Nucleic acids are composed of chains of nucleotides which consist of a sugar, phosphate group, and nitrogenous base. The two most common nucleic acids are DNA and RNA. DNA contains deoxyribose and thymine, while RNA contains ribose and uracil instead of thymine. Hybrid duplexes form between nucleic acids through base pairing between complementary bases. Previous studies show that hybrid duplexes with purine-rich strands are more thermodynamically stable than those with pyrimidine-rich strands. Molecular dynamics simulations were performed on various DNA-RNA and DNA-PNA hybrid duplexes to calculate entropy and better understand factors influencing hybrid stability. Results showed that as the number of purine bases on the DNA

1. Nucleic acids are macromolecules composed of chains of monomeric nucleotides.Nucleic acids are macromolecules composed of chains of monomeric nucleotides.
Nucleotides consist of a five-membered sugar ring, a charge phosphate group, and aNucleotides consist of a five-membered sugar ring, a charge phosphate group, and a
purine and pyrimidine base. The purine bases consist of adenine and guanine whichpurine and pyrimidine base. The purine bases consist of adenine and guanine which
contain two rings, while pyrimidine bases consist of thymine, cytosine, and uracil.contain two rings, while pyrimidine bases consist of thymine, cytosine, and uracil.
Two most common nucleic acids are DNA and RNA. DNA contains deoxyriboseTwo most common nucleic acids are DNA and RNA. DNA contains deoxyribose
sugar ring, while RNA contains a ribose. Furthermore all thymine bases are replacedsugar ring, while RNA contains a ribose. Furthermore all thymine bases are replaced
by uracil in RNA. Not so common is peptide nucleic acid (PNA), which is anby uracil in RNA. Not so common is peptide nucleic acid (PNA), which is an
artificially made “nucleic acid.” PNA is a DNA analogue that contains no sugar ring,artificially made “nucleic acid.” PNA is a DNA analogue that contains no sugar ring,
and has an electrically neutral pseudopeptide backbone; which means PNA is neitherand has an electrically neutral pseudopeptide backbone; which means PNA is neither
a peptide or a nucleic acid. Named peptide nucleic acid to emphasize their synthesisa peptide or a nucleic acid. Named peptide nucleic acid to emphasize their synthesis
as well as their relationship to nucleic acids.as well as their relationship to nucleic acids.
Hybrid duplexes form according to Watson-Crick base pairing: cytosine pairs withHybrid duplexes form according to Watson-Crick base pairing: cytosine pairs with
guanine by forming three hydrogen bonds, while thymine pairs with adenine byguanine by forming three hydrogen bonds, while thymine pairs with adenine by
forming two hydrogen bonds. In RNA, thymine is replaced by uracil. A hybridforming two hydrogen bonds. In RNA, thymine is replaced by uracil. A hybrid
duplex is formed when two different nucleic acids create a duplex.duplex is formed when two different nucleic acids create a duplex.
Previous studies show purine rich RNA/PNA strands form more stable hybridPrevious studies show purine rich RNA/PNA strands form more stable hybrid
duplexes with DNA than pyrimidine rich RNA/PNA strands. An experimental studyduplexes with DNA than pyrimidine rich RNA/PNA strands. An experimental study
of PNA duplexes, PNA(purine)of PNA duplexes, PNA(purine)DNA duplexes, PNA(pyrimidine)DNA duplexes, PNA(pyrimidine)DNA duplexes,DNA duplexes,
and DNA duplexes showed PNA(purine)and DNA duplexes showed PNA(purine)DNA duplexes are moreDNA duplexes are more
thermodynamically stable in comparison to PNA(pyrimidine)thermodynamically stable in comparison to PNA(pyrimidine)DNA duplexes. TheDNA duplexes. The
difference in entropy between individual single strands and the hybrid duplex wasdifference in entropy between individual single strands and the hybrid duplex was
greater for the pyrimidine duplex than the purine duplex as shown in the tablegreater for the pyrimidine duplex than the purine duplex as shown in the table
below:below:
