# The effect of DNA bases permutation on surface enhanced Raman scattering
spectrum

Shimon Rubin∗ Phuong H.L. Nguyen∗ Yeshaiahu Fainman  ∗ Equal contribution
Department of Electrical and Computer Engineering, University of California,
San Diego, 9500 Gilman Dr., La Jolla, California 92023, USA

###### Abstract

Surface enhanced Raman scattering (SERS) process results in a tremendous
increase of Raman scattering cross section of molecules adsorbed to plasmonic
metals and influenced by numerous physico-chemical factors such as geometry
and optical properties of the metal surface, orientation of chemisorbed
molecules and chemical environment. While SERS holds promise for single
molecule sensitivity and optical sensing of DNA sequences, more detailed
understanding of the rich physico-chemical interplay between various factors
is needed to enhance predictive power of existing and future SERS-based DNA
sensing platforms. In this work we report on experimental results indicating
that SERS spectra of adsorbed single-stranded DNA (ssDNA) isomers depend on
the order on which individual bases appear in the 3-base long ssDNA due to
intra-molecular interaction between DNA bases. Furthermore, we experimentally
demonstrate that the effect holds under more general conditions when the
molecules don’t experience chemical enhancement due to resonant charge
transfer effect and also under standard Raman scattering without
electromagnetic or chemical enhancements. Our numerical simulations
qualitatively support the experimental findings and indicate that base
permutation results in modification of both Raman and chemically enhanced
Raman spectra.

## Introduction

Surface enhanced Raman scattering (SERS) fleischmann1974 ; Jeanmaire1977 ;
albrecht1977  is an intriguing effect which results in several orders
amplification of Raman scattering cross section of molecules chemisorbed or
physiosorbed to a rough metal surface. In particular, SERS enhancement factors
(EFs), which characterize increase in molecular Raman scattering relative to
under non-SERS condition le2008principles , mostly stem from conjointly
operating electromagnetic enhancement (EM) and chemical enhancement (CE)
effects. While EM effect stems from local increase of electromagnetic fields
in so-called hot spots which contribute to both larger induced Raman dipole
and intensified radiation of the vibrating dipole through excitation of
plasmon resonances in the metal nanostructure (operating as plasmonic
nanoantenna moskovitz ; stockman ), CE effect leru2007 ; morton2011 ; leru2013
stems from changes of the Raman polarizability and of the molecular electronic
structure due to formation of chemical bonds between the relevant molecule and
the metal and therefore selectively operates on the formed metal-molecule
complex depending on its’ specific properties moskovitz ; jensen2008 . In
particular, CE effect may be accompanied by either resonant charge transfer
between the adsorbed molecule and the metal substrate kneipp2016  facilitated
by formation of charge-transfer states, or non-resonant (static) ground-state
charge redistribution due to overlap of metal and molecular orbitals
morton2009  and surface binding (see ding2017 ; langer2019  and references
within) leading to static far-from-resonance changes of the molecular
polarizability.

Due to the high sensitivity of the SERS process inherent to Raman-based
vibrational spectroscopy with narrow spectral lines, leading (under some
conditions) to single molecule detection nie1997 ; kneipp1997  as well as
single base sensitivity xu2015label ; guerrini2015  in simple DNA sequences,
SERS-based DNA sensing holds promise for numerous future bio-related
applications such as medical diagnosis, bio-analysis, and environmental
monitoring where composition and sequencing analysis of the information-rich
DNA molecules serve as one of the central tools. Furthermore, the significant
progress in more recent years allowing individual nucleobases resolution
he2018  achieved by employing the closely related tip-enhanced Raman
spectroscopy (TERS) stockle2000 ; anderson2000 ; hayazawa2000 ; pettinger2000
, and exploitation of CE effect freeman2014  to achieve higher specificity in
ssDNA sensing, both indicate potential applications of SERS/TERS for DNA
sensing. The latter include DNA characterization with a reduced number of
thermocycling steps in polymerase chain reaction (PCR) amplification
wu2020performance , mutation detection due to molecular conformation change
kowalczyk2019  or employing branched DNA technique which relies on the signal
amplification of the probe that binds to a specific nucleotide sequence
cheng2018 , which are typically more sensitive than conventional fluorescent
labeling (see for instance a recent work fu2019 ). Nevertheless, the extreme
sensitivity of SERS with respect to numerous factors such as substrate
quality, dielectric environment, as well as unknown molecule orientation,
occasionally leads to controversial results on gold harroun2018controversial
and silver freeman2016  substrates, indicating that further research is needed
to understand the basic physical mechanisms of plasmon-DNA interaction and how
to leverage them in order to enhance present capabilities, eventually leading
to bio-medical applications which require higher precision than achieved today
pyrak2019 . In particular, considering increasingly complex DNA sequences,
where each nucleotide in turn is composed of additional sub-units, is expected
to introduce novel mechanisms that affect the corresponding Raman and SERS
spectra; it is reasonable to assume that incorporating these effects might
improve the accuracy of future plasmonic-based detection schemes.

In this work we experimentally and numerically study, for the first time to
the best of our knowledge, the effect of intra-molecular interaction between
DNA bases on the resultant SERS and Raman spectra, by considering simple ssDNA
sequences which admit identical number of bases appearing at different order
along the sequence. Taking advantage of the controlled distance between DNA
bases in ssDNA molecules allows us to investigate how the position of DNA
bases and their nearest neighbors affect the frequency, RA (Raman activity)
and vibrational pattern of the corresponding normal modes. Fig.1 presents
schematic description of the key elements in our study which includes
silver/gold nanorod array serving as a substrate for adsorbed ssDNA 3-mer
strands, allowing to extract changes of the SERS spectra due to nucleobases
permutation, as well as different units/groups in a single DNA base which are
activated depending on their position in ssDNA molecule.

Figure 1: Schematic description of the underlying concept of our work. (a) Key
elements of the experimental setup presenting a silver/gold nanorod array
substrate of mean period $\Lambda$ and height $h$, hosting ssDNA 3-mers
allowing to compare SERS spectra of ACA with CAA and of CAC with CCA (only ACA
and CAA are presented in the scheme). The permutation of DNA bases in the
sequences leads to a change in the interaction between the DNA bases,
schematically represented as different bonds between the bases, and to
enhancement of different molecular vibrational modes with distinct dominant
frequency (b) and different kinetic energy distribution among the different
atom groups (c); relative disks’ size indicate the corresponding kinetic
energy stored in the relevant atoms at the dominant mode.

