Title: Dise
1Diseño de primers
2 Francis Crick
Alex Rich Leslie Orgel James
Watson
3Escenarios frecuentes en el diseño de primers
- Secuencia de DNA conocida
- Diagnóstico, genotipificación
- Tener cuidado si es DNA o cDNA
- Secuencia de DNA desconocida
- Se busca secuenciar el gen en cuestión
- Regiones conservadas en genes homólogos de
organismos cercanos - Extremos amino ó carboxilo terminal de la
proteína codificada es conocida
4Secuencia de DNA conocida
- Los primers se diseñan a partir de criterios de
optimalidad - Estabilidad térmica del complejo primer-DNA
- Estructura secundaria
- Dímeros
- Temperatura media de fusión
- Especificidad
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6PCR
1 copy
and - strands of template
forward primer
reverse primer
amplified DNA
5
3
3
5
2 copies
5
3
5
3
4 copies
etc.
8 copies
7Ciclos deTemperatura
- Temperatura de hibridación (annealing) (usual
45-60?C) allows primers to hybridize to template - Temperatura de extensión (usually 72?C) allows
polymerase to extend starting at the primer - Temperatura de denaturación (usually 95?C)
separates strands
8- Tiempo de vida media de Taq polymerasa
- aprox. 30 min a 95C,
- Es lar razón por la que después de 30 ciclos de
amplificación se pierde eficiencia - Es posible reducir la temperatura de
denaturación luego de 10 ciclos de amplificación
ya que la longitud media del DNA blanco se ha
reducido cercanamente al tamaño del amplicón
para templados de 300bp o menos, la temperatura
de denaturación puede reducirse a valores tan
bajos como 88C para un 50 de (GC) (Yap and
McGee, 1991), por lo que es posible llegar hasta
40 ciclos sin disminuir sustancialmente la
eficiencia de la enzima.
9Durante el PCR se da una liberación de
pirofosfato que juntamente con el producto van a
comportarse de manera inhibitoria
10Considerations About Primers
Characteristics of primers
Thoughts on primer design
Uniqueness
Specificity Specific for the intended target
sequence (avoid nonspecific hybridization)
Length
Base Composition
Internal Stability
Stability Form stable duplex with template under
PCR conditions
Melting Temperature
Annealing Temperature
Internal Structure
Compatibility Primers used as a pair shall work
under the same PCR condition
Primer Pair Matching
11Uniqueness
There shall be one and only one target site in
the template DNA where the primer binds, which
means the primer sequence shall be unique in the
template DNA. There shall be no annealing site in
possible contaminant sources, such as human, rat,
mouse, etc. (BLAST search against corresponding
genome)
Template DNA 5...TCAACTTAGCATGATCGGGTA...GTAGCAG
TTGACTGTACAACTCAGCAA...3
TGCTAAGTTG
CAGTCAACTGCTAC
NOT UNIQUE!
Primer candidate 1 5-TGCTAAGTTG-3
UNIQUE!
Primer candidate 2 5-CAGTCAACTGCTAC-3
12Length
Primer length has effects on uniqueness and
melting/annealing temperature. Roughly speaking,
the longer the primer, the more chance that its
unique the longer the primer, the higher
melting/annealing temperature. Generally
speaking, the length of primer has to be at least
15 bases to ensure uniqueness. Usually, we pick
primers of 17-28 bases long. This range varies
based on if you can find unique primers with
appropriate annealing temperature within this
range.
13Base Composition
- Base composition affects hybridization
specificity, melting/annealing temperature and
internal stability. - Random base composition is preferred. We shall
avoid long (AT) and (GC) rich region if
possible.
Template DNA 5...TCAACTTAGCATGATCGGGCA...AAGATGC
ACGGGCCTGTACACAA...3
TGCCCGATCATGCT
- Usually, average (GC) content around 50-60
will give us the right melting/annealing
temperature for ordinary PCR reactions, and will
give appropriate hybridization stability.
However, melting/annealing temperature and
hybridization stability are affected by other
factors, which well discuss later. Therefore,
(GC) content is allowed to change.
14Thermodynamics
- Gibbs Free Energy, G
- Describes the energetics of biomolecules in
aqueous solution. The change in free energy, ?G,
for a chemical process, such as nucleic acid
folding, can be used to determine the direction
of the process - ?G0 equilibrium
- ?Ggt0 unfavorable process
- ?Glt0 favorable process
- Thus the natural tendency for biomolecules in
solution is to minimize free energy of the entire
system (biomolecules solvent).
