter C, third letter U) and follow along in the table. You should arrive at
the box containing amino acid proline (P). Try another one. GAC leads to aspartic acid (D).
Not all 64 codons specify a single amino acid. Additionally, there are three that do not specify an
amino acid during translation. In humans, translation involves only 20 amino acids. Therefore,
several mRNA codon triplets may result in the same amino acid. Note that three codons are
called STOP codons. They are UAA, UAG, and UGA. Instead of translating to amino acids, they
tell the ribosome, which is making the protein, to stop the translation. In other words, they
indicate the end of the protein, which is usually before the end of the RNA. Similarly, there is
another codon called the initiator or start codon. It is AUG and codes for methionine, abbreviated
M. The start codon signals the ribosome to start the translation and causes the first amino acid in
the protein to always be methionine.
Spider Silk
Student 8
ACTIVITY 1-1
Translating Triples
Objective: Translate nucleotide codons to amino acids.
Materials:
Handout SS-H1: Translating Triples Worksheet
1. Below are the first 15 codons in a nucleotide sequence. Check to see that the first 10 codons
are translated correctly, and then use the table in figure 1.3 to fill in the last five amino acids
yourself.
atg agt tgg aca gcg cga ctt gct ctt cta ttg ctc ttt gta gct
M S W T A R L A L L
2. Translate the following codon sequences to amino acids.
a. atg ccc tgt gga gcc aca ccc tag b. atg acg gag ctt cgg agc tag
d. atg cgg ata aaa ata tcc aat tac agt
c. atg agc cag tac acc aca atg
3. Why are there 3 nucleotides in a codon? Why not 2? Why not 4?
4. How would you translate a sequence of 20 or 40 codons? Describe a more efficient method for
translation of long codon sequences.
5. Are there other ways to depict the genetic code? Find a different image or diagram and be
prepared to share it with your class.
From DNA to Protein
To review, the coding process starts with DNA, which is transcribed into RNA, which is then
translated into protein. Look back at Figure 1.2 to review this process. Actual photographs of the
process are shown in Figures 1.4 and 1.5.
In Figure 1.4, arrow “Begin” shows DNA strands while arrow “End” depicts RNA strands. The
direction of transcription shows shorter strands to longer strands. As shown, the transcription can
take place simultaneously at many places in a gene as multiple RNA polymerase molecules
move in series along the DNA.
Spider Silk
Student 9
From Wikimedia Commons http://commons.wikimedia.org/wiki/File:Transcription_label_en.jpg
Figure 1.4: Photomicrograph of RNA being transcribed from DNA.
In Figure 1.5, the start of translation is at the upper right (arrow). Note how the protein strands
are longer on the ribosomes that are further from the start of translation. As shown, many
ribosomes can simultaneously move along the mRNA, resulting in many copies of the protein
being produced at the same time. Note that translation similarly takes place simultaneously along
the RNA, as multiple ribosomes move along the strand.
Source: https://ib-biology2010-12.wikispaces.com/Transcription+and+Translation
Figure 1.5: Ribosomes and growing protein molecules strung along an RNA strand.
Spider Silk
Student 10
Lesson 2
Structure and Function
Structure
One of the most challenging problems in computer science is to determine the 3-dimensional
structure of a protein from its amino acid sequence. After the protein molecule is created, it folds
up into a 3 dimensional structure that is determined by the attractive and repulsive forces
between the amino acids and the water molecules in the cell. These forces are different between
different amino acids, so changing the amino acid sequence changes the 3 dimensional structure
of the protein. Thus, the shape of the protein is completely determined by the order of amino
acids in the sequence.
This problem of protein structure has captured the imagination of mathematicians and computer
scientists for several decades, and is still not adequately solved. For example, using some of the
world’s most powerful computers, it typically takes several weeks of computation time to predict
the structure of a protein molecule consisting of only a few hundred amino acids. Unfortunately,
the results aren’t always reliable!
Because of this computational difficulty, it is unlikely that we will be able to design proteins
from scratch. Instead we need to learn patterns from existing proteins. This is why it is
important to be able to compare the sequences of different protein molecules. The places where
the sequences are similar often correspond to similar features in the three dimensional structure.
We will come back to this idea after we talk about sequence databases.
Publicly available sequence databases are revolutionizing the study of molecular biology. These
databases exist worldwide and are maintained by institutions with funding from the U.S.
government and governments in other countries. For example, the U.S. National Institutes of
Health (NIH) through its National Center for Biotechnology Information (NCBI) maintains the
largest U.S. sequence database, called GenBank. Protein and DNA sequences discovered through
government-funded research must, by agreement, be added to these databases. Once added, they
are promptly shared worldwide.
The description “publicly available” means just that. Anyone can look at the information and all
that’s required is a computer with an Internet browser. Let’s take a look at some spider silk
proteins in the GenBank database.
ACTIVITY 2-1
Sequence Databases
Objective: Use a sequence database to examine patterns of DNA
Materials:
Handout SS-H2: Sequence Databases Worksheet
Computer (web site http://www.ncbi.nlm.nih.gov/[2])
Each sequence that is deposited in the GenBank database has a name given to it by the
researchers and a special unique number called an accession number. We can use the name to
look up the spider silk sequences we want. Later we can use the numbers to be sure we always
refer to the same sequences. Two types of silk mentioned earlier are major ampullate, which has
Spider Silk
Student 11
the name MaSP1, and minor ampullate, which has the name MaSP2. We will use these names to
find our sequences.
1. To go to GenBank, first google “NCBI” and click on the NCBI HomePage
http://www.ncbi.nlm.nih.gov/.[2] Notice at the top of the page there are a pull down menu for
which database to use, a blank space to enter your search item and a button labeled “Search.” In
the pull down menu select “Nucleotide.” In the blank space enter “MaSP1 spider” (without the
quotes) and click Search or press the Enter key. This will bring up a page showing the 21 MaSP1
or similar records of different organisms resulting from the search. The number “21” is used
here, but it may not still be “21” by the time you perform this search. These databases are
updated on a regular basis, by researchers worldwide. Click on the record labeled Accession:
AM259067. This will bring up a page of information about the MaSP1 as shown in Figure 2.1.
Figure 2.1: GenBank page from NCBI for MaSP1 in Euprosthenops australis.[2]
Spider Silk
Student 12
a. What is the name of the organism described on this page?
b. The information was published in an article entitled “N-Terminal Nonrepetitive Domain
Common to Dragline, Flagelliform, and Cylindriform Spider Silk Proteins.” N-terminal
refers to one end of the silk protein and this article discusses common features of several
different types of silk proteins. In what journal and year was the article published?
c. Where is the protein sequence of amino acids?
d. What does the entry labeled “CDS” stand for?
e. What are the first twelve entries in the protein sequence and what do they stand for?
f. What do you notice about the last four lines of the protein sequence?
2. Other lines under the “CDS” label give additional information. For example, the line
“15..>1196” means that the protein sequence is derived from the portion of the DNA sequence
starting at the 15th character and going beyond the 1196th character. The gene name, as we
already know, is shown to be MaSP1 and the protein product is called “major ampullate spidroin
1 precursor.”
a. What do you notice about the sequence shown in the section labeled ORIGIN? How is this
sequence different from the protein sequence discussed above?
b. What sequence is shown in the section labeled ORIGIN?
c. How long is this sequence?
3. Sometimes researchers want just the sequences without all the additional information. These
can be obtained by going to the top of the page, in the box labeled “Display,” and choosing
FASTA. That is the name of a formatting that gives just the sequence, in this case, the nucleotide
sequence, and a brief identification line preceded by the “>” symbol. “FASTA format” is often
used as input to computer programs that compare sequences. Now return to the GenBank
display.