In particular, we experimentally measure SERS spectra of two groups of isomers
classified according to the total number of nucleotides of a given type; group
($1$) comprised of ACA and CAA sequences which admit two adenines (A) and a
single cytosine (C), and group ($2$) comprised of CAC and CCA which admit a
single A and two C’s. We then analyze the corresponding SERS spectra and
compare them by constructing the corresponding statistical correlation
matrices which provides a quantitative metric to characterize the changes of
the spectra due to permutation of DNA bases. In addition to the experiments
where ssDNA molecules adsorbed directly to metal nanorod substrate array which
facilitates both EM and CE effects, we also consider Raman spectra of ssDNA
molecules in bulk solution without CE and EM effects as well as ssDNA
molecules adsorbed to gold and silver nanorod substrate arrays covered with a
$2$-nm thickness of Al2O3 dielectric film. The latter is thin enough to
facilitate EM effect but eliminate the CE effect, allowing to study the
difference between the various spectra of ssDNA molecules without the charge
transfer resonant effect freeman2014 . Furthermore, we employ density
functional theory (DFT) which became a widespread method for calculating
electronic excitations and related optical properties of molecules Ullrich2011
(including Raman polarizability), to study the permutation effect on Raman
spectra of ssDNA 3-mers with and without the CE effect. The latter is achieved
by introducing Ag4 silver nano-clusters huang2013  bond to each one of the
nucleotides, allowing to study the effect of static non-resonant (i.e. far
from resonance) CE effect on Raman spectra and kinetic energy distribution due
to electrostatic charge redistribution. For simplicity, our computational
model studies single orientation of DNA bases relative to the metal, and
therefore it is not used for quantitative comparison against experimental
results. In fact, predicting the binding sites of ssDNA molecules with the
metal and the resultant orientation of these molecules is still somewhat
controversial; e.g. adenine binding orientation harroun2018controversial  or
orientation dependence due to interaction with magnesium cations garcia2018
(which are used in our experiments), is expected to lead to considerable
variation in the corresponding spectra.

This work is structured as follows. First, we present DFT simulation results
which compare Raman spectra of ssDNA 3-mers under nucleobases permutation with
and without non-resonant CE effect. We then present experimental results of
the ssDNA 3-mers with an increasing number of enhancement effects; first we
present Raman spectra acquired in bulk solution without EM and CE effects,
then we present SERS spectra on nanorod array substrates with only EM effect,
and finally SERS spectra when both EM and CE effects are present. We analyze
the numerical and experimental data, determine prominent trends, and
distinguish the spectra of permuted ssDNA 3-mers based on the correlation
values of the elements in the corresponding statistical correlation matrix.

## Results

### Simulation results

Figure 2: DFT simulation results comparing between Raman spectra of ACA and
CAA isomers (group 1) with and without bonded three Ag4 nanoparticles. (a,b)
Present Raman spectra of ACA and of ACA-Ag12 molecules with dominant modes at
$775.52$ cm-1 and $1368.57$ cm-1, respectively, whereas (d,e) present Raman
spectra of CAA and CAA-Ag12 molecules with dominant modes at $775.98$ cm-1 and
$1368.16$ cm-1, respectively. (c,f) Relative kinetic energy distribution among
the different atoms at the dominant normal modes with red disks and green
disks corresponding to the cases with and without silver nanoparticles,
respectively. The disks with black contours in ACA and CAA molecules admit
kinetic energy values larger by a factors $1.22$ and $1.60$, respectively.

Fig.2 and Fig.3 present DFT simulation results of Raman spectra of ACA, CAA
(group 1) and CCA, CAC (group 2) sequences, as well as the same sequences
where each DNA base is also bound to Ag4 nano-particle. All calculated Raman
intensity results are normalized to unity, and Raman intensities of the cases
with metal particles admit values higher by approximately factor of five or
smaller. The broadening of the peaks is manually introduced by Lorentzian
functions with bandwidth full-width at half maxima (FWHM) of $12$ cm-1, where
$5-20$ cm-1 is usually employed to describe various broadening effects
le2008principles . Fig.2(c,f) and Fig.3(c,f) present the corresponding 2D
schematic representation of the 3-base long sequences where each nucleotide
consists of a phosphate backbone joined to a sugar (a.k.a. 2-deoxyribose due
to a missing hydroxyl) to which the base is attached, and different
nucleotides are linked through the phosphodiester linkage WatsonDNA . The
latter also leads to chiral and polar structure of the ssDNA molecule with
distinct ends labeled as 3′ and 5′. The red/green disks represent the relative
kinetic energy of each atom with/without CE effect at the corresponding
dominant vibrational mode; solid contour lines around few of the atoms
indicate that the relevant atom carries larger kinetic energy as described in
figures’ captions. We follow the common convention and write the sequences
from $5^{\prime}$-end to $3^{\prime}$-end WatsonDNA , where for instance, CAA
stands for $5^{\prime}-$CAA$-3^{\prime}$.

Our simulation results indicate that the modes can be classified according to
the groups that store the kinetic energy of the vibrating atoms, and that the
normal frequencies of these groups depend both on their position in the
sequence as well as on the closest neighbor DNA bases. For instance, the
frequencies and the RAs of the ring breathing modes (RBMs) of adenine or
cytosine bases, which involve relatively small number of atoms, depend on
their location in the sequence and are affected by the DNA bases permutation
as we discuss in the following. Furthermore, changing the number of DNA bases
leads to frequency splitting of the normal modes due to partial degeneracy
lifting which stems from normal modes dependence on the position along the
sequence.

Fig.2(a,b,d,e) present Raman spectra of ACA and CAA molecules, group (1),
showing intensification, decline and shift of the normal modes, where red and
green colors indicate the cases with and without Ag4 nanoparticles,
respectively. To demonstrate basic trends and patterns we analyze the Raman
spectra in the following four spectral regions: (1) $775-791$ cm-1, (2)
$1231-1238$ cm-1, (3) $1367-1377$ cm-1 and (4) $1541-1544$ cm-1, and use the
spectra presented in Fig.2 in conjunction with Table.1 summarizing modes’
frequencies, RAs, as well as the corresponding Raman active group in the
sequence. Note that in some cases the dominant peak is composed of several
peak of comparable Raman intensity, and therefore the value of the maximal
frequency presented in Fig.2(a,b,d,e) and Fig.3(a,b,d,e) is different than the
frequency of the corresponding dominant modes analyzed in Fig.2(c,f) and
Fig.3(c,f).