- ?G ?H - T?S
- ?H is enthalpy, ?S is entropy, and T is the
temperature in Kelvin. - Molecular interactions, such as hydrogen bonds,
van der Waals and electrostatic interactions
contribute to the ?H term. ?S describes the
change of order of the system. - Thus, both molecular interactions as well as the
order of the system determine the direction of a
chemical process. - For any nucleic acid solution, it is extremely
difficult to calculate the free energy from first
principle - Biophysical methods can be used to measure free
energy changes
15Internal Stability
Stability Profile Internal stability is
calculated with entropy values of neighbor
nucleotides. Usually, We draw a graph of ?G for
all nucleotides of the primers. This is known as
the stability profile.
163 Stability 5 Stability
Primer elongation starts at 3 end. Therefore, as
long as 3 end hybridizes to the template stably,
the elongation begins. 5 end sequence plays less
important role. This feature can be utilized for
modifying 5 end so that there will be a
restriction enzyme site. However, this feature
also brings out a problem if 3end of the
primer has 3 or more than 3 C/G, it can almost
bind stably to any site where there are 3
complement G/C bases.
Template DNA 5...TCAACTTAGCGTGATCGATTA...AAGATTC
GCGTTAGCTGTACACAA...3
5-AATCGATCTCGC-3
Ideal situation will be stable 5-termini less
stable 3-termini, which eliminates false priming
due to annealing of 3'-half of primer only. We
prefer the 5 end has 1 or two G/C bases (GC
clamp) and the 3 end has no more than 1 G/C base.
17Melting Temperature
Melting Temperature, Tm the temperature at
which half the DNA strands are single stranded
and half are double-stranded.. Tm is
characteristics of the DNA composition Higher
GC content DNA has a higher Tm due to more H
bonds. Calculation Method 1 (Base Composition)
Tm ( A T ) ? 2?C ( C G ) ? 4?C
(lt20bp) Method 2 (Salt Adjusted) Used by GCG
and Primer3 Tm 81.5 16.6 ? log10Na
0.41 ? GC 0.65 ? formamide 675/length
mismatch Method 3 (Nearest Neighbor) Used by
OLIGO ?H / (10.8 ?S R ? ln (c / 4))
273.15 16.6(log10K) where ?H is the sum of
enthalpy of the nearest neighbors, ?S is the sum
of entropy of the nearest neighbors, c is the
molar concentration of primer, and R is the gas
constant (1.987). As you can tell from the
equation higher GC, higher Tm Higher probe,
higher Tm higher K, higher Tm Differences are
sometimes significant, like 8 degrees, and
sometimes trivial, like 0.1 degree. Try different
software to calculate Tm. Pick the common value.
18Annealing Temperature
Annealing Temperature, Tanneal the temperature
at which primers anneal to the template DNA. It
can be calculated from Tm .
Tanneal Tm_primer 4?C or 0.3 ? Tm_primer
0.7 ? Tm_product 14.9 Where Tm_primer is the
melting temperature for primer and Tm_product is
the melting temperature for product.
To ensure that primers anneal to the template
before the two strands of template anneal to each
other, it required that the Tm_product Tanneal
30 ?C
19Stringency in Primer Annealing
- Stringency determines the specificity of the
amplified DNA product. Tanneal is the most
significant factor affecting the stringency in
primer annealing. - Tanneal too low ? less stringent ? primer
matches elsewhere - too high ? more stringent ? primer
may fail to match - Other factors
- GC GC pairs are more stringent than AT paris
- Salt Buffer
20Internal Structure
If primers can anneal to themselves, or anneal to
each other rather than anneal to the template,
the PCR efficiency will be decreased
dramatically. They shall be avoided.
However, sometimes these 2? structures are
harmless when the annealing temperature does not
allow them to take form. For example, some dimers
or hairpins form at 30 ?C while during PCR cycle,
the lowest temperature only drops to 60 ?C.
21Primer Pair Matching
Primers work in pairs forward primer and
reverse primer. Since they are used in the same
PCR reaction, it shall be ensured that the PCR
condition is suitable for both of them. One
critical feature is their annealing temperatures,
which shall be compatible with each other. The
maximum difference allowed is 3 ?C. The closer
their Tanneal are, the better.