4. Let’s confirm the translation of the nucleotide sequence for MaSP1. Look back at the printout.
At the top of the CDS section (remember, coding sequence), is a note that says it runs from
positions 15 to 1196. Look at the DNA sequence and find position 15. The sequence letters occur
in groups of 10 in rows of 60.
a. Starting at position 15, what is the first codon triplet?
b. Convert this nucleotide to its mRNA nucleotide to find the start codon and then translate
this codon to its associated amino acid.
______  ______  __________
DNA
mRNA
amino acid
Spider Silk
Student 13
Note the unique number which identifies this sequence in the database. It follows the word
ACCESSION and is “AM259067.” The number is also repeated elsewhere. If you ever want to
look this sequence up again, return to the NCBI HomePage. For “Search” choose Nucleotide.
Then enter AM259067 in the “for” field click “Go” and follow the links.
Practice
1. Use GenBank to find another sequence for MaSP1 from the same organism. Print out and
label a copy of the page. Is the amino acid sequence the same? Describe. Sometimes only
part of the sequence is shown.
2. Find another sequence for MaSP1 from a different organism. Print out and label a copy of
the page. What organism did you choose? Describe how the amino acid sequence is the
same or different as for Euprosthenops australis?
3. Find a sequence for MaSP2. Print out and label the page.
4. Get the FASTA format sequences for two versions of MaSP2. Print out and label the page.
Comparing Two Sequences
Let’s take a look at another MaSP1 sequence and see if it appears similar to the MaSP1 sequence
of Euprosthenops australis. Figure 2.2 shows the MaSP1 sequence from the spider Latrodectus
hesperus, otherwise known as the Western Black Widow spider.
Western Black Widow Spider
Photograph by B D (Flickr) [CC-BY-2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons
Spider Silk
Student 14
Many people assume these two species are related by a common ancestral spider species living
perhaps millions of years ago. Finding obvious similarity between the protein sequences would
support this assumption. The degree of similarity could even tell us how long ago the common
ancestor lived. Let’s look for that similarity.
Figure 2.2: Page from GenBank NCBI for MaSP1 in Latrodectus hesperus.[2]
Spider Silk
Student 15
The protein sequence in Figure 2.2 is again listed under “CDS /translation”. Notice that both
sequences begin with the amino acid methionine (M) as expected, but the next few letters are
different. Below are the first 10 letters of the Euprosthenops australis sequence and the first 10
letters of the Latrodectus hesperus sequence.
MSWTARLALL
MYS LS IQSDF
They don’t look similar at all. What should we do?
ACTIVITY 2-2
A Tale of Two Spiders
Objective: Finding similar amino acid sequences.
Materials:
Handout SS-H3: A Tale of Two Spiders Worksheet
Computer
1. Search for the Latrodectus hesperus in the GenBank web site.
2. Look through the first 120 letters of the Euprosthenops australis sequence and the sequence to
see if you can find any parts that look similar. Record what you find on a blank sheet of paper. In
order to assist you in identifying similar sections, the two sequences are labeled S1 and S2 and
every tenth letter is marked. Try to find portions of the sequence that match.
Euprosthenops australis vs. Latrodectus hesperus
S1 Euprosthenops australis
10
20
30
40
50
60
MSWTARLAL
L
LLFVACQGS
S
SLASHTTPWT
NPGLAENFM
N
SFMQGLSSM
P
GFTASQLDD
M
70
80
90
100
110
120
STIAQSMVQS
IQSLAAQGRT
SPNKLQALN
M
AFASSMAEIA
ASEEGGGSLS
TKTSSIASAM
S2 Latrodectus hesperus
10
20
30
40
50
60
MYSLSIQSDF
PTTTMTWSTR
LALSFFAVIC
TQSIYALGQG
NTPWSTKANA
DNFMNGFLSA
70
80
90
100
110
120
CAQSGVFSAD
QVDDMTTIGK
TLMIAMDKMG
GKISSSKLQA
LDMAFASSVA
EIATAEGGAN
Spider Silk
Student 16
3. Look at the first 10 letters in sequence S1 and the ten letters starting at position 15 in sequence
S2.
S1: M S W T A R L A L L
S2: M T W S T R L A L S
a. Is this a good match?
b. Place a star below the sequence letters that match. What do you notice about the stars?
Since we started 15 places into sequence S2 to find matches, this suggests that S2 is longer
on the left than S1.
4. Record and align the entries S1 : 84 – 100 with S2 : 97 – 113. Did you identify these two
portions of the sequence in part 2 above?
S1:
S2:
a. Is this a good match?
b. Mark the matching amino acids with a star. What can you say about the similarities of
these two species?
The results of your matching further suggest that these particular parts of the sequences may be
essential for the properties of the silk proteins because they have remained essentially unchanged
over millions of years during which the spiders and their proteins have diverged. We say that
these amino acids have been conserved.
Alignment
Obviously, looking through sequences to find similarities is tedious. We can use computers to do
it quickly and without errors by a process called alignment. This will be the subject of the
remainder of this unit. It is important to note that the success of an alignment program is
dependent on an understanding of the types of mutations that typically occur as proteins evolve.
We have seen the two most common types of mutations:
•
Substitution. In this case, one amino acid is replaced by another. In the first comparison
above, there were 4 substitutions: S  T, T  S, A  T, and L  S. We might accurately
conclude from this that S and T frequently participate in substitutions. In the second
comparison, there were 2 substitutions: N  D and
M  V.
•
Insertion/deletion. This occurs when a small piece is added or removed from one of the
sequences. In the first comparison in S2, there was an insertion of the first 14 amino acids.
That is why the matching started at amino acid 15.
Spider Silk
Student 17
A complete alignment of the sequences S1 and S2 is given in Figure 2.3. An alignment program
called CLUSTALW (we will examine this program in a later lesson)[3]. The line under the
sequences codes the alignment as:
* (asterisk)
indicates a match
: (colon)
indicates a common substitution
. (period)
indicates a less common substitution
- (dash)
indicates an insertion or deletion.
Figure 2.3: Alignment between the MaSP1 sequences in two spider species.
Alignment has proven to be a powerful tool in researching the causes of disease. An example in
humans involves the hemoglobin gene. Hemoglobin is the protein that carries oxygen in red
blood cells. Alignment of the hemoglobin gene from a healthy individual and from an individual
with sickle cell anemia shows a single substitution in the nucleotide at position 17 in the gene.
In a healthy individual, the 6th codon is “gag,” but in an individual with sickle cell anemia this
codon reads “gtg.” This results in a replacement of the amino acid glutamic acid (E) in the
healthy hemoglobin protein with valine (V) in the sickle cell protein, which ends up giving the
protein its unhealthy properties.
Spider Silk
Student 18
Alignments with more than two sequences are possible and can give more information about
conserved amino acids, that is, those amino acids that have not changed. The conserved portions
of the protein sequences are believed to be the most essential for protein function since they have
not mutated over the millions of years of evolution that separate the species. In the alignment in
Figure 2.4 a sequence has been added from a third spider, Argiope trifasciata, the Banded
Garden spider.
Photograph by Thomas Quine (Garden-Spider-2 Uploaded by High Contrast) [CC-BY-2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons
Notice that not only is the species different, but this is the sequence from the minor ampullate
silk protein, MaSP2. Note the very strong conservation in the ‘KLQALNMAFASSMAEIA’
region. This clearly indicates an important role for this part in these proteins.
Figure 2.4: Alignment between partial MaSP1 sequences in two spider species
and the MaSP2 sequence in a third.
Spider Silk
Student 19
Using Alignments to Predict Protein Structures
One final use for protein alignments is in predicting three-dimensional protein structure.
Understanding the structure is essential for understanding the properties of silk proteins.