Entropy Calculations of Hybrid Nucleic Acid SystemsEntropy Calculations of Hybrid Nucleic Acid Systems
Danyal Floisand and Tricia D. Shepherd
Department of Chemistry, Westminster College, Salt Lake City, UT, 84105
U. Deva Priyakumar, and A. MacKerell, J. Phys. Chem. B 2008, 112, 1515-1524
A. Noy, A. Perez, M. Marquez, J. Luque, and M. Orozco, J. Am. Chem. Soc. 2005, 127, 4910-4920
T. Cheatham, and P. Kollman, J. Am. Chem. Soc. 1997, 119, 4805-4825
A. Sen, and P. Nielsen, Biophysical J. 2006, 90, 1329-1337
S. Sen, and L. Nilsson, J. Am. Chem. Soc. 2001, 123, 7414-7422
H. Schafer, A. Mark, and W. van Gunsteren, J. Chem. Phys. 2000, 113, 7809-7817
I. Andricioaei, and M. Karplus, J. Chem. Phys. 2001, 115, 6289-6292
Acknowledgements:
Westminster College Gore Math/Science Summer Research Grant (2009)
ABSTRACT
BACKGROUND
RESULTS METHODS
CONCLUSIONS
REFERENCES
Molecular dynamic simulations are used to study the structure and stability ofMolecular dynamic simulations are used to study the structure and stability of
hybrid duplexes DNA·RNA and DNA·PNA in aqueous solution. DNA·RNA andhybrid duplexes DNA·RNA and DNA·PNA in aqueous solution. DNA·RNA and
DNA·PNA hybrid duplexes are biologically important molecules with potentialDNA·PNA hybrid duplexes are biologically important molecules with potential
therapeutic properties. Previous studies have shown that DNA·RNA andtherapeutic properties. Previous studies have shown that DNA·RNA and
DNA·PNA duplexes are significantly stabilized when pyrimidine bases (thymineDNA·PNA duplexes are significantly stabilized when pyrimidine bases (thymine
and cytosine) are attached to the DNA strand. In order to further investigate theand cytosine) are attached to the DNA strand. In order to further investigate the
stability and sequence-dependent structural effects, we performed molecularstability and sequence-dependent structural effects, we performed molecular
dynamics simulations using AMBER 9 on a series of DNA·RNA and DNA·PNAdynamics simulations using AMBER 9 on a series of DNA·RNA and DNA·PNA
duplexes systems for which the purine base content of the DNA strand wasduplexes systems for which the purine base content of the DNA strand was
systematically decreased from containing only purine to only pyrimidine bases. Asystematically decreased from containing only purine to only pyrimidine bases. A
comparison of the intramolecular entropy components of the backbones and basescomparison of the intramolecular entropy components of the backbones and bases
of the various hybrids are analyzed in order to better understand the stability ofof the various hybrids are analyzed in order to better understand the stability of
DNA·RNA and DNA·PNA hybrid duplexes.DNA·RNA and DNA·PNA hybrid duplexes.
• All calculations were performed using AMBER 9.All calculations were performed using AMBER 9.
• Staring duplexes were generated from a canonical A-type DNA duplex forStaring duplexes were generated from a canonical A-type DNA duplex for
DNADNARNA sequences and AB-type DNA duplex for DNARNA sequences and AB-type DNA duplex for DNADNA , PNADNA , PNAPNA , andPNA , and
DNADNAPNA sequences using the NUCGEN module of the AMBER program. The pdbPNA sequences using the NUCGEN module of the AMBER program. The pdb
file was then modified according to the following mapping scheme for DNAfile was then modified according to the following mapping scheme for DNARNA: onRNA: on
DNA strand remove N6 (except on adenine) then on RNA strand also remove N6, andDNA strand remove N6 (except on adenine) then on RNA strand also remove N6, and
H41 and H42 on uracil; and DNAH41 and H42 on uracil; and DNAPNA: (DNA) C5’-C4’-P’-C3’-O1’-C1’-O5’-PNA: (DNA) C5’-C4’-P’-C3’-O1’-C1’-O5’-
O3’O3’(PNA) C2’-N2’-N1’-C5’-C3’-C4’-C1’-C6’.(PNA) C2’-N2’-N1’-C5’-C3’-C4’-C1’-C6’.
• All standard atom types were defined according to the AMBER FF99 force field.All standard atom types were defined according to the AMBER FF99 force field.
The PNA backbone and base charges were obtained from T. Rathinavelan, and N.The PNA backbone and base charges were obtained from T. Rathinavelan, and N.