22Calculation procedure for extinction (absorption)
coefficient of DNA Extinction coefficient at 260
nm, 25 degrees of Celsius, and neutral pH for the
single-strand DNA is determined by the
nearest-neighbor method
23The following table contains extinction
coefficients l/(mmol.cm)
stack or monomer extinction coefficient
pdA 15.4
pdC 7.4
pdG 11.5
pdT 8.7
dApdA 13.7
dApdC 10.6
dApdG 12.5
dApdT 11.4
dCpdA 10.6
dCpdC 7.3
dCpdG 9.0
dCpdT 7.6
dGpdA 12.6
dGpdC 8.8
dGpdG 10.8
dGpdT 10.0
dTpdA 11.7
dTpdC 8.1
dTpdG 9.5
dTpdT 8.4
24Summary when is a primer a primer?
5
3
5
3
5
3
3
5
25Summary Primer Design Criteria
- Uniqueness ensure correct priming site
- Length 17-28 bases.This range varies
- Base composition average (GC) content around
50-60 avoid long (AT) and (GC) rich region
if possible - Optimize base pairing its critical that the
stability at 5 end be high and the stability at
3 end be relatively low to minimize false
priming. - Melting Tms between 55-80 ?C are preferred
- Assure that primers at a set have annealing Tm
within 2 3 ?C of each other. - Minimize internal secondary structure hairpins
and dimmers shall be avoided.
26Computer-Aided Primer Design
Primer design is an art when done by human
beings, and a far better done by machines.
- Some primer design programs we use
- Oligo Life Science Software, standalone
application - - GCG Accelrys, ICBR maintains the server.
- Primer3 MIT, standalone / web application
- http//www-genome.wi.mit.edu/cgi-bin/primer/pri
mer3_www.cgi - BioTools BioTools, Inc. ICBR distributes the
license. - Others GeneFisher, Primer!, Web Primer, NBI
oligo program, etc.
Melting temperature calculation software -
BioMath http//www.promega.com/biomath/calc11.htm
27Primer Design on the Web
- There are a bunch of good PCR primer design
programs on the web - Primer 3 at the MIT Whitehead Institute
- http//www.genome.wi.mit.edu/cgi-bin/primer/primer
3_www.cgi - Cassandra at the Univ. of Southern California
- http//www-hto.usc.edu/software/procrustes/cassand
ra/cass_frm.html - GeneFisher by Folker Meyer Chris Schleiermacher
at Bielefeld University, Germany - http//bibiserv.TechFak.Uni-Bielefeld.DE/genefishe
r/ - Xprimer at the Virtual Genome Center, Univ.
Minnesota Medical School - http//alces.med.umn.edu/rawprimer.html
28Secuencia de DNA desconocida
- Regiones conservadas en genes homólogos de
organismos cercanos
29- gtgi175637971-1014 Caenorhabditis elegans
essential CathePsin L (38.1 kD) (cpl-1), mRNA - ATGAACCGATTCATTCTTCTGGCACTGGTTGCCGCCGTCGTCGCCGTCAA