Determining structure is a long, costly laboratory process. The number of known structures is
only in the thousands while the number of proteins is in the millions. The known structures are
stored in the Protein Data Bank[4] or PDB found at http://www.rcsb.org/pdb/home/home.do.[5]
Unfortunately, no one has yet worked out the structures for spider silk proteins.
This is not unusual. In fact, it puts us in the position of scientists who study a new protein. We
can get some information about structure by asking which proteins in the PDB are similar to the
spider silk proteins. This question is answered by finding proteins that align well with all or part
of the spider silk proteins.
Searching the PDB yields several proteins that align with a small part of the Latrodectus
hesperus MaSP1 protein. Figure 2.5 shows the alignment with one of those proteins, subtilisin
Carlsberg, from the bacteria Bacillus licheniformis, abbreviated ‘1c3l’ (that’s one cee three el).
The alignment in Figure 2.5 shows another commonly used format that differs from that in
Figure 2.4. Letters in the middle of the alignment denote matches. Plus signs (+) indicate
common substitutions.
Figure 2.5: Alignment of part of MaSP1 from Latrodectus hesperus (top sequence)
with subtilisin Carlsberg (bottom sequence).
Figure 2.6 shows the three-dimensional structure of subtilisin. The spider silk protein may share
some of the structural features of this protein. In this “ribbon” image, the corkscrew shapes are
alpha helices and the arrows are beta sheets. These are common protein structures.
Licensed under Public domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:1st2.png#mediaviewer/File:1st2.png
Figure 2.6: Three-dimensional structure of subtilisin.
Spider Silk
Student 20
Lesson 3
Dynamic Programming
Have you ever been travelling to school or to go shopping and run into a detour? You have to
adjust your route. Perhaps this new route is not any longer, just different than the one you
normally travel. If you wanted to travel a different route every day, how many days would it be
until you took the same route to school twice?
ACTIVITY 3-1 The Path to Work
Objective: Explore the pattern of determining minimum paths.
Materials:
Handout SS-H4: The Path to Work Worksheet
Sally, a hard-working storekeeper in the city of Mandicy, has an unusually curious mind and
wonders about things that you and I might not realize need wondering about. Recently, she
discovered that there were 210 different ways that she could walk from her apartment to her
store. Believe it or not, this discovery has some bearing on our interest in spider silk. Here’s a
picture of Sally’s portion of the city of Mandicy. Her apartment building is located at “A,” her
store is at “S.” Two friends from her apartment also have stores near hers: Ted’s store is at “T”
and Rita’s store is at “R.”
1. How many blocks is the walk from Sally’s apartment to her store? Try a few different routes
and decide if the number of blocks is always the same.
2. Is the number of blocks found the minimum? The maximum? Explain.
3. Estimate without doing any calculations or making any lists how many ways there are for
Sally to walk to her store in the minimum number of blocks. Explain your reasoning.
One day Sally made a list of all the ways that there were, but that got very tedious. At first she
got “214" as the answer, but then she found that she had duplicates in her list. When she got rid
of the duplicates she had 207 ways, but she wasn’t completely confident that she hadn’t missed
any others. Finally, she settled on a list of 210 ways. She was confident about this number, but
was sure there must be a simpler way to figure this out.
Spider Silk
Student 21
4. Describe how you think Sally finally calculated the number with which she was confident.
Frustrated, Sally walked a block north to the store of her friend Ted and showed him her work.
Right away he said that the answer had to be at least 84. Stunned, she asked how he could know
such a thing. She discovered that she wasn’t the only curious person in her apartment building. It
turns out that years earlier, Ted had gotten curious about the same question and discovered that
there were 84 ways to walk from their apartment building to his store. He shared that he had
made a very systematic list of all possible ways. In fact, Ted still had his list and handed it to
Sally. Ted’s list, like the ones Sally had made, used “E” and “S” to denote walking a block east
or a block south.
5. If there are 84 ways to walk from the apartment building to Ted’s store, why does that mean
that there must be at least 84 ways to walk from the apartment to Sally’s store?
6. In comparing her list to Ted’s, how can Sally easily pick out her paths that should also be on
Ted’s list?
Sure enough, there were exactly 84 paths on Sally’s list that passed by Ted’s store. What about
all the other routes? There must be 126 of them, since she was confident about the 210 routes on
her list and 210 – 84 = 126. A portion of Sally’s list, with some of those passing Ted’s store
circled, is shown in the figure below.
Spider Silk
Student 22
7. What do you notice about all the non-circled routes? Describe the paths that these routes
represent.
Sally wondered if there was a convenient way to check if 126 routes pass by Rita’s store. Could
it be possible that Rita had also thought about this problem? Unbelievably, Rita had done that
calculation, shortly after hearing Ted’s story about his counting experience. She was quick to
point out that she was in a much more accessible location than Ted, for her list had a full 50%
more paths on it than Ted’s. That’s just the response Sally needed.
8. Why was Sally so excited with Rita’s statement?
Sally took Rita’s list and put it next to Ted’s. And there they were—all 210 paths that she had
found: 84 from Ted’s list and 126 from Rita’s list. She simply added an “S” to the end of each of
Ted’s and an “E” to the end of each of Rita’s, put them together and presto!
Practice
1. Complete the following grids to get a feel for Sally’s adventures on a slightly smaller scale.
For each figure, make list of all the ways to walk from the top-left corner to the bottom-right
corner, taking eastward and southward steps only. You can encode your different ways to walk
using the letters “S” and “E.” One of the paths is given for each figure.
a.
EEES
b.
EESS
c.
EEESS
2. Now match up each way to walk in the grids on the left with one of the ways to walk on the
grid on the right, in the fashion that Sally did in our story.
Counting Walks on a Grid
The problem that Sally was trying to solve is an example of a problem that is easily solved by a
method called dynamic programming. When using this method, we attempt to solve a given
instance of a problem by showing how the solution to that problem can arise from solutions to
similar, but smaller problems. For example, Sally saw that the number that she was looking for
Spider Silk
Student 23
as the solution to her problem, 210, was the sum of the solutions to two simpler problems,
namely those that Rita and Ted had already solved. Their problems were similar to hers, but were
both simpler because they involved counting paths to a location that was nine blocks away
instead of ten. In fact, Sally could have gotten her answer without making a list at all, if only she
had known that Ted and Rita had already solved the problems for their stores. She could have
just called them, asked for their numbers and added them.
You might then ask, how could Ted have gotten his answer? Who would he have called? Think
about this for a moment. Look at the figure below and decide whom Ted could have called in
order to be able to compute his answers without having to make his own list.
Did you conclude that Ted could ask g and h for their numbers, and then add them? If so, you
were correct: There are 56 ways to walk from A to g, and 28 ways to walk from A to h, and 56 +
28 = 84.
Whom should Rita call if she wanted to compute her answer of 126 the easy way? So that you
can check your answer, I’ll tell you that there are 70 ways to walk from A to f on that grid. Did
you get the right answer?
In general, then, we see that to obtain the number of ways to walk from A to any corner on this
diagram, we simply need to obtain the answers at the corners north of and west of our target
corner, and add them together. Does every question reduce to finding the answers to simpler
questions?
Let’s consider a corner at the top of our diagram, such as corner m.
Someone owning a store on this corner would have a very easy time determining the number of
walks from A to his or her store. Remember, we count only those walks that don’t “backtrack,”
Spider Silk
Student 24
that is, that make the trip in as few blocks as possible. For corner m, this would be six blocks and
there is exactly one way to walk from A to m on that grid, without backtracking. A person
making a list like Ted’s at corner m would have a list with one entry: EEEEEE. In fact, for every
corner along the top of that diagram, there would only be one way of walking to that corner in
the least blocks possible. The same would be true for the corners along the left side of that
diagram. There is exactly one way to walk the fewest blocks to each of those corners from A as
well. These corners are called the “base cases” of our dynamic programming solution.