YathindraYathindra FEBS J.FEBS J. 20052005,, 272272, 4055-4070. Sodium counter ions were added to the, 4055-4070. Sodium counter ions were added to the
duplexes which were then solvated with approximately 3,500 TIP3P water moleculesduplexes which were then solvated with approximately 3,500 TIP3P water molecules
in a truncated octahedron box extending 8in a truncated octahedron box extending 8 Å beyond the atoms of the duplexes.beyond the atoms of the duplexes.
• All duplexes were minimized using the SANDER module. For the DNAAll duplexes were minimized using the SANDER module. For the DNARNA andRNA and
DNADNADNA duplexes two minimizations were run, first minimization had the DNADNA duplexes two minimizations were run, first minimization had the DNA
strand restrained, and the second had nothing restrained. For the PNAstrand restrained, and the second had nothing restrained. For the PNAPNA andPNA and
DNADNAPNA hybrid duplexes four minimizations were run, first minimization had thePNA hybrid duplexes four minimizations were run, first minimization had the
duplex restrained, second had the PNA strand (or DNA strand) and PNA basesduplex restrained, second had the PNA strand (or DNA strand) and PNA bases
restrained, third had the bases restrained, and fourth had nothing restrained.restrained, third had the bases restrained, and fourth had nothing restrained.
• Finally, the system was heated from 0 K to 300 K over 40 ps, with the DNA strandFinally, the system was heated from 0 K to 300 K over 40 ps, with the DNA strand
weakly restrained. Production runs (NPT) were then performed using constantweakly restrained. Production runs (NPT) were then performed using constant
temperature and pressure. Simulation runs for 5 ns (DNAtemperature and pressure. Simulation runs for 5 ns (DNARNA) and 8 nsRNA) and 8 ns
(DNA(DNADNA , PNADNA , PNAPNA , and DNAPNA , and DNAPNA) at 300K and 1 atm.PNA) at 300K and 1 atm.
Figure 1: Comparison of backbone composition of DNA, RNA, and PNA.Figure 1: Comparison of backbone composition of DNA, RNA, and PNA.
Entropy CalculationEntropy Calculation
• MD coordinate trajectory:MD coordinate trajectory:
• RMSD fit MD coordinates to initial structure, than apply mass weighting:RMSD fit MD coordinates to initial structure, than apply mass weighting:
• Apply principal component analysis (PCA) to calculate mass weighted covarianceApply principal component analysis (PCA) to calculate mass weighted covariance
matrix. The individual elements of the covariance matrix σmatrix. The individual elements of the covariance matrix σ22
m.w.m.w. are:are:
• Diagonalize matrix and obtain a new PCA coordinate system matrix with 3N-6Diagonalize matrix and obtain a new PCA coordinate system matrix with 3N-6
eigenvalues or variances:eigenvalues or variances:
• Calculate entropy using all PCA modes and the Andricioaei and Karplus method:Calculate entropy using all PCA modes and the Andricioaei and Karplus method:
where ωwhere ωii are the eigenvalues (in frequency units) obtained by diagonalization of theare the eigenvalues (in frequency units) obtained by diagonalization of the
mass-weighted covariance matrix.mass-weighted covariance matrix.
X=(x1,x2,x3,..,xnf)
yi =M1/2
xi
(σm.w.
2
)i,j=(yi−<yi>)(yj−<yj>)
λii =(meffσPCA
2
)i
S=kB
αi
eαi
−1
−ln(1−e−αi
)




i=1
3N−6
∑ αi =
hωi
kBT
Tm
(°C)
ΔG
(kcal/mol)
ΔH
(kcal/mol)
ΔS
(cal/mol K)
PNAŸPNA 71.1 -16.6 -86.1 -224
PNA(purine)ŸDNA 1 65 -15.4 -87.6 -233.1
PNA(purine)ŸDNA 2 67.3 -16.1 -92.4 -245.8
PNA(pyrimidine)ŸDNA 1 39 -8.2 -35.3 -87.4
PNA(pyrimidine)ŸDNA 2 43.3 -8.8 -43.4 -111.7
DNAŸDNA 36.2 -4.5 -62 -185.5
Name
DNA sequence
of DNARNA duplex
Name
DNA sequence
of DNAPNA duplex
# of Purine
bases on DNA
1DR 3' C G A A G A G A A G 5' 1DP 3' C G A A G A G A A G 5' 9
2DR 3' C G A A C T G A A G 5' 2DP 3' C G A A C A G A T G 5' 7
3DR 3' C G A A C T C T A G 5' 3DP 3' C G A A C T C T A G 5' 5
4DR 3' C G T T C T C T A G 5' 4DP 3' C G T T C A C T T G 5' 3
5DR 3' G C T T C T C T T C 5' 5DP 3' G C T T C T C T T C 5' 1
• The 5 sequences identified in theThe 5 sequences identified in the
second column of the table to the leftsecond column of the table to the left
correspond to DNAcorrespond to DNARNA hybridRNA hybrid
duplexes. The fourth columnduplexes. The fourth column
corresponds to DNAcorresponds to DNAPNA hybridPNA hybrid
sequences. Also identified are thesequences. Also identified are the
corresponding number of purinecorresponding number of purine
bases on the DNA strand.bases on the DNA strand.