TTCGGCCAAGCTGTCCCGTC - AAATCGAGTCGGCCATCGAGAAATGGGACGACTATAAGGAGGACTTTGAT
AAGGAGTACTCGGAGAGCGA - GGAGCAGACCTATATGGAGGCATTTGTCAAGAATATGATCCATATTGAGA
ATCACAACAGAGATCACCGA - CTCGGAAGAAAGACATTCGAGATGGGATTGAATCATATTGCTGACTTGCC
ATTCAGCCAATACCGCAAAC - TCAACGGTTACAGACGTCTCTTCGGTGACTCCAGAATCAAGAACTCCTCC
TCTTTCTTGGCTCCATTCAA - TGTTCAGGTCCCAGATGAGGTTGACTGGCGTGATACCCACCTCGTCACTG
ATGTCAAGAACCAAGGAATG - TGCGGATCGTGCTGGGCCTTCTCCGCCACCGGAGCCCTCGAAGGACAACA
CGCTCGCAAGCTGGGACAAC - TCGTCTCCCTTTCCGAGCAAAACCTCGTCGACTGCTCTACCAAGTACGGA
AACCACGGATGCAACGGAGG - ACTCATGGATCAAGCTTTCGAGTACATTCGTGACAACCATGGTGTCGACA
CCGAGGAGTCATACCCATAC - AAGGGACGTGACATGAAGTGTCACTTCAACAAGAAGACCGTCGGAGCTGA
TGATAAGGGATACGTTGACA - CCCCAGAAGGAGATGAGGAGCAACTTAAGATCGCTGTCGCCACCCAAGGA
CCAATCTCTATTGCTATCGA - CGCCGGACACCGCAGCTTCCAACTTTACAAGAAGGGAGTCTACTACGATG
AGGAATGCTCATCCGAAGAG - CTCGACCACGGAGTGCTTCTCGTCGGATACGGAACCGACCCAGAGCACGG
AGACTACTGGATTGTCAAGA - ACTCGTGGGGAGCTGGATGGGGAGAGAAGGGATACATCCGTATCGCCCGT
AACCGCAACAATCACTGCGG - AGTCGCCACCAAGGCCAGTTATCCATTGGTCTAA
30- gtgi2518814970-1131 Brugia malayi mRNA for
cathepsin L-like cysteine proteinase, complete
cds - ATGAAGGCGTTTTTTATTCTACATTTAGCCAGTTTTCTCTTGCTTACTTA
TGCAAATCCACTTAATGAAC - TGGATAATGATGACACACCAGGTAAAATTCATACCTTGTATCAGCAGCAT
TATTCGAAGTATAAAACATA - TCTGAAAAAAATGGGCAAAAAACATGATCCATCTGTTCCGGAACCAATTC
GATTACTTAAATTTGTACAA - TCTTTGAAAATGATTGATGAACATAACCAGCGTTACAGTAAAGGATTGGA
AACATACAAAGTAGATCTGA - ACAAAATGAGCGATTGGACCGAAGAAGAGAAAGAAAGACTTCGGGGATAT
TATCCAAATTTGACTGAATA - TGCGGAAGGAGATTTAAGTAGAATAATCCGAGGAAATATAACAACAACAA
TACCAAAGTCTTTTGATTAT - AGAAAGAAAATAACTGTACTACCAGCATCAGATCAAGGTCGTTGTGGTGT
GTGTTTTATTTTCTCAGCAT - TAGGAGCGCTTGAAATGTATGTGGCGCTCAGGACTAAAAAACGGCCGGTA
AAACTATCAGTACAGGATGT - AATGGATTGTAGTGGAATGGAAAAATGCAAAGGAAGAGGCGGAAATGAAC
CTGCGGTTTTTCGTTGGGTT - GCTGAGCACGGTGTAAAGACCGATAAGAGTTACCCATATAAGGAAAATGA
TAGTGTTTCATGCCCGAGAA - ATACCCCACAACGACGAAAGTATGGTTTAGCTGATGCATTCTATTTACCT
CCTAGCAATGAACAAATTCT - CAAGAAGATACTAGCACTATATGGACCAGTTTGTGTATCGTTACATTCGT
CATTACAAAGTTTTGTAGCT - TATCGAAGTGGTATTTATAATGATCCAAAATGTCCAACTAATGCAGAAAA
AGTAAATCATGCGGTAATAG - CGGTTGGTTATGGTGTCCAGAATGGGATGGAATATTTTATCATCAAAAAC
AGTTGGGGCCCTACATGGGG - TCAAAAAGGATACGGTCGTATTCGCGCTGGGGTATTTATGTGCGGTATTG
GTCGTTTTTCGAACGTACCA - ATCTTCAAATGA
31- gtgi214896764-1068 Haemonchus contortus
cathepsin L cysteine protease (cpl-1) mRNA,
complete cds - ATGCTACGTCTGTTGTCGTTGGCGCTTCTATGCGCTGTAGTTTTAGCTAG
TATTGATGGGTTCAGAAGGC - ATGATCATGGCGTACGAGTGCACAGACAGAAAAGCCTTCGCCAAAAAATC
GACGAGGCTTTCAATAAATG - GGATGACTACAAGGAGACCTTTGGAAAGTCGTATGAACCGGATGAAGAGA