You could imagine Sally making two phone calls, to Ted and Rita, who say “hold on, I’ll call
you back with the answer in a moment.” And Ted and Rita each make two phone calls, and so
on. But when the call gets to a corner at the top of our diagram, such as vertex m, that person
does not need to make any call. He can simply say “one.” And the same would go for each
vertex along the left side of the diagram. Pretty soon, Ted and Rita will get responses (Rita, from
f and g, Ted from g and h), compute their answers and call Sally back, and then Sally can finally
compute the answer to her question.
We are now in a position to be able to compute the answer to Sally’s question pretty quickly, by
hand, without making lists of any sort. We will simulate this frenzy of phone calls on paper, but
only those phone calls that actually give an answer. Thus we will not simulate Sally making a
phone call until after Rita and Ted have already obtained their answers. This is another key
characteristic of dynamic programming algorithms: Asking the questions in the right order, so
that the answers to our questions have already been computed!
We’ll assume that Sally has initiated a whole cascade of phone calls full of questions, and we’ll
start filling in the answers as we can compute them. The first set of easy answers we can fill in
are those along the top and along the left. To each of these corners there is exactly one way to
walk from A, without backtracking. So let’s put “1" at all of those corners:
That’s a pretty good start. We’ve been able to label eleven corners with their answers--only 24
corners to go. Among the remaining corners there is only one whose answer we can compute
from the answers of its neighbors. Do you see which corner that is? Label this corner with its
answer.
Spider Silk
Student 25
The corner one block south then one block east of A is the one we can label at this point. That
corner would ask its neighbor to the north, “How many ways to your corner?” and get the answer
“one.” He’d also ask his neighbor to the west and get the same answer. Then adding those
answers he’d discover that there are 1 + 1 = 2 ways to walk from A to his own corner, and this is
obviously the right answer, since “SE” and “ES” are the only two ways form A to that corner.
This allows us to label one more corner:
Now there are two corners who can query their neighbors to get their answers. Find them, and
fill in the answers at those corners. Finish this grid by filling in the numbers at all the corners,
including Sally’s corner. If you get 210 for her corner, then you know you’ve done all your
arithmetic correctly.
Practice
A More General Situation. Suppose that Sally lived in a more interesting city, in which there
might be any number of blocks leading into a given corner. Such a city is shown below.
3. Label the corners in this diagram with the total number of ways to walk to each corner.
Spider Silk
Student 26
4. List all of the ways to walk to the corner labeled with a square and all of the ways to walk to
the corner labeled with a circle (one example is done for each corner).
To Square: ESS, To Circle: EES,
Shortest Paths
After Sally had figured out how to do dynamic programming, she decided to try to solve a more
useful problem: “What is the shortest route from her apartment building to her store?” By
“shortest” Sally means “the least number of steps.” To help her answer this question, Sally
walked every single block between her apartment and her store, counted the number of steps,
labeled each block on her diagram and studied the result. Sally’s diagram is reproduced below.
The diagram represents a significant amount of data. As we’ve already seen, there are 210
different ways for Sally to walk from her apartment to her store, so how should she determine the
shortest path? Naturally, Sally would like to find a better method than “check them all” to find
the shortest route.
Questions for Discussion
1. Why are the blocks labeled with different numbers? Explain at least 2 reasons.
2. Brainstorm possible methods for Sally to find the shortest route to her store.
3. Will the shortest route to Sally’s store necessarily be one of the 210 routes with the fewest
blocks? Explain why or why not?
Spider Silk
Student 27
The idea that eventually worked for Sally was very similar to the method she used for counting
the paths. Her thinking went like this: Suppose I call Rita and Ted again, and see if they have
solved this problem. That wouldn’t be quite as helpful as in the counting problem, because their
steps are not the same length as mine. But suppose, just for supposing’s sake, that they knew
exactly the least number of my steps that it would take for me to get to their stores, along the best
possible path. What could I do with that information?
Suppose the shortest path to Rita’s store takes 586 of Sally’s steps. You still do not know the
actual shortest path, but you know the shortest path will take 586 steps. And suppose you find
out that the shortest path to Ted’s store took 579 of Sally’s steps. Can you use that information to
find the length of the shortest path to Sally’s store? Look over Sally’s Steps Map and figure out
the least number of steps to get to Sally’s store.
The reasoning goes as follows: To walk to her store, Sally has two choices regarding what her
last block to the store ought to be. Either she walks from the north, via Ted’s store, or from the
west, via Rita’s store.
• The distance to Sally’s store from Ted’s store is 74 steps, and if we add that to 579 steps,
which is the shortest possible way to get to Ted’s store, we get a total of 653 steps.
• The distance to Sally’s store from Rita’s store is 65 steps, and if we add that to 586 steps,
which is the shortest possible way to get to Rita’s store, we get a total of 651 steps.
• Since 651 is less than 653, we ought to go via Rita’s store. We conclude that the shortest path
to Sally’s store consists of 651 steps and passes by Rita’s store.
This is another form of dynamic programming. Sally wanted to find the least number of steps to
her store, and was able to do so by obtaining the solutions to two smaller problems and using
them to find the solution to her problem.
Of course, the question remains as to how Sally could have obtained the solutions to those two
smaller problems. Imagine that Ted, Rita and all the other storekeepers took Sally-sized steps,
and that they all had access to Sally’s Steps Map. Then each storekeeper could call their two
neighbors, ask for the least number of Sally-sized steps to walk from A to those neighboring
stores and then use that information to find the least number of steps from A to their own store.
Once again, we have phone calls going in one direction (toward smaller, easier problems) and
answers coming back in the other direction.
Let’s see, for example, how we determined that the shortest path to Rita’s store is 586 steps.
When Rita asked her neighbor to the west for the length of the shortest path to that store, she got
the answer 519. Rita does not have to worry about how the shopkeeper obtained that answer.
She just takes it as a given that if she comes from the west, the best she can do from that
direction would be those 519 steps, plus the additional 67 steps along the block to her west, for a
total of 586. Similarly, she asks the shopkeeper to the north for the shortest path to his store, and
gets the answer 518. She then concludes that the shortest path to her store coming from the north
would be 518 + 79 = 597 steps. But since this is greater than the number of steps she can obtain
by coming from the west, that is, 586, Rita concludes that 586 is the best possible.
Spider Silk
Student 28
How did Ted obtain his number? The only piece of information you need that you don’t have yet
is that the shortest path to the store on the corner north of Ted’s store is 538 Sally steps.
So, just as we did with the counting problem, we can solve the “shortest path” problem at any
given corner by having the shopkeeper at each corner ask his two neighbors for the answers at
their corners, and use this information, together with the Sally’s Steps Map, to find the answer at
our given corner. In the case of the counting problem, we had some corners that were “base
cases,” that is, corners that did not need to place other calls to get their answers. What is the
situation in our present problem? Consider the figure below, which shows the top row of Sally’s
Steps map.
If one were to ask the rightmost corner shopkeeper in that map for the length of the shortest path
to that corner, she could not answer immediately. Although the only path to that corner is along
the top row of the map the total number of steps needed to get to that rightmost corner depends
on all of the numbers in that top row. The shopkeeper has two ways to determine the least
number of steps. One way is to consult Sally’s Steps Map and add all the numbers in the top row.
Another way is to simply do what all the other corners do: Call her neighbor, get the neighbor’s
answer, and then add 64, which is the number of steps along the block to his west. Note that
since hers has no block to her north in this diagram, she needs to call only one neighbor instead
of two, and she does not need to select the minimum, since there is only one way into her corner.
Shopkeepers along the north-most row can all do it this way, and the west-most shopkeepers
determine the minimum steps to their stores by calling only their neighbor to the north.