Spectral region (1): is dominant for ACA and CAA molecules due to normal modes
which involve 3′sugar, central (cen) sugar and the single C base. For ACA the
dominant frequency at $777.05$ cm-1, is mostly due to $775.52$ cm-1
(RA$=39.89$ Å4/amu) and $779.09$ cm-1 (RA$=30.32$ Å4/amu) modes. Both admit
kinetic energy concentrated at 3′sugar and C with different out-of plane and
ring breathing amplitude vibrations (see fig.2(c) for kinetic energy
distribution), whereas kinetic energy of $775.52$ cm-1 mode is also
concentrated at central sugar group. Interestingly, as we will see in the
following, normal modes with kinetic energy more concentrated mostly at one
group are more prone to splitting, i.e. appearance of similar modes with
closely separated frequencies at different groups.

In CAA molecule, which is obtained from ACA by permutation of $5^{\prime}$A
with C, a slight red shift is observed at the peak vibrational Raman intensity
to $776.80$ cm-1, mostly due to red shift of the $775.02$ cm-1 mode to
$775.98$ cm-1 (RA$=37.36$ Å4/amu) and to the decrease of RA of the $779.09$
cm-1 mode. Bonding to Ag4 nanoparticles results in a red shift of all modes in
both ACA and CAA molecules, slight decrease of some modes RA (e.g. $779.09$
cm-1) and more significant decrease of $778.08$ cm-1 RA mode in CAA.

Spectral region (2): describes asymmetric RBM vibrations of the single C base
and the attached sugar molecule. Permutation of $5^{\prime}$A with C
introduces a relatively minor change in the vibrational frequency from
$1231.00$ cm-1 to $1231.51$ cm-1 and to a slight increase in the corresponding
RA (from $47.57$ Å4/amu to $50.51$ Å4/amu). Bonding to Ag4 nanoparticles leads
to a blue-shift of the resonant frequency and to a decrease in the RA values.

Spectral region (3): describes two normal modes of two different A bases, with
practically identical atomic displacements, but with different frequencies due
to different position in the sequence. In particular, ACA admits second
dominant peak at frequency $1375.35$ cm-1 which is a contribution of the
following stretching-bending modes (which lead to change in bonds’ length and
angles): $3^{\prime}$A at $1374.37$ cm-1 (RA$=59.78$ Å4/amu) and similar mode
of $5^{\prime}$A at $1376.74$ cm-1 (RA$=50.11$ Å4/amu). From Table.1 below we
learn that under permutation these modes are concentrated at A bases, but with
slightly different values of frequency and RA. Under bonding to Ag4
nanoparticles all modes are intensified, slightly red shifted, and the
vibrational modes become concentrated also in the adjacent sugar groups.

Spectral region (4): presents vibrational modes of two A bases around $1542$
cm-1 with two slightly different frequencies. Permutation of $5^{\prime}$A
with C in ACA molecule leads to slight intensification of RA and red shift of
the vibrational frequencies, whereas bonding to Ag4 nanoparticles leads to
more prominent intensification of the RA values and red shift of practically
all modes.

Due to the chiral nature of DNA molecule, AAC sequence, obtained by permuting
C base with 3′A base in CAA sequence, is expected to admit a different Raman
spectra. Indeed in Supplementary Information we describe additional DFT
simulation results indicating a red shift of cytosine active mode in the
second spectral region compared to ACA and CAA sequences, and also lower RA
values of adenine modes in the fourth spectral region when bound to Ag4
nanoparticles.

Name |  | Frequency [cm-1]
---
| Raman Activity [Å4/amu]
---
| Mode location
---
ACA |  | $767.08$
---
$773.34;775.52;779.09$
$1231.00$
$1374.37;1376.74$
$1541.24;1542.54$
| $2.49$
---
$6.91;39.88;30.23$
$47.57$
$59.78;50.11$
$28.11;44.66$
| C
---
C; 3′ sugar, cen sugar, C; C, $3^{\prime}$ sugar
C, cen sugar
$3^{\prime}$A; $5^{\prime}$A
$5^{\prime}$A; $3^{\prime}$A
CAA |  | $766.82;778.08$
---
$775.98;776.94$
$1231.51$
$1374.52;1376.57$
$1541.86;1542.66$
| $6.47;18.45$
---
$37.36;17.45$
$50.51$
$57.40;54.16$
$29.33;47.09$
| C; C
---
C, 3′sugar, 3′PHB; C, 3′sugar, 3′PHB
C, cen sugar
3′A; cen A
cen A; $3^{\prime}$A
ACA-Ag12 |  | $783.65;790.48$
---
$1237.93$
$1368.57;1371.40$
$1542.92;1543.55$
| $23.76;38.14$
---
$21.12$
$208.06;110.78$
$149.83;106.66$
| C; C
---
C, cen sugar
$3^{\prime}$A, $3^{\prime}$sugar; $5^{\prime}$A, $5^{\prime}$sugar
$3^{\prime}$A; $5^{\prime}$A
CAA-Ag12 |  | $778.75;781.09$
---
$1237.37$
$1367.45;1368.16$
$1541.41;1543.41$
| $58.46;4.48$
---
$25.69$
$90.96;201.37$
$152.31;147.26$
| 3′sugar; C
---
C, cen sugar
cen A, cen sugar; 3′A, 3′sugar
cen A; 3′A
Table 1: DFT simulation results presenting the effect of C-3′A permutation as
well as bases bonding to Ag4 particles on the frequency and the Raman activity
of the normal modes in the four different spectral regions: $775-791$ cm-1,
$1231-1238$ cm-1, $1367-1377$ cm-1 and $1541-1544$ cm-1. Figure 3: DFT
simulation results comparing Raman spectra between CAC and CCA isomers (group
2) with and without three Ag4 nanoparticles. (a,b) Present Raman spectra of
CAC and of CAC-Ag12 at dominant modes $769.56$ cm-1 and $781.58$ cm-1,
respectively, whereas (d,e) present Raman spectra of CCA and CCA-Ag12 with
dominant modes at $775.78$ cm-1 and $1568.62$ cm-1, respectively. (c,f)
Relative kinetic energy distribution among the different atoms of the dominant
modes with red disks and green disks corresponding to the cases with and
without silver nanoparticles, respectively. The disks with black contours
around red and green disks in CAC molecule indicate atoms with kinetic energy
$2.46$ and $1.85$ larger, respectively, whereas in CCA molecules admit kinetic
energy values larger by a factors $2.19$ and $1.54$, respectively.