ACGACTACATGGAGGCCTTT - GTGAAGAACGTGATTCACATTGAGGAACACAATAAGGAACACCGTCTTGG
TAGGAAAACATTTGAAATGG - GTCTCAACGAAATTGCTGATTTGCCATTCTCACAATATCGAAAACTCAAC
GGGTATCGTATGCGTCGTCA - ATTTGGCGATTCCTTGCAGTCCAATGGTACCAAGTTTTTGGTTCCATTCA
ATGTTCAGATCCCGGAATCT - GTTGACTGGCGAGAGGAAGGACTTGTGACTCCAGTAAAGAATCAAGGAAT
GTGTGGATCATGTTGGGCGT - TCTCCTCTACTGGTGCTCTAGAAGGACAACATGCACGTGCCACTGGCAAG
CTGGTATCCCTTTCCGAGCA - AAATCTTGTCGATTGCTCAACGAAGTACGGAAACCATGGCTGCAACGGTG
GTCTTATGGATTTGGCATTT - GAATATATCAAGGAAAATCACGGTGTCGATACCGAAGATAGTTATCCATA
CGTCGGAAGAGAAACGAAAT - GTCATTTCAAGAGGAACGCTGTTGGAGCCGATGACAAGGGCTTTGTAGAT
CTTCCTGAAGGCGATGAAGA - GGCGTTGAAGAAAGCAGTTGCCACTCAAGGTCCAATTTCTATCGCTATTG
ACGCTGGTCACAGGTCATTC - CAGCTGTACAAGAAGGGAGTGTACTTTGACGAAGAGTGCTCGTCTGAAGA
ACTGGATCACGGTGTTCTTC - TCGTTGGATACGGTACTGATCCCGAGGCAGGAGATTATTGGCTTGTGAAG
AACAGCTGGGGACCGACTTG - GGGAGAGAAGGGATACATTCGCATTGCCCGTAACCGCAACAATCACTGCG
GTGTTGCAACAAAGGCCAGC - TACCCGCTCGTTTAG
32- gt(gi21483189lt1-53, 1121-1209, 1586-1725,
1806-1910, 2049-2183, 2239-2385, 2448-2537,
2616-2691, 2999-3107, 3188-3287) Dictyocaulus
viviparus cathepsin L (cpl-1) gene, partial cds - TTGCTTCTGTTCCTATGCGATTTAGCTTCAACTAAGATCGGTACACCTAG
AAAGCACGGATTTTATTCGG - AGAAACAGAAAAGTCTACGTCAGAGGATCGATGAGGCCTTTGGAAAATGG
GATGAGTATAAGATCAAATA - TGATAAACACTATGACCCTGAAGAAGAAAATGATTATATGGAGGCTTTTG
TAAAAAACATGATCCACATC - GAGGAGCATAATCATGAACACCGCTTGGGGCGAAAAACTTTCGAAATGGG
ATTGAACAATATCGCTGATC - TTCCTTTCTCGGAGTACCGCAAATTGAACGGTTACCGCCATCGTCGCTTA
TTTGGTGACTCTATGCGTAA - AAATGGCACGAAATTTTTAGTCCCTTTCAATGTCAAGGCGCCGGATTCAG
TAGATTGGCGAGAACATAAT - CTCGTTACTCCAGTAAAAAATCAAGGGATGTGTGGTTCCTGTTGGGCCTT
CTCCGCAACTGGAGCTCTCG - AAGGACAACATTTTCGTGCAACCGGAAAACTTGTTTCCTTGTCCGAACAG
AATCTGGTGGATTGTTCTAC - TAAATATGGAAACCATGGTTGTAACGGTGGTCTCATGGATTTGGCATTTG
AATACATAAAAGATAATCAT - GGTATAGATACTGAGGAGGGTTACCCTTATGTTGGCAAAGAGATGAGGTG
CCACTTCAAAAAGAGGGACA - TTGGAGCTGAAGATAGGGGGTTTGTAGATCTTCCAGAAGGAGACGAAGAT
GCCTTGAAGGTCGCTGTCGC - TACTCAGGGTCCTATTTCTATTGCCATTGATGCCGGTCATCGGTCTTTCC
AGTTATATAAAAAAGGAGTT - TATTTTGACGAGGAGTGTTCATCCGAAGAACTTGATCATGGAGTTCTTCT
TGTGGGTTATGGCACTGATC - CTGAAGCTGGCGACTACTGGATCATAAAGAATAGTTGGGGAACTAAATGG
GGAGAAAAGGGTTACGTTCG - TATCGCTCGGAATCGCAACAATCACTGCGGTGTGGCAACGAAGGCGAGTT
ATCCGCTCGTCTAA
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34Universal Primers
- Primers can be designed to amplify only one
product. - Primers can also be designed to amplify multiple
products. We call such primers universal
primers. For example, design primers to amplify
all HPV genes. - Strategy
- Align groups of sequences you want to amplify.