The numbers have to start somewhere. Which storekeeper(s) can definitely answer the question
“What is the length of the shortest path to your store?” right away, without making any calls or
doing any computation? Anyone calling the storekeeper at corner A where Sally’s apartment
building is located would immediately receive the answer 0, since Sally needs to take no steps to
get from her apartment building to her apartment building. So this corner is the only “base case”
for the shortest path problem.
We are now in a position to find the lengths of the shortest paths to all the corners in the Sally’s
Steps Map. The numbers for a few blocks in the northwest corner of the map are shown.
Spider Silk
Student 29
In the figure above, the bold numbers at each corner show the length of the shortest path to that
corner, while the numbers along the blocks indicate the number of steps Sally must take to
traverse that block. Additionally, the thickened path indicates those streets along which the
shortest route to a particular corner travels. For example, the path EESS results in the shortest
path of 264 steps to that resulting corner. The shortest path came from the north, leaving the road
from the west unshaded.
Practice
5. Complete Sally’s Steps Map and determine the actual shortest path from her apartment to her
shop.
Extension
1. A More General Situation. Suppose that Sally lived in a more interesting city, in which there
might be any number of blocks leading into a given corner as shown below. This city diagram
includes a few of the shortest path numbers for you and shades those blocks giving the shortest
route into a corner. Note that to find the corner labeled 22, we had to compare three different
sums from three different corners, and select the minimum. Also, when computing the number
15, we had a tie score. What do you notice about the blocks into that corner? Complete the
diagram to find the shortest path from A to S. List the directions associated with the shortest path
and the number of steps.
Spider Silk
Student 30
2. How many ways are there to walk from A to B on each of the figures shown below, where
each step must move either east, south or diagonally southeast?
A
A
B
B
Figure 1
Figure 2
A
A
B
B
Figure 3
Spider Silk
Figure 4
Student 31
3. The numbers on the edges of the graph below represent distances. What is the length of the
shortest path from A to B? How many routes achieve that length?
4. What is the length of the shortest path from A to B on each of the figures below, where each
step must bring you closer to B?
Spider Silk
Student 32
5. Find the length of the shortest path from A to S on the map below, and also identify the
shortest path by shading the appropriate edges. This problem is pretty close to ultimate problem
we will be addressing regarding spider silk!
Spider Silk
Student 33
Lesson 4
String Alignment
You might be wondering how the previous lesson’s topics of paths and shortest distances relate
to spiders and DNA. You will soon see that you are in a good position to solve some DNA
problems.
Mutations
Recall the basic theory of DNA evolution: A long time ago in a species far, far away there was a
gene X that described some protein that contributed to the life and health of that species. Over
the millennia this gene, X, together with the thousands of other genes in this species, changed in
various ways, leading to several different species that we can see today, all of which are
descended from that one ancestral species, and all of which carry some remnant of the gene X.
The diagram above gives an example (on a very small scale) of this type of action. At the top of
the tree diagram is the gene X in some now-extinct, ancestral species a long, long time ago. The
two genes just below that in the tree represent how the gene X looked in two species, also now
extinct, a long time ago. At the bottom of the tree we find how the gene X looks in four species
that are alive today. The variations seen among these genes today have arisen by various
mutations through the ages, as organisms passed their genetic material (DNA) to their offspring.
These mutations consist mainly of insertions, deletions and substitutions, as we discussed in
Lesson 1.
Let’s take a look at how the sequence at the top of the tree diagram mutated to become the
sequence below it, on the left. Here, the sequence “AATTGGGGCCCCA” became
“AATTGGGCCTCA.” One likely explanation is that one of the G’s got deleted, and that the
third C mutated to a T. The diagram below represents this explanation.
Spider Silk
Student 34
In this representation, the various nucleotides are aligned in columns to show which nucleotide
in the child species corresponds to each nucleotide in the parent species. We can see how the G
was deleted, because in the child species (below) there is a dash where the parent has a G. And
beneath one of the C’s in the parent, there is a T in the child.
The alignment diagram below shows one possible relationship between the sequence at the top of
the tree and its child on the right.
In this diagram, the hyphen “-“ in the top string represents a gap. This gap could be due either to
a deletion in the 1st string, or to an insertion in the 2nd string. In this example, we know it was an
insertion in the 2nd string because we know that the 2nd string evolved from the 1st string. But if
we don’t know the history, there is no way to know, just from comparing the strings, whether the
difference is caused by insertion in one string or deletion in the other. So, we use the gap symbol
to represent either of these possibilities.
In this case we also see one substitution mutation, where a T in the parent became an A in the
child. And we see one insertion mutation, where a G was inserted into the sequence in the child
just before the last A in the gene.
Now, you might have noticed that these are not the only possible ways to explain the observed
mutations. The following diagram shows three additional alignments that might explain the
relationship between the sequence at the top of the tree and its left child.
All three of these explanations are theoretically possible, though they seem to become
progressively less likely as you move from left to right across the table. Option 1 is essentially
the same as that given in the previous discussion, but the first G was deleted here while the
fourth G was deleted above. Option 2 also has a single deletion, but uses two substitutions to
explain the changes. Option 3 has many changes occurring.
Spider Silk
Student 35
Questions for Discussion
1. Are there other options that could explain the mutation from the top parent species to the
second level left child species? If so, list two.
2. Why is it that Option 1 feels more “right” than Option 3, even though, as far as we know,
either one could be historically accurate?
The generally accepted principle of Occam’s Razor asserts that, all other things being equal,
people prefer simpler explanations. For biologists, this principle, usually call the parsimony
principle, is heavily relied upon to make our best guesses about historical events that we have no
way of discovering exactly at this time. But gut “feelings” are hard to turn into computer
programs. What is needed is a scoring system.
A scoring system is an objective way to attach a numerical value to the quality of an alignment.
A sample scoring system to score the first four alignments given above of the sequence of the top
of the tree and its left child is as follows.
In each column of the alignment score:
+2 for each match
–1 for each mismatch
–2 for each gap.
For example, consider the alignment of the top sequence and its child to the right:
AATTGGGGCCCC-A
AATAGGGGCCCCGA
To score this alignment, we consider each column of the alignment separately and assign a value
to that column. The first three columns are matches, so each receives a score of +2, according to
the scoring system we gave. The fourth column, however, has a T in the first string and an A in
the second string, which is a mismatch, meaning that a mutation happened. Our scoring system
assigns this a value of –1, since we want our alignments to prefer matches over mismatches.
This reflects that successful mutations are rare. All of the scores have been entered in the table
below. Note the penultimate column, where we have put a gap into the first string to show an
insertion mutation. This column has a score of –2 according to our scoring system because
insertions are even rarer than substitutions.
Spider Silk
Student 36
Adding up the scores for each column we obtain a total score of 21 for this alignment.
Score each of the three alignments of the top sequence to its child below to verify the total scores
shown in the table.
This scoring scheme gives us an objective way to say which alignments are better and which are
worse. In this case, we would say that alignments that had a score of 19 were the best, while the
others were worse. But is 19 the best we can do? At this point, we do not know. Finding the best
alignment is the subject of the next section.
Alignments and Walks
Now is when all of the hard work of the previous sections pays off. All that we have to do at this
point is realize that string alignment is really a shortest path problem, and we’re done! Let’s find
the optimal alignment of the strings “ACC” and “GGC,” where ACC is the initial sequence on
top and GGC is the resulting sequence on the bottom. At the same time, let’s consider the table
shown below.