Consider now group (2) with sequences CAC and CCA, which are formed by
replacing one of the A bases in group (1) by a C basis. Following our
discussion above, we expect normal modes splitting for the two C bases and
less modes involving a single A base. Fig.3(a,b,d,e) present Raman spectra of
CAC and CCA molecules, and similarly to the discussion above for group (1), we
consider the following four spectral regions: (1) $766-790$ cm-1, (2)
$1230-1242$ cm-1, (3) $1367-1375$ cm-1 and (4) $1542-1574$ cm-1. We use Fig.3
results in conjunction with Table.2 summarizing modes’ frequencies, RAs, as
well as the active group in the sequences.

Spectral region (1): describes mode splitting due to a pair of C bases which
introduces additional normal modes. In particular, the modes $767.08$ cm-1 in
ACA sequence and $766.82$ cm-1 in CAA sequence split into the pair
$766.33,769.56$ cm-1 in CAC sequence and into the pair $764.82,766.11$ cm-1 in
the CCA sequence (see Table.2). Furthermore, the pair $775.98$ cm-1 and
$776.94$ cm-1, which involves several groups in CAA sequence, joins into
another mode which involves several molecular groups at frequency $779.33$
cm-1. Bonding to Ag4 nanoparticles leads to a drop in RA, especially for the
$769.56$ cm-1 mode in CAC sequence.

Spectral region (2): describes mode splitting of the $1231.00$ cm-1 and
$1231.51$ cm-1 C-based modes in ACA and CAA sequences (with single C),
respectively, to the C-based paired modes $1241.62$ cm-1, $1242.74$ cm-1 and
$1230.04$ cm-1, $1231.15$ cm-1 in CAC and CCA sequences (with two C’s),
respectively. Bonding to Ag4 nanopartices leads to decrease of all RAs except
for the $1242.74$ cm-1 mode in CAC sequence which increases from $17.47$
Å4/amu to $39.20$ Å4/amu.

Spectral region (3): describes the activity of a single Raman active A-based
normal mode, as opposed to a pair of similar A-based modes in group (1). Under
permutation from CAC to CCA the resonant frequency is red-shifted from
$1378.61$ cm-1 to $1374.32$ cm-1 with slight increase in RA as further
described in Table.2. Bonding to Ag4 nanoparticles leads to red shift and
intensification of this mode in both CAC and CCA sequences (see Table.2).

Spectral region (4): Under permutation of 3′C with A, RA of A mode in CAC
sequence increases from $35.28$ Å4/amu to $44.27$ Å4/amu in CCA sequence, and
to decrease of RA values of the C-based pair modes. Bonding to Ag4
nanoparticles leads to strong intensification of both modes in the CCA-Ag12
sequence. In particular, RA of cen C mode in CCA sequence with RA$=29.74$
Å4/amu increase to RA$=282.20$ Å4/amu in CCA-Ag12 sequence.

Name |  | Frequency [cm-1]
---
| Raman Activity [Å4/amu]
---
| Mode location
---
CAC |  | $766.33;769.56$
---
$773.42;773.78$
$779.33$
$1241.62;1242.74$
$1378.61$
$1545.30;1572.78;1573.49$
| $7.25;45.43$
---
$7.34;1.45$
$53.45$
$53.46;17.47$
$45.21$
$35.28;36.30;32.40$
| 5′C; 3′C
---
3′C; 5′C
3′sugar, cen sugar, cen PHB, 3′PHB, 3′sugar
5′C, 5′sugar; 3′C, 3′sugar
A
A; $3^{\prime}$C; $5^{\prime}$C
CCA |  | $764.82;766.11$
---
$775.78$
$778.20;779.45$
$1230.04;1231.15$
$1374.32$
$1542.30;1572.84;1573.99$
| $4.62;5.64$
---
$36.28$
$21.87;32.23$
$47.34;49.62$
$59.14$
$44.77;33.69;29.74$
| cen C; 5′C
---
cen C, 3′sugar, 3′PHB, 5′C
5′C; cen C, 3′sugar, 3′PHB
cen C; 5′C
A
A; 5′C; cen C
CAC-Ag12 |  | $767.73;769.56$
---
$781.58;782.66$
$1245.54;1250.79$
$1375.63$
$1546.52;1565.53;1568.45$
| $2.62;5.17$
---
$57.42;34.49$
$21.48;39.20$
$116.53$
$119.22;28.48;46.86$
| 3′C; 5′C
---
5′C; 3′C, cen sugar
3′C, 3′sugar; 5′C, 5′sugar
A, cen sugar
A; $3^{\prime}$C; $5^{\prime}$C
CCA-Ag12 |  | $767.95;769.68$
---
$783.26;789.02$
$1237.27;1238.13$
$1368.33$
$1543.09;1568.30;1569.83$
| $1.61;2.38$
---
$40.66;45.30$
$30.89;30.23$
$208.60$
$156.58;282.20;69.38$
| cen C; 5′C
---
cen C; cen C, PHB, 5′C
cen C; 5′C
A, 3′sugar
A; cen C; 5′C
Table 2: DFT simulation results presenting the effect of C-3′A permutation and
Ag4 nanoparticles bonding to the molecules, on the normal modes’ frequencies
and Raman activities in the four spectral regions: $775-790$ cm-1, $1230-1250$
cm-1, $1367-1379$ cm-1 and $1542-1574$ cm-1.

Due to chiral nature of DNA molecule ACC sequence, obtained by permuting A
base with 5′C base in CAC sequence, is expected to admit a different Raman
spectra. In Supplementary Information we describe additional DFT simulation
results which allow to compare ACC to other sequences. These include blue
shift of the cytosine modes in fourth spectral region, $1572.78$ cm-1 and
$1573.49$ cm-1 in CAC sequence to $1573.07$ cm-1 and $1576.45$ cm-1 in ACC
sequence. Furthermore, from Table.2 and Table.S1 we learn that cytosine modes,
$1568.30$ cm-1 and $1569.83$ cm-1, in CCA-Ag12 sequences experience blue shift
to $1570.39$ cm-1 and $1572.39$ cm-1 in ACC-Ag12 sequences accompanied with a
decrease in RA.