- Find the most conservative regions at 5 end and
at 3 end. - Design forward primer at the 5 conservative
region. - Design reverse primer at the 3 conservative
regions. - Matching forward and reverse primers to find the
best pair. - Ensure uniqueness in all template sequences.
- Ensure uniqueness in possible contaminant sources.
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40Nucleic-acid Base Codes
Symbol Meaning Symbol Meaning
A A S G or C
G G W A or T
C C H A, C, or T (G)
T T B C, G, or T (A)
R A or G V A, C, or G (T)
Y C or T D A, G, or T (C)
M A or C N A, C, G, or T
K G or T
Adapted from Mount, Bioinformatics Cold Spring
Harbor Laboratory Press, Cold Spring Harbor, NY
(2001)
41- Catep1w 5'KTG YGG WKY VTG YTK KRY BTT CTC3'
- Catep2w 5'GTA WCC YTT YTS DCC CCA 3'
- Estos primers son las secuencias degeneradas de
alinear los nematodes disponibles C.elegans,
Brugian, Haemonchus, Dyctiocaulus
42Secuencia de DNA desconocida
- Extremos amino ó carboxilo terminal de la
proteína codificada es conocida
43- P F T K
- CCn TTy ACn AAr
- Donde
- n A,C,G or Ty C,Tr A,G
441 fold sites M W
2 fold sites F Y H Q N K D E C
3 fold sites I
4 fold sites V P T A G
6 fold sites L S R
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46Our Focus the Helix-Coil Transition in DNA
- In particular, we focus on two related processes
- DNA melting
- B helix to two coils.
- DNA annealing
- two coils to a B helix.
- Understanding these
- aids in modeling more complicated transitions.
- e.g., many species.
47Stabilizing Interactions
- DNA B-Helix structure stabilized by
- hydrogen bonding between bases (minor).
- stacking between H-bonded
- base-pairs (primary).
- induced dipole moments in the p clouds of
adjacent heterocyclic rings. - stacking also sequesters hydrophobic rings.
- results in the characteristic helix shape.
- In DNA meltingthe helix destabilized
- generally implemented by increasing temperature,
T. - destabilizes the stacksunwinding the helix.
- unwound helix separates into free ssDNAs
(coils).
48Monitoring the Helix-Coil Transition
- Degree of stacking experimentally observable
- Let QB mean fraction of stacked base pairs.
- Ultraviolet absorbance at 260 nm (A260)
- inversely proportional to QB.
- the hypochromicity.
- DNA melting accompanied by _at_ 40 increase A260.
- A260 vs. T yields QB vs. T (melting curve).
49DNA Melting Curves
- QB decreases monotonically from 1 to 0.
- sigmoidal shape indicates DNA melting is
cooperative. - Temp. at which QB ½ is the Melting temperature
(Tm) - Width (DT) is non-zero (e.g., for 10-mers, DT _at_
10 oC). - Melting curves of longer DNAs show more
structure - several independently melting regions (ATs less
stable). - melting curve then a combination of several
sigmoids.
50DNA Renaturation
- Renaturation is the reverse of DNA melting.
- also called DNA annealing or hybridization.
- DNA renaturation is a much more complicated
process
51DNA reassociation (renaturation)
Double-stranded DNA
Denatured, single-stranded DNA
Faster, zippering reaction to form
long molecules of double- stranded DNA
k2
Slower, rate-limiting, second-order process
of finding complementary sequences to
nucleate base-pairing
http//www3.kumc.edu/jcalvet/PowerPoint/bioc801b.p
pt
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53Reversibility of DNA Melting
- Melting for short DNAs strictly reversible.
- Reversibility of DNA melting
- measured by a lack of hysteresis in the melting
curve. - DNA melting curve DNA renaturation curve.
- Validity of an equilibrium model of melting
assumes - melting slow enough to maintain equilibrium at
each T. - relatively slow heating/cooling
(0.1-0.2oC/minute). - failure to maintain equilibrium hysteresis in
the melting curve.