Spider Silk
Student 37
Imagine that you are standing in the shaded square in this table as you are considering how to
begin aligning these two strings. There are three possible ways to begin the alignment: Your
first column can be either
Suppose you chose
,
or
. What do these options mean in the table?
for the first column of your alignment. This would correspond to taking
an east step in your table, because you would have “used up” the A in the top string, but used
none of the letters of the second string. And if you chose
for the first column, that would
correspond to taking a south step, because you would not have used any letters from the top
string, but would have used the G from the bottom string. Choosing
for the first column
would correspond to taking a southeast diagonal step, because that column used up the first letter
of both strings. Suppose that we selected
as the first step of our alignment, stepping east in
our grid. Now we must select the second column of our alignment. Again, we have three
choices:
,
Suppose we use
or
, corresponding respectively to an east, south or diagonal step.
for this column, stepping diagonally in our grid.
Continuing in this fashion, we might arrive at the alignment
, for which the path is
shown below by the shaded squares. Please take a moment to make sure that you see how the
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alignment above and the walk shown below correspond with one another.
Is there a better path than the one shown above? Each of the choices in the alignment has an
associated score. Can you explain how you would obtain a score of -3?
Starting at the upper left box again, you get –1 if you use column
mismatch, and –2 for either of the choices
or
, because that is a
, because they use gaps. We can include
this information in the original table by writing the scores of taking each type of step in the space
between the corresponding squares.
Thus in the table below, on the left, we see that to walk east or south from the initially shaded
square we incur a score of –2, while walking on a southeast diagonal from that square we incur a
score of –1. The complete table-full of scores is shown in the table to the right.
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Questions for Discussion
3. Note that all the horizontal and vertical steps score –2. Why?
4. The diagonal steps are either +2 or –1. Explain why.
5. Find the score of the following alignment explicitly. Each column of the alignment
corresponds to some step on our grid.
a.
corresponds to an East step, since we use only an A from the top string. What score
does this step incur?
b.
corresponds to a Diagonal step, since we use a character from each string. What
score does this step incur?
c.
corresponds to a South step, since we use only a character from the bottom string.
What score does this step incur?
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d.
corresponds to another Diagonal step, since we use characters from both strings.
What score does this step incur?
6. Using a copy of the scoring table above, shade the squares that we walk through in this
alignment. Put into each shaded square the running total of the score of our alignment along the
path. Note that this is similar to what we did in trying to find the shortest path to Sally’s store!
ACTIVITY 4-1 A Corresponding Walk
Objective: Understand the correspondence between string alignments and walking on the
alignment table.
Materials:
Handout SS-H9: A Corresponding Walk Worksheet
Shown here is another example of an alignment and its corresponding walk.
Figure 4.1: Walk Lattice
1. Have one group member explain how the first column in the alignment corresponds to the
walk shown above. Remaining group members take turns to explain each subsequent column and
step in the walk.
2. Each of the choices made in the walk above has an associated score. Use the same scoring of
+2 for each match, -1 for each mismatch and -2 for each gap. Write the running total of the score
in the shaded boxes. What is the final score of the alignment walk depicted above?
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Before finishing this section, make sure you understand the correspondence between string
alignments and “walking” on an alignment table. Look back at Figure 4.1. Take note of the rows
and columns: There is one extra row and one extra column before beginning the characters of the
strings. This is required in order to give us a starting point for our walk, prior to using up any of
the characters in the alignment. Also, every alignment of these two strings corresponds to some
walk in the table from the northwest corner to the southeast corner, taking only east, south or
southeast diagonal steps. And in the other direction, every such way to walk corresponds to some
alignment. Thus, finding the optimal alignment of these two strings amounts to finding the
optimal path.
Practice
1. Give the alignment that corresponds to the walk
shown in the table to the right.
2. In each of the shaded boxes, put the running total
of the score of the alignment. Assume that we now
award +1 for a match, –1 for a mismatch and –2 for a
gap.
3. Find an alignment of these two strings that achieves
a better score.
4. Show the walk corresponding to your improved
alignment, by shading the walk in the table to the right.
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The Optimal Alignment Algorithm
You are now in a position to answer the question: “How can I find the optimal alignment
between two strings?”
Consider the same two strings examined previously and shown in the figures below. On the right
you see the table that we have been using, and on the left you see a map similar to the walking
maps from Lesson 3. Finding the alignment with the highest score is like finding the longest path
from Sally’s apartment to her store. Finding the longest path to Sally’s store (without
backtracking) is solved the same way as finding the shortest path, except that at each corner we
select the greatest sum instead of the least sum. Don’t worry about the negative numbers on the
“streets” of this map. Even though a negative number has no physical interpretation in terms of
steps, it works fine for our mathematical computations of addition and then comparison to select
the greatest number. The cumulative scores for paths along the top row, the left column and the
first diagonal square are completed. Using the given scores for the first step, the greatest is -1
and so the optimal alignment would use this path.
ACTIVITY 4-2 The Optimal Alignment
Objective: Find the optimal alignment for two sequences
Materials:
Handout SS–H10: The Optimal Alignment Worksheet
1. Use the map below to find the highest scoring path from A to S. Note that we still do not allow
backtracking, so that all travel must go in an east, south or southeast diagonal direction.
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2. Repeat the activity above, except this time perform the computation directly on the table
below. Fill in the numbers in the blank cells, using the numbers between the cells to tell the score
from cell to cell.
When you do string alignments in real life, you are not going to want to write in all of those
scores between the cells of your table. There is no need to do so since we know that any east or
south step will score –2, and Diagonal steps score either +2 or –1, depending on whether the
letters in the row and column into which we are about to step match or mismatch. We have done
this in the table below for the strings “AGCGT” and “CAGT.” Note that in addition to putting
the numbers into each cell, we have also marked where the greatest value came from by putting
lines between the cells, showing which “roads” we walked along to obtain the greatest value.
To build an optimal string alignment from a completed table, we start at the southeast corner and
walk back along our marked connectors until we reach the northwest corner. Note that trying to
walk the other way can get us stuck at a dead end, without reaching the southeast corner.
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Continuing the above example we find a way to walk back from the southeast corner to the
northwest corner. This path is shaded and yields the string alignment:
- AGCGT
CAG - - T
There are several ways to walk back along an optimal path. In this case there are six optimal
paths altogether, including the one we found above. While they each give a different alignment,
they will all have the same score, 0.
Practice
5. What alignment is implied by the following scoring matrix?
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6. How many optimal alignments are indicated by the following scoring matrix?
7. Here is the start of an alignment between "ACC" and "CGAA" with match score +2, mismatch
penalty –1, and gap penalty –2. Complete the matrix.
C
G
A
A
0
|
-2
|
-4
|
-6
|
-8
—
\
\
\
A
-2 —
\
-1
| \
-3
\
C
-4 —
\
0 —
| \
C
-6
-2
–5
8. Give all optimal alignments between "ACC" and "CGAA" with match score +2, mismatch
penalty –1, and gap penalty –2, using your work from the previous problem.
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9. Find the optimal alignment of the strings AGT and TGA, using match score +2, mismatch
score –7, and gap score –2.
10. Two DNA sequences derived from a common ancestor in an environment in which insertions
and deletions were much more likely than point mutations. To reflect this in an alignment, a
researcher assigns a match score of +3, a mismatch score of –1, and a gap "penalty" of +1.
Here is the resulting scoring matrix. Complete the matrix.
11. Can you see why under the (very artificial) scoring system given in the previous problem, an
optimal alignment of any two strings will never align two mismatched bases? In fact, what
relationship between the gap penalty and the mismatch penalty will guarantee this behavior?
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12. Consider the two alignments shown below of the two strings ACCGG and
TATGACCGGTTGTG:
The alignment on the left is preferable to the alignment on the right, because it preserves the
integrity of our first string much better than the alignment on the right does, but our scoring
system will give them equal scores. If we modify our scoring system so that it does not
charge for gaps at the beginning or end, then the alignment on the left will have a much
higher score, and will be preferred to the other alignment. This exercise will show us how to
modify our algorithm accordingly.