Importantly, as indicated in Fig.S1, each one of the ssDNA molecules ACA, CAA,
CAC, and CCA admit different spatial conformation. The different conformations
within each one of the groups (1) and (2), due to permutation modified
intramolecular interaction, leading to different distances between the atoms
and eventually to modification of normal modes and Raman/SERS spectra. We then
assume that the optimized geometry holds also for the case when the sequences
are bond to metal nanolusters, somewhat mimicking behavior of real molecules
acquiring a given shape prior to metal adsorption. Metal atoms further modify
polarizability properties of the ssDNA molecules leading to modification of
the SERS/Raman signal and the kinetic energy distribution of the dominant
modes as indicated above.

### Experimental results

Figure 4: Experimental results presenting mean Raman spectra and correlation
matrices of $30$ measurements of ACA, CAA, CAC and CCA, ssDNA molecules in
bulk solution. (a) Mean Raman spectra of ACA (blue) and CAA (red), and (b)
presents the corresponding statistical correlation matrix. (c) Mean Raman
spectra of CAC (blue) and CCA (red), and (d) presents the corresponding
statistical correlation matrix.

Fig.4 and Figs.5-7, respectively, present experimental Raman and SERS
measurement results under exciting laser of wavelength $785$ nm, where each
measurement is conducted separately on each one of the following molecules
ACA, CAA, CAC, CCA; the first and the second pairs are referred below as group
(1) and group (2), respectively.

Figure 5: Experimental results presenting the effect of permutation of DNA
bases, adsorbed to nanorod gold substrate covered with $2$ nm thick Al2O3
film, on the mean SERS spectra and correlation matrices without the CE effect.
The experimental set is comprised of $24$, $25$, $25$ and $22$ measurements of
ACA, CAA, CAC and CCA, ssDNA molecules, respectively. (a) Mean SERS spectra of
ACA (blue) and CAA (red), and (b) presents the corresponding correlation
matrix. (c) Mean SERS spectra of CAC (blue) and CCA (red) and (d) presents the
corresponding correlation matrix.

First, we consider Raman signal of ssDNA molecules in IDTE bulk solution, i.e.
without metal substrate and therefore without the accompanying EM and CE
effects. The order of magnitude of the EM enhancement factor, as defined
according to (leru2007, , eq.4), which compares the total SERS signal from a
given surface element per estimated number of molecules adsorbed to the
illuminated surface area, to the total Raman signal from a given spatial
illuminated volume (defined by beam waist and Rayleigh length) per number of
molecules in that volume, is $\sim 10^{2}$. Fig.4(a,b) and Fig.4(c,d) present
comparison between Raman spectra of group (1) and between group (2) sequences,
respectively, where for clarity of presentation range bars are presented at 12
points along the profile and indicate 95% confidence intervals on the mean.
Importantly, here and elsewhere unless otherwise specified, the experimental
data was subject to multiplicative-scattering correction (MSC) in order to
filter out various noises, such as multiplicative light scattering
Isaaksson1988 . In fact, unless ssDNA molecules directly adsorbed to the
metal, MSC is necessary to observe the emerging square regions in the
correlation matrices Fig.4(b,d) (as well as in Fig.5(b,d) and in Fig.6(b,d)).
The latter are defined as the ratio of the covariance of the two variates to
the variance product of the independent variates GibbonsChakraborti , admit
close to unity values in the self-correlation blocks (e.g.
$\rho(\text{ACA},\text{ACA})$, $\rho(\text{CAA},\text{CAA})$, and lower values
in the cross-correlation blocks (e.g. $\rho(\text{ACA},\text{CAA})$),
signaling a difference in Raman spectra due to nucleobases permutation.

Next we consider the case where ssDNA molecules are adsorbed to $2$ nm thick
Al2O3 dielectric film deposited on top of oblique-angled deposition (OAD)
barranco2016  fabricated gold nanorod arrays. In so doing we introduce EM
effect due to gold nanorod array but eliminate the resonant charge transfer CE
effect. Figs.5(a,c) present mean SERS spectra of ACA and CAA sequences,
respectively, accompanied by the corresponding statistical correlation
matrices Fig.5(b,d). The latter indicate a close to unity correlation in the
diagonal blocks and smaller correlation in the off-diagonal block which is
more visible between group (2) sequences.

Figure 6: Experimental results presenting the effect of permutation of DNA
bases, adsorbed to nanorod silver substrate covered with $2$ nm thick Al2O3
film, on the mean SERS spectra and correlation matrices without the CE effect.
The experimental set is comprised of $98$, $98$, $100$ and $96$ measurements
of ACA, CAA, CAC and CCA, ssDNA molecules, respectively. (a) Mean SERS spectra
of ACA (blue) and CAA (red), and (b) presents the corresponding correlation
matrix. (c) Mean SERS spectra of CAC (blue) and CCA (red) and (d) presents the
corresponding correlation matrix.

In order to eliminate charge transfer CE effect, we perform similar
experiments with ssDNA adsorbed to $2$ nm thick Al2O3 dielectric film
deposited on top of silver OAD nanorod arrays. Fig.6 presents the
corresponding experimental results where Figs.6(a,c) illustrate the mean
spectra of group (1) and (2) ssDNA, and Figs.6(b,d) present the correlation
matrices indicating the differences between the two groups. Similarly to the
case of gold nanorod arrays coated with Al2O3, presented in Fig.5 above the
observed differences between group (1) molecules are smaller than between
group (2) molecules; the results in Fig.6(a,b) lead to very close signal and
the sequences ACA, CAA adsorbed to silver nanorod array coated with Al2O3 are
practically indistinguishable. Interestingly, the pattern of smaller
differences between group (1) molecules than between group (2) molecules is
also consistent with the computational spectra which can be seen by visually
comparing the mean spectra of group (1) molecules, Fig.2(a) vs Fig.2(d), and
Fig.2(b) vs Fig.2(e); group (2) molecules, Fig.3(a) vs Fig.3(d), and Fig.3(b)
vs Fig.3(e) due to more pronounced changes of the $5^{\prime}$C relative to
$3^{\prime}$A due to A-C permutation of the nearest nucleobase.

Next we consider the case where ssDNA molecules are adsorbed to silver nanorod
arrays which support both CE and EM effects. Figs.7(a,c) present SERS spectra
of the four ssDNA sequences with similar range bars as presented in figures
above. Fig.7(b,d) present the corresponding statistical correlation matrices
indicating close to unity correlation in the diagonal blocks and smaller
correlation in the off-diagonal blocks. In fact, in this case MSC wasn’t
implemented and signal processing wasn’t necessary to observe the difference
between the permuted cases. Interestingly, unlike the case presented in Fig.5
and Fig.6 above, where differences between group (1) sequences are less
visible compared to differences between group (2) sequences, in this case the
differences between group (2) sequences is more visible compared to group (1)
sequences. We attribute this difference to more prominent CE effect of adenine
bases reported in the recent work Nguyen2020 .