• ΔΔSS == SSDNA strandDNA strand -- SSRNA(PNA) strandRNA(PNA) strand corresponding to the difference incorresponding to the difference in
entropy between the DNA strand and the RNA or PNA strand.entropy between the DNA strand and the RNA or PNA strand.
• All Atoms:All Atoms: ΔS is calculated using all the atoms on each strandΔS is calculated using all the atoms on each strand
of the hybrid duplexes. For both types of hybrids (DNAof the hybrid duplexes. For both types of hybrids (DNARNARNA
and DNAand DNAPNA) as the DNA strand contains more purine basesPNA) as the DNA strand contains more purine bases
(corresponding to experimentally less stable duplexes), a smaller(corresponding to experimentally less stable duplexes), a smaller
difference in entropy between the two strands is observed.difference in entropy between the two strands is observed.
• Base Atoms:Base Atoms: ΔS is calculated using only the base atoms onΔS is calculated using only the base atoms on
each strand of the hybrid duplexes. A large correlation iseach strand of the hybrid duplexes. A large correlation is
observed between the entropy of the base atoms and the numberobserved between the entropy of the base atoms and the number
of purine bases on the strand. The purine bases appear to haveof purine bases on the strand. The purine bases appear to have
less entropy regardless of the backbone type.less entropy regardless of the backbone type.
• Backbone Atoms:Backbone Atoms: ΔS is calculated using only the backboneΔS is calculated using only the backbone
atoms on each strand. For the PNA hybrid, the difference inatoms on each strand. For the PNA hybrid, the difference in
entropy of the backbone atoms shows almost no dependence onentropy of the backbone atoms shows almost no dependence on
purine content. For the RNA hybrid, the backbone entropy ispurine content. For the RNA hybrid, the backbone entropy is
larger for strands with more purine bases.larger for strands with more purine bases.
A. Sen, and P. Nielsen, Biophysical J., 2006 90, 1329-1337 Unique Properties of
Purine/Pyrimidine Asymmetric PNADNA Duplexes: Differential Stabilization of
PNADNA Duplexes by Purines in the PNA Strand.
• The number of purine bases on a strand in a hybrid duplex tends to correlate withThe number of purine bases on a strand in a hybrid duplex tends to correlate with
the values of entropy calculated.the values of entropy calculated.
• In general, purine bases have a smaller entropy per atom than pyrimidine bases inIn general, purine bases have a smaller entropy per atom than pyrimidine bases in
the hybrid duplexes.the hybrid duplexes.
• Overall DNAOverall DNARNA duplexes have less entropy than DNARNA duplexes have less entropy than DNAPNA duplexes.PNA duplexes.
• The entropy of the DNA strand is larger than PNA in DNAThe entropy of the DNA strand is larger than PNA in DNAPNA duplexes.PNA duplexes.
• The difference in entropy of the strands in DNAThe difference in entropy of the strands in DNARNA duplexes is smaller thanRNA duplexes is smaller than
DNADNAPNA duplexes.PNA duplexes.
• The PNAThe PNAPNA duplex overall has the highest entropy, and DNAPNA duplex overall has the highest entropy, and DNADNA duplex hasDNA duplex has
the least.the least.