There are two strings: "AACCTT" and "ACTACT"
a. Align them using the following scoring system: match = +2, mismatch = –1, initial
gaps and end gaps = 0, and all other gaps = –2. The first few entries have been filled in for
you, as has the final score, so that you can check your work.
b. How many optimal alignments are there?
c. Show the optimal alignments.
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Lesson 5
Aligning with Biology Workbench
The Student Interface to the Biology Workbench (SIB)[3] is a Web-based bioinformatics
resource. It provides a set of powerful tools to investigate problems in molecular biology—the
same tools used by research scientists. In the first activity of this lesson you will look at proteins
that make up the silk of two species of spiders. In the second activity you will add three more
proteins from three other species of spiders to your analysis.
ACTIVITY 5-1
Introduction to Using Biology Workbench
Objective: Introduce you to the Biology Student Workbench.
Materials:
Handout SS-H11: Introduction to Using Biology Workbench Worksheet
Computer
1. Go to the Student Interface to the Biology Workbench (SIB) website at
http://bighorn.animal.uiuc.edu/cgi-bin/sib.py[3].
a. Set up an account by following the instructions to register on the screen. Complete your
registration by supplying a user name and a password.
b. Return to the SIB page and log in. Click on NEW (see 1st arrow in Figure 5.1) to create a
new session. Name this session Spider Silk.
Figure 5.1: SIB Page Shot 1
2. Scroll down to the bottom of the page and place a check (click) in the box to the left of the
session that you just created.
a. Scroll back up to the top of the page and click the button labeled PROTEIN TOOLS (see
2nd arrow in Figure 5.1).
b. In the table on the protein tools page look for a row with a tool (button) called Ndjinn (see
3rd arrow in Figure 5.2).
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c. You are going to search for a specific protein. In the cell to the left of this tool there is a
search window (see 1st arrow in Figure 5.2). Type in Araneus gemmoides 1 tubuliform
spidroin.
Figure 5.2: SIB Page Shot 2
d. Next select a database to search by clicking (highlighting) GenBank Invertebrate
Sequences (see 2nd arrow in Figure 5.2).
e. Then click on the button labeled Ndjinn (see 3rd arrow in Figure 5.2). You should now
have a search results screen that resembles Figure 5.3.
f. Place a check in the box to the left of the match that has a rank of 0 (see 1st arrow in Figure
5.3).
g. Check that the protein description matches what you typed into the search window note
that it has a rank of zero.
Figure 5.3: SIB Page Shot 3
h. Scroll down to the bottom of the page and click on Import Sequence(s) (see 2nd arrow
Figure 5.3). You should now be back on the Protein Tools page (see Figure 5.2).
i. Repeat these steps to search for and import the protein Nephila clavipes tubuliform
spidroin.
3. Scroll down to the bottom of the page and select (click in the boxes) the 2 protein sequences
that you just imported (See 1st arrow in Figure 5.4).
Figure 5.4: SIB Page Shot 4
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To find out more about the animals these proteins come from click VIEW RECORD in the right
hand column (not shown in Figure 4). Use the information on this page to answer the following
questions about these animals.
a. What is the tubuliform silk used for in both species of spider?
b. Who was the researcher(s) who posted the amino acid sequence for both types of spider?
c. Where were these researchers working when they submitted this information to this web
site?
d. What type of molecule was translated to produce the amino acid sequence in this protein?
e. Are the molecule type, gene name, and protein name the same for both species?
4. Now click RETURN at the top of the page to go back to the Protein Tools page.
You will now compare the two proteins you have selected. Scroll down to the bottom of the page
and make sure both protein sequences are selected. Then click on the button labeled
CLUSTALW (see 1st arrow in Figure 5.5).
Figure 5.5: Protein Tools Page
This page shows a comparison of the sequence of amino acids from the two species. Answer the
following questions from this page.
a. What do the blue letters mean?
b. What do the asterisk, colons, and periods at the bottom of the alignment mean?
c. How many amino acids are there in each protein?
d. What is the alignment score?
e. What scoring matrix was used in this alignment?
5. Before exiting this screen click on the button IMPORT ALIGNMENT, which should take you
to a new screen. This is the screen showing the alignment tools available in Biology Student
Workbench. Scroll down the screen and select CLUSTALW.
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6. Click the button labeled BOXSHADE (see 1st arrow in Figure 5.6).
Figure 5.6: Alignment Tool
This display is a color-coded view of the alignment from the previous page.
Answer the following questions about this page.
a. What does the blue color mean?
b. What does the green color mean?
c. What does the yellow color mean?
d. What does consensus mean?
Amino Acid Scoring Matrices
When we aligned our DNA sequences, we used a simple scoring system that had one score for
matches, one for mismatches and one for gaps. When aligning amino acid sequences, a more
interesting scoring system, such as the Gonnet matrix shown below is used.
Figure 5.7: The Gonnet scoring matrix.
The numbers in the scoring matrix are related to the probabilities of a particular substitution
occurring and surviving in nature. Recall that the amino acid sequence of the protein is derived
from the nucleotide sequence in the DNA. Thus, a change in the amino acid sequence is actually
caused by a mutation in the DNA. Take a look again at Figure 1.3 in Lesson 1. Notice that
codons for some amino acids differ by only a single nucleotide. For example, the codons for
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Serine (S) (AGU and AGC) differ only in the middle nucleotide from codons for Threonine (T)
(ACU and ACC). In contrast, the codon for Tryptophan (W) (UGG) has nothing in common with
any of the codons for Asparic Acid (D). Thus, replacing a Serine with a Threonine occurs with
higher probability than replacing a Tryptophan by an Asparic Acid.
A much more important consideration, however, is whether the substitution actually survives in
nature. Recall that changing an amino acid can cause a change in the three dimensional structure
of a protein. If this change is large, it can completely change the properties of the protein. Most
mutations are bad! If the protein performs an important function in the organism, the modified
protein is no longer able to perform the work that it is supposed to do. As a result, the organism
is less likely to mature and reproduce. Thus, while many mutations happen in nature, most of
them don’t survive in the gene pool.
It turns out that many pairs of amino acids have very similar properties; so substituting between
them does not dramatically alter the protein. Thus, when we compare sequences found in nature,
we are more likely to see substitutions between similar amino acids, and less likely to see
substitutions between amino acids that have very different properties.
The numbers in Figure 5.7 provide scores that take these considerations into account. A negative
score means that the substitution is rarely found in nature, and a positive score means that it is
relatively common. To score an alignment, we look up the two amino acids in the table to find
what score to give if those two amino acids are aligned with each other. Then, as before, the
score of an alignment is the sum of the individual scores.
For example, the score for the alignment shown here would be 4.9, using a gap value of –5. (This
gap value is independent of the matrix, and was an arbitrary choice for this example.)
A
A
2.4
M
C
–0.9
I
I
4.0
N
D
2.2
E
–5
S
S
2.2
Similarly, when using our dynamic programming alignment algorithm to align amino acid
sequences, we would also use the scores from the matrix shown for any diagonal move
(corresponding to aligning a pair of amino acids). The problem is no more complicated, but it is
more tedious because we have to look up scores from a table. Computers, of course, do not mind
this.
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ACTIVITY 5-2
Comparing Spider Silk Protein
Objective: To compare the amino acid sequence of the silk protein from five species of spiders.
Materials:
Handout SS-H12: Comparing Spider Silk Protein Worksheet
Computer
1. Open the Student Interface to the Biology Workbench: http://bighorn.animal.uiuc.edu/cgibin/sib.py[3]. Login and open the session called “Spider Silk” that you created in Activity 5-1 by
following the directions in the RESUME row (see 1st arrow in Figure 5.8).
Figure 5.8: SIB Page Resume
2. Click on the button that says Protein Tools at the top of the screen (see 2nd arrow in Figure
5.8). The screen should now resemble Figure 5.9.