Figure 7: Experimental simulation results presenting mean SERS spectra of $25$
measurements of each ssDNA molecule adsorbed to nanorod silver substrate and
the corresponding statistical correlation matrices between the different
measurements. (a) Mean SERS spectra of ACA (blue) and CAA (red), and (b)
presents the corresponding statistical correlation matrix. Minimal values in
the first and second diagonal block of the statistical correlation matrix are
$0.991$ and $0.817$, whereas the off-diagonal blocks admit lowest values
$0.646$. (c) Mean SERS spectra of CAC (blue) and CCA (red). (d) Minimal values
in the first and second diagonal block of the diagonal matrix are $0.987$ and
$0.954$, whereas the off-diagonal blocks admit lowest values $0.903$.

### Methods

#### DFT simulation setup and governing equations

In this work we employ time-dependent functional density theory (DFT) by using
Gaussian $16$ software gaussian  at San Diego Supercomputer Center (SDSC) at
the University of California, San Diego XSEDE ) by implementing a built-in
Becke’s three-parameters hybrid functionals and Lee-Yang-Parr (B3LYP) electron
correlation; $6-31G^{*}$ basis set is used for H, C, P, O, N atoms and LANL2DZ
basis set is used for Ag atoms to achieve better accuracy. All simulated ssDNA
molecules were electrically neutral singlets, where additional protons bonded
to the oxygen atoms in the phosphate backbone screened the negative charge of
the phosphate group.

The Raman cross section of mode $k$, $\left(d\sigma/d\Omega\right)_{k}$, and
the corresponding Raman intensity, $I$, are given by

$\displaystyle\left(\dfrac{d\sigma}{d\Omega}\right)_{k}$
$\displaystyle=f\dfrac{(\nu_{L}-\nu_{k})^{4}}{\nu_{k}}B_{k}(T)S_{k},$ (1a)
$\displaystyle I$
$\displaystyle=\sum_{k}\left(\dfrac{d\sigma}{d\Omega}\right)_{k}L(\nu-\nu_{k}).$
(1b)

Here, $B_{k}(T)$ and $L(\nu-\nu_{k})$ are the temperature dependent correction
and the Lorentzian function centered at $\nu_{k}$ both given by

$\displaystyle B_{k}(T)$
$\displaystyle=1/\left(1-e^{-\nu_{k}/\nu_{T}}\right),\quad\nu_{T}\equiv
hc/(k_{B}T)$ (2a) $\displaystyle L(\nu-\nu_{k})$ $\displaystyle=\dfrac{1}{\pi
g}\dfrac{g^{2}}{g^{2}+(\nu-\nu_{k})^{2}},$ (2b)

respectively. Here, $h$, $c$, $k_{B}$, $T$ are the corresponding Planck’s
constant, speed of light, Boltzmann constant, room temperature, respectively,
whereas $g$ is the half-width at half height (HWHH) parameter of the
Lorentzian which represents broadening effects. Typically, for room
temperature values ($298.13$ K and $\nu_{T}=207.27$ cm-1) the temperature
dependent factor introduces correction below $10\%$ for frequencies above
$497.01$ cm-1.

#### Substrate and sample preparation

Silver and gold nanorod substrate arrays were fabricated using a single-step
OAD method barranco2016  by employing Denton Discovery Sputter system.
Nanorods formation is governed by the so-called “shadowing effect”; when a
material flux of deposited particles is made incident on the target surface,
initially formed nuclei structures prevent the deposition of later arriving
particles in regions situated behind them (see barranco2016  and references
within), thus leading to growth of only initial nuclei. In our case the
substrate is oriented at zenithal deposition angle $75^{o}$ leading to a
nanorod tilt angle of $60^{o}$ relative to the substrate normal. Fig.S2 in the
Supplementary Material section describes SEM images of a typical nanorod array
used in our experiments.

The metal nanorod arrays, which were used to eliminate charge trasfer CE
effect, were covered with $2$ nm Al2O3 thick film using Atomic Layer
Deposition (ALD); see Nguyen2020  for fabrication details and also sample
preparation steps. Briefly, the ssDNA solutions were prepared by diluting the
DNA stock solution in 4-(2-hydroxyethyl)-1- piperazine ethanesulfonic acid
(HEPES) and MgCl2. We then drop-casted this ssDNA solution onto the metal
nanorod substrate, let it dry overnight, rinsed with deionized water in order
to remove excess of crystallized salt and unbound ssDNA molecules, and then
blow-dried.

For acquisition of Raman spectra of ssDNA molecules suspended in bulk solution
we employed high throughput $5$ mm diameter Wilmad NMR tubes filled with ssDNA
sequences in IDTE buffer (pH $8.0$, $10$ mM Tris-HCl/$0.1$ mM EDTA) normalized
to a concentration of $100$ $\mu$M.

#### SERS and Raman measurement and data processing

SERS and Raman measurements were acquired with Renishaw inVia Raman
spectrometer by employing $10$ mW continuous $785$ nm excitation wavelength;
acquisition time of $5$ s per spectrum. The objective magnification used was
$50X$ with $NA=0.75$. The grating type used was $1200$ l/mm at $785$ nm, and
the grating setting was set to a static regime with spectrum range extending
between $600$ cm-1 to $1700$ cm-1 with spectral resolution around $1$ cm-1.
The mapping setting of the spectrometer was used to acquire $100$ measurements
from a total substrate area of dimensions $50\times 50$ $\mu m^{2}$; this area
is divided into $10\times 10$ square units, where the dimension of each area
unit is $5\times 5$ $\mu m^{2}$ and each acquired spectrum measurement is
taken from a different square area. Raman measurements of bulk solution (i.e.
without metal substrate) were performed by employing $50$ mW continuous $532$
nm excitation wavelength; objective magnification $5X$ with $NA=0.12$; grating
$1800$ l/mm.

After data acquisition, SERS/Raman spectra undergo the following signal
processing steps which include: baseline correction, cosmic ray removal and
MSC. The first two were implemented by employing built-in algorithms in
Renishaw WiRE 4 software with Gaussian smoothing window of length 20, whereas
MSC was implemented in MATLAB codes. These procedures lead to small artifact
regions with negative values of Raman intensity, which do not affect the
derived statistical correlation matrices.