# of
Purine
Sequence
Base
Composition
R = 9 G A A G A G A A G C G4A5C
R = 8 A G G T A A C G A G A4G4CT
R = 5 G A A G T C T T G C G3A2C2T3
• The top table on the right gives the entropy difference betweenThe top table on the right gives the entropy difference between
the purine rich DNA strand of the duplex (DRP/DD) and thethe purine rich DNA strand of the duplex (DRP/DD) and the
pyrimidine rich DNA strand of the duplex (DPR/DD). Thispyrimidine rich DNA strand of the duplex (DPR/DD). This
entropy difference is also given for PNA strands.entropy difference is also given for PNA strands.
• Overall, the DNA strand has more entropy when its purine richOverall, the DNA strand has more entropy when its purine rich
and in the hybrid duplex.and in the hybrid duplex.
• The PNA strand exhibits more entropy when its pyrimidine rich.The PNA strand exhibits more entropy when its pyrimidine rich.
• The bottom table on the right gives the entropy differenceThe bottom table on the right gives the entropy difference
between the same sequence of DNA (PNA) strand connected to thebetween the same sequence of DNA (PNA) strand connected to the
homoduplex and the hybrid duplex.homoduplex and the hybrid duplex.
• All atoms of the DNA strand give some inconsistency, butAll atoms of the DNA strand give some inconsistency, but
breaking it down to the backbone atoms of the DNA strand it isbreaking it down to the backbone atoms of the DNA strand it is
seen that the DNA strand has more entropy in the hybrid duplex.seen that the DNA strand has more entropy in the hybrid duplex.
• On the whole, the PNA strand has more entropy in theOn the whole, the PNA strand has more entropy in the
homoduplex.homoduplex.
DNA Strand PNA strand
(DRP - DPR)*100
(kcal/mol*K)
(DD - DD)*100
(kcal/mol*K)
(PRD-PDR)*100
(kcal/mol*K)
(PP-PP)*100
(kcal/mol*K)
R = 9 1.91 1.19 -2.18 -4.49
R = 8 2.57 -1.13 -4.26 -1.53
R = 5 0.87 -0.38 -2.14 -0.54
All Atoms Backbone Atoms All Atoms
(DD-DRP)*100
(kcal/mol*K)
(DD-DRP)*100
(kcal/mol*K)
(PP-PRD)*100
(kcal/mol*K)
R = 1 1.14 -0.61 9.69
R = 2 0.20 1.04 -3.75
R = 5 -1.70 -2.36 1.17
R = 5 -2.94 -2.46 2.77
R = 8 -3.50 -4.44 -1.02
R = 9 0.43 7.49 7.38
• The three sequences identified in the table to the left correspondThe three sequences identified in the table to the left correspond
to DNAto DNADNA, PNADNA, PNAPNA, DNAPNA, DNAPNA, and PNAPNA, and PNADNA duplexes.DNA duplexes.
The number of purine bases refer to the first strand of duplex. TheThe number of purine bases refer to the first strand of duplex. The
hybrid duplexes are referred to as DRP (DNAhybrid duplexes are referred to as DRP (DNAPNA) and PRDPNA) and PRD
(PNA(PNADNA), where R is replaced by the number of purines on theDNA), where R is replaced by the number of purines on the
first strand indicated for the duplex.first strand indicated for the duplex.
• The second sequence is the same as the Sen and Nielson paper.The second sequence is the same as the Sen and Nielson paper.
• The figure to the left displays the entropy values for the threeThe figure to the left displays the entropy values for the three
different sequences for each of the different duplexes:different sequences for each of the different duplexes:
DNADNADNA , PNADNA , PNAPNA, PRD, and DRP . Due to the differentPNA, PRD, and DRP . Due to the different
amount of atoms per system, the entropy values were normalizedamount of atoms per system, the entropy values were normalized
through division by the number of atoms.through division by the number of atoms.
• In general, the entropy of the PNAIn general, the entropy of the PNAPNA duplex is the largest,PNA duplex is the largest,
while DNAwhile DNADNA has the lowest. The difference of entropyDNA has the lowest. The difference of entropy
between P8D and D8P hybrids have a similar size gap to that ofbetween P8D and D8P hybrids have a similar size gap to that of
the Sen and Nielson paper. A gap is also seen for P5D and D5Pthe Sen and Nielson paper. A gap is also seen for P5D and D5P
hybrid duplexes.hybrid duplexes.