Figure 5.9: SIB Page Protein Tools
a. Type Uloborus tubuliform into the box that says “Enter your search in the box below” (See
1st arrow in Figure 5.9).
b. In the box labeled “Ndjinn” select the following database: Genbank Invertebrate
Sequences (see 2nd arrow in Figure 5.9).
c. Click on the button labeled “Ndjinn” (See 3rd arrow in Figure 5.9).
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3. Place this sequence into your session labeled Spider Silk by placing a check (click) in the box
to the left of the protein selected (See 1st arrow in Figure 5.10). Go to the bottom of the page and
click on Import Sequences(s) (See 2nd arrow in Figure 5.10).
Figure 5.10: SIB Page Selection to Import
4. Repeat this procedure for Argiope aurantia tubuliform. This will return several sequences.
Import the one with accession number 61387230.
5. Repeat this procedure for Deinopis tubuliform, importing sequence number 63054332.
6. Take a look at the five sequences at the bottom of your Biology Student Workbench page, and
make sure they are the ones shown in Figure 5.11. To compare the five sequences that are now in
your Spider Silk session, at the bottom of the page check all five sequences by placing a check
(click) next to each.
Figure 5.11: SIB Comparing Sequences
7. Now click on CLUSTALW in the tool column (See 1st arrow in Figure 5.12). This performs a
multiple sequence alignment of the five spider silk proteins that we have imported. Note that we
did not discuss how to do alignments of more than two sequences, but the basic idea is the same:
Use dynamic programming. Notice that the first step in aligning these five sequences was
performing all pairs of pairwise alignments.
Figure 5.12: CLUSTALW
Answer the following questions about the display on this page.
a. What is the length of each of the five protein sequences, in order from longest to shortest?
b. Find a stretch of five amino acids that is the same in all of the silk protein sequences, and
aligned. What are they?
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c. Which pair has the greatest pairwise alignment score? Write out the protein ID numbers of
the two that have this greatest alignment score.
d. Where is the output concerning the pairwise alignments?
e. What is the overall multiple sequence alignment score?
8. Click on the “Import Alignments” button at the top of this page. (See 1st arrow in Figure 5.13.)
This saves the work that CLUSTALW just did, so that we won’t have to perform this alignment
again. We’ll come back here later.
Figure 5.13: SIB Import Alignment
9. Click on the “Protein Tools” button at the top of the page. You should now be on the Protein
Tools page. Scroll to the bottom of this page—if the five spider silk proteins that you previously
imported are not still checked—check them (see Figure 5.11). Scroll up the page and click on the
button labeled AASTATS (see 1st arrow in Figure 5.14).
Figure 5.14: SIB AASTATS
Answer the questions below.
a. For each of the five spider species list the two amino acids that appear the most frequently
and how many times that amino acid appears in the spider silk protein.
Protein
Most common amino acid
Name
Freq.
Percent
2nd most common amino acid
Name
Freq.
Percent
b. According to the list you generated in Question a, which two proteins are most alike?
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c. According to the list generated in Question a, which two proteins are least alike?
d. Which amino acids never appear in any of these sequences?
10. Click on the “Return” button at the top of the page, returning you to the “Protein Tools”
page. At the top of the page, click the “Alignment Tools” button, bringing you back to the page
where we saved our CLUSTALW alignment. At the bottom of this page, select the check box
next to the names of our five spider silk proteins. Notice that there is only one check box there.
This is because the alignment of those five sequences is now to be treated as one large object
containing those five sequences as well as information on how they are aligned.
11. Click on the “DRAWTREE” button in the tools section of this page. This generates a graphic
showing the relationship between our five sequences. In figures such as these, the lengths of the
segments are used to indicate how different sequences are from each other. Thus, since the labels
ending in “231" and “237,” corresponding to Argiope aurantia and Araneus gemmoides
respectively, are the closest together on this tree, we conclude that their sequences are the most
closely related. Indeed, these two were the pair with the highest pairwise alignment score, as you
discovered in Question 3. Such trees are considered to be good guesses at the evolutionary
relationship between the proteins, and perhaps the species they came from.
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Glossary
Adenine - one of four nucleotide bases, abbreviated as the letter “A” in a DNA sequence.
Alanine - an amino acid found in spider silk, abbreviated as the letter “A” in a protein sequence.
Alignment - the process whereby different DNA or protein sequences are compared. The
sequences may be from the same or different individuals or from different species.
Arachnida - the class where spiders are classified in the animal kingdom. This class includes
scorpions, mites, and ticks.
Araneae - the order where spiders are classified in the animal kingdom. This order contains
thousands of spider species.
Arthropoda - the phylum where spiders are classified in the animal kingdom. This phylum
includes insects, arachnids, and crustaceans.
Base case - a sub-problem whose solution is obvious by inspection.
Codon - three letters from the nucleotide sequence that “codes” for an amino acid.
Conserved - term given to nucleotides or amino acids in a sequence that have not changed over
a long evolutionary time.
Cytosine - one of four nucleotide bases, abbreviated as the letter “C” in a DNA sequence.
Deletion mutation - the removal of a nucleotide from an ancestor’s DNA sequence.
DNA molecule - a chain of nucleotides, usually double stranded.
DNA nucleotide sequence - a chain of nucleotide bases – adenine (A), guanine (G), cytosine
(C), and thymine (T).
DNA sequence - see “DNA nucleotide sequence”
Dynamic programming - a process for finding the optimal solution to a problem by
systematically identifying and solving a sequence of similar sub-problems.
GenBank - one example of a sequence database.
Genome - all the DNA is an organism’s cell, usually all the chromosomes.
Glycine - an amino acid found in spider silk, abbreviated as the letter “G” in a protein sequence.
Guanine - one of four nucleotide bases, abbreviated as the letter “G” in a DNA sequence.
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Insertion mutation - the addition of a nucleotide into an ancestor’s DNA sequence.
Mutation - any change in a DNA sequence.
Optimal - best according to some specific criteria.
Parsimony principle - the principle that simpler explanations are more likely to be correct than
are more complicated explanations.
Protein molecule - a chain of amino acids.
Protein sequence - a sequence of letters selected from the twenty-letter amino acid alphabet
used to represent a protein molecule.
RNA molecule - a chain of nucleotides, usually single stranded.
RNA nucleotide sequence - a chain of nucleotide bases – adenine (A), guanine (G), cytosine
(C), and uracil (U).
Sequence database - a repository that stores the sequence information discovered in individual
laboratories.
Sequencing - the process by which a scientist extracts DNA or protein molecules from a subject
and then treats the extraction in a laboratory to reveal the types and order of nucleotides (DNA)
or amino acids (protein).
Spider silk proteins - contain a high percentage of two amino acids, alanine and glycine.
Substitution mutation - the replacement of one nucleotide of an ancestor’s genetic sequence
with a different nucleotide.
Transcription - the cellular process, involving RNA polymerase, which copies part of a DNA
sequence into an RNA sequence.
Translation - the cellular process, involving ribosomes, which converts the genetic code along
an RNA molecule into a protein sequence.
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References
[1] John Wiley & Sons, Inc.. (2007, April 6). Fascinating spider silk. ScienceDaily. Found at
www.sciencedaily.com/releases/2007/04/070405094039.htm.
[2] National Center for Biotechnology Information (NCBI). Found at
http://www.ncbi.nlm.nih.gov/.
[3] San Diego Supercomputer Center. Biology WorkBench. Found at http://workbench.sdsc.edu.
[4] Berman, H.M. et al. (1999). The protein data bank. Nucleic Acids Research. 28(1), 235-242.
[5] RCSB Protein Data Bank. An information portal to biological macromolecular structures.
Found at www.rcsb.org/pdb/explore.do?stuctureId=1c3l.
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