The statistical analysis was performed by employing built-in ’corrcoef’
function in Matlab (version 9.7.0.1261785 (R2019b), Natick, Massachusetts, The
MathWorks Inc.) which calculates Pearson’s correlation matrix $\rho(A,B)$ of
two random variables $A$ and $B$, defined as the ratio of the corresponding
covariance matrix (cov), divided by the corresponding standard deviations
$\sigma_{A,B}$, explicitly given by

$\begin{split}\rho(A,B)&\equiv\dfrac{\text{cov}(A,B)}{\sigma_{A}\sigma_{B}};\\\
\text{cov}(A,B)&\equiv\dfrac{1}{N}\sum\limits_{i=1}^{N}(A_{i}-\mu_{A})(B_{i}-\mu_{B}).\end{split}$
(3)

Here, cov reflects the amount of correlation between the magnitudes and
directionality (i.e. positive or negative) of random variables deviation from
the corresponding mean values $\mu_{A,B}$, normalized by standard deviations
$\sigma_{A,B}$. In our case $A$ and $B$ designate several tens of SERS/Raman
spectra which belong to group (1) and group (2), respectively, and $N=1021$ is
the size of each spectra.

## Discussion

In this work we experimentally and numerically studied the effect of spatial
arrangements of DNA bases in ssDNA 3-mers on SERS and Raman spectra. Our
experimental results, where CE and EM effects were gradually introduced into
the system, clearly indicate a difference between the acquired SERS and Raman
spectra of sequences which differ under permutation of the DNA bases, and our
DFT simulations provide qualitative evidence for dependence of normal mode
frequency of DNA base on position along the sequence, with and without CE
effect. In particular, DFT simulations without metal indicate that frequency
dependence and mode splitting are intrinsic property due to complex structure
of the molecule, being composed of basic units with permutation dependent
molecular conformations; complex interaction with the metal may intensify this
difference as it allows higher variability such as different orientation
relative to the metal surface. Furthermore, we expect that CE effect should
play much more significant role in highlighting differences between different
permuted molecules than EM effect; the plasmonic mode, which is responsible
for the EM enhancement factor, isn’t expected to be affected by refractive
index changes due to sub-nanometer molecular permutations. Nevertheless, more
realistic simulations are needed to provide quantitative agreement by
incorporating additional effects such as CE due to resonant charge transfer
between the adsorbed molecule and the metal substrate, as well as additional
dielectric layer between the molecule and the metal. While in this work we
considered only 3-base long sequences to simplify the system and potentially
enhance the effect, we expect this work to facilitate future theoretical
studies, as well as experimental TERS-based sensing platforms, which admit
sufficiently high spatial resolution to enable excitation of just few bases
downes2006 ; trautmann2017 ; liu2019 ; he2018  to study sensing of longer
ssDNA molecules where permuted nucleobases are embedded in a longer DNA
sequences. In particular, studying SERS/Raman spectra as a function of
intermolecular zhang2020  or nearest neighbor interaction may potentially
enable more accurate SERS-based sensing platforms and allow lower read-out
error needed to meet bio-applications pyrak2019 , support DNA memory
applications panda2018  and allow novel tool to control Raman/SERS response of
complex molecules. Furthermore, our DFT simulation, presenting mode splitting
and normal modes dependence on the position along the phosphate backbone, may
lead to a novel structure dependent mechanism for inhomogeneous broadening of
the peaks in complex molecules such as ssDNA sequences, which may be of
importance from both fundamental and application perspectives.

## Funding

This work was supported by the Defense Advanced Research Projects Agency
(DARPA) DSO, NLM, and NAC Programs, the Office of Naval Research (ONR), the
National Science Foundation (NSF) grants CBET-1704085, DMR- 1707641, NSF
ECCS-180789, NSF ECCS-190184, NSF ECCS-2023730, the Army Research Office
(ARO), the San Diego Nanotechnology Infrastructure (SDNI) supported by the NSF
National Nanotechnology Coordinated Infrastructure (grant ECCS-2025752), and
the ASML-Cymer Corporation.

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Funding: This work was supported in part by the National Science Foundation
(NSF), the Office of Naval Research (ONR), the Semiconductor Research
Corporation (SRC), the Army Research Office (ARO), DARPA, Cymer Corporation,
and the San Diego Nanotechnology Infrastructure (SDNI) supported by the NSF
National Nanotechnology Coordinated Infrastructure (grant ECCS-1542148).

Competing interests: The authors declare no competing financial interests.

Acknowledgments: This work used the Extreme Science and Engineering Discovery
Environment (XSEDE), which is supported by National Science Foundation grant
number ACI-1548562.

SI Supplementary Material for:
“The effect of DNA bases permutation on surface enhanced Raman scattering
spectrum”

Shimon Rubin∗, Phuong H.L. Nguyen∗, Yeshaiahu Fainman

∗ Equal contribution

Department of Electrical and Computer Engineering, University of California,
San Diego, 9500 Gilman Dr., La Jolla, California 92023, USA

##  S.1 Dominant modes of AAC and ACC molecules

DNA molecules are inherently chiral and therefore in addition to ACA, CAA, and
CAC, CCA sequences we also consider vibrational modes of AAC and ACC, which
are expected to introduce changes in the Raman spectra. Table.S1 and Table.S2
below, describe Raman modes in the spectral regions corresponding to regions
specified in Table.1 and Table.2, respectively, with less modes presented in
the first spectral region.

Name |  | Frequency [cm-1]
---
| Raman Activity [Å4/amu]
---
| Mode location
---
AAC |  | $767.87;775.38$
---
$1241.67$
$1376.36;1376.98$
$1541.47;1541.96;1576.51$
| $19.85;55.72$
---
$21.7$
$48.36;47.71$
$24.32;36.80;37.31;$
|  $3^{\prime}$ sugar, $3^{\prime}$PHB, C; C
---
C, $3^{\prime}$sugar
cen A, cen sugar; $5^{\prime}$sugar
$5^{\prime}$A; cen A; C
AAC-Ag12 |  | $784.36;772.09$
---
$1247.22$
$1370.59;1372.23$
$1542.26;1545.89;1570.77$
| $83.76;30.48$
---
$16.40$
$106.15;108.84$
$115.58;106.19;191.45$
| C; $3^{\prime}$sugar, $3^{\prime}$PHB, cen sugar
---
C, $3^{\prime}$sugar
$5^{\prime}$A, $5^{\prime}$ sugar; cen A, cen sugar
$5^{\prime}$A; cen A; C
Table S1: DFT simulation results presenting frequencies, RAs and the corresponding Raman active molecular groups in AAC and AAC-Ag12 molecules which belong to group (1). Name |  | Frequency [cm-1]
---
| Raman Activity [Å4/amu]
---
| Mode location
---
ACC |  | $776.46;779.19$
---
$1230.42;1242.28$
$1376.59$
$1542.21;1573.07;1576.45$
| $36.05;22.86$
---
$47.48;19.97$
$51.25$
$28.43;33.87;34.46$
|  $3^{\prime}$C; cen C, $3^{\prime}$C
---
cen C, cen sugar; $3^{\prime}$C, 3′ sugar
A, $5^{\prime}$ sugar
A; cen C; $3^{\prime}$C
ACC-Ag12 |  | $788.32;791.96$
---
$1232.33$
$1387.99$
$1561.19;1570.39;1572.39$
| $70.31;47.72$
---
$22.95$
$21.99$
$65.88;90.51;48.26$
| cen C; 3′C
---
cen C, cen sugar
A
A; cen C; 3′C
Table S2: DFT simulation results presenting frequencies, RAs and the
corresponding Raman active molecular groups in ACC and ACC-Ag12 molecules
which belong to group (2).

Fig.S1 presents the effect of partial bonding of Ag4 nanoparticles on the
emerging SERS spectra.

##  S.2 Spatial Conformations of ACA, CAA, CAC, and CCA molecules

The following image presents computational results of the optimized geometry
for group (1) and group (2) ssDNA molecules.

Figure S1: DFT results presenting optimized geometry of group (1) and group
(2) ssDNA molecules in the first and second rows, respectively. Red - oxygen
(O), blue - nitrogen (N), grey - carbon (C), white - hydrogen (H), orange -
phosphorous (P). In all molecules the orientation (coordinate system) was
fixed by fixing the orientation of the four O’s which are bond to P at
$5^{\prime}$ end. In particular P is chosen as origin; x-axis is parallel to a
pair of O’s where each O is connected to a single P and H atoms; y-axis is
antiparallel to the P-O bond where O is bond to C; z-axis (towards the reader)
is along the P=0 bond.

##  S.3 Additional details about fabricated nanorod array

Fig. S2 presents SEM image of a typical OAD-fabricated nanorod array. The
average height of the nanorods, is approximately $h=200$ nm, whereas the
average diameter of the rods is approximately $\Lambda=50$ nm for gold (and
$\Lambda=100$ nm for silver)

Figure S2: SEM image showing typical morphology of the OAD-fabricated gold
nanorod array.

Based on the width of the error bars, which represent standard deviation due
to measurements acquired at 25 different spatial locations on the substrate,
relative to the mean peak height, we conclude that the mean signal variation
across all spectral domains is approximately 6%.

Based on our recent work [41], where identical nanorod arrays were employed,
we bring here the corresponding values of the CE factors. In particular, these
are approximately $\sim 2-20$ for gold (depending on the spectral region) and
$\sim 2$ for silver. The latter were obtained by comparing between SERS
spectra of molecules adsorbed directly to the metal nanorod array to similar
array coated with a $2$ nm thick Al2O3 film, which eliminates potential
resonant charge transfer effect. Experimental measurement of total enhancement
factor, due to both EM and CE effects, requires determination of surface
concentration of adsorbed ssDNA molecules to the nanorod array after the
rinsing step, which is beyond the scope of this work.

##  S.4 Estimation for the EM enhancement factor

We define the EM enhancement factor (EF) for each one of the 3-mers employed
in this work as

$EF=\bar{I}_{SERS}/\bar{I}_{Raman},$ (1)

where $\bar{I}_{SERS}$ and $\bar{I}_{Raman}$ represent ”signal per molecule”,
i.e. the integral of SERS (or Raman) spectra ($I_{SERS},I_{Raman}$) over the
relevant spectral domain divided by the corresponding number of molecules
($N_{SERS},N_{Raman}$) in the illuminated region and also by the illumination
power $(P_{SERS},P_{Raman})$, allowing to write the equation above as

$EF=\dfrac{I_{SERS}}{N_{SERS}\cdot
P_{SERS}}\bigg{/}\dfrac{I_{Raman}}{N_{Raman}\cdot P_{Raman}}.$ (2)

Based on our experimental spectra, the ratios of the signals
$I_{SERS}/I_{Raman}$ for the sequences ACA, CAA, CAC, CCA are: $28.2$, $30.9$,
$22.0$, $42.2$, respectively; i.e. very similar and differ at most by a factor
approximately two. Next, $P_{SERS}=10$ mW, $P_{Raman}=100$ mW, leading to
$P_{SERS}/P_{Raman}=10$. Finally, we determine the number of active molecules
in each one of the cases. Assuming the 3-base molecules cover uniformly the
$5\times 5=25$ $\mu$m2 sampling area, and the in-plane area of the molecule is

$\text{length}\times\text{width}=(0.676\text{ nm}\times 3\text{ bases})\times
0.9\text{ nm}=1.82\cdot 10^{-6}\mu\text{m}^{2},$ (3)

yields the following number of molecules in the sampling area,
$N_{SERS}=25/(1.82\cdot 10^{-6})=1.37\cdot 10^{7}$. To determine $N_{Raman}$,
defined by,

$N_{Raman}=\text{illumination volume}\times\text{copies per volume},$ (4)

we estimate illumination volume as $\pi\omega_{0}^{2}L_{R}=2.36\cdot 10^{-13}$
l. Here, $\omega_{0}=\lambda/(\pi\cdot NA)=785\text{ nm}/(\pi\cdot
0.12)=2082.3$ nm is the radius of the Gaussian beam waist, $\lambda$ is the
wavelength of illumination laser in the free space, and NA is the
corresponding numerical aperture; $L_{R}=\pi\omega_{0}^{2}/\lambda=17352.7$ nm
is the Rayleigh length. The number of molecules per volume is a product of
molar concentration, $100$ $\mu$M $=10^{-4}$ m/l, with Avogadro number,
$N_{A}=6.02\cdot 10^{23}$ copies/m, leading to $N_{Raman}=1.42\cdot 10^{7}$
copies. Inserting, these parameters into the definition of the EF, yields the
following similar values,

$EF=2.93\cdot 10^{2},3.20\cdot 10^{2},1.04\cdot 10^{2},4.37\cdot 10^{2}$ (5)

for the sequences ACA, CAA, CAC, CCA, respectively.